=== === ============= ==== === === == == == == == ==== == == = == ==== === == == == == == == == = == == == == == == == == == ==== M U S I C T H E O R Y O N L I N E A Publication of the Society for Music Theory Copyright (c) 1995 Society for Music Theory +-------------------------------------------------------------+ | Volume 1, Number 3 May, 1995 ISSN: 1067-3040 | +-------------------------------------------------------------+ General Editor Lee Rothfarb Co-Editors Dave Headlam Justin London Ann McNamee Reviews Editor Brian Alegant Manager Robert Judd Consulting Editors Bo Alphonce Thomas Mathiesen Jonathan Bernard Benito Rivera John Clough John Rothgeb Nicholas Cook Arvid Vollsnes Allen Forte Robert Wason Marianne Kielian-Gilbert Gary Wittlich Stephen Hinton Editorial Assistants Christopher Pitchford Ralph Steffen All queries to: mto-editor@smt.ucsb.edu or to mto-manager@smt.ucsb.edu +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ 1. Target Articles AUTHOR: Johnson, Timothy, A. TITLE: The Computer Presentation of Musical Research: A Case Study KEYWORDS: HyperCard, CD-ROM, John Adams, computer-assisted instruction Timothy A. Johnson Mount Holyoke College Department of Music South Hadley, MA 01075 tjohnson@mhc.mtholyoke.edu ABSTRACT: The traditional format for the presentation of musical research, the journal article, makes referencing musical passages less direct than ideally desired. CD-ROM technology provides a means for the presentation of written comments and analytical sketches simultaneously with a recorded performance of the corresponding music. This article describes a computer project that uses CD-ROM technology to bridge the gap between analytical or theoretical comments and the sound of musical passages. The main goals of the article are to encourage the development of and provide guidance for similar projects. ACCOMPANYING FILES: johnson.hqx (a downloadable copy of the program) The copy of the program is available at fas.harvard.edu, in the pub/smt/mto/software directory. [1] The traditional format for the formal presentation of musical research, the journal article, makes referencing musical passages less direct than ideally desired. Although much theoretical and analytical work primarily focuses on the musical sounds themselves, scholarly views and explanations usually are accompanied only by cryptic references to these sounds in the form of written musical examples and references to scores by measure numbers. The lack of ready access to the sounds under discussion often makes the theoretical and analytical concepts presented difficult, if not impossible, to grasp fully. Despite the high level of ability among musical scholars in producing imagined aural recreations of such passages or in remembering past performances, many readers do not have the ability to conceive the sounds implied by unfamiliar musical examples precisely or will not take the time and trouble to obtain a score and recording of the works being discussed. And even those with exceptional score-reading abilities or memories likely would benefit from hearing a performance of the passages discussed. After all, sounding music--not music sounding in our heads--is what led most of us to devote our lives to its study (even if music sounding in our heads is what keeps us devoted). [2] CD-ROM technology provides a means for the presentation of written comments and analytical sketches simultaneously with a recorded performance of the corresponding musical passages. The compact disks may be accessed with precision, accurate to a 75th of a second. Using a programming software package such as HyperCard, an author may create links to immediately bring the reader/listener from analytical texts or graphics directly to the relevant passage on a compact disk. Thus, the musical sounds are readily available, eliminating the problems associated with providing only written references to the music. [3] In this article I will describe in detail a computer project that uses CD-ROM technology to bridge the gap between analytical or theoretical comments and the sound of musical passages.(1) First I will introduce some of the basic aspects of the musical theories presented in the program [section 4] and present some of the principal advantages of the use of this technology for the presentation of musical research [sections 5-6]. A detailed description of the computer program follows [sections 7-15]. Next I discuss the development effort required and relate some of the problems encountered in bringing the project to completion [sections 16-20]. Finally, an exploration of some pedagogical implications of the technology closes the article [sections 21-24]. The main goals of this article are to encourage the development of similar projects by outlining the motivation for and benefits of using this technology and to provide guidance to those who choose to undertake such projects through example and by identifying some potential pitfalls. Although a number of more polished commercial CD-ROM products dealing with similar analytical issues have appeared, the project described in this article represents a more informal model of the use of this technology, in which someone with little experience may develop a useful (though certainly less thorough) program.(2) In addition to providing a detailed description of the computer project in this article, the computer program itself may be downloaded (see list of accompanying files above) for exploration by readers of this journal who have access to a Macintosh computer, preferably with a CD-ROM and the suitable compact disks.(3) Although CD-ROM is an essential component of the project and the primary concerns discussed in this article, the computer program may be examined without access to a CD-ROM, though unfortunately no music will be played. ============================================= 1. An earlier version of this case study was supported by the Mount Holyoke College Technology Seminar, sponsored by a grant from the Pew Charitable Trusts. 2. Some excellent commercial CD-ROM software products include: Daniel Jacobson and Timothy Koozin, *The Norton CD-ROM Masterworks*, Vol. 1 (New York: W. W. Norton and Company, forthcoming in 1995); Daniel Jacobson and Timothy Koozin, *CD-ROM Listening Guides for The Enjoyment of Music, 7th ed. by Joseph Machlis and Kristine Forney* (New York: W. W. Norton and Company, 1995); William Renwick and David Walker, *CD-BRAHMS* (Hamilton, Ontario: McMaster University, 1994); Robert Winter, *Anton Dvorak, Symphony No. 9 in E minor: From the New World* (Irvington, N.Y.: Voyager, 1994); Robert Winter, *Igor Stravinsky, The Rite of Spring* (Santa Monica, Calif.: Voyager, 1992); and Robert Winter, *Ludwig van Beethoven, Symphony No. 9* (Santa Monica, Calif.: Voyager, 1989). 3. The following compact disks may be used with this program: John Adams, *The Chairman Dances*, San Francisco Symphony, Edo de Waart, cond. (Elektra/Nonesuch 9 79144-2); Adams, *Grand Pianola Music*, and Steve Reich, *Eight Lines* and *Vermont Counterpoint*, Solisti New York, Ransom Wilson, cond. (EMI CDC-7 47331 2); Adams, *Harmonielehre*, San Francisco Symphony, Edo de Waart, cond. (Elektra/Nonesuch 79115-2); Adams, *Harmonium*, San Francisco Symphony Orchestra and Chorus, Edo de Waart, cond. (ECM 1277); Adams, *Nixon in China*, Orchestra of St. Luke's, Edo de Waart, cond. (Elektra/Nonesuch 9 79177-2); *American Piano Music of Our Time*, Ursula Oppens, piano (Music & Arts CD 604). ============================================= [4] This computer program, prepared using HyperCard for the Macintosh, presents analytical and theoretical comments linked to musical sketches and compact disk recordings of passages from John Adams's music. The theory presented in the program identifies the seven chord successions used in passages that repeatedly alternate between two chords. The seven chord successions correspond to two more general procedures, called operations. These operations, taken singly or in combination, stipulate relationships between two chords based on either the circle of thirds, alternating between major and minor thirds, or on notes moving by half step. The computer program describes and displays each of the seven typical successions, and links these theoretical explanations to analytical sketches and recordings of the corresponding musical passages from a variety of Adams's pieces. In addition, a more extensive example from the first scene of the opera, *Nixon in China*, suggests that these successions connect different passages by providing recognizable chord root and quality relationships. [5] The interactive format of this program allows users to explore the ideas presented at their own pace and in their own way--spending more time to examine certain areas or to hear additional musical examples while skipping over areas of less interest. This format seems particularly appropriate for the presentation of theoretical or analytical material, since many ideas require explanation from a variety of approaches and in reference to multiple examples, while other ideas may be immediately grasped with little explanation or demonstration. Furthermore, the exploration of the theoretical and analytical ideas may be focused according to each user's own interests and background. [6] In addition to providing direct links to precise musical passages on compact disks and allowing individualized interactive access, the HyperCard platform also facilitates the production of animated sequences that can illustrate complicated theoretical concepts with ease and with little textual commentary. Thus, instead of describing how a collection of notes may be manipulated to produce a related collection, the manipulation procedure may be shown as a step-by-step process unfolding upon the screen. Even familiar concepts such as inversional symmetry may be shown clearly and succinctly by gradually inverting a collection of notes to yield the same collection through an animated process. Another advantage of CD-ROM technology is the capability of highlighting specific locations in an analytical sketch at the same time as the corresponding music plays. Consequently, the correlation between specific analytical symbols and the parallel location in the music are immediately apparent without reference to location cues such as measure number or section. Because of this coordination, even an uninitiated student of music theory cannot fail to grasp the relationship between elements of the analytical sketches and the relevant musical passages. [7] The following detailed description of the key features of the computer program (sections 7-15) will provide an account of the program to readers without access to a Macintosh and will offer commentary on the essential aspects of the program. In addition to their descriptive purpose, these remarks are intended to serve as a guide for the development of similar projects by identifying potential problems and suggesting possible solutions. Those who have the facilities to examine the program may wish to read this section while observing the relevant screens in the program, skimming over the descriptive material in this part of the essay and focusing on the commentary. [8] The title page, in addition to providing descriptive information about the program and its developer, invites the unassisted user to try the software program. The instruction, "click the mouse anywhere to begin," indicates the only knowledge necessary to get started--the recognition of a mouse and the initiative to press the button. After several informational screens and an opportunity to hear a sample from Adams's music, another introductory screen attempts to alleviate fears of computer novices through humor while clearly providing necessary information to more experienced users. The technologically aware user is instructed to click the mouse in a button to select the level of help, while the novice is advised to "click the mouse anywhere else if computers scare you!" Three levels of help are offered, ranging from no-help to virtual hand-holding, to provide flexibility for the different backgrounds of potential users. [9] The importance of getting users started and providing sufficient help cannot be overestimated in developing interactive programs. Unless the first screen is sufficiently inviting and uncluttered, many potential users may stare blankly at the screen hoping someone else will come along and demonstrate the program. The help provided for those who venture into the hyperspace created in the program is even more essential, since furnishing too much help will bore and annoy sophisticated users (which, judging by the recent exuberant activity on the music theory list, are becoming more and more common among music theorists), and too little help will leave many users confused and unable to continue. Instructions on the use of the software that are provided should be simple and gradual, and opportunities must be provided for the user to try the maneuvers necessary to run the program, accompanied by descriptive guidance. [10] The main menu screen serves as a home base for the user and supplies an outline of the entire program. However, unlike the table of contents in a book, clicking the mouse on any particular entry in the outline provides immediate access to that section of the program. Each button on the main menu screen provides access to different areas in the program, and all screens in the program provide a possible direct link back to the main menu. In this program, the seven typical chord successions are listed in the right column of buttons and are connected via lines to the buttons containing the corresponding operations listed in the left column. An overview button heads the list, centered at the top of the screen, and a button linked to a list of musical examples and the quit button appear centered at the bottom of the screen. The main menu functions as a familiar location from which to explore the entire program. Whenever the user becomes disoriented, a click of the mouse on any of the "return to main menu" buttons produces this recognizable screen from which a new course of exploration may be contemplated. [11] Choosing "Overview" from the main menu reveals background information about the theory as well as essential aspects of how the main menu is constructed. Relationships between the operations and the chord successions emerge graphically while theoretical commentary on some crucial aspects of the theory appears in text boxes. The overview, in addition to providing a brief synopsis of the musical theory, aids the user in understanding the construction of the program and suggests possible areas to explore. [12] Choosing one of the operations from the main menu provides a detailed description of that operation and its connection to the corresponding typical chord successions. Similarly, choosing any of the chord succession buttons from the main menu, in addition to showing its link to an operation, produces a graphical representation of the abstract idea and supplies a link to some musical examples that illustrate the theoretical device. For each typical succession, the user may choose to examine and hear any of the examples listed on the buttons in the center of the screen or may choose to return to the main menu or repeat the graphic portrayal of the chord succession. Choosing one of the musical examples reveals a screen that clearly displays the title and measure numbers of the selected passage and the theoretical construct under investigation at the top of the screen. The main portion of the screen is devoted to a sketch of the harmonic content of the passage. And the bottom of the screen provides an opportunity to learn about the sketch technique used in the project, displays the duration of the example, and gives the option of playing the example or exiting to the previous screen. A box highlighted in reverse video, indicating the section of the sketch being played, moves through the sketch as the recording is heard. [13] Check marks appear next to all example buttons after the corresponding example has been examined and heard. This signal allows the user to keep track of which examples have been explored and which remain, though these place indicators do not prevent users from returning to any of the examples for further study or replays. Similar check marks on the main menu help the user to keep tabs on progress on a grander scale. [14] The master list of musical examples, comprised of working buttons, provides alternative access to each of the examples in the program. Thus, users may choose to approach the theoretical and analytical information through the operations or chord-succession types listed on the main menu, as described above, or they may explore the examples according to individual piece titles and measure numbers. The check marks indicating progress appear on this screen even if the example was entered from the chord-succession screens. A Discography/Bibliography, presented using the analogy of index cards, gives the usual information a familiar feel despite the unfamiliar technological mechanism. A user may move through the entries in the bibliography by using the arrow buttons at the bottom of the screen or by "thumbing" through the index cards by pointing to the top right corner of the cards and clicking with the mouse. [15] Whereas most of the examples in this program are brief excerpts from a number of different pieces, a more comprehensive view of the first scene of *Nixon in China* appears as a separate example. Instead of a graphical representation of the various passages, this extended example simply lists the many typical chord successions and their associated chords that appear in repeated alternation in the scene. The entire scene may be played while tracking the various typical successions as shown by a highlighted box, or individual passages may be played by clicking on the various selections in the list. This example serves as a summary, where the typical chord successions may be considered in a broader context. [16] This profile of the computer program and its essential theoretical components identifies the key features of the project. Although many aspects described above are unique to this project, the general concepts are applicable to other future projects. Offering an inviting initial screen, providing appropriate help, linking all areas of the program to a central screen, and indicating progress through the program are all essential components of successful interactive computer programs. In addition, providing effective metaphors for familiar concepts, such as the bibliographic index cards described above, helps the user to become acclimated to the program more quickly. [17] The development of this project required a rather substantial initial investment of time and effort. Developing additional projects, however, would take far less time since familiarity with the software and with design strategies would accelerate the process considerably. This project took approximately two and a half months of full-time work to complete--beginning with *no* knowledge of HyperCard or CD-ROM technology, almost no Macintosh experience, but considerable experience working with IBM-compatible computers. Included in this time period was a four-day music-technology workshop at the University of North Dakota.(4) After the workshop, continual reference to a valuable resource by Daniel Goodman,(5) and considerable trial and error guided the advancement of this project. In the final stages the Academic Computing Staff at Mount Holyoke College provided invaluable assistance.(6) ============================================= 4. Although there are a number of fine workshops on HyperCard and CD-ROM, I chose this one for the opportunity to work with Tim Koozin and Dan Jacobson, a music theorist and a musicologist who both have had substantial experience in developing applications similar to this program. 5. The Complete HyperCard 2.2 Handbook, 4th ed. (New York: Random House Electronic Publishing, 1993). 6. I especially would like to thank Jurgen Botz, Vijay Kumar, and Kevin Prime. ============================================= [18] The development of this project required a Macintosh Computer with a CD-ROM drive, headphones or speakers with an amplifier, a full authoring version of HyperCard, a CD sound-driver, Voyager Audio Stack, and compact disks of the music under investigation.(7) The project initially cost approximately $1170 ($750, music-technology workshop including travel; $50, books; $120, compact disk recordings; $75, CD-Caddies; $150, Voyager Audio Stack software; $25, audio wiring), not including computer and CD-ROM hardware.(8) Completing additional projects, however, would require only the cost of the compact disk recordings. ============================================= 7. Similar projects may be produced using an IBM-compatible computer and a comparable software product to HyperCard such as Toolbook. For Macintosh computers a *full* version of HyperCard must be procured since, although Macintoshes are customarily shipped with HyperCard, a full authoring version is not always supplied. A CD sound-driver is software that allows CD-ROM to be used for sound production rather than just data storage, the Voyager CD AudioStack is a software program for the Macintosh that facilitates access to compact disks, and the compact disks used for this application are standard commercial CD recordings. 8. The development of this project was supported by a faculty research grant from Mount Holyoke College. ============================================= [19] This program was initially presented as a "poster" at the Annual Meeting of the Society for Music Theory, Kansas City, 1992. A major obstacle in presenting this project at a national conference was transporting computer equipment to the site. Although a laptop would have be ideal for this application, test runs on a Powerbook revealed a "bug" in Powerbooks making their use problematic and causing substantial levels of stress for the developer (the computer would "freeze" during relatively lengthy animated processes since the keyboard was not in use). Other problems involved the disparate speeds at which the animated sequences ran on different computers, negating the effects of working out precise timing for certain animated processes. This timing problem has become more of a factor as computers constantly increase in speed; therefore, the program has been revised to rely on clock time rather than the computer's internal processor speed. Fortunately, none of the problems encountered were insurmountable, and the presentation took place without incident. [20] Another important consideration in the development of this project was the desire to discuss pieces appearing on different compact disks. Since automatic CD-ROM changers are currently rare and prohibitively expensive, users of this program must frequently change from one compact disk to another--an awkward and somewhat confusing process. Placing all pieces on a single compact disk would be ideal but would require either permission from disparate recording companies or new recordings of the pieces under discussion--both of which would be too time-consuming and expensive for non-commercial projects such as this model. The ability to utilize standard, existing compact disks is one of the most compelling features of this technology, making its wide use among music theorists imaginable and making many pedagogical applications feasible, as discussed below. [21] The model described in this case study, though designed as a vehicle for the presentation of musical research, easily may be adapted for use with students. This project has a variety of instructional implications including interactive programs for students to explore individually (similar to the project described in this article), courseware for classroom presentations, and computer projects for students to prepare on their own. [22] Software may be developed for students to use at their own pace that would directly link sound materials with text and graphics. The interactive nature of the software would engage the student in a rather different way than traditional assignments, since the student would have more control over her or his learning pace and sequence. Furthermore, many students, when pressed for time, often seek to streamline their studies by ignoring the audio components of assignments, choosing instead to rely solely upon the written representation. The development of this software would virtually eliminate the potential for students to listen to the assigned aural material at a different time than when they studied the corresponding graphical images and text or for students to ignore the aural material altogether. In addition, such programs would assure the instructor that students will at least have access to all of the course materials at the same time. Furthermore, the use of an interactive format allows students of widely divergent backgrounds and interests to be actively engaged in their own education. The students choose which aspects of the material to study first and in what order to proceed. When a particular aspect of the material sparks their interest, they are free to explore it in detail before returning to more general information. [23] Creating interactive programs may be the most compelling application of the material presented in this case study; however, course material may be developed quickly by instructors that would give them immediate access to specific locations on any compact disk--providing more class time for discussion rather than just searching for the proper track and time segment. Sound examples may be further enhanced in a classroom presentation by linking the examples to simple graphical images scanned from any source or created by the instructor using the simple drawing tools provided with HyperCard.(9) The expandable nature of HyperCard allows classroom materials to be assembled gradually from year to year, spreading the preparation time over a number of years. The coordination of graphical images with sounds further improves the quality of classroom presentations; instead of hastily drawing examples on a blackboard, a copy of the original image may be projected on a screen at precisely the right moment. ============================================= 9. The sketches in this program were prepared using the drawing tools and the Petrucci type font. ============================================= [24] A third potential instructional application for this model is for students to design their own software programs. Instead of a term paper with written examples representing sounds pasted into the text, the students may link their ideas to the actual sounds of the music discussed. This method of presentation would give students access to sounds, graphics, text, and animation to describe their research results. This application of the technology would allow students with different abilities in expression to clearly present their ideas. Furthermore, more creative students would have an essential outlet for their creativity in courses that traditionally provide few such opportunities. In addition, in analytical assignments, students would be forced to grapple with the actual sounds they are discussing rather than taking them for granted from written representations, since at times some students complete their analytical projects without ever hearing the sounds implied by the scores provided for them, as mentioned above in connection with interactive programs. They simply apply the rules and conventions they have learned, ignoring the effect of the music in their analyses, and consequently miss the most compelling aspects of pieces by focusing instead on the mundane. [25] In summary this article has shown some of the advantages of developing interactive computer programs with CD-ROM, has described the development of one such project, and has discussed some pedagogical implications. This technology has a number of possible uses ranging from the formal presentation of musical research to a variety of pedagogical applications. Although developing similar projects requires considerable time and effort at first, the resulting coordination between theoretical/analytical ideas and the music upon which they are based suggests that this technology has the potential to surpass many traditional methods for the presentation of musical research. ======================================== AUTHOR: Kopp, David TITLE: On the Function of Function KEYWORDS: function, harmony, Riemann, Rameau, Weber David Kopp Brandeis University Department of Music Waltham, MA 02254-9110 kopp@binah.cc.brandeis.edu ABSTRACT: The concept of harmonic function, far from carrying a unitary and universally understood meaning, has signified many different things to theorists past and present. This essay examines some of the different meanings commonly associated with the term today, as well as aspects of the harmonic theories of Rameau, Weber, and Riemann, all regularly associated with the concept. Notions of chord identity, scale degree, and logical determinacy are considered. ACCOMPANYING FILES: mto.95.1.3.kopp1.gif mto.95.1.3.kopp2.gif mto.95.1.3.kopp3.gif [1] Harmonic function is a term which, although it may seem to express a simple and obvious concept, has grown uncommonly vague through use. Loosely put, function signifies harmonic meaning or action. But notions of what meaning and action constitute may take many forms. In our time, any search for a commonly accepted definition of function will be frustrated, for the meaning of the word has proved adaptable to support a wide variety of statements concerning harmony. For example, the harmonic meaning of chords is often attributed to each diatonic scale degree and their variants, serving as the roots of a variety of chords.(1) Thus we may say that A-flat major functions as III in F minor, as V in D-flat major, and as flat-VI in C major. The term function may also be used in a stronger sense to signify a concept of the intrinsic potentiality of a given chord to progress in a particular way or to a particular chord; thus we say that V expresses function in its tendency to progress to I. We may use the term to group chords with similar syntactic behavior, e. g. saying that II and IV often express similar function. We may link it to the primacy of tonic, dominant, and subdominant in the key. Or we may associate function with specific outcomes rather than with unitary scale degree identity.(2)The term may be associated with harmonic tendencies of individual chord tones as well as chords.(3) It may be correlated with phrase-based syntactic meaning.(4) The function concept has even been identified with a prolongational scale-step notion.(5) We often use the term function to denote meaningfulness or meaningful relation within a key, as opposed to "color," which signifies a relation without meaning in the tonal system. All of these and many more contrasting notions of chord identity, potentiality, and activity may be invoked by the same term. Yet we use it as if its meaning were fixed and intuitively evident. None of the harmony textbooks cited above, for example, treats function as a concept to be defined in its own right or contains an index entry for the term. ================================================== 1. "Each scale degree has its part in the scheme of tonality, its tonal function." Walter Piston and Mark DeVoto, *Harmony*, fourth edition, New York: Norton (1976), p. 49. 2. "The IV has three common functions. In some cases, IV proceeds to a I chord...More frequently, IV is linked with ii...(it may also go) directly to V..." Stefan Kostka and Dorothy Payne, *Tonal Harmony*, second edition. New York: Alfred A. Knopf (1989), p. 103. 3. This approach is used by Daniel Harrison in his recent *Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of its Precedents*, Chicago: University of Chicago Press (1994). 4. "In the Kuhnau, the tonic functions first as an *opening tonic* At the end it is a goal of motion, thus a *closing tonic*." Edward Aldwell and Carl Schachter, *Harmony and Voice Leading*, 2nd. ed., New York: Harcourt, Brace, and Jovanovich (1989), p. 84. 5. Willi Apel, *The Harvard Dictionary of Music*, 2nd. ed., Cambridge: Harvard University Press (1969), article on function. ================================================== [2] Furthermore, we commonly associate an idea of function with the thought of many theorists of common-practice tonality, and regularly identify the presence of "function" in theory which significantly predates the introduction of the formal concept. What we call function in these theories is not always the same thing, nor is it always what we may think it to be. It is a familiar idea that one's view of the past can be affected by one's own manner of thinking (6); familiar terms may particularly obscure. In the space of this short essay I cannot propose either to trace either the development of the functional idea through the history of theory or to identify all the theorists to whose work we attribute function. Instead, I will restrict my inquiry to an attempt to isolate and evaluate the aspect of three major theories of harmony customarily associated with the function concept, one each from the beginning, middle, and end of the common-practice period. I hope to show how different this aspect is in each case, and to argue that the use of the same term to describe each unduly denatures its effectiveness. ================================================== 6. Thomas Christensen has examined this issue in "Music Theory and its Histories," in *Music Theory and the Exploration of the Past*, ed. Hatch and Bernstein, Chicago: University of Chicago Press (1993). ================================================== [3] Our tendency to identify function extends back to accounts of Rameau, whose theory is often described in recent literature as elucidating the harmonic functions of chords. Without a doubt, notions of differentiated chord action are present in Rameau. But did he really describe a property of the tonal system properly characterized as function? His terms *tonique*, *dominante*, and *sous-dominante* certainly evoke associations with Riemann's three *Hauptfunktionen*. But where *Hauptfunktionen* define harmonic states of triads, Rameau's chord types do not. Their identities hinge on an extrinsic explanation. Rameau does not identify chord types with harmonic meaning and identity.(7) Rather, he concentrates on differentiating chords' tendencies to progress: *dominante* by descending fifth, *sous-dominante* by ascending fifth, and *tonique* by any acceptable fundamental bass interval. Rameau accounts for the constrained, motivated natures of *dominante* and *sous-dominante* by positing the universal presence of dissonant minor seventh and major sixth in them, whether actual or implied.(8) A *tonique*'s freedom to progress stems from the absence of added dissonance. Thus the motivating force behind these tendencies is not harmonic but contrapuntal: the addition of a dissonant pitch to a consonant formation is the necessary cause of the directed motion associated with certain chord types. Rameau observes that dissonance is required for the listener to desire the chords which follow.(9) Furthermore, only the *sous-dominante* as defined is completely specific to scale degree.(10) A dominante could be one of a number of diatonic seventh chords; the dominant seventh chord on the fifth degree required a special name, *dominante-tonique*.(11) And while Rameau originally specified the *tonique* for the first scale degree only, the prevalence of freely progressing roots on other scale degrees in his fundamental bass analyses obliged him eventually to distinguish between the true tonic and *notes cense'es toniques*, or seeming tonics.(12) Thus there is no one- to-one correspondence between the three chord types and the three primary chords of the key. Example 1 shows Rameau's 1760 analysis of a descending chromatic line with alternative *basses fondamentales*. It contains *dominantes* and *dominantes-toniques* on various scale degrees, also *toniques* and a *note cense'e tonique* in the first *b. f.* at letter *f*. ================================================== 7. Lester, op. cit., p. 207. Lester uses the term function but is careful to distinguish how Rameau's theory differs from modern ideas. 8. A thorough discussion of this "mechanistic" aspect of Rameau's theory is found in Christensen, *Rameau and Musical Thought in the Enlightenment*, Cambridge, England: Cambridge University Press (1993), pp. 106-7. 9. Rameau, *Traite' de l'harmonie*, Paris (1722), p. 53; *Nouveau syste'me de musique the'orique*, Paris (1726), pp. 56-57. Reissued in facsimile by the American Institute of Musicology, 1966-68. 10. Rameau (1726), pp. 38, 61. 11. Rameau (1722), pp. 203-4. 12. Rameau, *Code de musique pratique*, Paris (1760), pp. 81-82. Reissued in facsimile by the American Institute of Musicology, 1966-68. Example 1 from example p. 17. ================================================== [4] Does this constitute a theory of function? Rameau's theory contains no formal concepts of chord identity based on scale degree or of common harmonic identity shared by different types of chord. To a remarkable degree, the theory does contain a definite notion of how chords act differently from one another. But while Rameau does demonstrate that the coherence of progressions stems ultimately from the coherence of the triad,(13) he attributes the determined nature of these progressions to a contrapuntal tendency emanating from outside the triad, not from scale-degree identity. In this light, any view that Rameau's theory originates an idea of function as inherent potentialities of chord actions is compromised by the fact that for him these potentialities are in no way defined as inherent in triads themselves nor essentially in their position in the key, despite what is possible to read in behind what Rameau says. Rameau clearly perceived differences in chord action, accounting for them with his theory of added dissonance and the three chord types. However, his theory differs so dramatically from other conceptions of function that merely using the term to describe it necessitates a great deal of explanation as to what it really means. Claiming that function exists in Rameau unavoidably invites associations with the term which are not reflected in the theory. It would be useful to have more precise, dedicated terms to denote different conceptions of harmonic activity (e.g. notions of action-function, identity-function, hierarchic/syntactic-function, tonic-centering-function). Particular well-defined types of function could then be adduced in a more specific and meaningful way to clarify understanding of the essential nature of harmonic systems such as Rameau's. ================================================== 13. David Lewin documents this in "Two Interesting Passages in Rameau's *Traite' de l'harmonie*," In Theory Only 4/3 (1978):10. Also discussed in Christensen, op. cit., p. 106. ================================================== [5] Another theorist routinely identified with introducing functional thinking is Gottfried Weber. Typical is this comment on Weber's work by a mid-twentieth century historian of nineteenth-century harmonic theory: "The author believes Weber to be the first theorist to use Roman numerals as function signs."(14) This account suggests that Weber, writing in the 1820s, was devising signs to denote the concept familiar to us. While a clearly defined notion of function in harmony had not yet been introduced, it could indeed be possible that Weber sensed its existence and documented it in theory without being able to fully articulate its nature. But Weber was adamant that his theory was not meant to be a system explaining the genesis of chords and their actions.(15) He rejected rules and explanations for mechanisms properly linking chords; to do so would have been to unnecessarily forbid perfectly good progressions. Weber fully recognized the importance and ubiquity of I, IV, and V in the key. But at the same time, he permitted and even encouraged the use of any and all of the 6888 possible chord relationships he defined within and between keys, refusing to forbid anything.(16) He ascribed cadential power only to seventh chords resolving to triads; thus V7-I was his model cadence, V-I only a frequent progression between essential harmonies.(17) Moreover, Weber did not require the presence of the dominant in a modulation and even allowed for pieces containing no dominant at all.(18) Nor did he offer any explanation for the motivation and dynamics of chord progressions; he merely reported on the comparative strength and plausibility of as many of them as possible. ================================================== 14. Mark Hoffman, *A Study of German Theoretical Treatises of the Nineteenth Century*, Ph.D. dissertation, Eastman School of Music (1953), p. 65. The comment is innacurate; for a discussion of earlier numbering systems, see Joel Lester, *Compositional Theory in the Eighteenth Century*, Cambridge: Harvard University Press, (1992), pp. 207-08. 15.Weber, *Versuch einer geordneten Theorie der Tonsetzkunst*(1817), 3rd ed., B. Schotts So"hne, Mainz (1830-32), preface, pp. x-xi. 16. ibid., bk. II, pp. 187-88, 213. 17. His discussion of V-I comes in serial order between IV-vii and VI-ii during a taxonomic description of progressions by fourth (not fifth!). The discussion is one sentence long; since V-I is so common, Weber feels no need to explain it. Ibid., bk. II, pp. 231, 242. 18. ibid., bk. II, pp. 7, 102. ================================================== [6] In essence, Weber's theory identifies chords by their participation and position in a key, not by their relation to each other or their tendency to progress. His method attributed Roman numerals on a chord-by-chord basis: either a chord fit exactly into the prevailing key, or else it was defined as belonging to the closest possible key into which it fit. On this basis diatonic music was readily analyzed in a single key. But Weber had no concept of secondary/applied dominant by which to show basic hierarchic relationships of chords within the key, nor a theory of alterations by which to define variants of diatonic chords. Consequently, he analyzed stretches of music containing tonicizations of secondary degrees as quick successions of modulations to different keys. Highly chromatic passages of passing chords could, in his system, invoke one or more new keys with every chord.(19) Thus while Weber's Roman numerals do define chords by their identities within keys, they cannot demonstrate how successions of chords with any significant chromatic content display coherence within a single key, thereby depicting the syntactic connections which can represent function to us. Essentially, his Roman numerals designate chords: primary diatonic triads and seventh chords. They do not represent the scale degree rubrics we may associate with function, which do more to subjugate chord identity to the key. Accordingly, simply calling Weber's labels "function signs" can give a false impression that scale degrees themselves, not chords, are being designated. ================================================== 19. His analysis of a passage of his own music documents twenty keys in twenty-one measures, including chords which evoke two new keys simultaneously. Ibid., fig. 234, meas. 15-end. Example 2 shows an excerpt from this analysis (meas. 21-33). The attitude that individual chords may evoke a sense of key is not unique to Weber, but rather points to an attribute of thinking of the time. For example, A. B. Marx, writing in 1841, taught that even the dominant and subdominant triads, in their roles as principal triads of the key, bring with them a sense (*Erinnerungen*, or reminiscences) of their associated keys. Marx, *Die Lehre von der musikalische Komposition*, vol. 1, Leipzig: Breitkopf & Haertel (1841), p. 73. ================================================== [7] Moreover, these symbols are a far cry from the "functions" represented by Rameau's chord types. *Tonique*, *dominante*, and *sous-dominante* are defined by action -- their relation to the chord which follows. I, ii, iii, etc., are defined by identity -- their relation to a tonic. Used so broadly, these attributions of function may confound as much as they illuminate. It is interesting to note one shared idea: both theories require the presence of a dissonant seventh in order for the dominant to strongly imply the tonic. Neither attributes the will or power to progress to the fifth scale degree of itself. [8] Hugo Riemann's theory is indisputably a functional one in some sense, since it was he who popularized the term. But his notion of function and ours are worlds apart. In an early harmony treatise predating his introduction of the concept, Riemann demonstrates how a series of five chords containing direct chromatic relations, normally understood as passing through four keys, can be interpreted as belonging to a single key from beginning to end.(20) The progression, with its alternative analyses, is shown in Example 3. Riemann brings two lines of thought to bear here: first, the acknowledgement of the possibility of direct connections between the tonic and chords with chromatic content; second, the identification of chords containing chromatic pitches with diatonic chords from which they draw identity and meaning while retaining individual character. These lines of thought led to his concept of *Tonalitaet*, an expanded notion of key encompassing both diatonic and chromatic relations directly with the tonic, and to the mature concept of *Funktion* of the 1890s. Both concepts stem from his underlying urge to show that chromatic music retains and reinforces its essential tonal aspect rather than subverting it. ================================================== 20. Hugo Riemann, *Skizze einer Neuen Methode der Harmonielehre*, Leipzig: Breitkopf & Haertel (1880), pp. 67-69. ================================================== [9] While Riemann was developing the concept that eventually became *Funktion,* he also proposed an independent explanation of the mechanisms of chord connection. This was an exhaustive taxonomy based on intervals between roots and direction of progression.(21) Riemann retained this system of *Harmonieschritte* to explain chord progression even after introducing the *Funktion* idea; both are essential elements of his comprehensive harmonic theory. The advantage Riemann attributed to the *Harmonieschritte* system is that its particulars do not refer to key. He makes this clear in an impassioned refutation of Weber's Roman numeral notation, arguing for an essential identity of individual chord progression types existing independently of the character which they take on in the context of a key.(22) The system provides little explanation for motivational aspects of the progressions; it has no recourse to dissonance-based arguments such as those of Rameau and Weber. (23) ================================================== 21. This system was formalized by Henry Klumpenhouwer in a recent article in this journal: "Some Remarks on the Use of Riemann Transformations," Music Theory Online 0.9 (1994). 22. Riemann, *Katechismus der Musik*, Berlin: Max Hesse (1890), p. 65. 23. Scott Burnham has carefully investigated Riemann's reading of Rameau, and the differences in their harmonic concepts, in "Method and Motivation in Hugo Riemann's History of Harmonic Theory," Music Theory Spectrum, vol. 14/1, spring 1992. ================================================== [10] *Funktion*, on the other hand, has next to nothing to do with chord progression. Rather, it concerns the _meanings_ of the chords which progressions link. The principal significance of the functional archetypes Tonic, Dominant, and Subdominant is that they are the primary chords of the key, linked by the preeminent interval of the fifth. Scale degree identification per se is completely absent from the theory; any of the member pitches of a functional archetype can represent functional identity. By allowing for the identification of every possible diatonic and chromatic chord with one of the three functional archetypes, Riemann provided a means not otherwise available by which to understand these chords as exercising meaning within a prevailing key, rather than requiring constant reference to other keys. But a chord's *Funktion* does not specify its probable course of action. There is no counterpart in Riemann's theory to Rameau's doctrine of characteristic dissonances, differentiating the functions by their certain successors. Riemann's earliest writings do draw on Hauptmann's dialectic to substantiate the directed nature of familiar cadences.(24) But this aspect of logical necessity virtually disappears in later works. It would have been difficult to sustain as Riemann sought to account for every possible triadic progression within his theory.(25) Riemann's familiar prescription of T-S-D-T is often cited as an example of logical necessity in his functional theory. But perhaps his most characteristic argument for T-S-D-T appears in his composition treatise of 1902, rather than in the speculative works.(26) There Riemann painstakingly demonstrates to the student that the succession T-S-D-T strengthens the perception of tonic, while T-D-S-T weakens it. This argument is presented in terms of the favored choice among possibilities, rather than on the basis of any inherent properties of the functions themselves. While Riemann concludes that T-S-D-T is naturally smoother than T-D-S-T, there is nothing in his discussion to prove that the weaker cadence cannot be functional, nor that the stronger one is the only possible functional progression. The lesson is merely that T-S-D-T works and sounds better; the purpose of the discussion is chiefly to discourage the student composer from writing the progression from D to S.(27) ================================================== 24. Riemann, "*Musikalische Logik*", *Neue Zeitschrift fuer Musik* 28, (1872), pp. 279-82. 25. Harrison (op. cit., p. 282) views this development as an abandonment of higher principles, a deliberate move designed for pedagogical expediency and market favor. Alternatively, though, it could be seen as the progression from idealistic, derivative student work to a more mature and tempered approach, implicitly acknowledging the shortcomings of earlier ideas while advancing newer ones as fruitful intellectually as they were financially. 26. Riemann, *Grosse Kompositionslehre*, vol. I (1902), p. 33. 27. Further evidence comes from Riemann's principal analytic work, the complete Beethoven sonata analyses of 1918-20. T-S-D-T does predominate in the analyses; however, along with numerous other successions, Riemann identifies several instances of T-D-S-T, nearly always occurring in principal thematic areas. Riemann, *L. Van Beethovens saemtliche Klavier-Solosonaten*, vols. 1-3, Berlin: Max Hesse (1920). ================================================== [11] Carl Dahlhaus has examined Riemann's use of the terms *Funktion* and *Logik* and found both wanting. He has observed that while the term *Funktion* suggests a definite mathematical process by which to formally account for getting from chord X to chord Y, this kind of specificity is not to be found in Riemann's theory.(28) Likewise, Dahlhaus reproaches Riemann for claiming the attribute of musical logic for his system. Dahlhaus observes that, while the system does explain harmonic content of chords and the relations of chords within the tonal system, it must also supply rules and norms of harmonic progression in order to be truly logical. He finds that such rules are completely lacking in Riemann's system, which as a result appears more descriptive than logical. Ultimately, Riemann's functions inhere as tonal meanings in individual chords; they do not determine action from one to the next. One chord cannot imply another simply on account of its function. ================================================== 28. Carl Dahlhaus, "*Terminologisches zum Begriff der harmonischen Funktion*," *Die Musikforschung* 28/2 (1975), pp. 197-202. Newer mathematical approaches, such as the transformation system proposed by David Lewin, are sounder, but (deliberately) shift the focus of meaning from individual chords to progressions in order to rectify the perceived emptiness of Riemann's concept. Lewin, *Generalized Musical Intervals and Transformations*, New Haven: Yale University Press (1987), p. 177. Brian Hyer has also addressed this issue in his talk "The Concept of Function in Riemann," referenced in Burnham, op. cit., note 26; he argues a relational aspect for the *Funktion* concept. ================================================== [12] Clearly, Riemann's seminal idea is far removed from familiar concepts of function associating harmonic identity with scale-degree relations. But there is a more basic divergence having to do with the purpose of the systems. One way we use the term function is to signify the quality of harmonic relationship which makes music tonal. Used in this way it is an exclusive concept: there are functional relationships and there are non-functional relationships in harmony, with many different ways proposed to differentiate the two. For Riemann, function also represented that quality of harmonic relationship which makes music tonal. But his was an _inclusive_ concept. The objective of his elaborate system was to show that all possible chords and progressions could be accounted for in its terms as occurring within the key in relation to a tonic. While the cadential strength of progressions and their centrality to the key could vary, there was ideally no such thing as a non-functional progression within *Tonalitaet*. [13] What we are looking for in these older theories, I think, is a reflection of our belief that one of the important things chords do is imply other chords, and furthermore that they do so because of their function, whatever we understand that to be. All three of the theories discussed above fall short in this regard, each in its own way. Rameau provided an explanation showing how some chords imply other chords according to type, but ascribed their motivation to progress to non-chordal dissonance. Weber developed a way to clearly specify the position of each chord in its key, but allowed for all chord connections equally, and preferred not to speculate on motivational causes. Riemann explained harmonic coherence with a two-pronged approach: function specified the meaning of a chord in relation to its tonic and its key; the interval of root relation, which is independent of position in the key, specified the strength and directness of progressions. The motivational aspect of his theory was formulated as the concept of musical logic (not function), whose development he pursued early on but abandoned as his ideas matured. In our minds the lack of true teleological components in these theories of harmony can represent a serious shortcoming. Thus we may tend to read them in where they do not exist, or to lament their absence when it is undeniably perceived. It may be hard to imagine that all theorists of the common-practice era did not share our beliefs in the dynamic nature of harmonic identity, yet this is what close readings of at least these three theories reveal. But we need not conclude that these differences constitute failings on the part of the earlier theories. Rather, a clear understanding of the contrasts between earlier theories and our own can help to shed light on the expectations of our own time. [14] It has become natural for us to expect the ideal harmonic theory to explain how chord progressions are determined and goal- directed. Some of the responsibility for this, ironically, can be laid at Riemann's feet, for he was the one to introduce the term *function* in the first place. In his own work he explicitly associated *Funktion* with *Bedeutung*.(29) But the word naturally evokes more dynamic associations. After all, in everyday usage, the function of any object or concept has to do with what it does more than with what it is. It is inevitable that this sense of the word would have influenced our notion of harmonic function, leading us to associate the concept with the behaviors of chords and to transform it into an active verb ("functions as"). The positivistic model of much modern inquiry also orients us toward explanations which invoke logical determinacy. Moreover, the familiar feel of the term makes strict definition seem unnecessary. Yet this familiar feel derives more from informal usage (as the varied uses of the term cited at the beginning of this essay demonstrate) than from any rigorous and shared music-theoretic concept. Attempts to articulate the specific powers of chord function appropriately take the form of empirical summaries of chord behavior, such as the one quoted above in paragraph 1, note 2. It would be a formidable task to successfully formulate predictive rules to further specify exactly how and when each of the common functions of the IV chord as described must come into play. Such a fully rule-governed theory of harmonic function has proved on one hand to be an elusive goal, and on the other to be somewhat beside the point, since we have more satisfying deterministic explanations of music these days. ================================================== 29. This was his original definition of the term, I believe. Riemann (1890), p. 27. ================================================== [15] One of the principal teachings of Schenkerian theory is that the quality of goal-directedness in tonal music derives from short- and long-range contrapuntal and prolongational processes imbedded in the musical texture rather than from integral chord-to-chord progressions on the surface. If we accept this explanation of *Tonwille*, then perhaps it is unnecessary to require that our concept of harmonic function account fully for the same quality. A notion of function short on teleological implications might initially strike us as empty. But explanations of harmonic meaning and coherence remain necessary and important. If we limit our vision to recognizing diatonic scale-degree chords and their variants, then function becomes subsidiary in our minds to other musical processes. If, though, we open our view to imagine an enhanced system of diatonic and chromatic relations anchored to a tonic, something like Riemann's *Tonalitaet*, it may open our minds to contemplate in a positive way the greater structural potentials of the tonal system as exploited in mid-nineteenth to early twentieth-century music. Thus I would not like to suggest that we discard the function concept in our own descriptions of harmony or reject useful notions of harmonic identity and action. Function is a suggestive term which is still inspiring creative work in theory after over a century of use. But careful definition and elaboration is crucial. I do feel that we should be circumspect in attributing the function concept wholesale to theory before Riemann. The term carries so many associations for us that it is difficult not to read some of them into the historical subject, thereby occluding perception of subtle yet important differences from our own views. Even if we know exactly what we mean, there is no guarantee that our reader will accurately grasp our meaning when we use the term without scrupulous qualification, since there are so many acceptable interpretations of the concept. Furthermore, the widespread and casual use of the term nowadays has diminished its descriptive power. It may prove helpful to investigate our assumptions and more clearly articulate and differentiate the myriad concepts which function has come to represent for us. ============================================================ 2. Commentaries AUTHOR: Demske, Thomas TITLE: Response to Parncutt KEYWORDS: similarity, perception REFERENCE: mto.95.1.2.demske.art Thomas Demske Music Department Connecticut College 270 Mohegan Avenue New London, CT 06320 trdem@conncoll.edu [1] Richard Parncutt proposes a perceptual approach to similarity analysis based on, "average subjective judgment of global similarity by a representative group of listeners." Even if it were possible to achieve a general consensus on such a standard, I would be uncertain about how to apply it in musical contexts. [2] The "modified harmonic fluctuation" model of Messiaen's chord succession described in my essay was a rhetorical expedient. Most readers tentatively accepted the possibility of a connection between perceived breaks in surface continuity and low (whatever that means) REL, ASIM, and ATMEMB values. Competing clusters, based on different pivots or on different cutoff points relative to a single pivot, could thus presumably be evaluated according to how well they conformed to perception. (Recall that evaluation in general, and not perception in particular, was the focus of the essay.) But there are many basic difficulties here. One lies in identifying precisely what percepts might be appropriate testing grounds for the evaluation. (Cf. paragraph 16 in the essay.) Another is that of isolating the "similarity" relationship component from other factors contributing to a goal percept. (Cf. paragraph 17 in the essay.) [3] My working assumption throughout was that REL and comparable functions have something to do with perception. However valid that assumption may or may not be, the two problems mentioned above remain even for functions more securely grounded in that area. If I understand Professor Parncutt's paragraph 6 correctly, he is suggesting a table lookup function (?), where the table entries have been determined empirically through experimentation. I suppose that this means asking subjects to rate "global similarity" for 29 x 29 = 841 pairs of chords (or 841 x 2 = 1682, to check for immediate order effects). Perhaps the chords would be sounds, extracted from a single performance -- maybe normalized somehow, maybe not. It might even be possible (maybe!) to explain what "global similarity" means, so that subjects would have some idea of what to shoot for. [4] By construction, the proposed function should have something to do with perception. But how far would that "something" extend? Given competing clusters of the 29 chords under the proposed function, our hope would be to select only good clusters by listening to the piano ostinato. What to test against is the first decision: smooth progressions, surface grouping boundaries, shifts in large-scale harmonic region? Whatever we decide will likely require considerable extrapolation in order to relate it to the exhaustive process of discrete chord pairings used in deriving the function; each step in the extrapolation increases the distance between the function's application and its perceptual grounding. Next, given a goal percept, would we necessarily reject a clustering because it conflicts with the percept? Other factors not addressed through the experimental binary comparisons could take control in such situations -- contour changes; local tessitura; rhythm; clarinet, violin, and cello parts; voice leading. (Recent mto-list exchanges on enharmonicism seem especially relevant to me here.) The problem is in determining how far mitigating factors are operative, and how far they should be taken into account, when judging similarity-based boundaries according to perception. [5] David Lewin suggested in a recent mto-talk post that we drop the "similarity" label when referring to functions like REL, RECREL, etc. I suspect a wee bit of tongue-in-cheek here; I also doubt whether the SMT language police budget allows opening a new front in the continuing war on objectionable signifiers. So, what I suggest instead is that we recognize "context-free similarity" for the oxymoron that it is. (On a volunteer basis, of course.) Similarity presupposes a context. The context of REL is a particular intellectual apparatus. The context of (what I understand to be) Professor Parncutt's proposed similarity measure is a particular experimental setting. I would not at all suggest abandoning "similarity" functions. Like all reasonably well-developed constructs, they hold nice potential for theorists.(1) What I do suggest is applying more energy toward understanding their limits.(2) =============================== 1. See, for example, Chapter 6 of Marcus Castren's oft-mentioned dissertation, "RECREL: A Similarity Measure for Set-Classes" (Ph.D. diss., Sibelius Academy, 1994). Also, Allen Forte obtained remarkably interesting results some twenty-plus years ago with his R0, R1, R2, and Rp relationships (*The Structure of Atonal Music*, Yale University Press, 1973). Those relationships have been much maligned in the subsequent similarity literature. I think a more sympathetic re-evaluation, especially of Forte's analytical applications, could prove very illuminating. 2. Richard Hermann's response reached me only as I finished writing this. I will reply (if appropriate) after studying it. ============================================================== AUTHOR: Hermann, Richard TITLE: Towards a New Analytic Method for Post-Tonal Music: A Response to Thomas R. Demske KEYWORDS: similarity, atonal, post-tonal analysis, REL, set-theory, ASIM, ATEMB, contour theory, multidimensional similarity REFERENCE: mto.95.1.2.demske.art Richard Hermann University of New Mexico Department of Music Albuquerque, NM 87131-1411 harhar@unm.edu ABSTRACT: In an article entitled "Relating Sets: On Considering a Computational Model of Similarity Analysis," *Music Theory Online* 1.2 (1995), Thomas Demske criticizes some older published similarity relations and points to some general problems of analysis in post-tonal music. This response sketches a new analytical method for post-tonal music that places those similarity relations and other theoretical tools of the recent past in the context of some recent research and, in so doing, replies to some of the issues Demske raises. INTRODUCTION [1] In his article "Relating Sets: On Considering a Computational Model of Similarity Analysis," *Music Theory Online* 1.2 (1995), Thomas R. Demske seeks to use techniques of cluster analysis upon similarity relations found between pc- sets "abstracted from post-tonal analysis." He finds that the evaluation component that would define the boundary values for cluster analysis (which group similarity function return values between sets into rough equivalence classes) most difficult to find, that "the similarity relationship is too abstract to imply guidelines for its own application," and that "other potential criteria resist formal implementation." He further states that "other more commonly used tools in post-tonal analysis are susceptible to the concerns raised here." [2] Demske raises some important issues about the inherent nature and limitations of similarity relations, computational models, and typically used analytical techniques for post- tonal music. This response briefly reviews some his concerns but will not alleviate them. Instead, this response places similarity relationships into broader contexts and then suggests how they might reasonably be used with other post- tonal theoretical tools of fairly recent vintage. While my suggested approach might ease his discomfort somewhat, other interesting issues arise. Unfortunately, due to the broad issues summoned by Demske and due to the limitations of space in this forum, my response can only broadly sketch the approach. It is hoped that this response might spark continued responses upon the issues surrounding post-tonal theory; recent composition; history, analysis, perception and perhaps even the sociology of post-tonal music that Demske reopens or implies. FOUR OF DEMSKE'S DISSATISFACTIONS WITH ABSTRACT SIMILARITY RELATIONS [3] 1) The author seems to find fault with the fact that similarity relations lack transitivity, although he does not mention the transitive property in his essay. See his footnote three where he writes "Blind subset polling is a basic source of such barriers. Two REL calls with the same pivot may yield identical results, and yet differ with respect to the types of subsets counted. Ignoring the degree of this difference when comparing REL value spreads strikes me as questionable." Similar thoughts are found in paragraph [10]. [4] By definition, similarity relations lack transitivity. Thus, if transitivity is valued so highly that its lack becomes a standard for rejection of a theory, then much of value will be lost to post-tonal analysis. For instance, similarity relations might just be the class of tools best used to describe how change is accomplished from one process or segment to another differing process or segment within a work. Similarity relations might also be of analytical use in describing interesting instances of variation such as might occur in Schoenberg's concept of developing variations. Other compelling uses will be discussed shortly. [5] 2) Demske sees as flawed a situation where some collection of set-classes can be grouped together in different ways by the similarity relation REL depending upon which pc- set is selected as the "pivot" set-class. Again, see his third footnote and paragraph [10]. The pivot set-class is the set-class which is held as a constant in measuring the similarity relation with each of the other set-classes.(1) ================================ 1. Lewin has noted that Demske's use of REL is not completely in accord with Lewin's definition. Instead of a single pivot set-class, Lewin uses a collection of set-classes called TEST selected from the local context. REL measures similarity of other analytically interesting set-classes, collectively called COMPARE, with those from TEST. See Lewin's mto-talk message of 22 Mar 1995 and especially his "A Response to a Response: On PCSet Relatedness," *Perspectives of New Music* 18.1-2 (Fall-Winter 1979, Spring-Summer 1980): 498-502 where the definition of REL is found. ================================ [6] The flaw described in paragraph [5] above could be seen as a virtue. For instance, when a member of set-class 3-11 [037] is found at a temporal posterior border of an octatonic collection and as a temporal anterior border of an abutting diatonic collection, it seems reasonable and even desirable for formal and abstract similarity relations to yield different return values between the octatonic collection and the member of set-class 3-11 and between the diatonic collection and the 3-11 member in that context. The passage of time through the passage does change the "color" of the member of 3-11. [7] 3) Demske finds that intuition can be mightily strained in attending, in the abstract, to all of the possible similarity relations that occur between all of the set- classes. See his paragraph [12]. [8] While we need to be aware of the potentialities of similarity in the abstract, we only need in analysis to attend to those reasonable relationships pertaining to the piece or segment under consideration. [9] 4) The author seems to resist context sensitive criteria such as a selected collection of set-classes to be used as the metaphoric yardstick such as Lewin's TEST from which to measure similarity. See his paragraph [13] and footnote number four in that regard. [10] Context sensitive criteria seem reasonable when the repertoire under study has already shown that individual pieces inhabit the post-tonal pc set world in very different ways. Also, certain segments at various levels of formal design within the same piece may also inhabit that world in significantly different ways. TWO PROBLEMS ENCOUNTERED IN THE ESSAY [11] 1) At times Demske appears to veer between formalist theoretical statements or claims and phenomenological or perceptual observations and desires. He judges one by the values of the other. In paragraph [16] he writes: "The idea that any formal evaluation procedure could embrace all of the [analytical segmentational] possibilities seems untenable. On what bases would a partial set of possibilities be selected for implementation? Since the different criteria may address different---and possibly conflicting--aspects of perception, how would the application of one criterion be coordinated with that of another?" [12] All analysts must make decisions about what strikes them as the most salient or important features of the piece and then select the appropriate "formal evaluation procedure" designed to address those features. Certainly to run all possible theoretical tools at the piece in an analysis would quickly overwhelm the analyst with a plethora of analytical observations upon the data: most observations are likely to be true, but many may be of little significance, aural or otherwise. Thus, the selection and use of theoretical tools for analysis acts like a set of filters upon the analyst and the piece at hand. It seems then that Demske's disagreement may well lie with the selection of tools--that is, with what is to be considered perceptually important, rather than with the nature of the formalist tool itself.(2) If a carpenter selects a hammer to cut a board, then poor results can be expected. ================================== 2. In his mto-talk message of 30 March 1995, David Lewin writes: "While the word [similarity] is suggestive, it might be a good idea to stop using it in formal theoretical discourse, because the intuitions it invokes are not all that reliable. (Except we probably can't stop using it at this stage of matters, ...." I suggest that we retain the use of the word *similarity* for formal relations that possess reflexivity and symmetry, but lack transitivity as mathematicians would have it: see Seymour Lipschutz, *Discrete Mathematics*, (New York: McGraw-Hill, 1976): 28. We then might use Robert D. Morris's phrase *aural similitude*--from his "A Similarity Index for Pitch-Class Sets," *Perspectives of New Music* 18/2 (1979-80): 445-60, as Demske acknowledges in his paragraph 5--when we wish to discuss perceptual matters. I also propose that, following a suggestion of Morris's, we use the term *resemblance relation* when we discuss relations that model inclusion relations whether or not they are formally similarity relations. These relations then potentially model some modest sense of "aural similitude" in the abstract. Whether or not these relations actually do model perception in a specific passage depends upon whether the passage exhibits its materials in such a way that encourages its perception with that tool by a reasonably experienced listener. See Richard Hermann, "A General Measurement for Similarity Relations: A Heuristic for Constructing or Evaluating Aspects of Possible Musical Grammars," Ph.D. Dissertation, Eastman School of Music, University of Rochester, 1994: 1-119 for a classification system for resemblance relations and a mathematical and historical evaluation of published resemblance relations. See pages 123-36 for discussion and classification of all possible classes of resemblance relations. =================================== [13] 2) In the essay, the reader may get the sense that Demske expects too much from any given class of theoretical tools such as the here discussed similarity relations. For example, in traditional tonal music the theory of harmony fails in explaining supertonic expansions through voice- exchange and in progressions found within some sequences. Consider, for example, Mozart's *Piano Concerto* number 9 in E-flat major, K. 271/II at measures 28 through 30 as an instance of supertonic expansion, where a supertonic harmony at measure 28 is followed by a tonic in measure 29 (an "illegal" harmonic elision); or Bach's *Little Prelude*in C major, BWV 924, at measures one through three, as an instance of a sequence where the harmonies go "backward" along the circle of fifths (I-V-II- VI-III, "illegal" harmonic retrogressions). These can be found respectively on pages 132-33 and 253-254 in Aldwell and Schachter's *Harmony and Voice-Leading*, 2nd ed. New York: Harcourt Brace Jovanovich, 1989. The problem here is not so much with the theory of harmony--although it does have its well-known problems--but rather with knowing when the use of the theory of harmony is appropriate. In these tonal instances, the effects of structural outer voice counterpoint, form, rhythm and so forth inform how the theory of harmony--*Stufen* in this case--is reasonably to be employed. For instance in the case of the Mozart, analysts need to realize that the tonic harmony is not functional but rather is the result of harmonizing a deeper layer passing tone with an incomplete neighbor--a contrapuntal relation--between the outer voices. DEMSKE'S EXAMPLE OF ABSTRACT SIMILARITY RELATION FAILURE IN A PASSAGE FROM THE FIRST MOVEMENT, *LITURGE DE CRISTAL*, OF MESSIAEN'S *QUATUOR POUR LA FIN DU TEMPS* [14] In paragraphs [14] through [17] and their accompanying figures, Demske notes that--within the repeating sequence of 29 chords--his intuitions of aural similitude run counter to the rough agreement found in the analytical results of Lewin's REL, Rahn's ATEMB, and Morris's ASIM similarity relations upon this chordal sequence. Their results are elegantly displayed in Demske's Figure 5.(3) In the context he has shown, Demske's complaint that these abstract similarity relations yield poor results from the vantage of aural similitude is clearly on target: the master's hammer was the wrong tool indeed. Brian C. Robison, in responding to Demske's intuitions, brings his own more appropriate tool to bear upon the passage: it deals more directly with pitches of the score and gives a plausible explanation for Demske's intuitions.(4) Clearly, ASIM, ATEMB, and REL are too "coarsely grained" for this particular situation while Robison's more "finely grained" work is here more suitable. Perhaps in some other post-tonal music with frequent octave duplications the more coarsely grained tools would better reflect aural similitude than Robison's tool. =================================== 3. See John Rahn, "Relating Sets," *Perspectives of New Music* 18.2 (1979-80): 488-97 for information on his ATEMB. See footnote 1 above for information on Lewin's REL and footnote 2 above for information on Morris's ASIM. 4. See Robison's mto-talk postings of 29, 30, and 31 March 1995 in this regard. For a more in depth look at his theoretical work employed in those postings, see his "Modifying Interval-Class Vectors of Large Collections to Reflect Registral Proximity Among Pitches," *Music Theory Online* 0.10 (1994). For other theoretical work capable of addressing Demske's concerns in this chordal sequence, see Robert D. Morris, "Equivalence and Similarity in Pitch and their Interaction with Pcset Theory," an unpublished mss. delivered at the Society for Music Theory Annual Conference held at Tallahassee, November, 1995 and Richard Hermann, "Theories of Chordal Shape, Aspects of Linguistics, and their Roles in Structuring Berio's *Sequenza IV for Piano*," an essay from *Concert Music, Rock, and Jazz since 1945, Essays and Analytical Studies,* Elizabeth West Marvin and Richard Hermann, eds. Rochester, New York: University of Rochester Press, forthcoming. =================================== TWO FURTHER COMPLAINTS OF MINE ABOUT EXISTING RESEMBLANCE RELATIONS [15] 1) Until quite recently, resemblance relations have typically concerned themselves with resemblance between pitch-sets through the powerfully reductive concepts of pitch- class and set-class. Resemblance relations that address musical dimensions such as pitch-space, time, timbre, sound source direction, and so forth have just recently begun to appear. [16] 2) Apart from some work on serial music, I am aware of no work yet in print that simultaneously addresses resemblance relations in more than one musical dimension. In order to get a better fit between formal models and aural similitude for some important pieces in the repertoire, multidimensional resemblance relations need to be investigated.(5) =================================== 5. For some first steps in that direction, see Larry Polansky, "Morphological Metrics: An Introduction to a Theory of Formal Distances," in Proceedings of the International Computer Music Conference (San Francisco: Computer Music Association, 1987) and Richard Hermann, "A General Measurement for Similarity Relations:..": pp. 120-78 and "An Approach to Multidimensional and Multisubdimensional Similarity for Post- Tonal Music" delivered November 1995 at the Society for Music Theory annual conference, Tallahassee, Florida. Subdimensions can informally be understood through some examples: subdimensions from the dimension of time are duration, metric position, attack-point position, and so forth. =================================== TOWARDS AN ANALYTICAL METHOD FOR POST-TONAL MUSIC: A PROVISIONAL SKETCH [17] Another way of looking at this situation is in speculating that some sort of unknown or partially known "grammar" may well dictate when and where various existing post-tonal analytical tools are to be best employed. If that grammar is even partially known, it might even suggest where gaps in our knowledge need to be filled. It may be possible now to start the discussion of how some recent tools might fit together with older ones within an overall sketch of a new post-tonal analytical method. That we are likely to disagree on this sketched method is highly probable; note how difficult it is/has been to obtain general agreement on a precisely specified teaching methodology for tonal analysis. And that lack of agreement is over a repertoire that has enjoyed several hundred years of intense theoretical contemplation and analytical study. Nonetheless, we gain insight into what is lacking by evaluating how various methods of combining tools fare. As pieces inhabit the post-tonal worlds in different ways, I suspect that multiple methods of combining and selecting tools will be necessary. [18] Discussion of Demske's complaints about some abstract similarity relations has shown that in order to get formal analytical results that correlate with our sense of aural similitude, our tools must be employed at the correct level of precision. In the Messiaen example, the pitch-class/set-class similarity approach was counter-intuitive while a pitch-space approach was more successful. Recent developments in contour theory and investigations into different kinds of musical spaces now suggest that post-tonal analysis can have a variety of spaces available to it ranging from the most diffuse on up to the most precise.(6) On the most diffuse extreme, spaces whose elements lack identifiable intervals between them--called "preintervallic"--have been investigated and those investigations have yielded interesting insights into form and instrumental/relative register assignments.(7) More precise are spaces inhabited by the relative or ordinally based intervals found in the various contour theories. Here, only inequalities can rank the elements within the space. Note that Marvin and Hermann have also extended contour theory to musical dimensions other than pitch.(8) Next in precision are those intervals such as the familiar interval-classes that are collapsed from an infinite space onto a finite space through modulo arithmetic. And yet greater in precision are the absolute intervals, such as the distances between equal-tempered pitches. Certainly other kinds of intervals lurk in between these: see the Morris and Lewin writings of footnote six above. Recent theoretical developments in post-tonal theory occurring since ASIM, ATEMB, and REL have widened the scope for development of resemblance relations in other musical dimensions and subdimensions and have even started to show how they can be coordinated. See footnotes two and five above. With research continuing in the fields of musical spaces, resemblance relations in other musical dimensions, and multidimensional or multisubdimensional similarity, analysts will soon have a greater variety of tools to select in order to best model their perceptions of aural similitude. =================================== 6. See Robert D. Morris, *Composition with Pitch-Classes*, (New Haven: Yale University Press, 1987): pp. 23-7 and David Lewin, *Generalized Musical Intervals and Transformations* (New Haven: Yale University Press, 1987): pp. 16-30 for discussions of interval--of varying kinds--based spaces in several different musical dimensions. 7. See Richard Hermann, "On 'Preintervallic' Spaces and on Their Interactions with Some Intervallic Spaces,"unpublished mss. delivered November 1994 at the Society for Music Theory annual conference, Montreal, Canada. 8. The following is a bibliography of recent writings on contour theory by theorists: Michael L. Friedmann, "A Methodology for the Discussion of Contour: Its Application to Schoenberg's Music," *Journal of Music Theory* 29, 2 (Spring 1985): 223-248; Morris, *Composition with Pitch-Classes*, 26- 32; Elizabeth West Marvin and Paul A. Laprade, "Relating Music Contours: Extensions of a Theory for Contour," Journal of Music Theory 31, 2 (Spring 1987): 225-267; Michael L. Friedmann,"A Response: My Contour, Their Contour," *Journal of Music Theory* 31, 2 (Spring 1987): 223-248; Elizabeth West Marvin, "The Perception of Rhythm in Non-Tonal Music: Rhythmic Contours in the Music of Edgard Varese," *Music Theory Spectrum* 13 (1991): 61-78; Larry Polansky and Richard S. Bassein, "Possible and Impossible Melodies: Some Formal Aspects of Contour," *Journal of Music Theory* 36, 2 (Fall 1992): 259-279; Robert D. Morris, "New Directions in the Theory and Analysis of Musical Contour," *Music Theory Spectrum* 15, 2 (Fall 1993): 61-78; Richard Hermann,"A General Measurement for Similarity Relations: ...": 123-43; and Elizabeth West Marvin, "A Generalization of Contour Theory to Diverse Musical Spaces: Analytical Applications to the Music of Dallapiccola and Stockhausen," in *Concert Music, Rock and Jazz since 1945: Essays and Analytical Studies*. =================================== [19] When faced with music by composers such as Peter Maxwell Davies, Morton Feldman, or Ralph Shapey--to give only a few examples in which there is no known or reasonably convincing and widely accepted "grammar" to act as a guide in analysis--how might we more profitably proceed?(9) =================================== 9. Much of the musical "grammar" has been well established and accepted for the serial works of composers such as Schoenberg, Webern, Berg, and Stravinsky and for those serial composers such as Babbitt. So perhaps this methodological sketch has less import for that galaxy of the post-tonal universe. For a veritable *summa* of serial technique, see Robert D. Morris's *Composition with Pitch-Classes*. For an important and more recent study that greatly extends serial combinatorial theory through a partitional approach, see Brian Alegant's *The Seventy-Seven Partitions of the Aggregate: Analytical and Theoretical Implications*, Ph.D. Dissertation, Eastman School of Music of the University of Rochester, 1993. =================================== [20] After the analyst becomes thoroughly familiar with the music's sound and symbol, the first issue to be faced is segmentation: into what units should the piece be divided? Recent work by Polansky and Uno, following work by Tenney, use principles of Gestalt psychology to create computer-based formal procedural models for segmentation. These models are explicitly multidimensional. After Tenney, formal segments are called temporal gestalt units, and these formal units can nest within one another several layers deep. Gestalt psychology investigates the role of shape in perception. Thus, these shape oriented theories of segmentation are likely to coordinate well with the new contour space theories because they are also concerned with shape in various dimensions. In this light, contour theory can profitably be thought of as a kind of abstract master dimension. Segmentations that arise from formalist theories sensitive to the perceptual issues of shape will go a ways towards eliminating Demske's complaint of "blind subset polling." Lefkowitz and Taavola, Brinkman, and Hasty have also made contributions to this developing area of segmentation in post-tonal theory.(10) =================================== 10. See Larry Polansky, "Morphological Metrics: An Introduction to a Theory of Formal Distances," in Proceedings of the International Computer Music Conference, San Francisco: Computer Music Association; Yayoi Uno, "The Roles of Compositional Aim, Syntax, and Design in the Assessment of Musical Styles: Analyses of Piano Music by Boulez, Cage, Babbitt, and Xenakis Circa 1950," (Ph.D. dissertation, University of Rochester, 1994); David S. Lefkowitz and Kristen Taavola, "Generalizing Segmentation: A Multi-Dimensional Approach/Piece-Specific Weighting System," unpublished mss. given at the 1993 New England Conference of Music Theorists; Christopher F. Hasty, "Phrase Formation in Post-Tonal Music," *Journal of Music Theory* 28, 2 (Fall 1984): 167-190; and Alexander R. Brinkman, *Pascal Programming for Music Research*, (Chicago: University of Chicago Press, 1990), 783-97. For earlier foundational work in this area, see James Tenney, *Meta + Hodas and META Meta + Hodas*, 2nd ed. (Oakland: Frog Peak Music, 1988); James Tenney and Larry Polansky, "Temporal Gestalt Perception in Music," *Journal of Music Theory* 24, 2 (Fall 1980): 205-241 and their *Hierarchical Temporal Gestalt Perception in Music: A "Metric Space" Model* (Toronto: York University Press, 1978). =================================== [21] The next issue to be faced might best be described by the question: What levels of precision--that is what kinds of musical space--best capture the intuitions of relatedness and dissimilarity in the piece? Here, multidimensional or multisubdimensional similarity relations can act as a heuristic to narrow the number of interesting, potentially applicable musical spaces to those likely to yield the best results. Those multidimensional or multisubdimensional similarity relations yielding probabilistic return values scaled through standard deviation techniques can do an analysis of the potentials of the spaces themselves in the abstract, an *a priori* analysis. Then, those results can be compared with empirically derived results from the score: an *a posteriori* statistical and probabilistic analysis. Where the two sets of results do not significantly correlate, important features of a relevant grammar may have been identified. Follow up analyses of the segments--selected by shape based segmentation theories--could then be done using equivalence class analysis, resemblance relations, and so forth, designed for those specific musical spaces.(11) Relations, operations, and transformations that significantly preserve shape are preferred to those that do not preserve shape. This analytic process seems likely to reveal a good ratio of "hearable" structures to other less "hearable" structures. The fruits of those tailored analytical processes can then be organized as strings of operators, networks of various kinds, and so forth as is appropriate to the music.(12) =================================== 11. This approach has been employed with Luciano Berio's *Sequenza IV for Piano solo*. See Hermann, "A General Measurement for Similarity Relations: ....": pp. 201-34 and 252-54. The use of a redesigned contour theory along with a probability based similarity relation scaled by statistical techniques gives the flexibility to be able to deal simultaneously with various different kinds of musical spaces of differing cardinalities in an n-dimensional probability space. 12. See Morris, *Composition with Pitch-Classes* for technical information on groups of operators and their use in compositional designs; and David Lewin, *Generalized Musical Intervals and Transformations*: pp. 157-254 for technical information on the design of networks for analytic use, and his *Musical Form and Transformation: 4 Analytic Essays* (New Haven: Yale University Press, 1993) for extended analyses using networks. Many of the issues raised in this response have been commented upon by Jay Rahn. See his "From Similarity to Distance; From Simplicity to Complexity; From Pitches to Intervals; From Description to Causal Explanation," *Music Theory Online* 0.9 (1994). Other pertinent works of his are found in that article's reference list. =================================== CONCLUSION: A WISH [22] As these formalist techniques are all easily amenable to computer implementation--and many have been so implemented--I wish that these tools could all be found in one big sophisticated suite of software. Pieces could be encoded and loaded into database-like structures so that analysts could then follow their intuitions and call up the needed software tools designed for the specific kinds of musical spaces desired and use them on the work.(13) =================================== 13. A database structure for electronically "holding" encoded scores is already available. See Alexander R. Brinkman, *Pascal Programming for Music Research*, (Chicago: University of Chicago Press, 1990): pp. 137-154, 751-812, and 825-915. =================================== [23] Although much theoretical work has been done since ASIM, ATEMB, and REL made their first appearances in 1980--and only a small amount of the work could be cited here--much more yet remains to be done in understanding the various musical spaces and designing appropriate equivalence class and resemblance relation tools for them. One benefit of continuing this line of research is that "updating" ASIM, ATEMB, and REL for use in other dimensions and for use in multidimensional and multisubdimensional analysis is possible. Marvin and Laprade have already updated ATEMB for use with their contour theory (see footnote number eight). While other quite important contributions and issues such as timbre theory, atonal voice-leading, and the influence of feminist thought, among others, upon analysis of this repertoire can only be barely mentioned or imagined here, it is time to start the discussion of how and when it is appropriate to use various combinations of these theoretical entities. Demske's reminder about these issues deserves our serious attention, and calls for discussion to begin. REFERENCES CITED Aldwell, Edward and Carl Schachter. 1989. *Harmony and Voice- Leading*. 2nd ed. New York: Harcourt Brace Jovanovich. Alegant, Brian. 1993. *The Seventy-Seven Partitions of the Aggregate: Analytical and Theoretical Implications*. Ph.D. Dissertation, Eastman School of Music, University of Rochester. Bach, Johann Sebastian. *Little Prelude* in C major. BWV 924. Berio, Luciano. 1967. *Sequenza IV for Piano solo*. London: Universal Editions. Brinkman, Alexander R. 1990. *Pascal Programming for Music Research*. Chicago: University of Chicago Press. Demske, Thomas R. 1995. "Relating Sets: On Considering a Computational Model of Similarity Analysis." *Music Theory Online* 1.2. Friedmann, Michael L. 1985. "A Methodology for the Discussion of Contour: Its Application to Schoenberg's Music." Journal of Music Theory 29, 2: 223-248. Friedmann, Michael L. 1987. "A Response: My Contour, Their Contour." *Journal of Music Theory* 31, 2: 223-248. Hasty, Christopher F. 1984. "Phrase Formation in Post-Tonal Music." *Journal of Music Theory* 28, 2: 167-190. Hermann, Richard. 1994. "A General Measurement for Similarity Relations: A Heuristic for Constructing or Evaluating Aspects of Possible Musical Grammars." Ph.D. Dissertation, Eastman School of Music, University of Rochester. Hermann, Richard. 1994. "On "Preintervallic" Spaces and on Their Interactions with Some Intervallic Spaces," unpublished mss. delivered at the Society for Music Theory annual conference, Montreal, Canada. Hermann, Richard. 1995. "An Approach to Multidimensional and Multisubdimensional Similarity for Post-Tonal Music" unpublished mss. delivered at the Society for Music Theory annual conference, Tallahassee, Florida. Hermann, Richard. forthcoming. "Theories of Chordal Shape, Aspects of Linguistics, and their Roles in Structuring Berio's *Sequenza IV for Piano*." an essay from *Concert Music, Rock, and Jazz since 1945, Essays and Analytical Studies.* Elizabeth West Marvin and Richard Hermann, eds. Rochester, New York: University of Rochester Press. Lefkowitz , David S. and Kristen Taavola. 1993. "Generalizing Segmentation: A Multi-Dimensional Approach/Piece-Specific Weighting System." unpublished mss. delivered at the New England Conference of Music Theorists. Lewin, David. mto-talk postings of 22 and 30 March 1995. Lewin, David. 1980. "A Response to a Response: On PCSet Relatedness." *Perspectives of New Music* 18, 2: 498-502. Lewin, David. 1987. *Generalized Musical Intervals and Transformations*. New Haven: Yale University Press. Lewin, David. 1993. *Musical Form and Transformation: 4 Analytic Essays*. New Haven: Yale University Press. Lipschutz, Seymour. 1976. *Discrete Mathematics*. New York: McGraw-Hill. Marvin, Elizabeth West and Paul A. Laprade. 1987. "Relating Music Contours: Extensions of a Theory for Contour." Journal of Music Theory 31, 2: 225-267. Marvin, Elizabeth West. 1991. "The Perception of Rhythm in Non-Tonal Music: Rhythmic Contours in the Music of Edgard Varese." *Music Theory Spectrum* 13: 61-78. Marvin, Elizabeth West. forthcoming. "A Generalization of Contour Theory to Diverse Musical Spaces: Analytical Applications to the Music of Dallapiccola and Stockhausen." in *Concert Music, Rock and Jazz since 1945: Essays and Analytical Studies*. Rochester, New York: University of Rochester Press. Messiaen, Olivier. 1957. *Quatuor pour la Fin du Temps*. Paris: Editions Durand and Co. Morris, Robert D. 1980. "A Similarity Index for Pitch-Class Sets." *Perspectives of New Music* 18, 2: 445-60. Morris, Robert D. 1987. *Composition with Pitch-Classes*. New Haven: Yale University Press. Morris, Robert D. 1993. "New Directions in the Theory and Analysis of Musical Contour," *Music Theory Spectrum* 15, 2: 61- 78 Morris, Robert D. 1995. "Equivalence and Similarity in Pitch and their Interaction with Pcset Theory," an unpublished mss. delivered at the Society for Music Theory Annual Conference, Tallahassee, Florida. Mozart, Wolfgang Amadeus. *Piano Concerto* no. 9 in E-flat major. K. 271, 2nd mvt. Polansky, Larry. 1987. "Morphological Metrics: An Introduction to a Theory of Formal Distances." in Proceedings of the International Computer Music Conference. San Francisco: Computer Music Association. Polansky, Larry and Richard S. Bassein. 1992. "Possible and Impossible Melodies: Some Formal Aspects of Contour." Journal of Music Theory 36, 2: 259-279. Rahn, Jay. 1994. "From Similarity to Distance; From Simplicity to Complexity; From Pitches to Intervals; From Description to Causal Explanation." *Music Theory Online* 0.9. Rahn, John. 1980. "Relating Sets." *Perspectives of New Music* 18, 2: 488-97. Robison, Brian C. 1994. "Modifying Interval-Class Vectors of Large Collections to Reflect Registral Proximity Among Pitches." *Music Theory Online* 0.10. Robison, Brian C. mto-talk postings of 29, 30, and 31 March 1995. Tenney, James and Larry Polansky. 1978. *Hierarchical Temporal Gestalt Perception in Music: A "Metric Space" Model*. Toronto: York University Press. Tenney, James and Larry Polansky. 1980. "Temporal Gestalt Perception in Music." *Journal of Music Theory* 24, 2: 205-41. Tenney, James. 1988. *Meta + Hodas and META Meta + Hodas*. 2nd ed. Oakland: Frog Peak Music. Uno, Yayoi . 1994. "The Roles of Compositional Aim, Syntax, and Design in the Assessment of Musical Styles: Analyses of Piano Music by Boulez, Cage, Babbitt, and Xenakis Circa 1950." Ph.D. dissertation, Eastman School of Music, University of Rochester. ============================== AUTHOR: London, Justin M. TITLE: Misreading Meyer: a reply to Cochrane KEYWORDS: Cochrane, Meyer, conformant relationships, ontology, epistemology, hierarchic levels, closure, Deleuze, Narmour, Eco REFERENCE: mto.95.1.1.cochrane.art Justin M. London Carleton College Department of Music jlondon@carleton.edu ABSTRACT: A response to Richard J. Cochrane's article "The Phases of Fire" which appeared in volume 1.1 of this journal. Two main aspects of Cochrane's presentation are critiqued: (1) that in a number of substantial ways Cochrane has misrepresented Meyer's account of conformant relationships in musical structure (which Cochrane refers to as "Meyer's concept of 'conformancy'"), and (2) that the tripartite notion of model, copy, and simulacrum does not map onto musical structures in general and Meyer's account of conformant relationships in particular. [1] Let me begin by first citing a number of minor examples of where Cochrane, either explicitly or implicitly, misquotes or misconstrues various aspects of Meyer's argument. Right off the bat it should be noted that Meyer does not use the term "conformancy," but rather speaks of "conformant relationships."(1) Cochrane's transformation of this word from Meyer's adjectival use to a nominative reveals the way in which he has reinterpreted Meyer, as we shall see below. Another problematic alteration (in this case, an addition) to Meyer's argument is Cochrane's repeated use of the term "dialectic."(2) While Meyer does speak of the tension between musical continuity and musical closure--indeed this is one of the guiding principles of his entire book--it is not accurate to describe Meyer's view of music as dialectic or dialectical. Indeed, Meyer takes Reti to task for the latter's dialectical approach to musical structure and his reification (not to mention blatant overuse) of conformant relationships.(3) Yet another example of Cochrane's interpretive ventriloquism occurs in his summation and discussion of Meyer's "five factors for coherent musical structure."(4) Here Cochrane notes that "copies must be separable units, or poses," a grammatical construction which implies that "poses" is Meyer's term, whereas in fact it is Cochrane's. As a final example, Cochrane claims that Meyer's analyses "show a development of large-scale, or macro-dialectics . . . out of smaller dialectically constructed units, down to the micro-dialectical copy itself."(5) Here Cochrane seems to mistake hierarchic nesting (where in his characteristic fashion Meyer notes subordinate and superordinate relationships between various structural levels) with dialectic structure. Meyer explicitly denies that the structural patterns he describes are the product of recursive processes: The way in which a particular parameter acts in articulating structure may be different on different hierarchic levels. For example, on lower levels dynamics and orchestration tend to contribute to the articulation of rhythmic patterns, but on higher levels they generally serve in the structuring of large-scale formal relationships. . . . The syntax of particular parameters tends to change as one moves from one level of the hierarchy to another.(6) This is in flat contradiction to the kind of conformant relationships that Reti pursues and that I infer Cochrane to be describing. ================================================== 1. Cochrane, paragraph 1. 2. ibid., para. 3. 3. See *Explaining Music* (Chicago: University of Chicago Press, 1973) pp. 64-65. Though Meyer does entertain notions of music history in dialectic terms (ibid., pp. 56-59), this is a historical perspective, not an analytic one. 4. Cochrane, paragraphs 3 & 4. Actually, Meyer's "five factors" are not those which give rise to musical coherence, but are factors which delineate musical patterns, and to that end are mainly aspects of articulation and closure which serve to individuate units of musical structure (Meyer, p. 83). 5. Cochrane, paragraph 6. 6. Meyer, p. 89. ================================================== [2] Cochrane begins his essay by presenting Meyer's "formula" for gauging the strength of perceived conformance/musical similarity:(7) Regularity of Individuality of Similarity of pattern (schemata) . profile . patterning Strength of = _______________________________________________________ perceived variety of intervening temporal distance conformance events . between events With this equation (which Meyer presents as a summary to several pages of discussion) Meyer tries to unpack a relatively straightforward analytical notion: "the greater the variety of intervening events and the greater the separation in time between two comparable events, the more patent the shape of the model must be if a conformant relationship is to be perceived"(8). In his exegesis of this equation Cochrane misconstrues a number of its terms. First, Cochrane claims that "regularity of pattern . . . is the most ill-defined of terms, but it seems to mean simply that a pattern which is very complex will not be easily recognizable when it reappears."(9) Cochrane ignores/omits Meyer's inclusion of "schemata" in this term. Schemata are, of course, given substantial treatment by Meyer; indeed, a discussion of melodic schemata comprises the entire second half of Meyer's book. In context it is thus clear that by "regularity of pattern" Meyer means syntactic regularity--that is, the extent to which a particular musical shape can be recognized in terms of its relation to a stylistic archetype (e.g., a cadential progression characteristic of a particular style). This term has nothing to do with the relative complexity of any particular pattern. Next, "Individuality of profile" does not mean, as Cochrane claims, that "the pattern must not be too like the surrounding music," but rather that some aspects of the musical shape itself must be distinctive, and not just a presentation of generic syntactic patterns.(10) "Individuality" is thus included to balance the generic features of a particular motive that are recognized by the first term of the numerator (for example, a figure that is a triadic arpeggiation) with other features (such as a characteristic rhythm) which give the otherwise generic shape a particular identity. Likewise "Similarity of patterning" does not mean, as Cochrane claims, "similarity between copies of the model" (for of course this is precisely the product that the "Strength of perceived conformance" is supposed to represent), but rather the ways in which various parameters are involved in varying subsequent presentations of a musical shape. Finally, the product of this equation is not "strength of the conformant relationship" but rather the "strength of the *perceived* conformance." Meyer is keenly interested in the perceptual aspects of musical structure and musical experience. The terms in the numerator of the equation are those factors which make a particular musical shape easy to remember and recall when it re-appears, while the terms in the denominator are those factors which inhibit recall. Conformance is not simply a property of the musical object(s); rather it arises through our interaction with the musical object, hence Meyer's use of the term "conformant relationships" and not "conformancy." Meyer's essential question is not ontological, but epistemic. ================================================== 7. Meyer, p. 49; Cochrane paragraph 1. (Cochrane presents these terms in an abbreviated fashion, i.e., C = R.I.S./V.T). 8. Meyer, p. 49. 9. Cochrane paragraph 1. 10. This difference between generic structural patterns versus musical figures characteristic to a particular work has been discussed at some length by Eugene Narmour, who draws a distinction between "style structures" and "style shapes" in *The Analysis and Cognition of Melodic Complexity: The Implication-Realization Model,* (Chicago: University of Chicago press, 1992). ================================================== [3] Cochrane's misappellation of "conformancy" reveals his own ontological reification of conformant relationships. Given that Meyer is interested in *perceived* similarities between musical structures, it follows that he is less concerned with the "real" similarities and differences between musical objects as he is with the ways in which listeners come to make judgements regarding similarity and difference. The validity or invalidity of analytic/listening judgements based on conformace-as-heard (to paraphrase Clifton) informs Meyer's subsequent critique of Reti. Reti's analyses are called into question not because the conformant structures he finds are not there, but rather (a) because many of the relationships Reti claims to be present are not likely to be perceived as distinct instances of conformance, and (b) even if they are perceived (perhaps with the help of Reti's analyses) their musical relevance is often questionable. [4] At the core of Cochrane's critique is Meyer's omission/exclusion of "the simulacrum" in the latter's discussion of conformant relationships. Instead of speaking only of "models" and "copies," Cochrane believes that a third term--the simulacrum--must be introduced. It should first be noted that Meyer's use the term "model" (or "model event") differs substantially from Cochrane's. For Meyer "model" is simply the first instance of a distinct musical shape in a particular musical context, whereas for Cochrane "model" assumes a higher ontological status. Cochrane gives "a favorite example" to explain his notions of model, copy, and simulacrum: The idea of a table (model), the table (copy), and a sculpture of the table (simulacrum)."(11). Let us consider two ways in which this tripartite ontology might map onto a piece or pieces of music. Having done this we will be in a better position to evaluate Cochrane's claim that "Meyer . . . views a whole piece of music as governed by the logic of model and copy."(12) ================================================== 11. Cochrane, paragraph 7, from Gilles Deleuze, *The Logic of Sense* (London: Athlone, 1990) p. 257. For another (and extremely entertaining account) of the notion of simulacrum see Umberto Eco's discussion of "absolute fakes" in his *Travels in Hyperreality* (Orlando: Harcourt Brace Jovanovich, 1986), pp. 1-58. 12. Cochrane, paragraph 8. ================================================== [5] Let us first consider how the idea-table-sculpture example would map onto an entire piece of music and its relationship to other musical objects. Right off the bat we have the interesting problem of where to place the "model" of a particular piece--Is the "model" of Beethoven's 5th symphony an a-priori sound object which Beethoven was fortunate to discover (versus a musical object which Beethoven brought into existence through his creative actions)? Is it an ideal structure that exists only in Beethoven's head? Perhaps it is that ideal structure which is embodied in the score, or (since scores are only partial maps of the work-in-performance) in the apprehension of a score by a musically competent score-reader? Any one of these might serve as "models". Then we have particular performances of Beethoven's fifth. It is fairly safe to consider these, at least for the present purpose, as "copies" or instantiations of the ideal 5th symphony.(13) And clearly recordings of a particular performance could be considered copies. But what would count as a musical simulacrum, the analog to the sculpture of the table? Perhaps some transmogrification of the score? (this is not so far fetched, as we have everything from Switched on Bach to Hooked on Classics-- Beethoven's Fifth with a disco beat).(14) At the very least one would have to acknowledge that a simulacrum of Beethoven's fifth would be based upon an artwork--not a sculpture of a table, but a sculpture of a sculpture. Note that this relationship (sculpture #1 to sculpture #2) is one between two items in the same ontological category, not between items in different categories. ================================================== 13. In *Music, Art, and Metaphysics* (Ithaca: Cornell University Press, 1990, pp. 86-88) Jerrold Levinson draws a very useful distinction between "performances" of a work (which we usually get) versus "instances" of a work (which exactly and completely fulfill the musical directives embodied in the score as executed by competent players); under this framework "instances" could serve as "models" while "performances" would count as copies. 14. These are precisely the sorts of simulacra that Eco (op. cit.) discusses, e.g., Wax museum dioramas of Leonardo's "Last Supper" that purport to be *more real* and *more authentic* than Da Vinci's original painting. ================================================== [6] Cochrane does not concern himself with complete works as simulacra; his interest is in mapping the model-copy-simulacra onto intra-opus relationships. Let us examine this mapping with a concrete example. Consider the first four notes Beethoven's Fifth as "motive X." We then hear the next four notes. For the purposes of this discussion let us accept that we have two discernable structural units--we are not worried about which notes belong to which motive, etc., though of course these are often crucial questions. In comparing these two musical structures it would seem that we have but three options, as notes 5-8 can be (a) another instance of motive X, (b) something else--motive y (that is, not X), or (c) a variant of motive X--an X'. Of course, it is in option (c) where most of the musical and analytical fun is--what parameters are varied, what remains the same, and so forth. But what strikes one immediately is that we are not really dealing with a clear "model" which is ontologically prior to the "copy," as we are unable to determine what the "ideal" or platonic model of the 4-note motive might be. Maybe the model is notes 5-8 (as in a bit of artistic cleverness Beethoven has given us the copy first and then the model); maybe it is some other structure we have not yet hear (or may never hear). Happily, this is not what goes on when we attend to Beethoven's musical structure. What does seem to be going on are judgements of similarity between two musical objects on the same ontological plane. One need not appeal to any ideal structure in order to apprehend their relative similarity and/or salient differences. Here is an analogy: I have two red bricks which I will use in building a wall. They are both the same size and weight, but one is a little redder, while the other has a slightly rougher surface. Need I appeal to some Platonic brick in order to mediate my judgements regarding their similarity? The answer is no--I can attend to the relevant qualities (roughness, redness) to discern differences while my other perceptions (size, weight, shape, etc.) inform me of their similarity. [7] When we add the notion of the simulacrum into this context the difficulties in mapping the model-copy-simulacrum ontology to intra-opus relationships become even more acute. Do we really want to claim that the second and subsequent presentations of Motive X are somehow akin to sculptural representations of the first presentation? Cochrane warns us that this is not the proper arrangement of relationships: It is not that the simulacrum resembles the copy which resembles the model . . . the copy resembles the model, but the simulacrum resembles nothing, or rather: "If the simulacrum still has a model, it is another model, a model of the Other from which there flows an internalized dissemblance."(15) I am not quite sure what this means, but it at least seems clear that the simulacrum is not going to help us deal with the pragmatic question of whether or not the pattern formed by notes 5-8 of Beethoven's fifth symphony are similar to the pattern formed by the first four notes, and if so, on what would our judgement of similarity be based. Cochrane thus seems to be making a bit more than is perhaps warranted of the presence of iterable elements in musical syntax (this may well be an occupational hazard of post-Derridean philosophy). ================================================== 15. Cochrane, paragraph 8; the quote is from Deleuze, p. 258. ================================================== [8] At the end of the same paragraph Cochrane claims that Meyer "views a whole piece of music as governed by the logic of model and copy" and thus asks if Meyer thus prefers "a structurality [sic.] based on the single Ideal model, and the similarities and differences which the copies bear to it?" The answer to this question is clearly and easily no, as (again) this is the sort of "structurality" which Reti pursues and which Meyer critiques. Furthermore, Meyer does not claim that all hierarchic music is based on conformant relationships; conformant relationships are but one of several kinds of organizational strategies or "musical processes" on one level which give rise to coherent formal structures on higher levels (Meyer, pp. 88-97, as well as the quote given above). And while Meyer is a structuralist, he is one with a keen cognitive bent: musical structure is significant to the extent that we can make sense of it. Meyer's beef here, then, is not with hierarchic versus non-hierarchic music, but with intelligible versus unintelligible music. Meyer quotes Herbert Simon: If there are important system in the world that are complex without being hierarchic, they may to a consider- able extent escape our observation and understanding. Analysis of their behaviour would involve such detailed knowledge and calculation of the interactions of their elementary parts that it would be beyond our capacities of memory or computation.(16) Music, especially complex music, is not just something we hear--it is something we hear and remember. For without memory, without being able to apprehend and relate motives, phrases, sections and so forth, all one can do is listen to the succession of sounds. To put it another way, if one cannot remember a piece of music or passage, then one cannot make any determination of its complexity or coherence, its hierarchic or non-hierarchic nature. In *Explaining Music* Meyer's focus is not on the music, but on the explaining of it, on the epistemic limits to our understanding of musical structure. ================================================== 16. Meyer, p. 80; from Herbert A. Simon, "The Architecture of Complexity," *Proceedings of the American Philosophical Society* 106.6 (1962): 477. ================================================== AUTHOR: Parncutt, Richard TITLE: Response to Demske: Relating sets KEYWORDS: similarity, pc-sets, timbre, pitch commonality REFERENCE: mto.95.1.2.demske.art Richard Parncutt Depts of Psychology and Music Keele University Keele, Staffordshire ST5 5BG Great Britain r.parncutt@keele.ac.uk [1] Thomas Demske's thorough treatment of the similarity of pc-sets demonstrates how problematical it can be to derive a general and yet musically relevant similarity function. The essay highlights inherent weaknesses in the pc-set paradigm for post-tonal analysis, and suggests that perceptually based approaches may be more appropriate than approaches based purely on pc-sets. [2] First, there seems to be a tacit problem of definition. What exactly does it mean for two pc-sets to be similar? If we are to speak meaningfully about the similarity of two different pc-sets, then we must first of all satisfy ourselves that one and the same pc-set is highly similar to itself. Unfortunately, even this apparently trivial condition is not satisfied. To take a simple example: A melodic statement of {01369} sounds entirely different from the same tones heard as a sonority. And different voicings (inversions, spacings) of that sonority can sound more different from each other than similar voicings of different sets. It's familiar stuff: Octave equivalence ain't always valid. [3] *Perceptual* similarity may be a more promising starting point for a theory of similar pitch structures in atonal music. Demske makes several references to perception in his essay. Perceptual similarity is easy to define: It is the average subjective judgment of global similarity by a representative group of listeners. Theorists may be included as one of the groups. Of course, the results depend on musical expertise and experience -- as does the perception of listeners in the concert hall. [4] Unlike a pc-set-based theory of similarity, a perceptual theory must account for effects of voicing, onset asynchrony, spectral envelope, temporal envelope, and so on. Consider first an isolated pair of steady-state complex sonorities of the same loudness and duration. Their global similarity breaks down into similarity of pitch and similarity of timbre. Similarity of pitch in turn breaks down into two parts, depending upon whether individual pitches are perceived to fall in the same category (chromatic scale degree) or different categories. These two parts may be called pitch commonality and pitch distance (respectively); tentative algorithms are given in my book *Harmony: A Psychoacoustical Approach*, Springer 1989, and in my recent article in PNM. Different listeners emphasize different aspects of pitch similarity in their responses, depending on their orientation and experience. [5] Alternatively, we might look at the similarity of two melodic fragments. That depends on the similarity of their contours and of their underlying scales; for details see papers by Annabel Cohen, Jay Dowling, Marilyn Boltz, Mari Riess Jones, Lola Cuddy. This is quite a different affair from the similarity of sonorities, and needs to be treated independently. [6] For an appropriate set of stimuli for a perceptual experiment on similarity, we need not look past the piano chords in Messiaen's *Quatuor pour le fin du temps* analysed by Demske. A possibile experimental paradigm might involve presenting the chords in pairs to listeners and asking them to rate their global similarity. Then, model the results as a linear combination of pitch commonality and pitch distance. Finally, wonder about the effect of context on similarity judgments. Analogous effects in tonal music have been studied in some detail (see Carol Krumhansl, *Cognitive Foundations of Musical Pitch*, OUP 1990). ================================================== AUTHOR: Rothstein, William TITLE: The Tristan Chord in Historical Context: A Response to John Rothgeb KEYWORDS: harmony, recitative, intertextuality, Tannhaeuser, Purcell, Bach REFERENCE: mto.95.1.1.rothgeb.art William Rothstein Oberlin College Conservatory of Music Oberlin, OH 44074 frothstein@ocvaxa.cc.oberlin.edu ABSTRACT: John Rothgeb's analysis of the "Tristan chord" engages a large intertextual network, stretching back to the Baroque and centering on recitative. Examples of a specific figure of recitative, usually associated with the asking of a question, are presented and analyzed. Examples include passages in Wagner's operas before *Tristan*. ACCOMPANYING FILES: mto.95.1.3.rothstn1.gif mto.95.1.3.rothstn2.gif mto.95.1.3.rothstn3.gif mto.95.1.3.rothstn4.gif mto.95.1.3.rothstn5.gif mto.95.1.3.rothstn6.gif [1] Most of the discussion of Professor Rothgeb's article so far has focused, understandably, on enharmonic issues (e.g., can the TC be legitimately described as a half-diminished seventh chord?). In the process, it seems, the originality and cogency of Rothgeb's analysis of the TC in its *original* context--mm. 1-3 of the *Tristan* Prelude--has gone largely unremarked. (1) When I first read his essay, I found Rothgeb's analysis of these measures instantly convincing, and far superior to the conventional analysis of the TC's G#4 as an appoggiatura to A4 (the last eighth note of m. 2), or to William Mitchell's reading of a voice exchange within a composed-out V of A minor. The central feature of Rothgeb's analysis (see his Ex. 2) is his claim that G#4 properly belongs to the V chord of m. 3, but that a rhythmic shift--specifically, a measure-long anticipation--moves G#4 back to the downbeat of m. 2, thus displacing A4, the note that "properly" belongs to the French-sixth chord. This latter chord Rothgeb (along with many others) understands to be the chord "behind" the TC. (2) Unlike earlier authors, however, Rothgeb does not identify the displaced A4 with the eighth note at the end of m. 2. That A4, and the A#4 following it, Rothgeb reads as part of a slide embellishment--i.e., a passing motion--connecting the anticipated G#4 and the B4 of m. 3; the latter note arises from the voice-leading technique known as reaching-over (Schenker's *Uebergreifen*). ================================================ 1. In this response, I will use "TC" to mean exclusively the first verticality in m. 2 of the *Tristan* Prelude. Unlike Rothgeb, I accept the notion that this chord participates in a network of collections--all of them reducible, in the abstract, to the collection [3, 5, 8, 11] and its transpositions--extending over the entire opera. To my mind, it is this network that ultimately constitutes the "Tristan chord," not the specific manifestation in m. 2. However, a thorough understanding of the language of *Tristan* requires that each occurrence of the chord/collection be analyzed independently for its harmonic, contrapuntal, and (ideally) timbral context. It is the harmonic/contrapuntal analysis of mm. 1-3 that I find most exciting about Rothgeb's article. 2. A work cited in Allen Forte's recent response to Rothgeb (MTO 1.2 [1995]), the *Harmonielehre* of Louis and Thuille, accepts the TC as an independent augmented-sixth chord, adding it (and two others) to the inventory of augmented-sixth chords. I thank Daniel Harrison for bringing this fact to my attention. ================================================ [2] Rothgeb's Ex. 2 isn't as clear as it might be about the rhythmic process that, in his analysis, gives rise to the TC. My Ex. 1 paraphrases his Ex. 2 in such a way that rhythmic issues are brought to the fore. Ex. 1a is essentially the same as his Ex. 2a, except that chords are identified by their harmonic functions (T=tonic, P=pre-dominant, D=dominant), and the reaching-over-cum-voice-exchange is shown. Example 2b shows a rhythmic shift in the soprano, anticipating G#4 (the resolution of A4) and shifting B4 back to the downbeat of m. 2. (I will return to this form of the progression later.) Example 1c compounds the rhythmic shift by giving G#4 the *entire* value of the augmented-sixth chord; the resulting vertical sonority is, of course, the TC. Example 1d fills out the soprano's minor-third leap with passing tones, yielding Rothgeb's slide. Given the added passing tones, the alto's E4 would cause parallel fifths--the earlier "hidden fifths" having become open fifths--so D4 has been substituted; this is a common voice-leading contraction (a leading tone descends directly to a passing seventh, a chromatic semitone lower, instead of resolving upward as usual and then passing downward by whole step). Finally, Example 1e shifts the second passing tone in the slide, A#4, to the downbeat of m. 2. It will be noticed that Ex. 1e is virtually a durational reduction of Wagner's mm. 1-4; the principal difference is that m. 1 is represented in the example by a complete tonic triad. [3] I have followed Rothgeb's harmonic analysis thus far, but I don't really hear m. 1 as a tonic harmony in A minor. F4 sounds to me like a consonant chord tone, not an appoggiatura. Along with Deryck Cooke, I hear the ascending sixth A3-F4, in upbeat-to-downbeat-rhythm, as an arpeggiation from the fifth to the third of a D-minor triad, which proves to be IV of A minor (3); the other two ascending sixths, in mm. 5 and 8, are similarly arpeggiations from the fifth of a triad up to its third. I have added Example 1f to represent this hearing of m. 1. The bracketed sixth in the example represents the cellos' ascending sixth. The bass and soprano notes in parentheses are, to my ear, implied by the larger context; notice the chromaticized voice exchange between bass and alto. I hear G#4 as coming from the implied A4 (so does Rothgeb, but he hears the elided A4 in terms of I, not IV). The entire progression thus represents a motion from pre-dominant (IV) to dominant (V), with an augmented-sixth chord (an altered pre-dominant) in between. The alto's E4 is a passing tone, analogous to the eighth-note A4 in the soprano. It is a simple matter to substitute the first chord in Example 1f, IV, for the tonic triad in Examples 1a-1e; the progression from level to level remains essentially the same. ================================================ 3. See Deryck Cooke, "The Creative Imagination as Harmony," in Robert Bailey, ed., *Wagner: Prelude and Transfiguration from Tristan and Isolde* (New York: Norton, 1985), pp. 169-76. This essay is excerpted from Cooke's *The Language of Music* (Oxford, 1959). ================================================ [4] I now return to Example 1b, which, I here claim, forms part of the pre-history of the TC. Devotees of vocal music will quickly recognize the latter part of this example--everything, that is, but the opening tonic chord--as a common figure in recitative. With its half cadence and its rising melodic gesture, this figure was typically used by composers to set lines of text ending with a question mark. This "question" figure was taken over by Wagner in his early operas; it plays an especially important role in *Tannhaueser*. The same figure is transformed into the so-called Fate motive in the *Ring*. I was aware of the "question"/*Tannhaeuser*/*Ring* connection before I read Rothgeb's article, but his analysis of the TC adds *Tristan* to the intertextual network. [5] The earliest example of the "question" figure that I am aware of--but almost certainly not the earliest that exists--is the very opposite of a question: it is Belinda's announcement of Aeneas's first entrance in Purcell's *Dido and Aeneas* (see Ex. 2). Belinda's words are "how godlike is the form he bears." The example is in C major, although the succeeding passage is in G. The figure involves a bass motion from ^6 to ^5--here in major instead of the usual minor--with the downward melodic resolution, C5-B4, anticipated in the same way as in Example 1b. D5, at the end of the passage, comes from E5, the third of the tonic triad, which was itself reached by arpeggiation in the first two measures of the recitative. Thus the melodic structure is based on a pair of unfolded thirds: E5-C4 (mm. 2-3) is answered by B4-D5 (mm. 3-4). [6] Many examples of the "question" figure, and of figures closely related to it, occur in the cantatas of J. S. Bach. (Curiously, I have found no examples in Bach's Passions.) In each case, the bass progression is ^6-^5, usually in minor; often, but not always, the figure concludes a bass progression descending by step from I to V. The harmonic progression, naturally, is from pre-dominant to dominant, with IV6-V the usual choice. The melody, at the half cadence, features either an ascending leap or an ascending passing motion from ^#7 to ^2. Those examples that include melodic passing tones, naturally, recall the *Tristan* progression most closely. [7] Example 3, from Bach's Cantata No. 82 ("Ich habe genug"), is especially striking in connection with *Tristan*. (4) The middleground harmonic progression, beginning in m. 2, is I-IV-V in C minor. At the fourth quarter of m. 4 the bass moves from the root of IV, F2, to its third, A-flat2; at the same time, two tones of the V triad--B-natural and D--are anticipated (the continuo figure is 6/4/2+). The vocal line connects B3 and D4 with a passing tone, C4; in most editions (notably that of the Bach-Gesellschaft), D4 is embellished with an appoggiatura from below, so that the passing C4 is heard twice, once before and once after the bar line. (Example 3, from the Neue Bach-Ausgabe, does not show this appoggiatura, but a singer would probably add it--also an upper appoggiatura on the word "Erde.") If the lower appoggiatura were made chromatic--C#4 instead of C4--we would hear a progression very much like Wagner's, lacking only the augmented sixth in the 6/4/2+ chord and the seventh in the V. ================================================ 4. Readers who own the Dover volume "Bach: Eleven Great Cantatas" (New York, 1976) can find other examples of the "question" figure on p. 61 (m. 4 and mm. 8-9 of the tenor recitative "Wie hast du dich, mein Gott" from Cantata No. 21) and p. 157 (mm. 7-8 of the tenor recitative "Der Heiland ist gekommen" from Cantata No. 61). ================================================ [8] Example 4 is a voice-leading interpretation of Ex. 3. The passage is complicated, as one comes to expect of Bach. Level A, a foreground graph, omits the registral play of the vocal line, which descends into its lower octave to illustrate the "cool earth" ("kuehler Erde") into which the singer longs to be buried. Level B, a middleground layer, shows more clearly that the passage as a whole is governed by a series of parallel tenths between the bass and the vocal line; the bass leads. (5) The last two tenths of the series are displaced by anticipations and by an unfolding in the bass (shown at level A). C3--C4 in the graph--is anticipated at the end of m. 3, although it is sustained by the keyboardist through the first three beats of m. 4. B3 is anticipated on the fourth beat of m. 4, as indicated above. While F2 in m. 4 is the root of the IV harmony, the controlling bass tone within the larger progression is A-flat2, reached only at the fourth beat of the measure--precisely the moment when B3 is anticipated. Thus the tenth A-flat2/C4 is never explicitly represented at the musical surface (remember that the last sixteenth note of m. 4 is passing). The anticipation of B3 leaves time for the reaching-over of D4, a note that connects back to E-flat4 in m. 2. ================================================ 5. On the concept of leading and following linear progressions see Schenker, *Free Composition (Der freie Satz)*, trans. and ed. by Ernst Oster (New York: Schirmer Books, 1979), pp. 78-80. ================================================ [9] I do not know whether Wagner took the "question" figure from Bach, some of whose music he knew very well, or from later composers. Wherever he got it, he used it in *Der fliegende Hollaender* (I haven't looked for it earlier than that), and especially in *Tannhaeuser*. (6) In both operas, the pre-dominant chord used is generally an augmented-sixth chord of some kind; the minor third from ^#7 to ^2 is expressed as a leap, not a slide. If the local key is major, ^6 in the bass is typically flatted, as it must be if an augmented-sixth chord is to be used. ================================================ 6. In *Der fliegende Hollaender*, see Erik's question "Welch' hohe Pflicht?" in his dialogue with Senta. ================================================ [10] The figure appears frequently in Act 3, Scene 3 of *Tannhaeuser*. While it is not always used to express a literal question, the figure's searching quality captures nicely the restless unfulfillment of Tannhaeuser's quest. Interestingly, almost all appearances of the figure in this scene are in either A minor or C major, precisely the two keys used at the beginning of *Tristan*. Ex. 5 shows two of the figure's occurrences. The first, in A minor, sets a question from Wolfram to Tannhaeuser: "Zogst du denn nicht nach Rom? (Didn't you go to Rome?)" The second, in C minor/major, is of special interest because--in the vocal score, at least--it briefly introduces a transposition of the TC, on the last eighth note of the first measure (in fact, C4 is sustained by half the violas, so the chord is literally a French sixth). B-natural is, of course, an anticipation. Tannhaeuser is telling here of the mortifications he visited upon himself on his way to Rome (the text at this point is "vergoss mein Blut ich zu des Hoechsten Preis"). [11] The final link in the chain is the *Ring*. By the time he composed *Tristan*, Wagner had completed *Das Rheingold* and *Die Walkuere*, and had composed the first two acts of *Siegfried*. In *Die Walkuere*, the "question" figure appears most notably as the Fate motive; it also ends the "Todesklage" motive. The two motives are closely linked in Act 2, Scene 4, the "Todesverkuendigung." Whereas all earlier examples of the "question" figure have involved a melodic leap from ^#7 to ^2--the third and fifth, respectively, of the V triad--the basic form of the Fate motive involves a leap from ^2 to ^4, the fifth and seventh of V7. (7) This variant of the figure is made possible by the nineteenth century's acceptance of V7 as a legitimate goal for a half cadence. In Wagner's syntax, of course, such a V7 does not require conventional resolution, although the listener should (I think) still feel a yearning for such resolution. ================================================ 7. Several occurrences of the Fate motive in *Die Walkuere* explore still other tonal relationships. See, for example, Bruennhilde's question to Siegmund, "So wenig achtest du ewige Wonne?", in the "Todesverkuendigung." ================================================ [12] Ex. 6 shows two consecutive occurrences of the Fate motive in the "Todesverkuendigung." As in the Purcell example (Ex. 2), the text contains an exclamation, not a question: Siegmund asserts that he will not follow Bruennhilde to Valhalla ("zu ihnen folg' ich dir nicht!"). The passage as a whole is in F# minor, but the first statement of the motive sounds like A minor. The progression moves from a French-sixth chord to V; the anticipated leading tone, G#, forms the TC at its "home" transposition level. The following statement, in F# minor, represents the original form of the Fate motive, with a progression from an incomplete diminished-seventh chord, 6/4/2+ (cf. the Bach passage in Ex. 3), to V7. Wagner's spelling here suggests that the apparent D-minor triad is not the "real" chord in the motive's first measure, but that A is an accented passing tone *resolving* to G#. (8) (Hearing A in this way also makes the outer-voice parallel fifths easier to accept.) Notice that, in the final measures of *Die Walkuere*, Wagner changes his spelling from E# to F-natural, emphasizing the Phrygian progression from F-natural to E and thus the *plagal*--as opposed to pre-dominant--function of the Fate motive at the end of the opera. ================================================ 8. At the beginning of this scene, where the Fate motive appears at the same transposition level, A is a suspension. Its tendency to resolve *downward* is intensified there by the fact that its preparation is a dissonant seventh (V7 of E minor). ================================================ [13] I have tried, in this response, to support John Rothgeb's analysis of the TC indirectly, by drawing a thread back through history. The conceptual evolution of the TC shown in Ex. 1 mirrors, to a remarkable degree, the historical evolution of the "question" figure, much of which took place within Wagner's oeuvre. Wagner's seeming preoccupation with this figure supports the notion that, in the opening measures of *Tristan* (if nowhere else), ontogeny recapitulates phylogeny. The gradual dissolution of tonal syntax that *Tristan* did so much to further made continued evolution of this sort extremely problematic. In terms of tonal syntax--harmony and voice leading--*Tristan* represents a station very near the end of the line. ===================================================================== 3. Review AUTHOR: Smoliar, Stephen W. TITLE: Book Review: Robert Cogan, *New Images of Musical Sound*, Harvard University Press, 1984. KEYWORDS: Fourier analysis, music analysis, phonology, sonology, auditory perception Stephen W. Smoliar National University of Singapore Institute of Systems Science Heng Mui Keng Terrace Kent Ridge, SINGAPORE 0511 smoliar@iss.nus.sg ABSTRACT: While Robert Cogan's *New Images of Musical Sound* is now over ten years old, the applicability of Fourier analysis as a basis for music theory is still a relevant issue. This review attempts to put Cogan's work into both a technical perspective, regarding what sound analysis technology now supports, and a theoretical one, regarding his attempt to build a theory on the foundations of phonology. From a technical point of view, it is now far easier to approach analysis as Cogan has done; but his attempt to build a theory suffers from some significant weakenesses. ACCOMPANYING FILES: mto.95.1.3.smoliar1.gif mto.95.1.3.smoliar2.gif THE NEED TO LOOK AT SOUNDS [1] This book is now over ten years old. However, a recent discussion thread on mto-talk was addressing the applicability of Fourier analysis as a basis for music theory; and, in the course of this discussion, David Lewin was kind enough to observe that Robert Cogan had already discussed some of these issues. It therefore seemed appropriate to return to this book and see how it has withstood the past decade. [2] Cogan's primary interest is in music analysis. Given how much disagreement there has been over just what music analysis is all about, he clarifies his own position in his final chapter: "To analyze is to create a map or model--a model that reveals certain functions and relationships" (p. 153). He then develops this point along a line very similar to one which John Roeder recently presented in *Music Theory Online* (1): "A model itself can be verbal, numerical, or graphic, and the preceding chapters have employed (to varying degrees) all of these means: commentaries, tables of oppositions, and spectral photos" (Cogan, p. 153). Roeder's own interpretation of the graphic had more to do with the use of diagrams to explicate mathematical relationships (2); and, of course, just about every form of music notation is also graphic. However, Cogan's approach is far more direct: He is interested in graphics to the extent that they satisfy his need to *look at sounds*, and his thesis is that this need may be best satisfied by spectrographic traces of those sounds. In this way what the eye sees in such traces can supplement what the ear hears, perhaps even informing the mind of structural details which are not immediately apparent in the course of listening. ================================================ 1. Roeder, J. 1993. "Toward a Semiotic Evaluation of Music Analysis," Music Theory Online 0.5: 4. 2. Ibid, 8. ================================================ [3] Before examining the specifics of this approach, it is worth reviewing some of its general virtues. Most important is what may be called Cogan's attempt to "conquer time." Sound cannot exist without the passage of time; but, during that passage, the sound goes as soon as it comes, so to speak. An instant cannot be scrutinized because, once scrutiny begins, the instant is gone. Cogan's images, on the other hand, are *traces* which remain in the present long after the sound has faded into the past; and, unlike the sounds themselves, those traces *can* be scrutinized in as much or as little time as the mind chooses to allocate. Music notation, of course, has the same advantage of timelessness; but notation is, at best, a *prescription* for sound. Cogan has attempted, for purposes of *description*, to capture *the sound itself*. [4] Another advantage to Cogan's approach is its scalability. By suitably compressing the time scale, one can take in the entirety of any sound event in a single glance. Of course if that event happens to be all of *Goetterdaemmerung*, that single glance is not likely to take in very much detail; but one can then adjust the time scale in order to examine greater detail. In other words if the data are appropriately captured, the observer can control what that single glance encompasses, moving between coarse and fine detail at will. The variable time scale provides an *implicitly hierarchical* view of the sounds of any musical experience, which gets away entirely from the symbolic representations of hierarchy found in the approaches of Heinrich Schenker (3) and Eugene Narmour (4). ============================================== 3. Schenker, H. 1956. *Der Freie Satz*, O. Jonas, editor, Vienna: Universal Edition. 4. Narmour, E. 1977. *Beyond Schenkerism: The Need for Alternatives in Music Analysis*. Chicago: The University of Chicago Press. ============================================== [5] However, spectrographic traces are only one of many ways in which sound events may be represented visually (5). There is also the waveform itself: a display of how, for example, a loudspeaker cone physically vibrates with the passage of time. This is again a display with the advantage of scalability; but, in this case, we have to be more careful about the scales at which we choose to examine the signal. When we go down to the millisecond level, we can see the actual periodic waveforms associated with isolated pitches. However, the *shape* of such a waveform depends not only on its *harmonic* content (as revealed by a spectrogram) but also on the *phase* associated with each of the component frequencies. The problem is that significant differences in phase do not necessarily imply differences in what is heard (6). Figure 1 illustrates two waveforms, each of which is represented by a single cycle. Both waveforms have the same harmonic content in identical proportions; but, in the second waveform, the first and second harmonics are cosines, rather than sines, which means they have been phase-shifted by 90 degrees. However, in spite of the obvious differences in appearances, these waveforms are indistinguishable to the ear. ============================================== 5. Aigrain, P., *et al.* 1995. Representation-Based User Interfaces for the Audiovisual Library of the Year 2000, *Proceedings: Multimedia Computing and Networking 1995*, A. A. Rodriguez and J. Maitan, editors, SPIE, pp. 35-45. 6. Risset, J.-C. 1991. Timbre Analysis by Synthesis: Representations, Imitations, and Variants for Musical Composition, *Representations of Musical Signals*, G. DePoli, A. Piccialli, and C. Roads, editors, Cambridge: The MIT Press, pp. 7-43. ============================================== [6] On the other hand if we view these waveforms at a *macroscopic*, rather than *microscopic*, level, they have at least the potential of being more informative. Figure 2, for example, is the entirety of the Aloys Kontarsky recording of Karlheinz Stockhausen's "Klavierstueck III" (7). This display tells us nothing about notes or the serial structure of the pitches, but it *does* show how those notes are grouped into *gestures* and how the intensities of those gestures are modulated. ============================================== 7. The sound was digitized from the vinyl Columbia recording, 32 31 0008; these recording sessions were supervised by Stockhausen. ============================================== [7] Before examining *any* such visual approach in greater detail, however, we should also be sober enough to recognize that *biological* support is not encouraging. One thing we know for certain is that the path from ear to brain is decidedly different from that from eye to brain (8). Thus, if the biological substrates differ, it is unlikely that principles which dictate how we identify objects and structures in what we see are necessarily going to carry over into what we hear. Furthermore, much of this distinction has to do with the necessity to account for time in auditory perception. It is all very well and good to synthesize visual traces which "freeze" the passage of time; but once the stimuli are "frozen," they can no longer be auditory. If time "stops" then so do the stimuli; and any attempt to abstract away from the passage of time runs the risk of also abstracting away certain attributes and relations which may be most critical to how those stimuli are perceived and interpreted. ============================================== 8. Gibson, J. J. 1983. *The Senses Considered as Perceptual Systems*. Westport: Greenwood Press. ============================================== COGAN'S APPROACH [8] Probably the element which has changed the most in the ten years since Cogan published these results has been the supporting technology. Cogan's data were collected during the years 1980 and 1981 in the Sonic Analysis Laboratory at the New England Conservatory. The very first sentence in the book acknowledges the support of Dale Teaney and Charles Potter from the IBM Watson Research Center: "Without their professional and personal initiatives, the process would have become available to musicians much later than it did" (p. v). [9] Given the extent to which computers have become part of our day-to-day lives, it is hard to believe that, when these data were being collected, personal computing did not yet exist. Much of what we now take for granted could not even be imagined in 1980, making it somewhat difficult to infer from the description in Appendix A just what instrumentation Cogan actually used to arrive at the spectrum photos which lie at the heart of this book. He *does* tell us that the "spectrum analyzer was a thirty-three- millisecond fast Fourier transform instrument, capable of analyzing sounds in five continguous octave registers simultaneously" (p. 155); so we can conclude that at least *some* of the equipment was digital. On the other hand the images appear as if they were photographed from a rather conventional (and probably temperamental) analog oscilloscope; and there is no doubt that he had to use photography (rather than, for example, laser printing) to capture those images (not to mention physical acts of cutting and pasting his photographs, rather than composing his images with software assistance). However, there are also references to dynamic controls which could be adjusted, with little reference to what exactly is being controlled. [10] One thing is certain: Anyone interested in undertaking a similar project today is going to have a far easier time of it. These days it is pretty difficult to find a personal computer which *lacks* some form of audio input, not to mention direct capture of data from audio compact disc recordings. It is quite likely that Cogan could now carry all the examples from his book around in a laptop computer, examining and listening to his data while on a flight surrounded by other users who are buried deep in their spreadsheets and games (all of whom, collectively, are probably radiating enough frequency to give the pilot a whole new patch of gray hairs). Put another way, this is no longer a big deal, which means that, putting a more positive slope on the situation, it is now the sort of thing we can expect any resourceful undergraduate to do. [11] To be a bit more fair, all this means is that *collecting* data is no big deal. The "real deal" is what happens next. Therefore, I would like to be relatively brief in reviewing the data which Cogan actually collected and focus more attention on how he then undertook to develop a theory from them. THE EXAMPLES [12] Part I of the book is essentially an exposition of seventeen spectrum photos. These are collected into four chapters: Voices, Instruments, Large Mixed Ensembles, and Electronic and Tape Music. Each chapter, in turn, attempts to explore considerable variety in its subject matter. Thus, the Voices chapter covers Gregorian chant, Tibetan Tantric chant, Billie Holiday singing "Strange Fruit," and Gyorgy Ligeti's "Lux Aeterna." The instrumental examples include a Balinese gamelan, a Ludwig van Beethoven piano sonata recorded on both a forte-piano and a modern instrument, the second of Igor Stravinsky's "Three Pieces for String Quartet," the latter two of Anton Webern's Opus 7 ("Four Pieces for Violin and Piano"), and the third etude from Elliott Carter's "Eight Etudes and a Fantasy" (the only example of winds). The mixed ensembles include both instruments and voices. The first two examples compare the "Confutatis" from Wolfgang Amadeus Mozart's *Requiem* with the "Tibi Omnes Angeli" from Hector Berlioz' *Te Deum*. This is followed by the first of Claude Debussy's orchestral "Nocturnes," the brief orchestral interlude which follows Marie's murder in Alban Berg's *Wozzeck*, and Edgard Varese's *Hyperprism*. In contrast the final chapter is rather sparse in its examples: the Introduction to Milton Babbitt's "Ensembles for Synthesizer," the "Fall" movement from Jean-Claude Risset's *Little Boy* suite, and Cogan's own "No Attack of Organic Metals." Nevertheless, the overall variety of the entire collection is quite satisfying; and it is gratifying to see that Cogan deliberately avoided concentrating on the music of Dead White European Males. THE THEORY [13] What is less satisfying about Part I of the book is that it is primarily anecdotal. As one proceeds through the images, one gets the feeling that Cogan is saying, "Here is something interesting. Here is something else interesting. Here is yet another interesting thing." After a while, even the most generous reader is likely to erupt: "YES! I agree! There *are* interesting things here! Do you also have an interesting *theory*?" [14] Cogan attempts to confront this question with Part II of his book. This is a decidedly shorter part of the entire volume; and, unfortunately, it is also noticeably weaker. Some of its weaknesses may be more apparent because of what we have learned over the last ten years; but, even in his own time, Cogan was failing to do justice to his subject matter in several significant ways. [15] In order to develop his theory, Cogan turns to *phonology*, that division of linguistics which is concerned with the *sounds* of language, as opposed to either syntax or semantics. This was not, even in its own time, a particularly new idea. Gottfried- Michael Koenig had organized an Institute for Sonology at the University of Utrecht in a deliberate attempt to generalize phonological theory to encompass other sources of sound (such as experiments in electronic and computer music which particularly interested Koenig); and some of the earliest research concerned with developing a sonological theory was undertaken by Otto Laske (9). It is therefore unfortunate that Cogan gives no indication of either Koenig or Laske, either the theory or practice of their work, or even the *idea* of generalizing from phonology to sonology. Instead, his primary foundations seem to rest on the work of Roman Jakobson (10) and N. S. Trubetzkoy (11). There seems to be little acknowledgment that there might be any *other* foundations, such as those which were pursued by Morris Halle and Noam Chomsky (12); so the reader is left with the uneasy feeling that Cogan decided to pursue this particular approach because it looked good at the time. ============================================ 9. Laske, O. 1972. "On Problems of a Performance Model for Music" (Technical Report, Institute of Sonology, Utrecht State University): 29. For a critical review of this work, see Smoliar, S. W. 1976. "Music Programs: An Approach to Music Theory Through Computational Linguistics," Journal of Music Theory 20.1: 105-131. 10. Jakobson, R., and Waugh, L. 1979. *The Sound Shape of Language*. Bloomington: Indiana University Press. 11. Trubetzkoy, N. S. 1969. *Principles of Phonology*, C. A. M. Baltaxe, translator, Berkeley: University of California Press. 12. Chomsky, N., and Halle, M. 1968. *The Sound Pattern of English*. New York: Harper & Row. ============================================ [16] What interested Cogan most was Jakobson's desire to describe sounds in terms of *oppositions*. This amounts to describing the quality of a sound in terms of where it is situated between two contrasting extremes. For example, the grave/acute opposition distinguishes between concentration of sounds in low and high frequencies, respectively. On the other hand the centered/extreme opposition addresses whether there is frequency activity at the extremities of the spectral range or only in some more limited middle range. Cogan presents thirteen of these oppositions; and, while he is very up front about the fact that this list may not be complete, the idea of building such a list in the first place lies at the heart of his theory. [17] This approach is not unfamiliar in the technology of signal analysis. However, what Jakobson called *oppositions* are now more commonly known as *features*; and, when several of these are collected together, the results are called vectors in a *feature space* (13). Feature vectors have become invaluable tools for the description and recognition of both visual and auditory signals; but, like most other tools, they religiously follow the GIGO (Garbage-In-Garbage-Out) Principle. If they are not used properly, they are likely to yield results which are, at best, questionable. Therefore, it is important to review some questions which need to be asked before feature vectors are invoked as a descriptive tool. =============================================== 13. Gianotti, C. 1993. Analysis of Economic and Business Information, *Handbook of Pattern Recognition and Computer Vision*, C. H. Chen, L. F. Pau, and P. S. P. Wang, editors, Singapore: World Scientific, pp. 569-594. =============================================== [18] Perhaps the most important question to be asked of any feature is: *Can it be effectively calculated?* This question has been deliberately formulated using the language of Alonzo Church (14); so a positive answer implies that there is some *effective algorithm* which may be applied to the input, whether from spectra or waveforms, which will assign a value for that feature in a reproducible manner. Cogan is quick to point out that his feature values are context-dependent; but that does not preclude their being effectively computed. Computation may just have to look at a broader span of time than, say, thirty-three milliseconds. However, while Cogan is certainly *trying* to be specific in describing his features, effective computation appears to be beyond his scope. =============================================== 14. Church A. 1965. An Unsolvable Problem of Elementary Number Theory, *The Undecidable: Basic Papers On Undecidable Propositions, Unsolvable Problems And Computable Functions*, M. Davis, editor, Hewlett: Raven Press, pp. 88-107. =============================================== [19] The opposite question is: *What can be reconstructed from a feature vector?* One of the interesting things about the spectrum is that it can be used to reconstruct the original sound (15). Given a feature vector, can it be used to construct *any* sound? The context-dependent nature of Cogan's approach to description definitely works against him on this count. However, even if his value assignments were *less* context-dependent, it is unclear that one could ever look at a feature vector and hear anything remotely relevant in "the mind's ear." =============================================== 15. Butler, D. 1992. *The Musician's Guide to Perception and Cognition*. New York: Schirmer: 208. =============================================== [20] This leads to yet another question: *How do we compare feature vectors for similarities?* This is a familiar problem in visual processing. While any color can be easily described as a weighted sum of red, green, and blue sources of light, colors which are visually similar do not always have similar weight contributions. Color similarity is usually better represented in terms of a different set of descriptors, commonly called luminance, hue, and saturation (16). The two sets of descriptive vectors are equally effective in reconstructing a color, but the second representation facilitates identifying colors which are *perceptually similar*. Thus, even if we have an effective set of features for describing sounds, until we know how to relate those features to auditory perception, we have little more than a mathematical abstraction. =============================================== 16. Luong, Q.-T. 1993. Color in Computer Vision, *Handbook of Pattern Recognition and Computer Vision*, C. H. Chen, L. F. Pau, and P. S. P. Wang, editors, Singapore: World Scientific, pp. 311- 368. =============================================== [21] The moral of the story is that the path Cogan has chosen is probably heading in the right direction, but he has not yet properly equipped himself for the journey. Fortunately, our understanding of auditory perception has come a long way since Cogan's book appeared (17). If Cogan is no longer interested in the trip, others can look where his finger is pointing and set off on their own. Thus, the weakness of the theoretical portion of this book should not be seen as a condemnation of Cogan's approach to collecting data but as an incentive to apply our increased knowledge of both signal analysis and perception to go forth and do a better job. =============================================== 17. One may gain a good appreciation of how long we have come from Butler, op. cit. =============================================== CONCLUSIONS [22] Is the trip going to be worth making, bearing in mind, for example, the biological conflict between what we hear and what we see? If the purpose of the trip is to try to reduce all that is auditory to the visual, then, most likely, the trip will be doomed to failure. However, as Cogan observed, images are but one of many approaches to description; and no one approach will ever do all the work (18). So we should not expect images of either spectra or waveforms to yield *all* the secrets of any musical experiences. This should not be the purpose of the trip. Instead, one should undertake the trip to learn, in more specific ways, what these image data both *can* and *cannot* tell us. If we undertake this task seriously, we are likely to find that those data can, indeed, tell us things which cannot be readily accommodated, if at all, by other modes of description. Such a discovery will leave us better equipped than ever for future analyses of music and a firmer sense of the capabilities of music theory. =============================================== 18. Smoliar, S. 1994. "Comment on John Roeder's Article," Music Theory Online 0.6: 7. =============================================== 4. Announcements A. SMT Special Interest Group in the Philosophy of Music (1) SMT 1995 -- SPECIAL SESSION The ad hoc steering committee is pleased to announce that its proposal for a special session on "Analysis and Meaning in Music" has been accepted for the 1995 meeting of SMT in New York. The session, the topic of which was chosen from suggestions offered by members of the group, comprises papers by theorists and musicologists that examine the question of musical "meaning" -- its constitution in music, in discourse about music, and its role in musical analysis -- and a response from a philosopher. The panel for the session is as follows: Leo Treitler, City University of New York "Nelson Goodman's Concepts of Reference and Metaphorical Exemplification and 'Postmodern' Ideas of Music as Play of Signifiers" Robert Snarrenberg, Washington University in St. Louis "Tones and Words in Schenker's Representation of Content" Stephen Peles, Washington University in St. Louis "Musical 'Meaning' and Talk About It" Naomi Cumming, Queen Elizabeth II Research Fellow of the Australian Research Council "Gesture and Meaning" Jenefer Robinson, University of Cincinnati, will present a response to the four papers, and Marianne Kielian-Gilbert, Indiana University, will serve as the session's moderator. (2) ORGANIZATIONAL MEETING The steering committee has also arranged for an organizational meeting to be held at the New York conference on Friday evening from 5:30-6:30 p.m. On the agenda for discussion will be such matters as how best to organize the group, what sorts of activities we should carry on (e.g., distribution of bibliographies, establishment of an internet discussion group, proposing special sessions or arranging for other kinds of meetings at the annual SMT conference, etc.). If you have suggestions for the agenda that you wish the steering committee to consider beforehand, please send them to Robert Snarrenberg at . (3) DISCUSSION GROUP Though it was not our intention, many who responded to our initial announcement of the group's formation appear to have thought this would become an electronic discussion group. As suggested above, a proposal of this nature could be considered at the organizational meeting in New York. Meanwhile, there are already several discussion lists that may be of interest to members: Narramus, Musical-Aesthetics, and The American Society for Aesthetics List. Queries about Narramus should be directed to Flo Martin at , queries about Musical-Aesthetics to Richard Cochrane at , and queries about the ASA-List to Stan Godlovitch at . ------------------------------------------------- The Philosophy of Music Ad Hoc Steering Committee ------------------------------------------------- Joseph Dubiel (Columbia Univ.) Marion A. Guck (Washington Univ.) Janet Hander-Powers (Topsfield, MA) Marianne Kielian-Gilbert (Indiana Univ.) Fred Everett Maus (Univ. of Virginia) Robert Snarrenberg (Washington Univ.) Alicyn Warren (Univ. of Virginia) ================================================== B. THE MIDDLE AGES IN CONTEMPORARY POPULAR CULTURE: CALL FOR PAPERS An Interdisciplinary Conference McMaster University Hamilton, Ontario, Canada March 29-31, 1996 Keynote Speaker: Derrick de Kerckhove Director of The McLuhan Program in Culture and Technology University of Toronto We invite proposals for a conference exploring the general theme of "The Middle Ages in Contemporary Popular Culture." This theme is intended to be as open-ended as possible and can be approached from any number of directions. Possible topics include, but are not limited to: * Marketing the middle ages in music (Gregorian chant, Hildegard of Bingen), novels, movies, TV series, video games and CDRom *New millenarianisms, Satanic cults and witchcraft *The middle ages in nationalist ideologies *The middle ages as an attraction for tourists: visits to archeological sites, medieval fairs, feasts and pageants Papers from a broad range of academic disciplines are welcome. A number of special cultural events are also planned, including musical performances, films, a display of books, videos and interactive multimedia products. Please send 250-word abstracts in English or French (for twenty-minute papers) BY SEPTEMBER 30, 1995, to: Madeleine Jeay or Susan Fast Dept. of French School of Art, Drama and Music McMaster University McMaster University Hamilton, Ontario Hamilton, Ontario L8S 4M2 L8S 4M2 Phone (905) 525-9140 ext. 23754 ext. 23670 e-mail: jeaymad@mcmail.cis.mcmaster.ca fastfs@mcmail.cis.mcmaster.ca FAX: (905) 577-6930 If you have a fax number or e-mail address, please send it along with your proposal. Presented by the McMaster Medieval and Renaissance Media Team ============================================== B. Feminist Theory and Music 3: Negotiating the Faultlines Center for Ideas and Society Highlander Hall, University of California, Riverside, June 15-18, 1995 The two previous "Feminist Theory and Music" Conferences (Minneapolis, 1991 and Rochester, 1993) opened a dialogue about issues of gender and sexuality in music making and in critical discourse about music. A primary goal for this third meeting continues to be "to develop a critical language, common to all the subdisciplines of music, that intersects with the insights of feminist theory." In addition it has the aims of providing a supportive environment for new approaches and ideas, of continuing the dialogue within and among diverse scholarly interests and musical traditions, and of negotiating the faultlines that have created divisions in our disciplines. With over eighty participants in formal sessions, panel discussion, and concerts, it promises to be a celebration as well as an interrogation of a lively new field. 1995 Steering Committee: Philip Brett (chair) Jann Pasler Gretchen Horlacher Jennifer Rycenga Susan McClary 1995 Program Committee: Roberta Lamb Jann Pasler (chair) Susan McClary Jennifer Rycenga Mitchell Morris Janika Vandervelde Presenters: Peter Antelyes Geraldine Finn Fred Maus Robin Armstrong Robert Garcia Sam McBride Raphael Atlas Dana Gooley Maryann McCabe Paul Attinello Shannon Green Donna McCabe Christina Baade Heather Hadlock Andra McCarthey Prateeti Punja Ballal Lydia Hamessley Martha Mockus Elaine Barkin Wendy Heller Julia Moore Christine Bezat Leslie Hiers Thomas Nelson Joanna Bosse Ellie Hisama Nancy Newman Daphne Brooks Bruce Holsinger Pauline Oliveros Jeanice Brooks Nadine Hubbs Kitty Pappas Lori Burns Jennifer Hughes James Parsons James Buhler Brian Hyer Sanna Pederson Virginia Caputo Monika Jakuc Karen Pegley Theo Cateforis Maria Johnson Judith Peraino Marcia Citron Elizabeth Keathley Elizabeth Randell Barbara Coeyman Elizabeth Kertesz Ivan Raykoff Renee Coulombe Marianne Kielian-Gilbert Sonnet Retman Brian Currid Rosemary Killam Eva Rieger Suzanne Cusick Michelle Kisliuk Cristina Ruotolo Cynthia Cyrus Kevin Kopelson Milton Schlosser Joke Dame Romy Kozak Jeff Schwartz William DeFotis Karissa Krenz Anne Lineback Seshadri Claire Detels Elisabeth Le Guin Jennifer Shaw Leslie Dunn Judy Lochhead Catherine Parsons Smith Linda Dusman Renee Cox Lorraine Elizabeth Tolbert J. Michele Edwards Margaret Lucia Riitta Valkeila Melina Esse Pam Madsen Ellen Waterman Robert Fink Anne McNeil Sherri Wilcauskas Su Zheng Program Thursday, June 15 1-2.30 Session 1A Trespassing Mediums Session 1B Music and AIDS 3-4 Panel Negotiating the Faultlines 4.45-5.30 Study Sessions 5.30-6.30 Reception 6.30-8 Concert Friday, June 16 8.30-10 Session 2A Renaissance Women's "Self-fashioning" Session 2B Romantic Binarisms Session 2C Gender Tensions in Musical Voice 10.30-12 Session 3A Service, Rights, and the Bourgeoisie's Exercise of Power Session 3B Fragile Femininities Session 3C Technology, Oliveros, and the New Music Listener 12-1 Lunch 1-2.30 Session 4A Representation if Women in Early Modern Europe Session 4B Engendered Pedagogies: Theoretical & Historical Perspectives 3-4 Panel Myths and Methods of Music Education 4.45-6.15 Keynote address: Pauline Oliveros 6.30 Dinner 8 Concert Monika Jakuc Saturday, June 17 8.30-10 Session 5A Difference and Reception in Early 20th-century America Session 5B Ethel Smyth Session 5C Reading Pop 10.30-12 Session 6A Freedom, Power, and Music in Willa Cather's America Session 6B Women of the Piano Session 6C Rowdy females and ecriture feminine 12-1 Lunch 1-2.30 Session 7A Negotiating Power: Egalitarianism across Cultures Session 7B Gender Dysphoria and Male Fantasy 3-4 Panel Feminisms across Generations 4.45-5.30 Study Session Women-in-Music Courses 5.30-6.30 Reception 6.30-8 Concert Sunday, June 18 8.30-10 Session 8A Music on the Couch: the Dialectics of Desire Session 8B Queer Effects Session 8C Race and Nostalgia--Some American Musical Crossovers 10.30-12 Session 9A Interiority and the Other Session 9B Body and Instrument Session 9C Women in Film 12 Concert Transportation Travel arrangements are being handled by Canyon Crest Travel/American Express (5225 Canyon Crest Drive, Suite 1, Riverside, CA 92507). They are able to offer discounts of 5% on the Super Saver rates (non-refundable, Saturday-night stay-over) on two major airlines (probably United and American). To make reservations, contact Patty Jimenez (or Raquel De Nucci) at (800) 544-6633 or (909) 788-7611 during office hours only: M-F 7:30-5:30, Saturday 9-1 (PST). The nearest airport is Ontario, California, with flights to most major hubs by American, Delta, United, and also Southwest. Transport from the airport to Riverside is not easily available or cheap. A University van shuttle service will be set up, and we will meet you if you let us know your flight and arrival time. Fares may be cheaper if you fly into Los Angeles International Airport, but keep in mind that transport into Riverside from LAX is costly. You will either need to rent a car or take the Super Shuttle (one way, two people, $74). If you drive to Riverside, Highlander Hall is opposite the University Avenue offramp on Highway 60 (East). There is ample parking both at the University and the Center for Ideas and Society. Amtrak stops at San Bernadino ten miles away at which point you will need to connect on the RTA Shuttle. Downtown Riverside is also served by Greyhound. Hotel accommodations A block of rooms has been reserved at the Marriott Courtyard for conference attenders at $49 per night. There are doubles and singles available both for that price. Please call (909) 276-1200 and ask for the Feminist Theory and Music 3 rooms. Other accommodations include: The Mission Inn exclusive (909) 784-0300 Hampton Inn moderate (909) 683-6000 Super 8 rock bottom (909) 682-9011 Those attending the conference are urged to make bookings soon, since June 17 is graduation day for the University. Meals There are restaurants up and down University Avenue, where Highlander Hall is located, but we are also arranging to have delicious boxed lunches available for Friday and Saturday. Please address any queries to Philip Brett or Lea Appleton, conference organizer, at (909) 787-3138 or by fax to (909) 787-4651, or by e-mail: pbrett@mail.ucr.edu; appleton@mail.ucr.edu (if these addresses don't work, try @ucrac1.ucr.edu) ___________________________________________________________________________ Registration form Name:________________________________________________________________ Address:_____________________________________________________________ Street:______________________________________________________________ City, State, Zip (Country)___________________________________________ Daytime phone:____________________ Evening Phone:____________________ Conference fees Indicate applicable fee category ______ Early registration (before June 1) $50.00 ______ General registration (after June 1) $60.00 ______ Student (include photocopy of current academic ID, $25.00 ______ Single day registration, $25.00 ______ Single day student registration, $10.00 Meals ______ Lunch (Friday) $7.50 ______ Lunch (Saturday) $7.50 Please specify special dietary needs:________________________________ Please make checks payable to "UC Regents" and send with completed form to Feminist Music and Theory 3 Department of Music University of California Riverside, CA 92521-0325 ================================================ D. Society for Seventeenth-Century Music: Call for Papers Fourth Annual Conference April 11-14, 1996 Wellesley College (near Boston, Massachusetts) Papers are solicited on all aspects of seventeenth-century music, including the history of music, performance practice, dance, theater, visual arts, and other topics related to the musical culture of the century. Various formats for presentations will be considered, such as: --20-25 minute lectures with recorded or live illustrations --sessions of 3-4 short (5-10 minute) statements on an issue --lecture-recitals (30-45 minutes) --seminars on a specific work or topic --workshops All proposed presentations will be considered on their individual merits, but proposals for grouping papers into integrated sessions are also welcome. All sessions will be plenary and will include extensive time for discussion; typical sessions will consist of two papers with musical illustration and discussion. Papers may be read in any language, but detailed abstracts for non-English language papers will be required. No topic will be excluded categorically; any national focus, methodology, or genre will be welcomed. Only one abstract will be considered from any individual, and 1995 presenters should not submit abstracts for 1996. Abstracts will remain anonymous until the final formulation of the program. The committee will complete its work before 15 January 1996, at which time those accepted for the program will be asked to make a firm commitment, to specify equipment needs (such as audio-visual aids), and to provide an electronic copy of the abstract for posting and for reproduction in the program booklet. Guidelines for Abstracts: --Summarize the content of the presentation (not just the underlying issues or methodology). --State any anticipated needs for special equipment at the end of the abstract. --Limit the length to no more than two pages. --Send one copy identified with your name, address, telephone, fax, and e-mail address (as applicable). --Send four copies without identification of the author. --Do not send tapes or related materials at this time. --Mail no later than 6 October 1995. --Send to: Prof. Bruce Gustafson, SSCM Program Committee Chair Department of Music Franklin & Marshall College Lancaster, PA 17604-3003 --Abstracts from abroad may be sent by fax (one copy only) to Bruce Gustafson at (1) 717 291-3639. Program Committee: Bruce Gustafson, chair (Franklin & Marshall College), Robert Kendrick (Harvard University), Lois Rosow (Ohio State University), Louise Stein (University of Michigan). ========================= B_Gustafson@acad.FandM.edu Bruce Gustafson, Professor of Music, Chair voice 717 291-4011 Franklin & Marshall College, Lancaster, PA 17604-3003 fax 717 291-3969 337 West James Street, Lancaster, PA 17603 voice & fax 717 299-2116 520 East 20th St., 5-D, New York, NY 10009 voice & fax 212 674-5226 =========================================================== 5. Employment POSITION/RANK: Lecturer/senior lecturer in composition INSTITUTION: Music Department, University of Sheffield, UK QUALIFICATION: PhD in Composition preferred, strong record of publication (music and/or written research) DUTIES: teaching composition to undergraduates and postgraduates, supervision of research students (in composition), possibly teaching a course in some aspect of contemporary repertoire. The successful candidate will join a permanent staff of eight, and will be expected to have a particularly strong research profile. The post has been created specifically to enhance the research standing of the department in composition. Experience of working with digital music technology would be an davatage, though not essential. The post is tenable from September 1995 or as soon as possible thereafter. SEND: For application procedures and further particulars, contact The Director of Human Resource Management, Western Bank, Sheffield S10 2TN tel. 114 282 4144 quoting reference no. R600. Please send a small selection of scores/tapes with applications. DEADLINE: 1st June 1995 CONTACT: Eric Clarke Music Department, University of Sheffield, Sheffield S10 2TN, UK e.f.clarke@sheffield.ac.uk tel.: 114 266 7234 fax: 114 266 8053 ======================================= 6. New Dissertations AUTHOR: Doerksen, John F. TITLE: "A Theory of Set-class Salience for Post-tonal Music, with Analyses of Selected Lieder by Anton Webern." INSTITUTION: University of Western Ontario, Faculty of Music, London, Ontario, Canada N6A 3K7 BEGUN: March 1993 COMPLETION: June 1994 ABSTRACT: This dissertation treats the question of hierarchical structure in post-tonal music. Its principal invention, the salience theory, offers a systematic means of interpreting the structural weight of a musical event. The salience theory, of which Allen Forte's genera theory and a rather regimented segmentation strategy form two aspects, purports to model post-tonal compositions as series of events. Many events share structural and contextual properties, some of which I identify and specify as event-classes (ECs). Each pc set within a composition, through its association with ECs, achieves a numerical ranking that reflects its relative salience--the more times a pc set instantiates an EC, and the broader the range of ECs it instantiates, the greater its structural role is deemed to be. While the salience theory has generalizability as its ultimate goal, the purview of the present study is limited to selected atonal Lieder of Anton Webern. KEYWORDS: Webern, post-tonal, salience, matrix, event, segmentation, Forte, genera TOC: Chapter 1. Introduction Trends in Hierarchical Analysis using Set Theory The Salience Theory: Introduction and Context Chapter 2. Exclusivity Index: The Representation of Genus Uniqueness The Exclusivity Index A Reinterpretation of Two Analyses by Forte Chapter 3. The Salience Theory: Its Derivation and Implications Salience Theory Definitions Events and Event-classes The Salience Matrix Segmentation and the Salience Theory Chapter 4. Analyses of Selected Webern Lieder Introduction "Dies ist ein Lied" (Op. 3/1) "Du, der ichs nicht sage" (Op. 8/1) "Der Tag is vergangen" (Op. 12/1) "Nachts" (Op. 14/5) "Dormi Jesu" (Op. 16/2) Chapter 5. Conclusions Macro-salience: the Five Lieder Combined Future Research CONTACT: Voice: (519) 888-0641 or (519) 884-1970 (ext. 2153) ============================================================ AUTHOR: McCallum, Peter, H.J. TITLE: The Analytical Significance of Beethoven's Sketches for the String Quartet in F major, opus 135 INSTITUTION: University of Sydney, Department of Music, NSW 2006, AUSTRALIA BEGUN: August, 1987 COMPLETION: March, 1995 (under examination) ABSTRACT: The thesis is an analysis and transcription of the surviving sketches of Beethoven's String Quartet in F major, opus 135 from the point of view of analytical theory. Music analysis contains both explicit and implied assumptions which can, in part, be tested against the composer's own working drafts and sketches. The intention is not to invalidate theory but to contextualise it. Important among these assumptions are those which concern themselves with intentionality and unity. For the first movement, the sketches suggests combinatorial strategies which could be set against organicist metaphors, while the drafts for the development raise issues of large-scale voice leading and the structural significance of register. Discussion of the sketches for the second movement revolves around phrase structure and hyperrhythm, while those for the third movement are pertinent to motivic unity and the structural function of register. The sketches for WoO 196 suggest a tension between the demands of motivic identity and voice-leading which was carried over into the finale of opus 135. The thesis concludes that the unity of this work is most usefully seen, not in terms of its immanent integrity, nor in terms of its contribution to the organicist narratives, but rather as the result of a set of responses by its composer to the interaction of sometimes conflicting compositional habits, aesthetic values and circumstances. KEYWORDS: Beethoven, sketch study, analysis, unity, compositional process, genesis, Schenker TOC: VOLUME I: ANALYSIS ABSTRACT i ACKNOWLEDGMENTS ii LIST OF TABLES vi LIST OF FIGURES vi ABBREVIATIONS vii INTRODUCTION 1 Chapter 1 1 Thesis 1 PART 1: THEORY 7 Chapter 2 Analysis and Sketch Study 7 Positivist Musicology and Modernist Analysis 7 Postmodern Thought and New Approaches to Contextuality 14 Sketch Study, Organicism, Schenker and Schenkerians 16 Contextualising Analysis 21 PART 2: PRELIMINARIES TO THE ANALYSIS 31 Chapter 3: Historical and Biographical Background 31 Chronological and Biographical Issues Relevant to the Analysis 31 Chapter 4: Sources 48 Definitions Relating to the Sources 49 Background 52 Previous Literature on the Sketches for opus 135 54 Survey of the Individual Manuscripts 56 The Desk Sketchbook: Kullak 56 The Pocket Sketchbooks: Autograph 9, Bundle 4 and Autograph 10, Bundle 1 57 The Pocket Sketchbooks: Artaria 205, Bundle 3 and MS 62/66 58 The Sketch Miscellanies: Artaria 216, Artaria 210 and Artaria 209 62 Vienna A74A 64 PART 3: THE SKETCHES 77 Introduction to Part 3 77 Chapter 5: Preliminary Ideas and Tonal Overviews 79 Preliminary ideas 82 First Preliminary Idea 83 Second Preliminary Idea 87 Third Preliminary Idea 92 Tonal Overviews 95 First Overview 95 Second Overview 97 Chapter 6: The First Movement 103 Introduction 103 Catalogue of Sketches for the First Movement 104 Beginnings and Endings 107 The Sketches 118 Towards Integration: the Motive of the Third 141 The Drafts for the Development in Artaria 216 150 The Development in Score Draft 1(b) 155 The Development in Score Draft 2 157 Score Draft 2(b) 158 Chapter 7: The Second Movement 168 Motives: Unity and Parody 169 Draft in Artaria 205, Bundle 3, pp. 30-32, 28 192 Score Draft 1 195 Score Draft 2 200 Drafts for the trio section 207 Score Draft 1 213 Score Draft 2 214 Score Draft 3 215 Score Draft 4 216 Chapter 8: The Third Movement 227 Unity and Disruption 230 The D Theme within opus 131 234 Tonal overview for opus 131, VI-VII 237 `Su?er ruhegesang' sketch 240 Kullak f. 46r, f. 47r 242 Issues in Analysing Variations 243 `2tes Stuck' sketch 248 Score Sketches for Variation 2 248 Score Draft 1 249 Score Draft 2(a) 249 Score Draft 2(b) 249 Fragment 1 250 Score Draft 3 251 Score sketches for Variation 4 252 Chapter 9: The Sketches for WoO 196 262 Counterpoint, Semantics and Syntax 262 Historical Background to WoO 196 266 The Sketches for WoO 196 274 Chapter 10: The Fourth Movement 284 Subject and Countersubject 287 Paths from F major to A major 303 Towards Thematic Integration 307 The Question Reached With Difficulty 319 The Second Theme 324 CONCLUSION 342 Chapter 11: 342 BIBLIOGRAPHY 353 VOLULME II: TRANSCRIPTIONS INTRODUCTION 1 A Note on the Transcriptions 1 Layout of Volume II 5 TRANSCRIPTIONS AND FACSIMILES 10 DESK SKETCHBOOKS 10 Sketches for opus 135 and related material in Kullak 10 Facsimile of Kullak, f. 39r, 39v 48 INDIVIDUAL LEAVES IN DESK SKETCHBOOK FORMAT 51 Vienna A74A 51 POCKET SKETCHBOOKS 53 Sketches for the D theme as Coda for opus 131 in Autograph 9, Bundle 4 53 Sketches for the D theme as Coda for opus 131 in Autograph 10, Bundle 1 56 Sketches for opus 135 and related material in Artaria 205, Bundle 3 58 INDIVIDUAL LEAVES IN POCKET SKETCHBOOK FORMAT 83 MS 66(6) 83 SCORE SKETCHES 88 Score Sketches for the First Movement 88 Facsimile of Artaria 216, p. 85 88 Score Draft 1 (a) 90 Score Draft 1 (b) 97 Facsimile of Artaria 210, p. 319 106 Fragment 1 108 Fragment 2 111 Facsimile of Artaria 216, p. 69 116 Score Draft 2 (a) 118 Score Draft 2 (b 135 Discarded Autograph Fragments 146 Other Score Fragments 153 Score Sketches for the Second Movement 158 Score Draft 1 158 Score Draft 2 165 Score Draft 3 173 Score Draft 4 182 Fragments 197 Score Sketches for D theme as Coda for opus 131 205 Coda for draft autograph of opus 131, VII 205 Sketch for transition to D Coda 210 Score Sketches for the Third Movement 212 Score Draft 1 212 Score Draft 2 (a) 217 Facsimile of Artaria 209, p. 39 226 Score Draft 2 (b) 228 Score Draft 3 235 Fragments 246 Score Sketches for the canon, WoO 196 "Es muss sein" 253 Facsimiles of sketches and autograph for the canon, WoO 196 "Es muss sein" 260 Score Sketches for the Fourth Movement 268 Score Draft 1 268 Score Draft 2 283 Score Draft 3 288 Fragments 293 RECONSTRUCTED POCKET SKETCHBOOK Pocket Sketchbook MS 62/66 INSERT IN BACK COVER CONTACT: Sydney Conservatorium of Music, Macquarie St, Sydney 2000, Australia, Voice:61 2 230 3759 Fax: 61 2 230 3747, email petermc@pitt.conmusic.su.oz.au ================================================= AUTHOR: Nelson, Mark, D TITLE: "Quieting the Mind, Manifesting Mind: The Zen Buddhist Roots of John Cage's Early Chance-Determined and Indeterminate Compositions" INSTITUTION: Princeton University BEGUN: June, 1989 COMPLETION: February, 1995 ABSTRACT: In the course of his engagement with Zen Buddhism in the early 1950's, John Cage began to regard music as a discipline comparable to sitting meditation. Music, he discovered, could function as a vehicle with which one might curb the inveterate thinking that artificially separates human beings from the 'divine' flood of perceptual experience. Cage aspired to immerse musicians and listeners in this flood. He turned to chance operations as essential aids with which to minimize ego-involvement in determining musical continuity; and the radical alterations of his methods for harnessing chance paralleled substantial refinements of his aesthetic creed. After examining fundamental tenets of Zen Buddhist thought, this paper considers Cageian assimilations of that thought, with particular focus upon 'nothing,' the composer's adaptation of the Zen concept of 'emptiness'. Such philosophical ground is then used as the basis for integrated discussion of the synergic evolutions of Cage's aesthetic perspective and musical style in 1948-1960. The indeterminate scores -- which may be viewed as challenging puzzles for David Tudor, as incipient 'circus situations,' and as utterly flexible tools facilitating the mining of any facet of the unpredictable and manifold universe -- are portrayed as apotheoses of Cage's Zen-informed activity of the 1950's. KEYWORDS: indeterminacy, chance, Zen Buddhism, non-intention, I Ching, Variations TOC: Chapter 1 Reconsidering Music's Purposes Chapter 2 Zen Buddhism Chapter 3 Cageian Echoes of Zen Buddhist Doctrine Chapter 4 Accomplishing Nothing, Educing Nothing Chapter 5 Early Glimpses of Non-Intention Chapter 6 First Freedoms from the 'accretions of habits and tastes': Concerto for Prepared Piano and Chamber Orchestra Chapter 7 Charts, Chance Chapter 8 'the music is there befOre /it is writteN: Music for Piano (Indeterminacy I) Chapter 9 The Synthesis of the Time-Length Pieces Chapter 10 Enacting Process: Indeterminacy II CONTACT: 3042 Shore Drive Crawfordsville, IN 47933 Voice: 317 866-1552 nelsonm@scholar.wabash.edu ================================== AUTHOR: Rupprecht, Philip, E. TITLE: Tonal Stratification and Conflict in the Music of Benjamin Britten INSTITUTION: Yale University, Music Dept., 143 Elm St., New Haven CT 06520 BEGUN: 10/90 COMPLETION: 11/93 ABSTRACT: This theoretical study explores tonal instability in Britten's music via analytic readings of six works. Tonal stratification describes a division of registral space into discrete layers--strata--each associated with a recognizably independent functional-tonal process. Conflict in Britten's music is felt as a clash of opposing focal pitches. Salient pitch dualisms undermine the security of key definition associated with triadic monotonality. A wide registral gap between strata dismantles the harmonic integration of voices over a bass. Chapter 1 surveys tonal conflict in earlier styles, and in polytonality. Analyses of the song "London" (1965) and Noye's Fludde (1957) explore the role of tonal prolongation in stratified textures. Chapters 2-5 treat four works in detail. In Billy Budd (1951), chromatic tonal uncertainty (a B/Bb dualism) affects foreground motivic detail and larger linear motions. Triadic dualisms in the 1963 Nocturnal for guitar are read in light of symbolic tensions in the work's poetic source. Linear-analytic readings here replace the conventional consonance/dissonance dyad with a register-specific intervallic model (congruency/discrepancy) to capture the equivocal nature of harmonic relations between registers. Analysis of "Die Heimat" (1958) examines formal articulations in a song whose counterpoint of strata appears only loosely coordinated. The multivalent textural interactions in the 1962 War Requiem grow from a precarious tension between the axial centricity of the C/F# Bell-tritone and the vestigial gravitational force of D minor. KEYWORDS: stratification, texture, tonality, register, prolongation, uncertainty, bitonality, dualism, inversion, conflict TOC: Chapter 1: Tonal Stratification and the definition of musical conflict Chapter 2: Tonal Stratification and Uncertainty: The Billy Budd Prologue Chapter 3: Tonality and the Presence of the Past: The Nocturnal after John Dowland Chapter 4: Synchronicity of Process in a Stratified Texture Chapter 5: Conflict as Premise: The First Movement of the War Requiem (327 text pages) CONTACT: 412 2nd St, Brooklyn, NY 11215 ======================================== AUTHOR: Scotto, Ciro, G TITLE: "Can Non-Tonal Systems Support Music as Richly as Tonal Systems?" INSTITUTION: University of Washington BEGUN: September, 1991 COMPLETION: December, 1995 ABSTRACT: Can non-tonal systems support music as richly as the tonal system? The question has many possible interpretations, and each interpretation requires a different type of answer. Moreover and more important, each interpretation of the proposition and its corresponding answer directs the investigation down a different path. A proposition's context often determines its sense, and determining a proposition's sense is one method of specifying its interpretation. Chapter one begins by examining the role context plays in establishing the proposition's sense and the role context plays in determining the sense of a musical expression in music. The sense of a musical expression in music leads to a discussion about expressed and unexpressed music theories which lays the groundwork for establishing the context and sense for proposition P . This essay examines proposition P in the comparative context. The goal of the investigation in this context is to build bridges between domains by integrating tonal structures, such as prolongation and structural levels, and non-tonal structures, such as trichords and uniform trichordal arrays, into a single system called the hybrid system. However, since a recent argument has suggested that the design of compositional systems may be limited by certain cognitive constraints, the author addresses this question in depth in chapter one before constructing the hybrid system. Since uniform trichordal arrays form the hybrid system's rear end, and since uniform trichordal arrays are a subclass of the class of self-deriving rows, chapter two constructs a detailed model of all self-deriving rows. Using the model of self-deriving rows as a foundation, chapter three constructs a model of the subclass of uniform trichordal arrays, while chapter four compares the subclass of self-deriving rows capable of generating uniform trichordal arrays to other self-deriving rows capable of generating other array types and twelve-tone arrays in general. Chapter five begins the transformation of a uniform trichordal array's structure into the foundations of the hybrid system. Chapter six integrates uniform trichordal arrays and tonal theory to produce the engine that drives the hybrid system. Chapter seven demonstrates how intra-set-type relations translate into inter-set-type relations, and finally, chapter eight briefly reexamines proposition P. KEYWORDS: non-tonal system, tonal system, cognitive constraints, self-deriving rows, structural levels, hybrid system TOC: Chapter 1: Philosopheme 1 Review of Meaning and Truth 2 Meaning in Music 14 Context, Meaning, and Theory 23 Expressed and Unexpressed Theories 28 Context 38 Lerdahl's Cognitive Constraints 41 Universals 62 Representations 70 Linguistics, Psychology, and Generative Music Theory 81 The Terms of Proposition P 121 Outline of the Hybrid System 139 Chapter 2: Ampliation--A Model of Self-Deriving Arrays 2.1 Towards a Model of Self-Deriving Arrays 145 Set Properties and Folding Sub-Category 3 Type 2 Arrays 164 Partitioning Type 1 and Type 2 Arrays into Subclasses 171 Pruning Table 2.4 by Means of Algorithms for Type 1 and Type 2 Self-Deriving Arrays 193 2.2 Type 1 Combinations 195 Subclass 1a--General 195 Algorithm for Type 1 Subclass 1a Arrays 201 Preliminaries 201 Procedure 208 Procedural Changes 216 Multiple Orderings, Cycle Length, and Hidden Cycles 221 Merging Schemata 234 Subclass 1c--General 240 Algorithms for Type 1 Subclass 1c Arrays T0-TnIR/TnI-TnR Special Case 243 T0-TnIR/Tn-TnIR 248 Procedural Changes 253 T0-TnIR/TnM-TnIMR 268 Subclass 1b--General 277 Algorithm for Type Subclass 1b Arrays T0-TnR/TnM-TnMR 280 T0-TnR/TnIM-TnIMR 286 Subclasses 1d and 1e--General 292 Algorithms for Type 1 Subclasses 1d and 1e Arrays T0-TnMR/Tn-TnMR, T0-TnMR/TnIM-TnIR, and T0-TnIMR/TnM- TnIR 294 T0-TnMR/TnM-TnR, T0-TnIMR/Tn-TnIMR, T0-TnIMR/TnIM-TnR 300 2.3 Type 2 Combinations Preliminaries 306 Subclass 2a: Hexachords 325 Algorithm: Partition Identity Arrays 326 Commentary 328 Subclass 2a: Tetrachords 329 T0-Tn/TnR 334 T0-Tn/TnM 335 T0-Tn/TnMR 337 Commentary and Summary 338 Subclass 2b: Hexachords 339 Algorithm: Partition Identity Arrays 340 Commentary 346 Algorithm: Intersecting Partition Arrays, Subclass 2b, Schema 3-3, T0-TnI/TnR Combination 347 Algorithm: Intersecting Partition Arrays, Subclass 2b, Schema 3-3, T0-TnI/TnIR Combination 352 Commentary 355 Algorithm: Intersecting Partition Arrays, Subclass 2b, Schema 4-2 358 Subclass 2b: Tetrachords 359 Algorithm: Partition Identity Arrays 360 Summary 362 Subclass 2c: Hexachords 363 Algorithm: Partition Identity Arrays 363 Commentary 366 Subclass 2c: Tetrachords 367 Algorithm: Partition Identity Arrays 367 Summary 370 Subclass 2d: Hexachords 371 Algorithm: Partition Identity Arrays 371 Commentary 374 Algorithm: Intersecting Partition Arrays, Subclass 2d, Schema 3-3, T0-TnIM/TnMR Combination 375 Subclass 2d: Tetrachords 381 Algorithm: Partition Identity Arrays 381 2.4 Summary 383 Chapter 3: Cosmogony--Uniform Trichordal Arrays Preliminaries 385 Algorithm for Generating a Uniform Trichord Array from a Seed Array 399 Structural Model of Uniform Trichordal Arrays 419 Chapter 4: Alternative Worlds--Semi-Uniform Trichordal Arrays and Non-Self-Deriving Arrays Prelininaries 473 Generating a Semi-Uniform Trichordal Seed-Array from an Alternative-Merging Schemata 481 Three-Lyne Self-Deriving Arrays 487 Non-Self-Deriving Arrays 494 Chapter 5: The Hybrid System--from Array to Schema Uniform Trichordal Arrays: Definition of Function 500 Array as Schema: From Pitch-Class to Pitch 512 2'Schematic Structure as Compositional Determinant From Order to Content 519 Chapter 6: The Schema of Causality 537 Exposition and Translation 538 Trichord Progressions: Part I 580 Trichord Progressions: Part II 614 Translevel Connections 653 Chapter 7: Second Plane Tertiary Structures 673 Chapter 8: Epilogue 703 Bibliography 716 Appendix i: Common-Tone Vectors for Hexachords Under M5 and M7 728 Appendix ii: Hexachordal Information for the Generation of Uniform Trichordal Arrays and the Arrays They Generate 733 Appendix iii: Trichord Partitioning Patterns for Uniform Trichordal Arrays 845 Appendix iv: Detailed Trichord Vectors for Tn/TnI Type Hexachords 858 Appendix v: Episodes for Guitar 871 Appendix vi: Tetralogy 886 CONTACT: 5009 40th Ave NE, Seattle, WA 98105 Voice: (206) 525-8190 ================================= AUTHOR: Squibbs, Ronald, J. TITLE: "Analytical Issues in Recent Instrumental Works of Iannis Xenakis" INSTITUTION: Yale University, Dept. of Music, 143 Elm Street, New Haven, CT 06520 BEGUN: 9/92 COMPLETION: 3/96 ABSTRACT: This dissertation confronts some of the problems involved in the analysis of post-war avant-garde music by focusing on the recent instrumental music of Iannis Xenakis. This study presents comprehensive analyses of a group of solo and chamber works in an effort to uncover some of the general structural principles underlying this important composer's msuic. The analytical method developed for this study takes into account several aspects of the music, including its pitch structure, textural features, and temporal structure. A survey of the composer's most important theoretical concepts and compositional techniques is presented as a necessary preliminary to the introduction of the analytical methods that are used thoughout the dissertation. The relationship of the mathematical theory of probability to the composition of Xenakis's stochastic music is discussed in detail and the structural ramifications of this compositional method are explored in the analyses. The use in Xenakis's compositional process of techniques of transformation derived from the graphic arts in is also discussed with reference to particular works. In conclusion, Xenakis's position among his contemporaries, both serialists and non-serialists, is considered in light of the preceding analyses. KEYWORDS: Xenakis, analysis, 20th-century, music since 1950, pitch sets, compositional technique, mathematics, graphic composition, stochastic music TOC: 1. Introduction, 2. Compositional Technique and Analytical Method, 3. Works for Solo Piano, 4. Works for Solo Strings, 5. Chamber Music, 6. Conclusions CONTACT: 1164 Whitney Avenue, Apt. J, Hamden, CT 06517 voice: (203) 782-9885 ============================================ AUTHOR: Thomas, Margaret E. TITLE: "Polytempo as Temporal Dissonance in the Player Piano Studies of Conlon Nancarrow" INSTITUTION: Yale University, Department of Music, 143 Elm St., New Haven, CT 06520 BEGUN: Sept., 1992 COMPLETION: Sept., 1995 ABSTRACT: This dissertation focuses on the extreme form of polyphony created by the simultaneous, seemingly uncoordinated streams of music that are so common in Conlon Nancarrow's Studies for player piano, and the philosophy of musical rhythm and time embodied therein. My analyses are guided by two qualities I believe to be elemental to the Studies: multidimensionality and temporal dissonance. Multidimensionality refers to the stratification of musical time into two or more asynchronous layers, as created foremost by the simultaneous use of conflicting rhythms, meters, and/or tempos. Temporal dissonance can result from a work's multidimensionality: Nancarrow views the conflicting rhythmic organization of contemporaneous layers as dissonant, to varying degrees, depending on the precise relationship of the layers. In the course of the dissertation I examine approximately two-thirds of the Studies. CONTACT: e-mail: thomare@minerva.cis.yale.edu ================================================= AUTHOR: Waters, William, J. TITLE: "A Study of Temporal Change in the Recorded Performances of Igor Stravinsky's, `The Rite of Spring'." INSTITUTION: Florida State University, Humanities Department, Tallahassee, FL, 32306 BEGUN: January, 1994 COMPLETION: December, 1995 ABSTRACT: This study will provide a comprehensive evaluation of the recorded performances of Igor Stravinsky's "The Rite of Spring" concentrating on changing interpretations with regard to tempo in general, and the idea that musical works are performed slower today than in the earlier part of this century (as promulgated by Harold Schonberg, Robert Philip, Sandra Rosenblum, et al) in particular. Chapter one will present timings for approximately ninety recordings from 1929 to 1993 in terms of minutes and seconds. Chapter two will focus on those sections of the work exhibiting a marked shift in tempo by employing a computer program (TempoMapper) to construct temporal maps. This type of analysis was used as early as 1964 by Robert King. However, the present study borrows from a more recent method employed by Jos Bowen. In Chapter three (and several subsequent ones) the focus of the study will shift from where changes of tempo have taken place to the thorny question of why. Factors to be considered include changes in the recording medium, the growing emphasis on detail in modern recordings, and showmanship of conductors. KEYWORDS: Stravinsky, "Rite of Spring," tempo, performance practice, performance trends, sound recordings, "TempoMapper," computer-aided analysis TOC: NA CONTACT: Bill Waters, Pensacola Jr. College (LRC), 1000 College Blvd., Pensacola, FL 32504 (wk) or 1175 Peperidge Dr., Pensacola, FL, 32504 (hm) Voice: 904-484-2058(wk) 904-494-9058(hm) e-mail: bwaters@pjc.cc.fl.us ========================================================================== 7. Communications 1. MTO Access Survey 2. Guide to Web Tools 3. HTML Essays 4. MTO Database ========================== 1. MTO Access Survey Thanks to all who kindly replied to the MTO access survey I sent out toward the beginning of April. Here are the results: Access methods No. of users ~~~~~~~~~~~~~~ ~~~~~~~~~~~~ mto-serv 54 ftp 18 gopher 12 www 50 none 33 This was primarily an informational survey; some who expressed concern that www might "elbow out" other methods should not worry! We realize that not everyone has high-powered technology easily available and will continue to strive to make MTO accessible to as many as possible, as conveniently as possible. At the same time, a number of respondents were excited about the prospects of www. We will be moving toward more html documents (in addition to ascii versions) in the future (see below for the first). As an indication of the usage of the www access method, here is a week-by-week tally of www accesses to SMT documents: Week MTO SMT ~~~~ ~~~ ~~~ March 24-31 151 120 April 1-6 106 107 April 7-14 114 107 April 14-21 112 134 April 21-28 94 95 April 28-May 5 98 128 May 5-12 103 80 Robert Judd MTO Manager 5/15/95 ================================================================ 2. Guide to Web Tools* This provides information for MTO subscribers regarding A. gaining access to world-wide web B. editing documents for www browsers *This "Guide to Web Tools" is available as www-tools.txt in the pub/smt/mto/docs directory on the host fas.harvard.edu. It can be retrieved either through anonymous FTP, or with the MTO FileServer, mto-serv. ======================================================================== A. Gaining access to www www is a means for viewing documents via the internet. Those with www capabilities can use graphic interface (mouse) with point-and-click uploading and downloading of documents, including visual and aural images. The usefulness of this technology for MTO seems clear. To gain access to www documents one needs a "browser," a program that does the work of processing data so that it appears correctly on a local screen. If you have e-mail capabilities, you can gain access to www documents. The question you need to answer is "which method is best for me?" The answer depends on your hardware and electronic connection methods. 1) web documents via e-mail ~~~~~~~~~~~~~~~~~~~~~~~~~~~ All web documents are available via e-mail. Simply send a message to the following address: listserv@w3.mail.org include the text line send e.g. send http://smt.ucsb.edu/mto/index.html The document will be mailed to you. 2) basic browsing connection: Lynx ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The most straightforward and "plain" browser is Lynx, which is intended for running on mainframes. It is useful in that it does not require high-power modems or SLIP/PPP connection (more on that later). All you do is log on to your e-mail account and run Lynx, just as you might run your e-mail program. While it does not enable full graphic interface (no mouse), it does allow for document reading and enables easy downloading of all graphics and text files. It is quite similar to "gopher" in general appearance. If you do not have Lynx running locally chances are that your system administrator will load it and make it available if you ask him/her. The Lynx "help" and "commands" pages are essential; be sure to read them, so that you can utilize the program's potential. 3) intermediate connection: SlipKnot ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If you have a PC running Windows, a unix e-mail account and a fast modem (9600 baud and up) you can get full graphic access to www through a program called SlipKnot. It is shareware and requires registration after a short trial period. It is available only in a PC version at present. SlipKnot's primary feature is that it DOES NOT require SLIP or PPP or TCP/IP services. SlipKnot is being published by MicroMind Inc. as restricted shareware. The SlipKnot 1.0 distribution file (approx. 1.2 MB) is available for downloading from the following sites: Site Directory File ----------------------------------------------------- In North America: oak.oakland.edu /SimTel/win3/internet slnot100.zip ftp.uoknor.edu /mirrors/SimTel/win3/internet slnot100.zip ftp.netcom.com /pub/pbrooks/slipknot slnot100.zip In the U.K.: src.doc.ic.ac.uk /computing/systems/ibmpc/simtel-win3/internet slnot100.zip In Australia: ftp.bf.rmit.edu.au /pub/pc/www/slnot100.zip For help on installation, there is a step-by-step procedure both in the included READ.ME file and inside the SlipKnot Help screens. There is also a SlipKnot FAQ file dedicated to installation questions; please retrieve it via anonymous FTP from one of addresses below if you have any problems: interport.net /pub/pbrooks/slipknot sntfaq1.txt If you have a WWW browser (lynx and www are fine), then SlipKnot's Home Page can be accessed at: http://www.interport.net/slipknot/slipknot.html 4) full connection: Mosaic ~~~~~~~~~~~~~~~~~~~~~~~~~~ If you have an ethernet connection, OR your e-mail mainframe allows for SLIP/PPP access and you have a fast modem, you can utilize the fully powered www browsers now available. The most popular browser is Netscape, available via anonymous ftp from the following address: ftp.mcom.com (Many other ftp sites have the program available. Ask locally if you need help.) Netscape is available in Mac and PC formats. At the moment (5/15/95) the most effective version is 1.1, released at the end of April. There are many other browsers available (e.g. Cello, NCSA Mosaic, Omniweb), but none as popular. Q: How do I know if I have ethernet or SLIP/PPP? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A: Ask your local e-mail help contact. (SLIP = Serial Line Internet Protocol; PPP = Point to Point Protocol; both enable more efficient modem communication.) If you are on a public internet-access site such as CompuServe or America Online, SLIP/PPP may be available to you for a hefty monthly fee; you might want to look for newer internet service providers, who can give this type of connection to you for $10-20 a month. Modem users need "socket" software to enable SLIP/PPP connection. One of the most popular (for PCs) is Trumpet Winsock. If you would like to obtain a copy of this product you can find it at the anonymous ftp site ftp.utas.edu.au. The file, twsk10a.zip, is located in the /pc/trumpet/winsock directory. A copy of this Shareware product may also be had at the NCSA anonymous ftp server, ftp.ncsa.uiuc.edu. The file, winsock.zip, is in the /PC/Mosaic/sockets directory. (There are many other sites that make this program available; ask locally for assistance.) Q: How do I download files via anonymous ftp? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A: See the MTO Guide for full details on how to use anonymous ftp. To receive the current Guide send the following one-line message: information mto-list to the address: listproc@husc.harvard.edu and the Guide will be mailed to you. +-+-+-+-+-+-+-+-+-+- B. Editing documents for html browsers HTML (hypertext markup language) is understood by all WWW browsers. Its purpose is to make documents and links to documents or images easily accessible across the networking spectrum. For the purposes of MTO, authors need only be concerned with essential style elements: managing titles, headers, footnotes, images (graphics) and the like. MTO articles will not normally contain links to other documents (other than graphics files). Since HTML is so simple, a few minutes reading one of the guides to html writing is well worth the time spent. The standard starting point is the HTML Primer: http://www.ncsa.uiuc.edu/General/Internet/WWW/HTMLPrimer.html Other manuals and tutorials include Peter Flynn's "How to write HTML": http://kcgl1.eng.ohio-state.edu/www/doc/htmldoc.html and Ian Graham's guide to HTML: http://www.utirc.utoronto.ca/HTMLdocs/NewHTML/htmlindex.html The Lynx help file is also useful in this regard. For more extended editing you might want to consider an HTML editor, which makes it easy to enter the specific codes. The following is a list of a few HTML editors; others are available as well. Re this list: HTML Assistant (for PCs) and Rick Giles (for Macs) have been used and endorsed by MTO editors. Let us know if you have others you can recommend. 1. Macintosh a. Rick Giles (giles@dragon.acadian.ca) need SE/30, Mac III or other computer with 68020/compatible CPU; System 7 or higher, 2 MB RAM ftp: cs.dal.ca dir: /giles/HTML_Editor_1.0.sit.hqx b. Billy Lee (billy@gizmo.dt.navy.mil) BBEditLiet at info-mac locations get: bbedit-lite-232.hqx bbedit-html-ext-b3.hqx 2. IBM-PC/Compatible a. HTML Assistant site: ftp.cs.dal.ca dir: htmlasst file: htmlasst.zip or .exe file (self-extractor) b. HotMetal site: ftp.ncsa.uiuc.edu dir: /Web/html/hotmetal/Windows file: hotmetal.exe Here is a WWW site for information on HTML Editors: http://info.cern.ch/hypertext/WWW/Tools/Overview.html To read a document on learning about HTML: http://cs.dal.ca/ftp/htmlasst/lernhtml.html Robert Judd MTO Manager 5/15/95 ========================================================================== 3. HTML Essays This issue of MTO includes a rudimentary example of an HTML document, William Rothstein's response to John Rothgeb's MTO 1.2 essay on the "Tristan Chord." The musical examples are integrated into the text, and the footnotes, rather than following each paragraph as in the text-only version of MTO, may be viewed by clicking on footnote reference numbers. Links at the end of each foonote lead back to the appropriate point in the text. In addition to permitting such links and text-graphics integration, HTML allows control over paragraph and character formatting (e.g. italics and diacritical markings for foreign-language characters). Now that MTO is being distributed on the World-Wide Web, I would like to encourage prospective authors to consider submitting essays formatted with the HyperText Markup Language (HTML), not really a computer language but rather a set of "tags" that control the display of text in a Web browser. Robert Judd, MTO Manager, has prepared a document (described above) that explains how to get HTML editors for various hardware platforms. Further questions about HTML editors, or about Web browsers, should be addressed to him. 4. MTO Database Subscribers should be aware of the MTO database, which indexes all articles, commentaries, and reviews published in the journal according to author, title, and keywords. The database is updated with each new issue. The database does not include the author-title listings for dissertations postings included in MTO. The file diss.index, alphabetized by authors' last names, is comprehensive listing of dissertation postings. The MTO Guide explains how to use the database. In brief, to do a search, send an email message to mto-serv@husc.harvard.edu. In the body of the message (not in any of the header lines) include the word "path" followed by your full email address (Bitnet-only users must include .BITNET), and one or more of the other lines listed after the "path" line: path YourEmailAddress search ITEM=article, review, talk search AUTHOR=LastName search TITLE=TitleWord(s) search KEYWORDS=Keyword(s) search REFERENCE=ReferenceFile(s) Don't forget the "equals" sign! The ITEM= line specifies whether the desired item is an article, review, or a commentary (= talk). These can be combined with Boolean operators (or, and). The AUTHOR= line would be filled in with an author's last name. The TITLE= line would be filled in with one or more words from the title of the item, if known. The KEYWORDS= line can include a single word, or may be filled in with two or more keywords linked with Boolean operators. The REFERENCE= line is specifically for locating commentaries on a particular article. The line is filled in with the standard MTO filename of the article for which a user wishes to locate commentaries published in MTO. For complete instructions on searching the database, consult the Guide. Please report any typographical or other errors discovered in the database to the General Editor (address below). Lee A. Rothfarb, General Editor Music Theory Online University of California, Santa Barbara mto-editor@smt.ucsb.edu =================================== 8. Copyright Statement +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ Copyright Statement [1] Music Theory Online (MTO) as a whole is Copyright (c) 1995, all rights reserved, by the Society for Music Theory, which is the owner of the journal. Copyrights for individual items published in MTO are held by their authors. Items appearing in MTO may be saved and stored in electronic or paper form, and may be shared among individuals for purposes of scholarly research or discussion, but may *not* be republished in any form, electronic or print, without prior, written permission from the author(s), and advance notification of the editors of MTO. [2] Any redistributed form of items published in MTO must include the following information in a form appropriate to the medium in which the items are to appear: This item appeared in Music Theory Online in [VOLUME #, ISSUE #] on [DAY/MONTH/YEAR]. It was authored by [FULL NAME, EMAIL ADDRESS], with whose written permission it is reprinted here. [3] Libraries may archive issues of MTO in electronic or paper form for public access so long as each issue is stored in its entirety, and no access fee is charged. Exceptions to these requirements must be approved in writing by the editors of MTO, who will act in accordance with the decisions of the Society for Music Theory. +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ END OF MTO 0.0 (mto.pak.yy.v.i)