=== === ============= ==== === === == == == == == ==== == == = == ==== === == == == == == == == = == == == == == == == == == ==== 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) 1994 Society for Music Theory +-------------------------------------------------------------+ | Volume 0, Number 9 July, 1994 ISSN: 1067-3040 | +-------------------------------------------------------------+ General Editor Lee Rothfarb Co-Editors Dave Headlam Justin London Ann McNamee Reviews Editor Claire Boge Consulting Editors Bo Alphonce Thomas Mathiesen Jonathan Bernard Ann McNamee John Clough Benito Rivera Nicholas Cook John Rothgeb Allen Forte Arvid Vollsnes Marianne Kielian-Gilbert Robert Wason Stephen Hinton Gary Wittlich Editorial Assistants Natalie Boisvert Cynthia Gonzales All queries to: mto-editor@husc.harvard.edu +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ 1. Target Articles A. Henry Klumpenhouwer, Some Remarks on the Use of Riemann Transformations B. Jay Rahn, From Similarity to Distance; From Simplicity to Complexity; From Pitches to Intervals; From Description to Causal Explanation -------------------------------------------------- AUTHOR: Klumpenhouwer, Henry TITLE: Some Remarks on the Use of Riemann Transformations KEYWORDS: Riemann, harmonic dualism, Wagner Henry Klumpenhouwer University of Alberta Edmonton, Alberta T6G 2C9 userklum@mts.ucs.ualberta.ca ABSTRACT: The essay examines Lewin's and Hyer's use of transformations derived from Riemann's work, and suggests a number of revisions. An expanded collection of transformations is introduced and used in an short analysis of excerpts from Wanger's *Ring*. ACCOMPANYING FILES: mto.94.0.9.klumpenhouwer.fig (= examples) mto.94.0.9.klumpenhouwer.app (included at end here) [1] In this paper I suggest revisions to an analytical methodology developed in Lewin 1987, 1992 and Hyer 1989. Their work draws upon certain themes in Riemann's writings in order to construct procedures for investigating harmonic relationships in Wagner, procedures that also engage transformational approaches to analysis. My revisions also refer explicitly to Riemann's writing, but they refer to an earlier stage in his career, and in particular to his *Skizze einer Neuen Methode der Harmonielehre* (Riemann 1880). I. Chord Models and Chord Transformations. [2] Hyer (1989) develops a group of transformations on triads from a collection of four relations generally associated with Riemann's work: parallel, relative, leittonwechsel, and dominant. Lewin (1987, 1992) begins with a somewhat larger number of basic transformations. A few originate in Riemann (parallel, relative, leittonwechsel). Others (mediant, submediant) are adapted from other theorists. And still others (slide relation) are constructed by Lewin himself. [3] Example 1 investigates how these transfor- mations interact with the triads or klangs they relate. Example 1a is a network of three arrows labelled with Riemann transformations, and three nodes containing klangs. The relationship between C major and E minor is interpreted as leittonwechsel (L), defined by Lewin as a transformation on triads that maintains the two pitches that form a minor third (mod 8ve), and moves the remaining pitch one semitone so as to form another triad (1992, 49). The network interprets the relationship between E minor and G major as an instance of the relative transformation (R), which maintains the two pitches that form a major third (mod 8ve), and moves the remaining pitch a whole tone so as to form another triad. The arrow that extends from C major to the G major is labelled with the subdominant transformation (S), which transposes a klang by a perfect fifth up. The network suggests the following functional equality: L followed by R yields S. [4] Aside from node content, the network given in example 1b is very similar to the network in example 1a. Both networks have leittonwechsel and relative labels on corresponding arrows. But while the arrow on example 1a that extends from C major to G major is labelled with the subdominant transformation (S), the corresponding arrow on example 1b (extending from A minor to D minor) is labelled with the dominant transformation (D), which transposes a klang up a perfect fifth down. The network in example 1b, contrary to the network in example 1a, suggests that L followed by R yields D. [5] The difference bothers me because the difference (and other similar differences in the system) is brought about by separating dualist chord models from dualist transformations (leittonwechsel, relative) and then using those transformations in conjunction with functions or relations (dominant, subdominant, submediant, mediant) derived from fundamental-bass conceptions of chord structure. My point here is not that Hyer and Lewin have been unfaithful to the wishes of Riemann. My point is that technical properties of leittonwechsel and relative transformations--in particular the property that they are their own inverses-- induce what amounts to a dualist relationship between major and minor chords. For instance, as one examines the values and arguments on the relevant function table of the leittonwechsel transformation, one sees that in general the transformation changes the modality of a major triad to its parallel minor and transposes a major third up, while it changes the modality of a minor triad to its parallel major and transposes a major third *down*. The reversal of direction that accompanies the reversal in modality is the imprint of dualist thinking. The imprint is indelible: the only way to avoid the dualism is to redefine the transformation so that its function table reverses the modality of a triad and transposes it a certain directed interval regardless of modality. But that would simply turn leittonwechsel either into Lewin's SUBM (submediant) transformation or into his M (mediant) transformation, depending on the chosen directed interval. [6] I have not faulted Hyer and Lewin with having misrepresented Riemann's work because I do not count that as a fault, and because there is a sense in which an uncomfortable juxtaposition of dualist and non-dualist thinking is a prominent characteristic of Riemann, particularly of his later work: the well-known contemporary critique of Riemann in Belinfante 1904 makes this very point. In fact, it could be fairly argued that in what follows it is *I* who will be misrepresenting Riemann. My own distortions (as far as I can tell) involve projecting a particular ideational structure on Riemann's transformations (as they appear in the *Skizze einer Neuen Methode der Harmonielehre*), and then appropriating the transformations for analytical purposes other than those discussed by Riemann, who seems most interested in using transformations to chart out the topographies of his *Dur-Moll* and *Moll- Dur* systems. Following Lewin and Hyer, I will be interested in extending the use of Riemann's transformations to seek out repetitions of harmonic patterns, which are then presented as motivic. [7] Accordingly, my proposed revision of the analytical methodology involves firstly turning away from non-dualist transformations adapted from dominant, subdominant, mediant, and submediant relations, and secondly identifying in Riemann 1880 a less conflicted group of transformations. [8] Since the transformations I shall be discussing *do* compel a dualist conception of triads, it will be worthwhile to establish at least the dominant features of such a view. But because Riemann's own explanation of chord dualism is premised on the existence of harmonic undertones, I shall use an alternative yet functionally equivalent explanation, developed from Hauptmann's discussion of major and minor triads (1853, 25-35). [9] Hauptmann assigns three "functions" to pitches that constitute major and minor triads: unity (*Einheit*); duality or separation (*Zwei- heit*); union (*Verbindung*). The three func- tions are labelled respectively I, II, and III for reference, and are assigned to triad members according to two rules: 1) I and II form a perfect fifth (mod 8ve); 2) I and III form a major third (mod 8ve). The rules stipulate that only the pitch that acts as I or the *Einheit* participates in both the perfect fifth (mod 8ve) and the major third (mod 8ve) relationships. [10] Example 2 distributes the three symbols I, II, III among the pitches that form a major triad. Example 2a calculates which two pitches may be assigned I and II under the first rule above. Since the formalism asserts only that I and II form a perfect fifth, a perfect fourth, or one of their compounds, we cannot determine the assignment of function labels beyond what is shown in the example: F is either I or II; Bb is also either I or II. To decide which is I and which is II, we need to carry out rule 2. Example 2b calculates which pitches may be assigned I and III under the second rule above. Since the formalism asserts only that I and III form a major third, a minor sixth, or one of their compounds, we cannot determine the assignment of function labels beyond what is shown in the example: Bb is either I or III; D is also either I or III. But by combining the results of the rule assignments in examples 2a and 2b, we know that Bb must be I: only Bb par- ticipates in a perfect fifth (mod 8ve) relation- ship and a major third (mod 8ve) relationship. If Bb is I, F must be II, and D must be III. [11] Examples 3a, 3b, and 3c carry out on a minor triad the procedures for assigning the functions I, II, and III. Example 3a calculates which pitches may be assigned I and II under the first rule above. Since the formalism asserts only that I and II form a perfect fifth, a perfect fourth, or one of their compounds, we cannot determine the assignment of function label beyond what is shown in the example: F is either I or II; Bb is also either I or II. To decide which is I and which is II, we need to carry out the second rule. Example 3b calcu- lates which pitches may be assigned I and III under rule 2. Since the formalism asserts only that I and III form a major third, a minor sixth, or one of their compounds, we cannot determine the assignment of function beyond what is shown in the example: F is either I or III; Db is also either I or III. But by combining the results of the rule assignments in examples 3a and 3b, we know that F must be I: only F participates in a perfect fifth (mod 8ve) rela- tionship and a major third (mod 8ve) relation- ship. And if F is I, Bb must be II, and Db must be III. [12] Comparing the assignment of function labels in minor triads and major triads, Hauptmann analyzes the constitutive perfect fifths and major thirds as intervals directed upwards: in major klangs the two intervals extend respectively from I to II and from I to III; in minor klangs the two intervals extend respectively from II to I and from III to I. In major klangs, says Hauptmann, the pitch that acts as I *has* a perfect fifth and major third, while in minor klangs the pitch that acts as I *is* a perfect fifth and major third. [13] Under Hauptmann's explanation, a dualist model organizes aural sensations in roughly the following way: When listening to a triad, pick out a major third or its inversion, and pick out a perfect fifth or its inversion; when you do, you will become aware that one pitch in the triad member is overdetermined, and thereby seems more prominent than the others. By way of contrast, a fundamental bass model organizes sensations in roughly the following way: When listening to a triad, reorganize it so that it takes up the smallest registral space and so that only thirds and fifths are formed; assign prominence to the lowest pitch and take note of the quality of the third between that pitch and the next lowest. And a figured bass model orga- nizes aural sensations in roughly the following way: When listening to a triad, concentrate on the lowest-sounding pitch, and assign it promi- nence; imagine a third and a fifth above the lowest pitch (the qualities of which are deter- mined by a contextual diatonic collection); pitches that do not lie a diatonic third or fifth above the prominent pitch are momentarily displacing the pitches that do. The degree to which figured bass and fundamental bass proto- cols have been hypostatized by theorists (to the extent that many will claim that one or the other defines more or less the response end of a reflex arc) is something worth worrying about. [14] In the course of this paper we shall represent klangs as ordered pairs. The first element defines Hauptmann's I-function or *Einheit* (*not* the *Grundton*). The second element defines the klang's modality. "+" represents a major (or over or super) klang, or a "positive" *Einheit* Hauptmann calls it. "-" represents a minor (or under or sub) klang, or a "negative" *Einheit*. The klangs in examples 2c and 3c are respectively represented as (Bb,+) and (F,-). II. Schritts and Wechsels. [15] Having established the relevant chord model, we can now investigate appropriate transformations. We begin by examining Riemann's Schritts, the first of two classes of transformations he presents in *Skizze einer Neuen Methode der Harmonielehre*. Quintschritt (abbr. Q) transposes a klang by the directed interval that extends from I to II. In the case of (C,+), where C functions as I and G as II, the relevant interval is a perfect fifth up. Accordingly, Q(C,+) = (G,+). In the case of (C,-), where C functions as I and F as II, the relevant interval is a perfect fifth down. Accordingly, Q(C,-) = (F,-), i.e., a Bb minor triad. [16] Gegenquintschritt (abbr. -Q) transposes a klang by the directed interval that extends from II to I. In the case of (C,+), where G functions as II and C as I, the relevant interval is a perfect fifth down. Accordingly, -Q(C,+) = (F,+). In the case of (C,-), where F functions as II and C as I, the relevant interval is a perfect fifth up. Accordingly, -Q(C,-) = (G,-). Q and -Q are inverse-related transformations. [17] Terzschritt (abbr. T) transposes a klang by the directed interval that extends from I to III. In the case of (C,+), where C functions as I and E functions as III, the relevant interval is a major third up. Accordingly, T(C,+) = (E,+). In the case of (C,-), where C functions as I and Ab functions as III, the relevant interval is a major third down. Accordingly, T(C,-) = (Ab,-). [18] Leittonschritt (abbr. L) transposes a klang by the directed interval yielded by the composing the relevant directed intervals of Q and T. In the case of (C,+), the composition of Q (a perfect fifth up) and T (a major third up) produces a major seventh up. Accordingly, L(C,+) = (B,+). In the case of (C,-), the composition of Q (a perfect fifth down) and T (a major third down) produces a major seventh down. Accordingly, L(C,-) = (Db,-). [19] Ganztonschritt (abbr. G) transposes a klang by twice the directed interval that extends from I to II. Hence, G = Q2. In the case of (C,+), where C functions as I and G as II, the relevant interval is two perfect fifths up, viz., a (compounded) whole tone up. Accordingly, G(C,+) = (D,+). In the case of (C,-), where C functions as I and F as II, the relevant interval is two perfect fifths down, viz., a (compounded) whole-tone down. Accordingly, G(C,-) = (Bb,-). [20] Kleinterzschritt (abbr. K) transposes a klang by the directed interval that extends from II to III. In the case of (C,+), where G functions as II and E functions as III, the relevant interval is a minor third down. Accordingly, K(C,+) = (A,+). In the case of (C,-), where F functions as II and Ab functions as III, the relevant interval is a minor third up. Accordingly, K(C,-) = (Eb,-). [21] Riemann only discusses these six schritts. Following the pattern established by the pair quintschritt/gegenquintschritt, we can define four more schritts: gegenterzschritt (abbr.-T), gegenleittonschritt (abbr. -L), gegenganztonschritt (abbr. -G), and gegenkleinterzschritt (abbr. -K), which will be inversely-related to terzschritt, leittonschritt, ganztonschritt, and kleinterzschritt respectively. Two others, which we shall call identity (abbr. I) and tritonusschritt (abbr. R) are generated by demands of group structure. Appendix I lists all twelve schritts, and provides paradigms for each. Those not explicitly defined by Riemann are given in angle brackets. [22] The names of the transformations help us remember their particular effect: an X-schritt transposes by the *magnitude* X (where X is a German interval designation) in the direction determined by the operand: major (or over) klangs extend X upwards; minor (or under) klangs extend X downwards. Gegen-X-schritt may be taken either to reverse the direction of X, or to replace the magnitude X with its inverse. Accordingly, X-schritt and gegen-X-schritt are inverses. Kleinterzschritt and its gegen-form are the only schritts that do not follow the pattern: one needs provisionally to take kleinterz as signifying a major sixth. [23] Schritts combine according to the following rule: Xschritt*Yschritt = (X+Y)schritt In other words, summing the directed intervals of composed schritts (and reducing any compounds) yields the appropriate product schritt. For example, Composing K and T in the context of major klangs yields -L, since a major sixth up (the directed interval by which K transposes major klangs) and a major third up (the directed interval by which T transposes major klangs) sum to a minor ninth up, a compound of a minor second up (the relevant directed interval by which -L, the inverse of L, transposes major klangs). Composing K and T in the context of minor klangs still yields -L, since a major sixth down (the directed interval by which K transposes minor klangs) and a major third down (the directed interval by which T transposes minor klangs) sum to a minor ninth down, a compound of a minor second down (the relevant directed interval by which -L, the inverse of L, transposes minor klangs). [24] Since schritts are quantities that combine under simple addition, the group is commutative: in general X*Y = Y*X. [25] But schritts only relate klangs of the same genus. Wechsels, the second class of transformations presented in Riemann 1880, relate klangs of opposing genera. [26] Seitenwechsel (abbr. W) inverts a klang about I (or about I and I). The transformation reflexively maps the major klang and the minor klang whose I-functions are executed by the same pitch. In other words, it exchanges "positive" and "negative" forms of the same *Einheit*, so that W(C,+) = (C,-), and W(C,-) = (C,+). Seitenwechsel appears in Goetschius 1917 (114) as his "stride relation," defined as "a perfect fifth downward from any major keynote, and upward from any minor keynote, with a change in mode." [27] The remaining wechsels may be construed as the composition of some schritt and seitenwechsel. Terzwechsel (abbr. TW) transposes a klang by the directed interval that extends from its I to its III, that is, applies terzschritt, and then inverts the result around its I, that is, applies seitenwechsel. One might then understand the designation "terzwechsel" as an elision of "terzschrittseitenwechsel." Terz(schritt) only affects the first element of an order pair; (seiten)wechsel only affects the second element. In the case of (C,+), TW(C,+) = W(E+) = (E,-); in the case of (C,-), TW(C,-) = W(Ab,-) = (Ab,+). TW is functionally equivalent to Lewin's and Hyer's relative transformation (abbr. R), and may be alternatively defined as the inversion of a klang about I and III. [28] Leittonwechsel (abbr. LW) is the composition of leittonschritt (L) and seitenwechsel (W). In the case of (C,+), LW(C,+) = W(B,+) = (B,-); in the case of (C,-), LW(C,-) = W(Db,-) = (Db,+). LW may be alternatively defined as the inversion of a klang about II and III. [29] Riemann defines three more wechsels: quintwechsel (abbr. QW), ganztonwechsel (abbr. GW), and tritonuswechsel (abbr. RW). Quintwechsel is functionally equivalent to Lewin's and Hyer's parallel transformation (abbr. P), and may alternatively defined as inversion of klang about I and II. Six more wechsels are constructed by extending the idea of composing gegenquintschritt, kleinterzschritt, gegenkleinterzschritt, gegenleittonschritt, gegenterzschritt, and gegenganztonschritt in turn with seitenwechsel. Appendix II lists all twelve wechsels, and provides paradigms for each. Those not defined explicitly by Riemann are given in angle brackets. Appendix III provides rules and relevant examples for combining the twenty-four schritts and wechsels given in the first two appendices. The group is simply-transitive: in particular, for any two klangs j and k, there exists a unique member of the schritt-wechsel group S such that S(j)=k. The analytical use of groups with the property are considered in Lewin 1987. III. Analysis. [30] Examples 4 and 5 investigate some possibilities of schritts and wechsels by using them as arrow labels on network analyses of two excerpts from Wagner's *Ring*. Both networks are developed from analyses recently presented in Lewin 1992: example 6 is based on Lewin's figure 3b, which studies the harmonic structure of the Valhalla theme as it appears in *Das Rheingold* sc.2; example 7 is based on Lewin's figure 4b, which studies the harmonic structure of the same theme as it appears in *Die Walkuere*, act II, sc. 2. The networks are not exactly as they appear in the cited figures in Lewin 1992. The networks that appear in examples 6 and 7 were designed to have the same node-and-arrow configurations, viz., to contain the same number of nodes and arrows, with corresponding arrows extending in the same direction, while Lewin's figures were constructed to serve other analytical purposes that did not require identical node-and-arrow configurations. In any case the divergences from Lewin's figures are slight and the networks in examples 6 and 7 are well-formed according to standards of the relevant methodologies. [31] The nodes in examples 6 and 7 are filled with triads construed according to the fundamental bass model, and are represented by the relevant fundamental bass and an indication of the third's quality. The arrow labels are Lewin's designations: L represents leittonwechsel; P, parallel; S, subdominant; D, dominant. LP represents the composition of L and P. Comparing the left sides of example 6 and 7, we see that they are identical except for node content, and are thus strongly isographic structures. The right sides of examples 6 and 7 are not identical: while the node and arrow configurations are the same, the corresponding arrow labels are different. The transformations L and LP on the left side of both networks invoke dualism on the relevant nodes. (P is neutral with respect to chord model.) Traveling to the right side of each network, one is constrained by the transformations S and D to adopt a non-dualist conception of major and minor chords, to shift from Riemann to Rameau. Accordingly the Bb major/Bb minor nodes in example 6 and the E major/E minor nodes in example 7 are ideational pivots that need to be conceived within both frameworks. [32] Example 4 adapts example 6 to conform to the present methodology: harmonies are represented by the dualist ordered pair format, and arrows are relabelled with the appropriate schritt or wechsel. Only leittonwechsel appears on both example 6 (as L) and example 4 (as LW). Quintwechsel (QW) replaces parallel (P), and terzschritt (T)--which uses as its paradigm the directed interval the extends from I (Gb) to III (Bb) in the (Gb,+) klang--replaces LP, the composition of L and P. Quintschritt (Q) and its inverse, gegenquintschritt (-Q), transformations premised on the interval between I and II, replace the two S arrow labels. [33] Example 5 carries out similar changes on example 7. Comparing examples 4 and 5, one sees that the corresponding arrow labels are strictly identical. The shift from the analysis in examples 6 and 7 to the analysis in examples 4 and 5 allow us then to assert a strong isography between the harmonic relations in two Valhalla themes. With respect to node content, one could assert that the network in example 4 is a positive or major form of the network in example 5. [34] I will not pretend that schritt and wechsel transformations are the only way to establish a link between the two Valhalla themes. One could replace L and LP on example 6 by Lewin's submediant transformation (SUBM) and the composite transformation SUBMP respectively, and replace L and LP on example 7 by Lewin's mediant transformation (M) and the composite transformation MP respectively, thereby shifting the networks entirely into the discourse of fundamental bass theory. Corresponding arrows on example 6 and 7 would then be labelled by inverse-related (Rameau-) transformations. Bibliography Balinfante, Ary. 1904. De leer der tonale functien in conflict met die der polaire tegenstelling. *Orgaan van de Vereeniging van Muziek-Onderwijzers en -Onderwijzeressen* IV.9: 1-2. Goetschius, Percy. 1917. *The Theory and Practice of Tone-Relations*. New York: Schirmer. Lewin, David. 1987. *Generalized Musical Intervals and Transformations.* New Haven: Yale University Press. ---. 1992. Some Notes on Analyzing Wagner: *The Ring* and *Parsifal*. *19th Century Music* 16.1:49-58. Hauptmann, Mortiz. 1853. *Die Natur der Harmonik und der Metrik*. Leipzig: Breitkopf und Haertel. Hyer, Brian. 1989. "Tonal Intuitions in 'Tristan und Isolde'.* Ph.D. diss., Yale University. Riemann, Hugo. 1880. *Skizze einer Neuen Methode der Harmonielehre*. Leipzig: Breitkopf und Haertel. ------------------------------------------ APPENDIX I Schritts [I] (C,+) --> (C,+); (C,-) --> (C,-) [-L] (C,+) --> (Db,+); (C,-) --> (B,-) Ganztonschritt [G] (C,+) --> (D,+); (C,-) --> (Bb,-) [-K] (C,+) --> (Eb,+); (C,-) --> (A,-) Terzschritt [T] (C,+) --> (E,+); (C,-) --> (Ab,-) Gegenquintschritt [-Q] (C,+) --> (F,+); (C,-) --> (G,-) [R] (C,+) --> (F#,+); (C,-) --> (F#,-) Quintschritt [Q] (C,+) --> (G,+); (C,-) --> (F,-) [-T] (C,+) --> (Ab,+); (C,-) --> (E,-) Kleinterzschritt [K] (C,+) --> (A,+); (C,-) --> (Eb,-) [-G] (C,+) --> (Bb,+); (C,-) --> (D,-) Leittonschritt [L] (C,+) --> (B,+); (C,-) --> (Db,-) APPENDIX II Wechsels Seitenwechsel [W] (C,+)<-->(C,-) [-LW] (C,+)<-->(Db,-) Ganztonwechsel [GW] (C,+)<-->(D,-) [-KW] (C,+)<-->(Eb,-) Terzwechsel [TW] (C,+)<-->(E,-) [-QW] (C,+)<-->(F,-) Tritonuswechsel [RW] (C,+)<-->(F#,-) Quintwechsel [QW] (C,+)<-->(G,-) [-TW] (C,+)<-->(Ab,-) [-KW] (C,+)<-->(A,-) [-GW] (C,+)<-->(Bb,-) Leittonwechsel [LW] (C,+)<-->(B,-) APPENDIX III Rules for Combining Schritts and Wechsels Xschritt * Yschritt = (X*Y)schritt Q*L = Q+L = R Xschritt * Ywechsel = (X*Y)wechsel Q*LW = (Q+L)W Xwechsel * Yschritt = (X*-Y)wechsel QW*L = (Q-L)W = -TW Xwechsel * Ywechsel = (X*-Y)schritt QW*LW = (Q-L) = -T ============================================== AUTHOR: Rahn, Jay TITLE: From Similarity to Distance; From Simplicity to Complexity; From Pitches to Intervals; From Description to Causal Explanation KEYWORDS: similarity, proximity, structure, simplicity, complexity, pitch, interval, psychoacoustics, Gestalt, behaviorism, psychology, perception, logic, definition, theorem, proof, postulate, John Rahn, Jay Rahn, Nelson Goodman, nominalism, individual, part, whole, platonism, number, set, description, explanation Jay Rahn York University (Canada) Atkinson College Fine Arts Department 4700 Keele Street North York, Ontario M3J 1P3 relation@vm1.yorku.ca ABSTRACT: Words and phrases specifying similarity and distance abound in musical discourse. This essay explores such pitch-predicates as "matches", "is in the vicinity of, and "is closer to ... than to". Sought here are ways in which pitch and pitch-interval predicates might be inter-connected logically. Within a nominalist framework, an orderly progression from pitch- to pitch-interval-predicates can be proven and interpreted in terms of simplicity. Also indicated are connections between the present formulation and issues of (i) dimension- ality and explanation in psychoacoustics, Gestalt psychology, and behaviorism, and (ii) nominalism and the "numerological fallacy" in music theory. KEY TO LOGIC SYMBOLS: (x)(....) = for any thing, x, .... .... <--> .... = .... if and only if ....; .... iff .... .... v .... = .... and/or ....; (vel; inclusive or) .... . .... = both .... and .... -.... = not ....; it is not the case that .... .... --> .... = if ...., then .... (:Ex)(....) = there is at least one thing, x, such that .... ...+... = ...plus...; all the parts of individual..., as well as all the parts of individual... (including any parts common to both ... and ...); the sum of individuals ... and ... (which is, itself, an individual) [0] INTRODUCTION [0.0] Words and phrases specifying similarity and distance abound in musical discourse. For example: (i) two notes or tones (or even passages or pieces) are often characterized as matching, being the same, like each other, or similar in pitch (or pitch-structure), and (ii) pairs of sounds are frequently described as differing, contrasting, or being remote, far apart, or distant -- all these, in varying degrees or amounts (e.g., somewhat, extremely, etc.). Between twosomes that are precisely the same in some respect, and those which are exceedingly distant, one recognizes intermediate cases. One asserts, for instance, that two sound-events, a and b, are (i') next, or adjacent, to each other (i.e., neighbours, in some sense), or (i'') closer, or nearer, to one another (i.e., than a and/or b are/is to yet another sound-event, c). [0.1] "Common sense" acknowledges as orderly, or linear, a progression from sameness (i), through adjacency (i'), to relative proximity (i''), and onward to remoteness (ii). Things that do not match, differ. Of those that differ, the closest are those that are adjacent. And among non-adjacent things, one can distinguish degrees of distance. Despite the continuity of this progression, common sense also acknowledges that sameness is "qualitative," whereas distance is "quantitative." Nonetheless, one might contend that things which are relatively similar are also relatively close in some "dimension" (e.g., pitch), and that, within a single dimension, far-apart things are very dissimilar. [0.2] Particular traditions of musical thought (e.g., in psychoacoustics) comprehend similarity and distance as polar opposites along single continua (e.g., scaled or gradated in difference-limens or mels: cf. Stevens and Davis 1983, 76-98). By contrast, other lines of musical inquiry (e.g., inspired by Gestalt psychology: cf. Koehler 1947, 84-85 and 117-18) dichotomize in this regard, understanding similarity (or sameness) and proximity (or distance) as distinct principles of perceptual organization or grouping. [0.3] The present study probes the notion that, in such a musical dimension as pitch, there might be continuity between similarity and distance. The investigative strategy undertaken here is to pursue, until an impasse is reached (if at all), the possibility that there might be an unbroken progression from similarity to distance. In the development that follows, I try to clarify ways in which one might distinguish (or not) pitches from intervals. Attempted is the formulation of a common groundwork for dealing with similarity and distance in pitch. As far as possible, pitch- and interval-predicates are defined in terms of a single, maximally economical, basic, primitive predicate, so that (i) necessary, logical connections between predicates can be proven, or (but only if need be) postu- lated -- albeit, one seeks, in a maximally coherent manner, and (ii) stages or gradations between similarity and distance (e.g., comprising next-to and closer-to relations) can be identified clearly. A further tactic adopted in this account construes predicates of similarity and distance in terms of simplicity and complexity (i.e., "structure") and emphasizes, in this connection, relations between parts and wholes and between statements that can be true of a single thing and statements that only can be true of more than one thing. [0.4] The formulation of pitch that follows does not involve numerical modeling (i.e., as such). In this way, an effort is made here to prevent, or at least forestall, systematically and fundamentally, lapses in discourse that might produce instan- ces of the "numerological fallacy." As John Rahn notes at the outset of his exposition of the "integer model of pitch" (1980, 19 -- John Rahn's emphases asterisked: *...*): ... all sorts of things can be proven true of integers -- see any book on number theory. It does *not* follow that, because we are using integers to name pitches (or grapes, [etc.]), all those things that are true of integers are going to be true of pitches (or grapes, [etc.]). We must carefully determine the limits of similarity between integers (with their structure) and pitches (with their possible structures). To do otherwise would be to fall into the *numerological fallacy*. [0.5] To this end, instead of being framed in terms of numbers, the following formulation is cast in terms of things that are neither numbers nor sets; that is, what follows is cast in a nominalist outlook (for which, see Goodman 1966) and accor- dingly framed in terms of "individuals," as well as predicates that specify relations between, or among, such individuals. In this sense, general music-theoretical traditions that form an immediate background to the present study are Aristoxenian rather than Pythagorean, nominalist rather than platonist. [0.6] An idea that guides the present exposition is that two things might constitute a relatively simple whole, and, corres- pondingly, be relatively similar, or close, to one another, to the extent that they are described in terms that can be used to describe a single thing. Initial stages of the subsequent ac- count involve relations of matching, adjacency, and proximity, and explore a sense in which these correspond, respectively, to situations of increasing complexity. [1] MATCHING [1.0] If two things match in pitch, they form a simpler pair than if, all other aspects being the same, they had differed in pitch. The criterion, or benchmark, is a single, inherently pitched thing, which (i) cannot differ, in pitch, or pitch-wise, from itself, and (ii) if inherently pitched, necessarily is the same, in pitch, as itself. Concerning (ii), one can define an inherently pitched thing as follows (1): DEFINITION: (x)(IPx <--> xPRx) For any thing, x, x is inherently pitched if and only if x is pitch-related to x (i.e., to itself). ======================================================== (1) In this and following formulations, such a phrase as "is inherently pitched" can be replaced by such phrases as "is heard as inherently pitched", "is heard as being inherently pitched", etc. -- see below. Note also that inherent pitchedness here differs from pitchedness, which, in Jay Rahn 1992, 165, is a "property" of any thing, x, if and only if there is at least one thing, y, such that x is pitch-related to y. The subsequent theorems claimed in the latter study which depend on this definition of pitched (P) things can be proven for inherently pitched (IP) things. ======================================================== [1.1] The two-place predicate "is pitch-related to" can be defined in the following way: DEFINITION: (x)(y)(xPRy <--> xAHy v yAHx) For any thing, x, and any thing, y, x is pitch-related to y if and only if x is at least as high as y and/or y is at least as high as x (cf. Jay Rahn 1992, 164-65). [1.2] The predicate "matches, in pitch," can be defined as follows: DEFINITION: (x)(y)(xMPy <--> xAHy . yAHx) For any thing, x, and any thing, y, x matches, in pitch, y if and only if x is at least as high as y and y is at least as high as x (cf. ibid., 167). [1.3] From these definitions, one can prove the following theorem: THEOREM: (x)(IPx <--> xMPx) Proof: (x)(IPx <--> xPRx) (x)(xPRx <--> xAHx v xAHx) (x)(xAHx v xAHx <--> -(-xAHx . -xAHx)) (x)(-(-xAHx . -xAHx) <--> -(-xAHx)) (x)(-(-xAHx) <--> xAHx) (x)(xAHx <--> xAHx . xAHx) (x)(xAHx . xAHx <--> xMPx) -- i.e., MP is reflexive for any inherently pitched thing. [1.4] The other portion (i) of the criterion arises directly from the following definition for pitch-difference: DEFINITION: (x)(y)(xDPy <--> xPRy . -xMPy) For any things, x and y, x differs, in pitch, from y if and only if x is pitch-related to y and x does not match, in pitch, y (cf. ibid., 172). [1.5] As a relation, pitch-matching is proven (above) to be reflexive for any inherently pitched thing whatever. As well, pitch-matching has been proven, in an earlier study, to be symmetric for any pair of things whatever (i.e., pitched or non- pitched, inherently so, or not: ibid., 168): THEOREM: (x)(y)(xMPy <--> yMPx) [1.6] Additionally, it can be proven that if any two things, x and y, match, in pitch, then each is pitch-related to the other even if "they" are precisely the same thing (i.e., even if x=y): THEOREM: (x)(y)(xMPy --> xPRy . yPRx) [1.7] If, amidst the "booming, buzzing confusion" of Nature, one acts in an AH-manner, that is, if one "hears" certain things "as" being at least as high as others (or even as themselves), an immediate consequence of the energy expended in such an act of hearing is that one's world divides into things that are entirely unpitched and things that are inherently, and/or non- inherently, pitched. The single inherently pitched things are heard as matching themselves in pitch. Such singletons consti- tute a template, or model, for pitch-simplicity, or pitch- singleness; pitch-matching necessarily holds within inherently pitched things (i.e., "severally", e.g., within each of the two inherently pitched things of a pair) but might not hold between or among them (i.e., "jointly", e.g., between the two inherently pitched things of such a pair). Two inherently pitched things that match pitchwise constitute a simpler pair than two that do not match in pitch, at least with respect to pitch, all other factors being equal. [1.8] "A pitch" can be regarded merely as a sum of all, and only, certain things that match each other in pitch (cf. ibid., 165 on "pitch-identity wholes" and Goodman 1966 on sums of indivi- duals, which, as sums, are, themselves, individuals). Unless there were at least one instance of non-matching, or diffe- rence, in pitch, between two of them, then all pitched things would be heard as matching in pitch. In such a situation of universal non-differentiation in pitch (i.e., obtaining between any and all pitched things), all pitched things would be heard as "parts" of "a" single "pitch". That is, only "one pitch" would be heard and would comprise all, and only, the pitched things. [1.9] Behaviorally, however, it is generally advantageous for a listener that hears pitchwise to hear with optimum pitch acuity (e.g., relative to an immediate biological niche), that is, to hear as few things as possible as matching in pitch. To be sure, each inherently pitched thing necessarily matches itself in pitch. But in such an instance, pitch-matching is just another name for pitched-ness. Pitch-matching relations are not effectively significant, or important, for a listener, unless they hold between non-identical things (i.e., between, for in- stance, acts of hearing, x and y, where -(x=y)). [2] VICINITY [2.0] In the present formulation, every inherently pitched thing is regarded as being "in its own pitch vicinity." As well, all things that match each other in pitch, whether inherently pitched or not, are held to be pitch "neighbors." This general sense of pitch-neighborhood or -vicinity is conveyed as follows: DEFINITION: (x)(z)(xIPVz <--> xNMTJHTz v zNMTJHTx) For any things, x and z, x is in the pitch-vicinity of z if and only if x is no more than just higher than z and/or z is no more than just higher than x. DEFINITION: (x)(z)(xNMTJHTz <--> xAHz . -(:Ey)(xHTy . yHTz)) For any things, x and z, x is no more than just higher than z if and only if x is at least as high as z and there is no thing, y, such that x is higher than y and y is higher than z. DEFINITION: (x)(y)(xHTy <--> xAHy . -yAHx) For any things, x and y, x is higher than y if and only if x is at least as high as y and y is not at least as high as x.(2) ======================================================== (2) As defined here, IPV is more general (i.e., is less determi- nate) than NP ("is next, in pitch, to"), as defined in ibid., 172. E.g., for any things, x and y, xIPVy might hold even if xHTy, but xHTy excludes the possibility of xNPy. ======================================================== [2.1] It can be shown that xMPz is a special case of xIPVz only if there is no "intervening" thing, y. Such a situation would arise in an instance of "Shepard's tones" (cf. Shepard 1964), where, arranged in "descending" semitones, the first might be heard as matching the thirteenth, and yet as higher than the twelfth, which would be heard as higher than the thirteenth. Important to emphasize is that the "illusion" of Shepard's tones depends on temporal succession and is not merely a matter of pitch, as might be a (hypothetical) Shepard's "sonority". In the present formulation, matching in a vicinity is linear, not cyclic, and a pitch-vicinity comprises not only pitch-proximity, but concomitant temporal closeness too. [2.2] If xIPVz and x does not match z pitchwise, then xHTz or zHTx. Such cases are similarly linear, and involve always an HT-relation. Such an HT-relation constitutes a significant arti- culation in the continuity from matching to distance, for no thing whatever can be higher than itself. In this way, vicinity- relations straddle singleness and multitude. [2.3] The present sort of distinction, i.e., between matching and vicinity, arises "for free," as it were, once such a predicate as AH is let loose in the world. The differences in definition between matching and vicinity involve, in their respective formulations, merely differences in their patterning of quan- tifiers, conjunctions, modifiers, individual-variables, and the AH predicate. If one hears in an AH manner, opportunities to make such a distinction can arise (if the world is, in fact, truly characterized according to first-order logic). [2.4] Defining vicinity relations widens the net of simplicity that can be caught in a formulation. Single inherently pitched things (even single inherently pitched sums of individuals, which are themselves individuals) supply a criterion for asserting the simplicity of pairs of things, whether the things are individuals and/or sums of individuals, and whether the pairs are, pitch-wise, both matching and neighbors, or merely neighbors. The relatively weak, indeterminate specification that pitch-vicinity things (x and z in the definition) need merely be pitch-related (insofar as xAHz and/or zAHx), rather than, say, different in pitch (i.e., by virtue of one being higher than the other), widens the net considerably. [3] INTERIORITY [3.0] Concerning the following succession of letters: a b c, one can say, informally, that a is closer to b than (it, i.e., a, is) to c, and conversely, that c is closer to b than to a. As well, informally, b is closer to a than a is to c, b is closer to c than c is to a, b is closer to the sum of a and c (i.e., a+b) than a is to c, and so forth. Abbreviating the first two statements as aCb, and cCb,a, respectively, one can characterize closeness relations in the larger succession: a b c d, as follows: aCb,c; aCb,d; aCc,d; bCc,d; cCb,a; dCb,a; dCc,a; dCc,b; aCb+c,d, and dCb+c,a. [3.1] A corresponding pitch-predicate, "is, in pitch, at least as close to ... as to", can be defined as follows: DEFINITION: (x)(y)(z)(xPACy,z <--> xPOSy,z) For any things, x, y, and z, x is, in pitch, at least as close to y as (x is) to z if and only if x is, in pitch, on the opposite side of y from z. DEFINITION: (x)(y)(z)(xPOSy,z <--> xHSy,z v zHSy,x) For any things, x, y, and z, x is, in pitch, on the opposite side of y from z if and only if x is on the high side of y from z and/or z is on the high side of y from x. DEFINITION: (x)(y)(z)(xHSy,z <--> xAHy . yAHz . xAHz) For any things, x, y, and z, x is on the high side of y from z if and only if x is at least as high as y, y is at least as high as z, and x is at least as high as z.(3) ======================================================== (3) As defined here, PAC is more general than NICP ("is non- intervallically closer, in pitch, to ... than to") in ibid., 172-73. ======================================================== [3.2] Pitch-closeness and pitch-sidedness of this sort can be formulated in terms of things that comprise, or include, pitchwise, other things (or themselves), as follows: DEFINITION: (x)(y)(z)(x+zCPy <--> xPOSy,z) For any things, x, y, and z, the sum of x and z comprises, pitch- wise, y if and only if x is, in pitch, on the opposite side of y from z. [3.3] The partially-ordered character of pitch-comprising relations can be provided for in terms of pitch-interiority (or pitch-insideness): DEFINITION: (w)(x)(y)(z)(x+yPIw+z <--> w+zCPx . w+zCPy) For any things, w, x, y, and z, the sum of x and y is, pitchwise, inside, or interior to, the sum of w and z if and only if the sum of w and z comprises, pitchwise, x, and the sum of w and z comprises, pitchwise, y. [3.4] As well, one can prove that things which form pitch-, pitch-matching, and pitch-vicinity relations constitute pitch-interiority relations, but not necessarily *vice versa*. For example, within a pitch-interiority framework, possible situ- ations involve xHTy, yHTz, and xHTz, and xHTy, yHTz, and xMPy (the latter corresponding to a moment of "dis-illusion-ment" in hearing Shepard's tones). [4] POSSIBLE STEPS TOWARD INTERVAL PREDICATES [4.0] Interiority relations exhaust the farthest reaching possi- bilities for specifying degrees of pitch-distance within the AH-dimension. Whereas one can acknowledge (i.e., for any w, x, y, and z -- see above) that w+z is more inclusive than w+y or x+z, one cannot specify, in the most general way, whether w is more distant from y than x is from z, or w is farther from x than y is from z, or w forms a larger interval with x than x forms with y, etc., except, for example, by (i) specifying that all non-matching vicinity-pairs are equidistant (i.e., taking non-matching vicinity as the "unit" or "degree" of pitch gradation), or (ii) resorting to a predicate other than AH. [4.1] Plausible predicates to perform such functions include "is at least as large as", "is at least as much larger than ... as ... is than", "is at least as much higher than ... as ... is than", and "is at least as much larger than its next to largest part, as ... is than its next to largest part" -- cf. Jay Rahn 1994b, where the arguments might be individual-variables (e.g., w, x, y, z, above) or sums of individual-variables, which are themselves individual-variables (e.g., w+x, w+y, ..., above). Each such predicate can be regarded as introducing a novel "dimension" into a formulation (e.g., a dimension of pitch-inter- val, pitch-proportion, or pitch-proportionateness -- as distin- guished from pitch). And each can yield matching, vicinity, and interiority relations in its respective dimension. [4.2] Alternatively, one could "count" overlapping vicinity- pairs by, for example, (i) defining a special case of pitch- vicinity, namely, discrete pitch neighbor-hood: DEFINITION: (x)(y)(xDPNy <--> xIPVy . xDPy) For any things, x and y, x is a discrete pitch-neighbor of y if and only if x is in the pitch vicinity of y, and x differs, in pitch, from y, and (ii) applying the label "pairwise twofold" to the sums of such discrete-vicinity pairs as w+x and x+y (i.e., w+x+y) and x+y and y+z (i.e., x+y+z), the label "pairwise three- fold" for the sum of such a pair as w+x, x+y, and y+z (i.e., w+x+y+z), etc. Such a formulation could suffice in certain situa- tions (e.g., where the semitone functioned as the DPN unit, in total-chromatic pieces, or passages). However, much music, if not most, is not totally chromatic. Instead, diatonic and pentatonic works, for example, are generally "gapped" (i.e., relative to the twelve-semitone collection, or aggregate). In order to specify that, for instance, e-f was half as large as f-g, or as much smaller than f-g as g-b-flat was than b-flat-d, would require such a postulate as the following:(4) POSTULATE: (x)(y)(z)(xDPNy . yDPz . zPOSy,x . -yDPNz <--> (:Ey')(y'POSy,x . zPOSy',y . yDPNy')) ======================================================== (4) Postulates are regarded here as asserting the existence of at least one thing, whereas definitions do not make such an ontological claim (cf. Goodman 1961, 6 -- or Goodman 1972, 343-44). ======================================================== [4.3] Nonetheless, among things that are partially ordered in pitch, one can specify certain degrees of proximity based on discrete-vicinity, or "unit," relations -- for example, as follows: DEFINITION: (x)(y)(z)(x+zJLPy+z <--> xDPNy . zPOSy,x) For any things, x, y, and z, the sum of x and y is just (i.e., by one "unit") larger, in pitch, than the sum of y and z if and only if x is a discrete pitch-neighbor of y, and z is, pitchwise, on the opposite side of y from x. [5] CHALLENGES OF NOMINALISM [5.0] As Nelson Goodman indicates (1966, 41), "To reconstruct in the language of individuals [i.e., as distinguished from sets and numbers, as such] all of mathematics that is *worth saving* is a formidable task that need not concern us here. It will be enough to consider typical arithmetical statements used in ordinary discourse [my emphasis]." At the conclusion of his subsequent preliminary survey of ways in which mathema- tical statements can be "de-numerated", and "dis-membered" (my terms -- to which one could add "de-generated"), Goodman stresses (1966, 45) that the "effort to carry out a construc- tive nominalism is still so young that no one can say exactly where the limits of translatability lie. We have seen above that some statements that look hopelessly platonistic yield to nominalistic translation and the full resources available to the nominalist have not by any means been fully exhausted as yet." [5.1] More recent studies have attempted non-numerical ren- derings of mathematics on quite a large scale (notably, Field 1980 and Hellman 1989, the former not without controversy). However great their eventual success might be, attempts at modeling music by means of nominalistic formulations, or, alternatively, by means of the mathematics of sets and numbers, should be assessed not only systematically and philosophically, but also by considering seriously what is "worth saving" in accounts of music. Arguably, pitchedness (inherent or not), matching, vicinity, and interiority, none of which presumes an intervallic dimension, i.e., distinct from the AH-dimension, are worth saving. Nonetheless, after more than two millenia of music theory, it is still not entirely clear just what else is worth saving for a theory of pitch -- or how it might best be saved. [6] FROM DESCRIPTION TO CAUSAL EXPLANATION [6.0] Quite surely, insights of Gestalt psychology into musical structure are worth saving in music theory. However, whereas Gestalt approaches provide valuable descriptions of musical activity, the explanatory status of such accounts is generally questionable (cf. Skinner 1974, 29 and 71-75 on "topography" or mere description, as contrasted with causal explanations of behavior). Nevertheless, the Gestalt principles of similarity and proximity, drawn here into a single account, can be outfitted with causal force by construing as reinforcing the sorts of simplicity considered in the present study (cf. also Jay Rahn 1994a). [6.1] For example, things (i.e., stimuli) that are heard as matching pitchwise can be considered to constitute the immediate reinforcers of acts (i.e., responses) of hearing things, in general, in an AH-manner. By virtue of being heard as matching in pitch, such stimuli as x and y immediately become a pair of things that have been heard as matching pitchwise. Such a pair is a reinforcing stimulus, or reinforcer, for the relevant acts of "hearing as." Such acts can be designated x' and y', as in the following, behavioral postulate: POSTULATE: (x)(y)(xHAHy <--> (:Ex')(:Ey')(x'Hx . y'Hy . x'AHy')) For any things, x and y, x is heard as being at at least as high as y if and only if there is at least one thing, x', and there is at least one thing, y', such that x' is a hearing of (i.e., an act of hearing, or an auditory response to) x, y' is a hearing of y, and x' is at least as high as y'. [6.2] The latter postulate distinguishes between stimuli and responses and can be considered to occupy a territory that straddles descriptive music theory and the causal formulations of behaviorism. In this postulate, the HAH- and AH-predicates are morphologically identical. Each merely orders pairs of things; that is, neither involves presumptions, or axioms, of reflexivity, symmetry, etc., and both presume only that the distinction between xy and yx might be significant within its respective (HAH- or AH-) "dimension". Accordingly, one can reason about HAH-things in a manner quite parallel to ways, out- lined above, for reasoning about AH-things. [6.3] The preceding postulate can be replaced and extended in significance by the following: POSTULATE: (x)(y)(xMPy <--> (:Ex')(:Ey')(x'SHx . y'SHy . x'HAHy' . y'HAHx' . x'+y'Rx+y)) For any thing, x, and any thing, y, x matches, in pitch, y if and only if there is at least one thing, x', and there is at least one thing, y', such that x' stimulates the hearing of x, y' stimulates the hearing of y, x' is heard as being at least as high as y', y' is heard as being at least as high as x', and the sum of x' and y' reinforces the sum of x and y. [6.4] Fashioning nominalistically an account of reinforcement presents formidable challenges (cf. Jay Rahn 1993). Among these is distinguishing between earlier and later instances, or portions, of stimuli and responses. That reinforcement often develops in a curvilinear manner can also be problematic. Just as one can eat too much, beyond a certain point one can be satiated by repetition and other kinds of similarity. As bore- dom sets in, sorts of stimuli that formerly had been reinfor- cing become aversive. One way of preventing something from becoming "too much of a good thing" involves rendering it less thing-like: less simple, less "singular". Between the extreme possibilities of a world where (i) every inherently pitched thing differed in pitch from every other and (ii) every (inhe- rently or non-inherently) pitched thing matched pitchwise every other (including itself), lies a region in which music has specialized. Moreover, music has specialized in a world where salience is sought and reinforced. [6.5] Stimuli that are heard as pitchwise matching constitute reinforcers of acts of pitchwise hearing. Stimuli that escape or "e-lude" the net of matching-relation simplicity might be caught by the discrete-vicinity net. Those that elude discrete-vicinity might be trapped by relations of interiority, which can, in turn, vary in their degrees of simplicity. Moreover, interiority- simplicity can been shown to abound generally in the middles of things, i.e., of individual-sums. That the highest degree of pro- portionateness between things that differ in (e.g., pitch-inter- vallic) size arguably obtains between a thing and its (precise) half indicates the possibility of coherent continuity in a pro- gression of simplicity reinforcement that might extend beyond AH- relations into the "truly intervallic". And that highest and lowest things stand out, are salient, or "edgy", not only derives from the general paucity of adjacency or interiority relations in which they participate but also renders them "excellent," "privileged," "prime" candidates for "resolution," that is, for being heard, by way of other, simplifying relations, as (proper) parts of relatively simple, reinforcing wholes (e.g., as the soprano-bass "skeleton" of a complex texture, or as the "exo- skeleton" (my term) of a "contour" -- on which see Morris 1993). REFERENCES CITED Field, Hartry. 1980. Science without Numbers: A Defence of Nominalism. Princeton, NJ: Princeton University Press. Goodman, Nelson. 1961. Science and Simplicity. Washington, D.C.: Voice of America (repr. *In* Nelson Goodman. 1972. Problems and Projects. Indianapolis: Bobbs-Merrill. 337-46). ______. 1966. The Structure of Appearance. Indianapolis: Bobbs- Merrill. Hellman, Geoffrey. 1989. Mathematics without Numbers: Towards a Modal-Structural Interpretation. Oxford: Clarendon Press. Koehler, Wolfgang. 1947. Gestalt Psychology. New York: Liveright (repr. New York: New American Library). Morris, Robert D. 1993. "New Directions in the Analysis of Musi- cal Contour." Music Theory Spectrum 15, 2: 205-28. Rahn, Jay. 1992. "An Advance on a Theory for All Music: At-Least- As Predicates for Pitch, Time, and Loudness." Perspectives of New Music 30, 1: 158-83. _____. 1993. "A Nominalist Formulation of Basic Terms in Radical Behaviorist Theory." unpub. ms. Toronto: the author (formulations distributed in 10pp. handout of Jay Rahn. "Imaginary Entities in a Phenomenal Theory of Music." paper presented at Annual Confe- rence of Society for Music Perception and Cognition. University of Pennsylvania. Philadelphia. June). ______. 1994a. "Outline of a Causal Theory of Music." paper pre- sented at Graduate Music Theory Colloquium, Eastman School of Music. Rochester. February. ______. 1994b. "A Non-Numerical Predicate of Wide Applicability for Intervallic Relations in Music." paper presented at the Sim- posion International de Muzicologie: Muzica si Matematica, Bucha- rest. May. Rahn, John. 1980. Basic Atonal Theory. New York: Longman. Shepard, Roger N. 1964. "Circularity in Judgments of Relative Pitch." Journal of the Acoustical Society of America 36, 2346-53. Skinner, B.F. 1974. About Behaviorism. New York: Vintage. Stevens, Stanley Smith and Hallowell Davis. 1983. Hearing: Its Psychology and Physiology. 2nd ed. New York: American Institute of Physics for the Acoustical Society of America. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* 2. Commentaries None this issue 3. Reviews None this issue 4. Announcements a. "Gender Trouble" in Music Research: Theoretical Challenges, Problems, and Approaches b. Humdrum Toolkit Seminars c. New mailing list: music-and-moving-pictures d. Computer Music Journal (CMJ) Internet Archive ---------------------------------------------- A. "Gender Trouble" in Music Research: Theoretical Challenges, Problems, and Approaches Pre-conference Roundtable for the Joint Meeting of the American Folklore Society and the Society for Ethnomusicology, Milwaukee WI Wednesday, 19 October, 1994 1-5 p.m. $10 registration fee The pre-conference rountable, jointly sponsored and convened by SEM and AFS, will feature an afternoon devoted to the open exchange of ideas and work in progress. The conveners seek to promote interdisciplinary dialogue among reseachers working in diverse fields, including ethnomusicology, folklore, anthropology, and musicology, who are also engaged or interested in feminist and/or gender approaches to the study of music. To this end the rountable will feature a discussion of recent writings in the above fields and brief presentations from a number of scholars on their work in progress and the kinds of gender troubles--or theoretical and methodological challenges and questions--it provokes. Issues which MIGHT be addressed, but in no way are limited to, include: --How do we account for gender in our disciplinary environments? --Where are there collisions between feminist perspectives and those of our musical discipline? --How do we account for the lived experience of women's lives? --How do we account for the interactive and even contradictory understandings of male and female, masculinity and femininity? --What can we learn from each other as ethnomusicologists, anthropologists, folklorists, or musicologists? Throughout the afternoon there will be time for on-going responses to presentations from attendees. Students are especially encourages to take part. The $10 registration fee will cover refreshments and the set of readings to be discussed. Readings will be sent to all registered attendees well in advance of the pre-conference date. For more information, or it you are interested in participating, please contact either Susan C. Cook or Elizabeth Tolbert Susan C. Cook Elizabeth Tolbert School of Music Peabody Conservatory of the University of Wisconsin Johns Hopkins University Humanities--455 N. Park 1 Mt. Vernon Place Madison WI 53706 Baltimore MD 21202 scook@macc.wisc.edu tolbert@jhunix.hcf.jhu.edu -------------------------------------------- B. Humdrum Toolkit Seminars ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ + + + Humdrum Toolkit Seminars + + + + August 17-20 August 25-28 + + + ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ MTO Subscribers may be interested to learn of two 4-day seminars introducing the forthcoming Humdrum Toolkit. The Humdrum Toolkit is a set of 60 general-purpose software tools intended to assist music scholars in posing and answering research questions. Humdrum allows researchers to encode, manipulate, and output a wide variety of musically-pertinent representations. Humdrum is NOT (1) a MIDI sequencer, (2) a music printing package, or (3) a computer sound synthesis language. The emphasis is on posing and answering questions about music. For example: * In Bartok, are dissonances more common in strong metric positions than in weak metric positions? * What passages of the original `Salve Regina' chant are preserved in the settings by Tomas Luis de Victoria? * In Urdu folk songs, how common is the so-called "melodic arch" -- where phrases tend to ascend and then descend in pitch? * Which of the Brandenburg Concertos contains the B-A-C-H signature? * Identify all the harmonic contexts in which Handel doubles the leading- tone. * Which of two English translations of Schubert lyrics best preserves the vowel coloration of the original German? * Is there evidence of greater metric syncopation in late Mozart than in early Mozart? * After the V-I progression, which harmonic progression is most apt to employ a suspension? * Are crescendos in Wagner more strongly associated with rising pitch than is the case for other composers? * Which of several MIDI performances displays the greatest contrast in dynamics between the initial thematic statement and the thematic return? Humdrum can encode information in an unbounded variety of forms, such as French lute tablatures, conducting gestures, or perceptual data. Users are free to concoct their own task-specific representations -- such as schemes to represent Telugu notation, Dagomba dance, or Schenkerian graphs. Humdrum tools can transform, classify, coordinate, transfer, transpose, restructure, and otherwise manipulate both pre-defined and user-defined information. Humdrum provides extensive facilities for pattern searching. Tools are also provided that can charcterize the similarity between various types of information according to user-defined criteria of similarity. Humdrum will be of potential benefit to anyone wishing to pursue systematic investigations of musical information. This includes the posing of "factual" questions about music, and the testing of hypotheses about musical organization. In short, Humdrum may prove useful to music theorists, ethnomusicologists, historical musicologists, psychomusicologists, music librarians, dance scholars, linguists, and others. The Toolkit was designed for the UNIX operating system. However, with appro- priate UNIX utilities, the humdrum tools will also work under DOS or OS/2. The Humdrum Toolkit will soon be distributed on a non-profit basis by the Center for Computer Assisted Research in the Humanities, Menlo Park, CA. Although humdrum provides unprecedented opportunities for processing music- related data, becoming a proficient user is not trivial. Learning humdrum is comparable in complexity to learning C, perl, or kornshell programming. In order to assist scholars wishing to make use of Humdrum, two 4-day seminars will be held at the University of Waterloo, in Waterloo, Ontario (Canada), August 17-20 and August 25-28. The cost of the seminar is C$560 (approximately $400 US). This seminar price includes: daily lectures and tutorials, a complete copy of the Humdrum Toolkit software, an Installation Guide, a Humdrum User's Guide, a 350-page Humdrum Reference Manual, an electronic edition of the 48 fugues from J.S. Bach's Well-Tempered Clavier, and a VHS videotape containing review tutorials. Further information concerning the seminars, and concerning Humdrum in general, is available by request. The following further information is available: * Electronic brochure describing the Humdrum seminars in further detail. * Overview of Humdrum features. * A 750-line Humdrum FAQ (Frequently Asked Questions) * A 50-minute VHS videotape demonstration of Humdrum can be ordered for $16 Canadian ($11.50 US). N.B. The videotape is currently available in North American NTSC format only. Requests for further information should be addressed to: dhuron@watserv1.uwaterloo.ca The deadline for pre-registration is July 1, 1994. Distribution of the Humdrum Toolkit to the scholarly community is supported in part by a grant from the Social Sciences and Humanities Research Council of Canada. David Huron University of Waterloo dhuron@watserv1.uwaterloo.ca ------------------------------------------------- C. New Mailing List: music-and-moving-pictures A new list, music-and-moving-pictures has been established in England. The list was set up to open discussions about the techniques, aesthetics and future of music for film, television, video, computer animation, drawn animation, virtual reality simulators, games, and new areas, as yet to be invented. It is not essentially a list about hardware or software developments (the emusic list does that very well). The apparent need for this list arose out of designing and running a PGDip/MA course in Electro-Acoustic Music for Film & Television. Attempts to locate serious information about the aesthetics of film and television music revealed that relatively little has been published in these areas (the Library of Congress lists only 150 books at most, and several of these are reprints). The list, therefore, has as one of its goals the encouragement of serious discussion of the above topics, and the possibility of Networked publication. Questions about the list can be addressed to me: Stephen Deutsch: e-mail: sdeutsch@bournemouth.ac.uk Vox; (0202) 595102 FAX (0202) 595350 smail: Bournemouth University Department of Media Production Talbot Campus Fern Barrow Poole Dorset, UK BH12 5BB To subscribe write to mailbase@mailbase.ac.uk join music-and-moving-pictures your name your name should be 1st name space 2nd name Example: join music-and-moving-pictures joe joeson --------------------------------------------- D. Computer Music Journal (CMJ) Internet Archive Announcing the Computer Music Journal Internet Archive and World-Wide Web Home Page This archive is a set of files that are stored on two Internet-accessible servers--one at MIT and one at Stanford--for the use of CMJ readers and members of the computer music community in general. The "root" directories are for the archive are "mitpress.mit.edu:/pub/Computer-Music-Journal" and "ccrma-ftp.stanford.edu:/pub/Publications/cmj." The archive includes the tables of contents, abstracts, and editor's notes for the last several volumes of CMJ (including the recent bibliography, diskography, and taxonomy of the field), a number of useful CM-related documents such as the full MIDI and AIFF format specifications, a lengthy reference list, the guidelines for manuscript submission, and the full text of several recent articles. The files in these directories can be copied via anonymous Internet ftp file transfer, and there also is a World-Wide Web (WWW) "home page" in the file named "CMJ.html" that contains useful pointers into the archive (and elsewhere) and provides hypertext access for users of web browsers such as the NCSA's Mosaic. The document reproduced below is part of the archives and describes its contents in more detail. The two URLs for the Computer Music Journal WWW home page are "file://mitpress.mit.edu/pub/Computer-Music-Journal/CMJ.html" and "file://ccrma-ftp.stanford.edu/pub/Publications/cmj/CMJ.html". Please note that neither of these machines run local http servers, so Mosaic users should access them using the file URLs as above. Comments and suggestions are invited from readers/users about what if of use to you and what should be stored here. Stephen Travis Pope Computer Music Journal, CNMAT/U.C.Berkeley stp@CNMAT.Berkeley.edu, (510) 644-3881 ------------------------------------------------------ Filename: mitpress.mit.edu:/pub/Computer-Music-Journal/README Computer Music Journal Internet Archive README File This document describes the files related to Computer Music Journal that are available from the Internet server mitpress.mit.edu in the directory /pub/Computer-Music-Journal and also in the directory /pub/Publications/cmj on the server ccrma-ftp.stanford.edu at Stanford. The top-level directory has a Hypertext Mark-up Language (HTML) document for use as a "home page" with World-Wide Web (WWW) browsers such as the NCSA's Mosaic. It is in the file named CMJ.html and contains useful hypertext pointers into the archive (and elsewhere). CMJ subscription information can be found in the file Subscribe.t. The file named ls.lR contains a UNIX-style full directory listing of the archive (i.e., the output of the UNIX shell command "ls -lR").. There are several kinds of files kept in the various subdirectories of the directory where this README file is found. The subdirectories contain: Contents--tables of contents and abstracts from Computer Music Journal EdNotes--editor's notes and commentaries Authors--guidelines and templates for authors Documents--other computer music-related texts References--computer music reference lists Texts--full-text of several Computer Music Journal articles More details are given in the README files within each subdirectory, which are collected together in the file Index.t (ASCII) and Index.ps.Z (compressed PostScript). Please send comments and suggestions about what you'd like to find here to the editors at CMJ@CNMAT.Berkeley.edu. ------------------------------------------------------ Filename: mitpress.mit.edu:/pub/Computer-Music-Journal/Contents/README This directory contains ASCII text files with the tables of contents and article abstracts for the last few volumes of Computer Music Journal. Eventually this will be augmented by some sort of database allowing keyword, author, or other queries against all back issues of Computer Music Journal. ===================================== CMJ Topical Overview Volumes 13-18 (1989-94) ===================================== CMJ 13:1 Spring 1989--Clara Rockmore [Green] CMJ 13:2 Summer 1989--Object-Oriented Software CMJ 13:3 Fall 1989--Neural Nets and Connectionism--1 CMJ 13:4 Winter 1989--Neural Nets and Connectionism--2 CMJ 14:1 Spring 1990--New Performance Interfaces--1 [Blue] CMJ 14:2 Summer 1990--New Performance Interfaces--2 CMJ 14:3 Fall 1990--Analysis/Synthesis, Pitch Detection--1 CMJ 14:4 Winter 1990--Analysis/Synthesis, Lisp--2 CMJ 15:1 Spring 1991--Interactive Algorithmic Composition [Yellow] CMJ 15:2 Summer 1991--CAMP, Performance Rules CMJ 15:3 Fall 1991--IRCAM Musical WorkStation CMJ 15:4 Winter 1991--Dream Machines: John Pierce at 80 CMJ 16:1 Spring 1992--Advances in AI for Music--1 [Red] CMJ 16:2 Summer 1992--Advances in AI for Music--2 CMJ 16:3 Fall 1992--Computer Music Systems CMJ 16:4 Winter 1992--Physical Modeling 1 CMJ 17:1 Spring 1993--Physical Modeling 2 [Orange] CMJ 17:2 Summer 1993--Synthesis and Transformation CMJ 17:3 Fall 1993--Music Representation and Scoring--1 CMJ 17:4 Winter 1993--Music Representation and Scoring--2 CMJ 18:1 Spring 1994--Music Representation and Scoring--3 [Yellow] CMJ 18:2 Summer 1994--Composition and Performance in the 1990s--1 CMJ 18:3 Fall 1994--Composition and Performance in the 1990s--2 -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Filename: mitpress.mit.edu:/pub/Computer-Music-Journal/EdNotes/README This directory contains the full text of the Computer Music Journal Editor's Notes from 1991 through the present, including the Journal's annotated bibliography, diskography, and taxonomy of the field, and a note on electronic network-accessible resources that are relevant to computer music researchers. The file Topics.t (included below) lists the titles of the notes. ===================================== Topics of Editor's Notes for "Computer Music Journal" 15:3 - 18:3 ===================================== CMJ 15:3 (Fall, 1991) "The First Dilemma: The Marginalization of `Art Music'" CMJ 15:4 (Winter, 1991) "The Second Dilemma, or Tape Music--the Poor Cousin" CMJ 16:1 (Spring, 1992) "For Lack of a Better Word by Any Other Name" CMJ 16:2 (Summer, 1992) "The Composer and the Computer" CMJ 16:3 (Fall, 1992) "Performing with Active Instruments" CMJ 16:4 (Winter, 1992) "New Music Delivery" CMJ 17:1 (Spring, 1993) "Dancing about Architecture?" CMJ 17:2 (Summer, 1993) "Placing Max in Perspective" guest-edited by Brad Garton and Robert Rowe CMJ 17:3 (Fall, 1993) "The Basic Computer Music Library" CMJ 17:4 (Winter, 1993) "An Incomplete Diskography of Computer Music CMJ 18.1 (Spring, 1994) "A Taxonomy of Computer Music CMJ 18.2 (Summer, 1994) "Electronic Resources for Computer Music CMJ 18:3 (Fall, 1994) "Why is Good Electroacoustic Music So Good? Why is Bad Electroacoustic Music So Bad?" -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Filename: mitpress.mit.edu:/pub/Computer-Music-Journal/Authors/README This directory contains the style guidelines for authors, general instructions to contributors, and the (still to come) full style sheet for Computer Music Journal. There are also two document template files, one for MS-Word on a Macintosh, and one for FrameMaker on an UNIX workstation. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Filename: mitpress.mit.edu:/pub/Computer-Music-Journal/Documents/README This directory and its subdirectories contain a variety of computer music-related documents from various sources. Readers are encouraged to submit new documents for archival here by contacting the editor, Stephen Travis Pope, at stp@CNMAT.Berkeley.edu. The directory MIDI contains a version of the MIDI specification (grabbed from the server at csuhayward.edu--California State University, Hayward). The directory SoundFiles contains several documents describing various sound file formats. AIFF-c.ps.Z The "current" description of the AIFF sound file format. Can be obtained from ftp.sgi.com in the directory /sgi. AudioFormats2.10.t Guido van Rossum's excellent sound file format paper. From guido@cwi.nl. AudioFormats2.resp.t STP's extensions to Guido's document: The EBICSF sound file system. BICSF.t The description of the Berkeley/IRCAM/CARL sound file format. The top level directory contains the following files. Benchmarks.src.tar.Z The benchmarks used in the article comp-languages Carter Scholz's list of Computer Music Languages (csz@well.sf.ca.us). ircam.papers The IRCAM research-paper list from Music Research Digest. midi-archives A list of ftp and mail-based archives on the Internet that contain MIDI related stuff, and a list of midi mailing lists from Piet van Oostrum (piet@cs.ruu.nl). notation-pgms Music Notation Programs - a list to answer a FAQ from Dennis O'Neill (denio@seismo.CSS.GOV). -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Filename: mitpress.mit.edu:/pub/Computer-Music-Journal/References/README (Rudimentary) Computer Music Reference List This should eventually become an annotated (with well-selected keywords) reference list that can be searched with a full-text retrieval engine like WAIS. (Any volunteers?) Please feel free to send in your submissions (in exactly this format, please) to cmj@CNMAT.Berkeley.edu. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Filename: mitpress.mit.edu:/pub/Computer-Music-Journal/Texts/README This directory contains (as an experiment) the full text of two recent Computer Music Journal articles. If you find this useful, send us mail. The two articles are included in PostScript and ASCII formats, and can be freely copied provided that the copyright notices are maintained. The Interim DynaPiano: An Integrated Computer Tool and Instrument for Composers, Stephen Travis Pope Appeared in Computer Music Journal 16:3 Fall, 1993 Files: IDP.ps.Z Compressed PostScript of the text and figures IDP_MODE.t.Z Compressed ASCII of the text Machine Tongues XV: Three Packages for Software Sound Synthesis Stephen Travis Pope Appeared in Computer Music Journal 17:2 Summer, 1993 Files: SWSS.text.ps.Z Compressed PostScript of the text SWSS.figs.ps.Z Compressed PostScript of the figures SWSS.t.Z Compressed ASCII of the text -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- Please send comments and suggestions about what you'd like to find here to the editors at CMJ@CNMAT.Berkeley.edu. stp 1994.06.10 *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* 5. Employment Lectureship in Music Technology, University of Glasgow, Scotland Applications are invited for this new post in the newly established Centre for Music Technology. The Centre is a collaboration between the Departments of Music and Electronics and Electrical Engineering, with representation from the Department of Computing Science. It provides a structure for co-ordinating the necessary interdisciplinary developments to advance the teaching and research in its topic area. The appointee will be joining a team of academic and technical staff who have at their disposal two audio labs, two recording and production studios and a network of more than 40 UNIX (NEXTSTEP) workstations. Primary teaching responsibilities will be in support of the Music component of the B.Sc in Electronics with Music. The appointed person will be expected to join in a process of curriculum development in relation to this new degree, focussing on the introduction of independent learning technologies, the integration of contributing subject areas and the development of links with the professional, manufacturing and commercial world involved with aspects of music technology. Relevant areas of expertise include theory and practice of recording and sound diffusion, software music systems (eg csound), and electroacoustic music including composition. The post will be for three years in the first instance on the Lecturer A scale ( 13,601- 18,855). Appointment on the Lecturer Grade B scale not exceeding 20,442 may be possible for an exceptionally well-qualified and experienced candidate. Starting date will be from 1 August, 1994. Informal enquiries may be made to Dr. S. Arnold, Department of Music, University of Glasgow, tel (from UK): 041 330 5509, or (from abroad) +44 41 330 5509 (e-mail: stephen@music.gla.ac.uk). The successful applicant will be eligible to join the Universities' Superannuation Scheme and the Universities' Supplementary Dependants' Pension Scheme. Further information regarding these schemes is available from the Superannuation Officer, who is also prepared to advise on questions relating to the transfer of superannuation benefits. Applicants are asked to provide a brief note on the state of their health. The University of Glasgow is an equal opportunities employer. Those who wish to be considered should send to the Academic Personnel Office, University of Glasgow, Glasgow, G12 8QQ, not later than 20th June, 1994, eight copies of a statement of their qualifications and experience. Testimonials are not required but the names and addresses should be given of three persons to whom reference may be made. In reply, please quote reference number 8323 *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* 6. New Dissertations a. Burns, Kristine H., "The History and Development of Algorithms in Music Composition, 1957-93," Ball State University, School of Music, 1994 b. Harley, Maria A., "Space and Spatialization in Contemporary Music: History and Analysis, Ideas and Implementations," McGill University, 1994 c. Hoffman, Stanley M., "Extended Tonality and Voice Leading in Twelve Songs, Op. 27, by Alexander Zemlinsky," Brandeis University d. Rust, Douglas, "A Theory of Form for Lutoslawski's Late Works," Yale University, 1994 e. Sheinberg, Ester, "The Semantics of Irony In Shostakovich," (in progress) University of Edinburgh, Scotland f. Taylor, Stephen A., "The Lamento Motif: Metamorphosis in Ligeti's Late Style," Cornell University, 1994 ==================================================== AUTHOR: Burns, Kristine H. TITLE: "The History and Development of Algorithms in Music Composition, 1957-93" INSTITUTION: Ball State University, School of Music, Muncie, IN 47306 BEGUN: February 1993 COMPLETION: April 1994 ABSTRACT: The purpose of this dissertation is to trace the history and development of algorithms in music composition from ca. 1957 to 1993 and to clarify related terminology from the contexts of computer science, information science, and music theory and composition. The term "algorithm" has been adopted from the fields of computer science and information science; however, in some cases its misappropriation has caused confusion in meaning. The dissertation consists of three main sections, beginning with an extensive definition of the term algorithm. Historically and currently, there are three major approaches to algorithmic composition with computers: 1) algorithms for sound synthesis; 2) algorithms for compositional structure; and 3) algorithms for the correlation of sound synthesis with structure. This dissertation will trace developments from the latter two categories, algorithms for the generation of the micro- and macrostructural elements of music composition. KEYWORDS: algorithm, music, composition, information science, computer science TOC: Chapter 1--Description of the Dissertation Chapter 2--Terminology Chapter 3--A Review of the Literature Chapter 4--Algorithmic Developments Prior to 1957 Chapter 5--Principle Composers of Algorithmic Composition, 1957-1972 Chapter 6--Intermediate Developments in Algorithmic Composition Chapter 7--Algorithms in Music Composition, 1983-1993 Chapter 8--Chronological List of Algorithmic Compositions, 1957-1993 Chapter 9--Conclusion CONTACT: 36 N. Pleasant St. #8, Oberlin, OH 44074 216-774-4225, 775-8748, FBURNS@ocvaxa.cc.oberlin.edu ------------------------------------------------------ AUTHOR: Harley, Maria, A. TITLE: "Space and spatialization in contemporary music: History and analysis, ideas and implementations" INSTITUTION: McGill University, Faculty of Music, 555 Sherbrooke Street West, Montreal, Quebec H3A 1E3, Canada BEGUN: September, 1988 COMPLETION: June, 1994 ABSTRACT: This dissertation presents the history of *space* in the musical thought of the 20th century (from Kurth to Clifton, from Varese to Xenakis) and outlines the development of *spacialization* in the theory and practice of contemporary music (after 1950). The text emphasizes perceptual and temporal aspects of musical spatiality, thus reflecting the close connection of space and time in human experience. A new definition of spacialization draws from Ingarden's notion of *the musical work*; a new typology of spatial designs embraces music for different acoustic environments, movements of performers and audiences, various positions of musicians in space, etc. The study of spatialization includes a survey of the writings of many composers (e.g. Ives, Boulez, Stockhausen, Cage) and an examination of their compositions. The final part of the dissertation presents three approaches to spatialization: Brant's simultaneity of sound layers, Xenakis's movement of sound, and Schafer's music of ritual and soundscape. KEYWORDS: space, spatialization, contemporary music, space-time theory, philosophy of science, phenomenology, Roman Ingarden, Henry Brant, Iannis Xenakis, R. Murray Schafer TOC: Part One: Concepts of space. I. The meaning of "space." II. A history of concepts of space in music. Part Two: Spacialization in theory and practice. III. Music in space and the idea of spatialization. IV. Spatialization and the musical work. V. Spatial designs in contemporary music. Part Three: Implementations (three composers). VI. Experimental tradition in the "spatial music" of Henry Brant. VII. Spatial sound movement in the instrumental music of Iannis Xenakis. VIII. Soundscapes and rituals in the music of R. Murray Schafer. CONTACT: Address: 6105 - 28th Ave., #19, Montreal, Quebec H1T 3H7 Voice: (514) 728-5892 Fax: (514) 398-8061 -------------------------------------------- AUTHOR: Hoffman, Stanley M. TITLE: Extended Tonality and Voice Leading in Twelve Songs, Op. 27 by Alexander Zemlinsky INSTITUTION: Brandeis University Department of Music, Slosberg Bldg., 415 South Street, Waltham, MA 02254 BEGUN: September, 1990 COMPLETION: February, 1993 ABSTRACT: Alexander (von) Zemlinsky (1871-1942) was not only a renowned composer, but was also highly regarded as a conductor. Although he was Schoenberg's teacher and brother-in-law, and a friend to both Webern and Berg, Zemlinsky never composed twelve-tone music. His compositions reflect an individualistic reaction to several of the prevailing modes of composition during a time of great political, social, and artistic upheaval. Zemlinsky's late compositions employ extended tonality and voice leading in a personal way. No published theoretical writings offer a detailed analytical approach to the mature compositions of this post-Romantic composer. For this reason, as well as for the music's beauty and integrity of craftsmanship I wrote on Zemlinsky's Twelve Songs, Op. 27 composed in the years 1937 and 1938. This work offers twelve microcosmic examples of his mature compositional style. Each song posesses unique musical qualities worthy of analysis. The major topic for discussion in this paper will be Zemlinsky's use of extended tonality, with considerable emphasis placed upon voice leading considerations. Other issues covered will include the contention that Op. 27 is a song cycle, not merely a set of twelve songs, and that tonal forces govern the organization of the piece as a whole. The form of each song, including phraseological interpretations, the possible expressive motivations behind the choice and ordering of the texts, and the word-painting will be addressed. In addition, differences between Zemlinsky's manuscript and the published score will be discussed. KEYWORDS: tonality, modality, intervalic, phrasing, cyclic, word-painting African-American, Sanskrit, German, Jewish TOC: Chapter 1 - Song 1, Chapter 2 - Songs 2-6, Chapter 3 - Songs 7-9, Chapter 4 - Song 10, Chapter 5 - Song 11, Chapter 6 - Song 12 CONTACT: Stanley M. Hoffman Voice: 617-893-0702 Fax: 617-437-0222 E-Mail: Smhoff@aol.com The UMI order number for this doctoral dissertation is 9317084 -------------------------------------------------------------- AUTHOR: Rust, Douglas, M. TITLE: "A Theory of Form for Lutoslawski's Late Symphonic Works" INSTITUTION: Yale University BEGUN: March, 1992 COMPLETION: September, 1994 ABSTRACT: This dissertation develops the notions of "musical character" and "musical action" in selected works from Witold Lutoslawski's late symphonic works, to produce a method of form analysis that yields insight into the poetics of the composer's musical creation. One paragraph in Steven Stucky's book (Lutoslawski and His Music [Cambridge, 1981],127) introduces the idea of musical character as a legacy from Lutoslawski's composition teacher, Witold Maliszewski, who would label individual passages in Beethoven sonatas with one of four musical characters: introductory character, transitory character, narrative character, or finishing character. This dissertation applies the same four labels to individual passages in Lutoslawski's late works, based upon the composer's insistence--in a recent interview with the author--that the Maliszewskian concepts continued to influence his compositional designs. Lutoslawski's term "musical action" describes how the interaction of all the individual passages in a piece contributes toward an overall dynamic shape that leads the listener through the form. The interaction of character and action in the form analysis of Lutoslawski's late symphonic works helps us to understand the normative features of his large-scale closed forms and to interpret the meaning of unusual features in individual works. KEYWORDS: Lutoslawski, 20th Century, Symphonic, Form, Maliszewski, Chain TOC: Prologue, 1. Harmony, 2. Musical Character, 3. Musical Action, 4. Chain Form, Epilogue CONTACT: 211 Nicoll St., New Haven, CT 06511, 203/624-7878 ----------------------------------------------------------- AUTHOR: Sheinberg, Ester TITLE: The Semantics Of Irony In Shostakovich (in progress) INSTITUTION: University Of Edinburgh, Scotland, Faculty of Music, Alison House, 12 Nicolson Square, Edinburgh EH8 9DF, tel. 31-650-2422, fax 31-650-2425 BEGUN: OCTOBER, 1992 COMPLETION: JUNE, 1995 ABSTRACT: The music of Shostakovich demonstrates certain kinds of irony, parody and the grotesque, showing the composer's kinship with literary and theoretical writers of the time, including Tynianov, Sollertinsky and Bakhtin. He is known to have had connections with some of these. Musical irony is analyzed and found to be indicated by particular markers. A typology of irony is then illustrated from Shostakovich's music, and to some degree from the music of others. KEYWORDS: Shostakovich, irony, semantics, semiotics, parody, grotesque Dr. Raymond Monelle R.Monelle@music.ed.ac.uk Faculty of Music, Tel: 031 650 2430 University of Edinburgh, Fax: 031 650 2425 Alison House, 12 Nicolson Square, EDINBURGH EH8 9DF --------------------------------------- AUTHOR: Taylor, Stephen Andrew TITLE: The Lamento Motif: Metamorphosis in Ligeti's Late Style INSTITUTION: Graduate School Cornell University Ithaca, NY 14853 BEGUN: May 1992 COMPLETION: May 1994 ABSTRACT: Gyorgy Ligeti has spoken of a "stylistic caesura" in his music that occurred around 1980. Since then, melody has become more important in his music, as well as elaborate polyrhythm and a strange, new harmony which, as Ligeti has said so often about his music, is "neither tonal nor atonal." He lists among his new influences the music of sub-Saharan Africa, the Carribean, and Malaysia, as well the player-piano music of Conlon Nancarrow and the beautiful, fractal images of deterministic chaos discovered by Benoit Mandelbrot. Behind all these new influences, though, the music of his native Hungary and of his countryman Bela Bartok stands out more clearly than in any music Ligeti has composed since he left his homeland in 1956. This essay examines Ligeti's late style (for he has said this will be his last) by concentrating on four movements which all use the same theme, a chromatically falling lament: the last movement of the Horn Trio (1982); the sixth Piano Etude, Automne a Varsovie (1985); and the second and third movements of the Piano Concerto (1985-88). These pieces not only let us see how Ligeti uses the same idea in different contexts; they also provide an overview of Ligeti's late style. KEYWORDS: Ligeti, Gyorgy, Horn Trio, Etudes pour piano, Piano Concerto, Lamento TOC: 1. Introduction: The Lamento Motif and Ligeti's Late Style 2. Trio for Horn, Violin, and Piano: Fourth Movement, "Lamento" 3. Piano Etude No. 6, Automne a Varsovie 4. Concerto for Piano and Orchestra, Second and Third Movements 5. Ligeti's Late and Early Styles: Full Circle Appendix A List of Works, 1978-April 1994 Appendix B Selected Discography Appendix C Analytical graph of melodies in the Lamento of the Horn Trio Appendix D Analytical reduction of Etude No. 6, Automne a Varsovie Bibliography CONTACT: Stephen Taylor Department of Music Pittsburg State University Pittsburg, KS 66762 voice: (316) 232-7026 fax: (316) 232-7515 *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= 7. Communications Subscribers will recall that a survey regarding access to and use of the World-Wide Web (W3) was distributed to everyone prior to the broadcast of MTO 0.8, and then once again in the Communications section of 0.8. Despite two distributions the number of responses was regrettably low: out of over 500 subscribers, less than 10% (46) filled in and returned the questionnaire. The poor response might indicate indifference, lack of time, or mailing problems. In any case, the trend of the responses from the first survey distribution to the second remained stable: a majority of MTO subscribers (74%) are equipped to use W3, though only a little over half (56%) read their email (including MTO) on a machine that has access to W3. The number of times that subscribers use W3 averages out to between 2-3, though some use W3 as often as 10-15 times weekly. Almost 90% said they would read a multi-media version of MTO if it were available, and roughly 89% would make the commitment to learn the HyperText Markup Language (HTML) in order to prepare texts for a multi-media, hypertextual version of MTO. If these statistics are any indication of subscribers' readiness to embrace W3, then MTO will, in time, begin to offer a multi-media version of the journal. As originator and present editor of MTO, I certainly would like to see it take advantage of the unique opportunities offered by network technology--the very things that distinguish the journal. However, "network technology" is an evolving, moving target. Standardization across so many hardware platforms and operating systems is fraught with complexities. Many of these can be hidden behind user-friendly interfaces, but only at the cost of escalating demands on users' equipment, as well as on the network itself. The staff of MTO could make a full-time job just out of pursuing the latest advances and adapting them for our use, and in the process lose sight of the very purpose of the journal: disseminating and discussing ideas, not experimenting with network technology. MTO should be a scholarly forum, not a technological laboratory. We should explore the technology and adopt it insofar as it serves the objectives of a scholarly publication. However, when technology begins to drive our efforts, we have missed *our* target. As the survey showed, just over half of the respondents read email on machines with W3 access. Still, that leaves nearly half who don't, can't, or don't care to use W3. A multi-media MTO will put Bitnet subscribers out of the picture altogether. W3 tools are not yet completely stabilized. Demands on the network have increased markedly, decreasing its speed and taxing the patience of users who access large files (e.g. graphics and sound). Although a clear majority of respondents expressed a willingness, in the abstract, to learn HTML, when reality hits, how many will actually do it? Some HTML editors have become available, but how many authors will set aside their cherished word-processing programs, mastered with considerable time investment, in order to learn a new program whose usefulness may, for the time being, be limited to MTO? Moving MTO into the W3 arena means a number of changes for the editorial and production staff, and for distribution and archiving procedures. More staff will be necessary to check and, if necessary, edit texts. More storage space must be secured at various sites in order to archive files, particularly large sound files. Site managers must be recruited to oversee such storage sites. Appointing staff and establishing storage sites will take time. MTO cannot enter the W3 arena overnight. Further, the network still has some distance to go before W3 is stable, reliable, efficient, and generally "comfortable." MTO is an evolving medium in an evolving environment. The journal and its subscribers will prepare and be ready for W3 when W3 is ready for them. Lee A. Rothfarb, Editor Music Theory Online 8. Copyright Statement +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ Copyright Statement [1] Music Theory Online (MTO) as a whole is Copyright (c) 1994, 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 0.9