=== === ============= ==== === === == == == == == ==== == == = == ==== === == == == == == == == = == == == == == == == == == ==== 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) 1999 Society for Music Theory +-------------------------------------------------------------+ | Volume 5, Number 2 MARCH, 1999 ISSN: 1067-3040 | +-------------------------------------------------------------+ General Editor Eric Isaacson Co-Editors Henry Klumpenhouwer Catherine Nolan Lawrence Zbikowski Reviews Editor Robert Gjerdingen Manager Ichiro Fujinaga mto-talk Manager Jay Rahn Consulting Editors Bo Alphonce Richard Littlefield Jonathan Bernard Thomas Mathiesen John Clough Benito Rivera Nicholas Cook John Rothgeb Allen Forte Arvid Vollsnes Stephen Hinton Robert Wason Marianne Kielian-Gilbert Gary Wittlich MTO Correspondents Peter Castine, Germany Marco Renoldi, Italy Wai-ling Cheong, Hong Kong Ken-ichi Sakakibara, Japan Tore Ericksson, Sweden Roberto Saltini, Brazil Gerold W. Gruber, Austria Michiel Schuijer, Holland Tess James, England Uwe Seifert, Germany Henry Klumpenhouwer, Canada Panos Vlagopoulos, Greece Nicolas Meeus, Belgium, France Arvid Vollsnes, Norway Editorial Assistants Elisabeth Honn Arthur Samplaski Michael Toler Brent Yorgason All queries to: mto-editor@smt.ucsb.edu or to mto-manager@smt.ucsb.edu +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ 1. Target Article AUTHOR: Soderberg, Stephen TITLE: White Note Fantasy KEYWORDS: Eytan Agmon, John Clough, Jack Douthett, David Lewin, maximally even set, microtonal music, hyperdiatonic system, Riemann system, efficient linear transformation Stephen Soderberg Library of Congress Music Division 101 Independence Avenue SE Washington, DC 20540 ABSTRACT: This article is a continuation of White Note Fantasy, Part I, published in MTO Vol. 4, No. 3 (May 1998).  Part II combines some of the work done by others on three fundamental aspects of diatonic systems: underlying scale structure, harmonic structure, and basic voice leading. This synthesis allows the recognition of select hyperdiatonic systems which, while lacking some of the simple and direct character of the usual ("historical") diatonic system, possess a richness and complexity which have yet to be fully exploited. PART II: A FEW HYPERTONAL VARIATIONS Contents 5. Necklaces 6. The usual diatonic as a model for an abstract diatonic system 7. An abstract diatonic system 8. Riemann non-diatonic systems 9. Extension of David Lewin's Riemann systems References 5. NECKLACES. [5.1] Consider a symmetric interval string of cardinality n = c+d which contains c interval i's and d interval j's. If the i's and j's in such a string are additionally spaced as evenly apart from one another as possible, we will call this string a "necklace." If s is a string in Cn and p is an element of Cn, then the structure ps is a "necklace set." Thus , , and are necklaces, but , , and , while symmetric, are not necklaces. i and j may also be equal, so strings of the form are valid necklaces. Specific necklaces can be formed by substituting any appropriate integers for i and j; e.g., <113113>, <772772>, <8181818>, and <23323332333>. If s = <181> and p = 3, then ps = {3,4,2} is a necklace set in C10. [5.2] MAXIMALLY EVEN STRINGS. After John Clough and Jack Douthett (1), we will define a maximally even (ME) interval string as the string of m intervals in Cn (so m <= n) that meets two criteria: (1) is a necklace; (2) the elements of are either k or k+1. If s = is a maximally even string, and p is an element of Cn, then the structure ps will be called a maximally even set. Familiar examples of ME strings are <23223> (pentatonic), <2212221> (diatonic), <222222> (whole-tone), and <21212121> (octatonic). While we will be concentrating mostly on generalizing the diatonic, it will become apparent that many of our results will apply to other ME, and even non-ME, necklaces. ============= 1. John Clough and Jack Douthett, "Maximally Even Sets," Journal of Music Theory 35.1 & 2 (1991) : p.96. ============= [5.3] ME STRING TOKENS. As pointed out by Clough and Douthett, m and n determine a unique ME set, i.e., = iff m=p and n=q. Thus our notation is both necessary and sufficient to identify an ME string. But, although all ME strings are necklaces while all necklaces are not ME, any ME string can be taken as a token for an infinite "class" of necklaces. For instance, s = <1121112> is maximally even, but all strings of the form are necklaces, whether they are ME or not (e.g., <2212221> is ME, <1161116> is not ME, <5525552> is not ME, <5565556> is ME, etc.) Thus we will use the notation <(m;n)> to denote the class of all necklaces that can be derived from by substituting other integers for 's elements. <(7;12)> then denotes all strings of the form , and we will write <(7;12)> DEF <9222922> if we need a specific string example from the class.(2) The need for specification is due in part to the fact that WARP is sensitive to the rotation of its generic and scale strings, as will now be made evident. ============= 2. There is some redundancy in this notation since any necklace class has any number of ME tokens; for example, <(7;12)> represents the same necklace class as, say, <(7;9)> and <(7;16)>. While it would be more cumbersome and less intuitive, this notation could be improved by partitioning all ME strings with M(m,x,k) defined as all strings of the form where m,x,k are integers with m >= 1; x = 1,2,...; k <= [[m/2]]; xm%y >= m; and % stands for "plus or minus." N(m,x,k) would then represent all necklaces which can be derived from any member of M(m,x,k) by substitution. Or, using the "generating" case and the above notation, we might simply use N(m,k) defined as <(m;m+k)>. Thus <7;12>, <7;9>, <7;16>, as well as <1171117> and so on, all belong to the necklace class N(7,2) = <(7;9)> = . ============= [5.4] MAXIMALLY EVEN WARPS. If q = and r = are ME strings, they automatically fulfill the inequality conditions in the definition for the r-WARP of q: (u = #(q)) <= (v = SUM(q) = #(r)) <= (w = SUM(r)). serves as a generic string and as a scale string. But generally, two necklaces q = <(u;v)> and r = <(v;w)> are not WARP-compatible unless SUM(q) = #(r). [5.5] Let q = <3;11> and r = <11;13> be two ME strings. If we stipulate permutations q = <3;11> DEF <344> and r = <11;13> DEF <11211111211>, then WARP(q,r) = <445>, and the resultant string is a permutation of the ME string <3;13>. But if we choose a different permutation of q, q' = <3;11> DEF <434>, WARP(q',r) = <535> which, although it is a necklace in the <(3;13)> class, is not ME. Now let x = <11;18> DEF <12212212212>. WARP(q,x) = <567> and WARP(q',x) = <657>, both of which are asymmetric (and thus, of course, neither ME nor necklaces). If we generalize without caution, the WARP may be undefined. For example, if p = <(3;11)> DEF <177>, then WARP(p,r) is undefined since SUM(p) = 15 does not equal #(r) = 11; but if p' = <(3;11)> DEF <155> we have WARP(p',r) = <166>. [5.6] Again let q = <3;11> DEF <344>. If we now stipulate the 0- permutation of the scale string as r(0) = <11;13> DEF <11211111211>, then WARPSET(q,r) = {<445>, <445>, <454>, <355>, <355>, <355>, <445>, <454>, <454>, <355>, <355>}. Let a = <445>, a' = <454>, and b = <355>; then CHORDSET(q,r) (based on the scale {0,1,2,4,5,6,7,8,9,11,12}) is {0a, 1a, 2a', 4b, 5b, 6b, 7a, 8a', 9a', 11b, 12b}.(3) ============= 3. This particular WARPSET presents a situation that occasionally arises when resultant strings are symmetric. Note that a' is a circular permutation of a, i.e., a and a' represent the same shape, so for any p in C13, (p,a') = (p-4,a) (mod 13) (see [1.13] in Part I). If we "canonize" a = <445> as the "correct" string form and require that all a-based structures be put in that "root position" form, the CHORDSET given in [5.6] must be abandoned for {0a,1a,11a,4b,5b,6b,7a,4a,5a,11b,12b). This in turn makes scale elements 4, 5, and 11 into roots which can be associated with both a and b strings, whereas scale elements 2, 8, and 9 can't be associated as roots with any chords. ============= [5.7] While much of what we are about to discuss can be said about necklaces generally, it will be most profitable to concentrate on maximal evenness, but we will still generalize when doing so points to interesting relations and structures. We will now adopt the following notation for WARPSETs whose generic and scale strings are both maximally even: WARPSET(,) = ||u;v;w|| Thus the designation "maximally even" applied to a WARP refers only to the variable strings (i.e., the generic and scale strings) since, as noted, resultant strings may not be maximally even. [5.8] I = is a left identity (generic) string, and J = is a right identity (scale) string for ME WARPs. Thus WARP(I,) = WARP(,J) = . [5.9] DIATONIC STRINGS. Using Clough and Douthett's Theorem 2.2 (4), for any odd x > 1, a diatonic string is any ME string of the form d = = , where j is a substring of (x-3)/2 2's and k is a substring of (x-1)/2 2's. For any pitch class p, pd is a (hyper)diatonic set based on p. For p=0, x 2(x-1) d (p,d) 3 4 <121> {0,1,3} 5 8 <21221> {0,2,3,5,7} 7 12 <2212221> {0,2,4,5,7,9,11} 9 16 <222122221> {0,2,4,6,7,9,11,13,15} ... ... ... ... We will now focus closely on WARPSETs of the form ||w;x;2(x-1)|| and their related CHORDSETs as we generalize the usual diatonic. ============= 4. Clough and Douthett, op. cit., pp.170-71. ============= 6. THE USUAL DIATONIC AS A MODEL FOR AN ABSTRACT DIATONIC SYSTEM. [6.1] RD(1). To model the usual diatonic in the notation presented in Part I, we will make the following assignments: In C7, J = <7;7> = <1111111> g = <3;7> DEF <223> p = 0 X = WARPSET(g,J) = ||3;7;7|| Y = pJ = {0,1,2,3,4,5,6} Z = CHORDSET(X) and in C12, h = <7;12> DEF <2212221> q = 0 W = WARPSET(g,h) = ||3;7;12|| H = qh = {0,2,4,5,7,9,11} K = CHORDSET(W) The usual diatonic system(5), in our present terminology (see [2.25]), is then the ordered triple RD(1) = (W,H,K). Since (X,Y,Z) (=) (W,H,K), the entire model can be displayed as a set of correspondences: ___________C7_____________ ___________C12______________ / \ / \ X Y Z W H K <223> = g 0 {0,2,4} = 0g <435> = t 0 {0,4,7} = 0t <223> = g 1 {1,3,5} = 1g <345> = t' 2 {2,5,9} = 2t' <223> = g 2 {2,4,6} = 2g <345> = t' 4 {4,7,11} = 4t' <223> = g 3 {3,5,0} = 3g <435> = t 5 {5,9,0} = 5t <223> = g 4 {4,6,1} = 4g <435> = t 7 {7,11,2} = 7t <223> = g 5 {5,0,2} = 5g <345> = t' 9 {9,0,4} = 9t' <223> = g 6 {6,1,3} = 6g <336> = u 11 {11,2,5} = 11u Names for the strings <435> = t, <345> = t', and <336> = u have been assigned to identify the usual major, minor, and diminished triads respectively.(6) ============= 5. "System" is used here in the sense of the ordered triple of [2.25] in Part I. "Diatonic system" may be confused with that term as used by C&D (---) and Agmon (---), and for that reason we will mostly use the term "Riemann Diatonic System" introduced below. 6. Diatonic tetrachords (e.g., the dominant 7th-chord) are not included here since they would unduly complicate the present study. But the reader may want to keep these important structures in mind as we procede since they present an interesting dilemma. In the usual diatonic system, clearly one could view a 7th-chord as either a triad with an added third *or* the complement of a triad with respect to the diatonic scale (at the end of the day they produce the same structure). However, as the reader may note after reading about the next RD system, these two possible construction principles, when lifted into RD(2), produce different results. In RD(2) the basic structure is a 5-note chord. If we use the additive principle, the "hyper7th-chord" will have six notes. But if we use the complement principle, the "hyper7th-chord" will have eight notes. ============= [6.2] The interval matrix for the diatonic scale string, which is not partitioned, is / 2 5 0 0 0 0 0 0 0 0 0 0 \ | 0 0 4 3 0 0 0 0 0 0 0 0 | | 0 0 0 0 6 1 0 0 0 0 0 0 | MINT(h) = | 0 0 0 0 0 1 6 0 0 0 0 0 | | 0 0 0 0 0 0 0 3 4 0 0 0 | | 0 0 0 0 0 0 0 0 0 5 2 0 | \ 0 0 0 0 0 0 0 0 0 0 0 7 / and this yields the ic-mapping in C7 in C12 1 --> 1,2 2 --> 3,4 3 --> 5,6 4 --> 6,7 5 --> 8,9 6 --> 10,11 7 --> 12 (=0) As noted above, dealing with non-partitioned interval matrices can be somewhat complex, and we purposely have chosen examples which avoid them. However, in this case, the ambiguity presented by the tritone does not present any unusual difficulties. If we wish to write the vector associated with MINT(h), it is helpful to display it thus: U(h) = [254361 1634527] instead of [254362634527]. The vector can then be "partitioned" as [2,5;4,3;6,1 1,6;3,4;5,2;7] so that U'(h) = [2+5;4+3;6+1; 1+6;3+4;5+2;7] = [7777777] = U(J) Keeping the usual caution in mind while dealing with the tritone in vector applications, we can then write the corresponding interval- class vector relationships on which generic covariance is based: V(h) = [254361] V'(h)= [2+5;4+3;6+1] = [777] = V(J) [6.3] Thus by G-COV, the partition sum ic-vector of any string in W will equal V(g). W contains only two unique strings, t (t') and u, for which V(t) = V(t') = [001110] and V(u) = [002001], so V'(t) = V'(t') = [0+0;1+1;1+0] = V'(u) = [0+0;2+0;0+1] = [021] = V(g). If we had chosen a different string for g we would have created a different white note system, but by G-COV the same partition-vector pattern would still hold due to the diatonic scale string being held constant; however, we would then be headed in a direction which would soon diverge radically from our chosen diatonic model. [6.4] The important thing to take from G-COV, with respect to RD systems, is the characteristic partition pattern imposed by the scale string which will always be of the int-multiplicity form [a,b; c,d; ...; p,q; q,p; ...; d,c; b,a; z] and which can always be reduced to the ic-multiplicity form [a,b; c,d; ...; p,q]. The sum of the elements in any comma-separated pair in both forms will always equal the sum of the elements in the scale string (i.e., z). [6.5] To investigate scale covariance in RD(1) we now concentrate on ic-vectors spanning sets in the generic system (X,Y,Z). From this point on, when dealing with ic-vectors, we will adopt the more intuitive and widely used notation which places the ic0 multiplicity as the first vector component. Thus V(pg,(p+1)g) = [0513] for g = <223> indicates that between the sets, say, {1,3,5} and {2,4,6}, there are 0 ic0's (no common tones), 5 ic1's, 1 ic2, and 3 ic3's. [6.6] Given the generic string g = <3;7> DEF <223> as before, if p is any pitch class in C7, then pg is a triad in Z and (p+t)g is pg's t- transpose. The following list exhausts the possible ic spanning vectors for Z (% indicates plus-or-minus) V(pg,pg) = [3042] V(pg,(p%1)g) = [0513] V(pg,(p%2)g) = [2142] V(pg,(p%3)g) = [1323] The distribution of components in this list isn't as random as it might at first appear since it derives from the list of interval spanning vectors U. The reader will note that the ic-vector is simply the int-vector with the non-zero components "folded back" on their inversions. For U(pg,(p+1)g) we have: [ 0 3 0 2 1 1 2 ] | | | | | | | int: 7=0 1 2 3 4 5 6 ic: 0 1 2 3 3 2 1 \ \ \___/ / / \ \_________/ / \_______________/ and [0302112] --> [0513]. The pattern behind the ic vectors listed is then made clear by listing the int vectors for the same sets: U(pg,(p+1)g) = [3021120] U(pg,(p+2)g) = [0302112] U(pg,(p+3)g) = [2030211] U(pg,(p+4)g) = [1203021] U(pg,(p+5)g) = [1120302] U(pg,(p+6)g) = [2112030] U(pg,(p+0)g) = [0211203] (= U(g)) (note that we retain the ic0 component in the last position here since this display is taken directly from MINT(g) -- see [3.11-14] in Part I). [6.7] We can now relate any ic vector spanning two sets in K to one of the spanning vectors just listed for Z since, by S-COV, the partition- sum ic vector spanning any pair of sets in K will equal the ic vector spanning a corresponding pair of sets in Z. Some examples, referring back to the system correspondences in [6.1], are: V(9t',2t') = [1121130] V'(9t',2t') = [1;1+2;1+1;3+0] = [1323] = V(5g,1g) V(4t',5t) = [0230121] V'(4t',5t) = [0;2+3;0+1;2+1] = [0513] = V(2g,3g) V(5t,7t) = [0141021] V'(5t,7t) = [0;1+4;1+0;2+1] = [0513] = V(3g,4g) [6.8] By S-COV, the list of ic spanning vectors in [6.6] summarizes all the voice-leading possibilities for any pair of triads in Z and thus in K as well. If we display this list as an "available voice- leading" matrix for interval classes, /3042\ AVLIC(Z) = |0513| |2142| \1323/ it can be read in two ways. First, any given row indicates the multiplicity of generic interval classes spanning two triads in Z or the multiplicity of diatonic interval classes spanning two corresponding triads in K. For example, row 3 indicates the voice- leading multiplicities found in V(pg,(p%2)g), so all seven of the corresponding chord pairs in K (whose "roots are a major or minor third apart") have available connections of 2 ic0, 1 ic1/ic2, 4 ic3/ic4, and 2 ic5/ic6. Second, any column will list all possible chord pairs spanned by a given interval class. If we wish to conduct an "interval class search" -- say we wish to know how all possible chord progressions in K are spanned by a perfect or diminished fifth - - we simply go to the fourth column (representing ic3 in C7 which corresponds to ic5/ic6 in C12) and read down: there are 2 fifths available between correspondents of pg and pg; 3 fifths between correspondents of pg and (p%1)g; 2 between corespondents of pg and (p%2)g; and 3 between correspondents of pg and (p%3)g. [6.9] We can also form the more complete "available voice-leading" matrix for intervals, /3021120\ |0302112| |2030211| AVLINT(Z) = |1203021| |1120302| |2112030| \0211203/ and make interval-spanning statements about corresponding chords of the same sort as we did for interval-class spans. Due to AVLINT's symmetry ((row m, column n) = (row n, column m)), we can state a more general theorem relating chord pairs which can be extended via S-COV to correspondence-related white note systems. We state it here without proof and using int rather than ic notation. [6.10] For any integers p,x,y in the chromatic white note system (A,B,C) which has been generated by a generic string g, #intx(pg,(p+y)g) = #inty(pg,(p+x)g). For example, returning to g = <2,2,3> and (X,Y,Z) in the usual diatonic world, this theorem tells us, among many other things, that #int5(pg,(p+1)g) = #int1(pg,(p+5)g) = 1. To give us some idea of the amount of information packed into an AVLIC or AVLINT matrix, we can translate this example (by correspondence) into more familiar diatonic language, remembering that int5 and int1 in C7 "translate" to int(8- or-9) and int(1-or-2), respectively, in C12. What the example says, loosely, is that there is always one (and only one) 6th within a diatonic scale that can be found to span two triads within that scale whose roots are a 2nd apart and furthermore this implies that there is always one (and only one) 2nd within that same scale that can be found to span two triads within that scale whose roots are a 6th apart. [6.11] The theorem in [6.10] will, of course, hold for any simple white note system, not only those generated by ME strings. Its application is intimately related to the principle of scale covariance, since changing the scale string while keeping the generic string will consistently yield the same values for corresponding sets, but changing the generic string will normally yield different AVLINTs.(7) ============= 7. The reader is invited to generate and compare the AVLINTs for the three other possible triadic white note systems which can be associated with the usual diatonic string using g = <115>, <133> (necklaces) or <124> (asymmetric). It is then an interesting exercise to search for non-diatonic scale strings for each of these generic strings which might be profitably employed as a basis for compositional praxis (both inside and outside C12). ============= [6.12] Finally, cover covariance (C-COV) in RD(1) is particularly interesting. The C-7 chromatic scale Y = {0,1,2,3,4,5,6} can be covered by the g-triads in Z in a number of ways, but we know that any minimal cover of Y must consist of three triads. Perhaps the most important cover of Y is the one which, by correspondence, underlies the "dominant" related triples in K: COVER1(Z) = {pg, (p+3)g, (p-3)g}. For istance, setting p = 5, R = {5g,1g,2g} = {{5,0,2},{1,3,5},{2,4,6}} and R//Y (see [4.16-19] in Part I). Also note the common-tone relationships among these triads: #int0(pg,(p+3)g) = #int0(pg,(p-3)g) = 1 but #int0((p+3)g,(p-3)g) = 0. The only other minimal cover from Z is of the form COVER2(Z) = {pg, (p+1)g, (p-1)g}. with the common-tone relationships: #int0(pg,(p+1)g) = #int0(pg,(p- 1)g) = 0 and #int0((p+1)g,(p-1)g) = 2. Any triple in Z which cannot be expressed in one of these two forms (COVER1 or COVER2) will not cover Y (e.g., {0g,2g,3g} will not cover Y). [6.13] Now, bracketing possible psycho-acoustical, semiological, sociological, and historical "reasons" (which we've at least been trying to avoid up until now at any rate -- saving them for later to sit in judgement on any synthetic structures we might come to enjoy), is there any reason that we might expect a privileged status for either COVER1 or COVER2? This is tantamount to asking: Is there really any (non-bracketed) reason to "prefer" progressions whose roots are a diatonic 4th-or-5th apart to those whose roots are a 2nd-or-7th apart, or vice versa? Well, if we examine the possible (diatonicized) triads in K corresponding to the sets in Z (refer back to the correspondence chart in [6.1]), we note that, for whatever choice we make for a correspondence to COVER2, the resulting cover of H will be "mixed" with respect to chord "quality." For example, the cover {2t',4t',5t} contains two minor and one major triad. On the other hand, the choices corresponding to COVER1 yield two possibilities: "mixed" and "pure." With respect to symmetry, COVER1 can retain the kinds of (mirror) "quality" symmetries found in COVER2 while adding a kind not found there: two unique covers which each contain three chords of the same quality. Furthermore, COVER1 seems to most directly point to the overall inversional symmetry at the heart of RD(1) through the partition of K by major, minor, and diminished chords: R1(Z) = {5t,0t,7t} R1'(Z) = {2t',9t',4t'} R2(Z) = {11u} where R2 is a sort of "residue" set. So, fully aware that this is a choice made, in this particular context, by a preference for maximal symmetry coupled with a desire to discover as much variety as possible, we will privilege the sets R1 and R1' and call them "Riemann covers."(8) ============= 8. Clearly the converse, a preference for maximal variety coupled with a secondary desire to discover as much symmetry as possible, is most attainable by choosing COVER2 -- or by choosing neither or both. In the larger sense, if we were to adopt a preference for variety throughout, we could have stopped with Part I since, when we find ourselves in any (structured) musical universe, what we can say about any string can be said about symmetric strings as well, and cover covariance is simply an objective fact associated with whatever system we happen to find ourselves in at the moment. But in beginning Part II by focusing on necklaces and then on maximal evenness and (hyper)diatony we already (perhaps covertly) stated a preference for symetric structures which a fortiori guides our present and subsequent choices. ============= [6.14] A Riemann cover R will always have the following characteristics ($(A) indicates the interval string associated with set A): (1) The set R contains three chords which will be labelled S, T, D. (2) #int0(S,T) = #int0(T,D) = 1 (3) #int0(S,D) = 0 (4) $(S) = $(T) = $(D) (5) V(T,S) = V(T,D) (6) S.&.T.&.D = H (7) There is an inversion of R, R' = {S',T',D'}, such that R' is a Riemann cover. [6.15] Any CHORDSET whose scale string is (hyper)diatonic and that generates a Riemann cover will be called a Riemann Diatonic (RD) system. As we shall soon see, the usual diatonic based on ||3;7;12||, which we have been calling RD(1), represents the "smallest" or "first" such system available. This represents a somewhat different approach to what David Lewin has called "Riemann Systems"(9). The two approaches will be reconciled shortly, but a more complete congruence will not be demonstrated at this time. Our purpose here is more toextend systems rather than to simply find an alternate path to those that are known (and have been extensively used) in C12. ============= 9. David Lewin, "A Formalized Theory of Generalized Tonal Functions," Jounal of Music Theory 26.1 (1982) ============= [6.16] The triple {S,T,D} and its inversion display a characteristic pattern when projected onto a C12 circle. We plot the "roots" of each chord triple {5t,0t,7t} and {2t',9t',4t'} as vertices for the two triangles (5,0,7) and (2,9,4) on C12 (see Figure 1). Note that the two triangles overlap one another. A more complex version of this configuration will be met in RD(2)'s Riemann covers where we will find four overlapping triangles. In other words, where RD(1) has two "natural tonics" (the apexes of the triangles--one (right) "major" and one (left) "minor"), RD(2) will have four "natural" tonics, each supported by its own "dominant" and "subdominant." In general, any system RD(n) (to be defined) will have 2n, or n pairs of, Riemann covers. ****FIGURE 1**** [6.17] Note that nothing has yet been said about the cardinality of the basic RD(1) chords, so in higher RD systems the basic chords need not be triads. Nor has any stipulation been made concerning the specific shape (string) of the chords, so "dominant," "mediant," and any other intervallic constituents are temporarily left undefined. 7. AN ABSTRACT DIATONIC SYSTEM. [7.1] Let us assume that the set of strings W = ||3;7;12|| in RD(1) is the first member of a series of similar RD WARPSETs ||x;y;z||. We first note, given that the scale string must be diatonic (an assumption that can be stretched within limits -- see [] below), there can't be any other WARPSET of the form ||3;y;z|| since (from [6.14]) chord T must have one (and only one) tone in common with both S and D, and only y=7 satisfies that condition, concomitantly fixing z=12. So we begin by varying x. x=4 won't work since, to satisfy the common- tone condition, this would imply a WARPSET of the form ||4;10;z||, and <10;z> can't be diatonic since 10 is even; and the same applies for any even x. x=5 is the next possibility. Here the common-tone condition demands a WARPSET of the form ||5;13;z||, and the diatonic string from y=13 is <13;24>. In fact, as we will now see, the system (W',H',K') based on ||5;13;24||, which will be labelled RD(2), is the next RD system. After confirmation of this fact, we will return to find a general expression for any RD system. [7.2] RD(2). We begin by making the following assignments: In C13, J' = <13;13> = <1111111111111> g' = <5;13> DEF <23233> p = 0 X' = WARPSET(g',J') = ||5;13;13|| Y' = pJ' = {0,1,2,3,4,5,6,7,8,9,10,11,12} Z' = CHORDSET(X') and in C24, h' = <13;24> DEF <2222212222221> q = 0 W' = WARPSET(g',h') = ||5;13;24|| H' = qh' = {0,2,4,6,8,10,11,13,15,17,19,21,23} K' = CHORDSET(W') [7.3] Since (X',Y',Z') (=) (W',H',K'), we can display RD(2) fully by the following table of correspondences: ____________C13____________ _______________C24______________ / \ / \ X' Y' Z' W' H' K' <23233>=g' 0 {0,2,5,7,10} = 0g' <46365> = r 0 {0,4,10,13,19} = 0r <23233>=g' 1 {1,3,6,8,11} = 1g' <45465> = s' 2 {2,6,11,15,21} = 2s' <23233>=g' 2 {2,4,7,9,12} = 2g' <45465> = s' 4 {4,8,13,17,23} = 4s' <23233>=g' 3 {3,5,8,10,0} = 3g' <45456> = s 6 {6,10,15,19,0} = 6s <23233>=g' 4 {4,6,9,11,1} = 4g' <36456> = r' 8 {8,11,17,21,2} = 8r' <23233>=g' 5 {5,7,10,12,2}= 5g' <36456> = r' 10 {10,13,19,23,4}= 10r' <23233>=g' 6 {6,8,11,0,3} = 6g' <46365> = r 11 {11,15,21,0,6} = 11r <23233>=g' 7 {7,9,12,1,4} = 7g' <46365> = r 13 {13,17,23,2,8} = 13r <23233>=g' 8 {8,10,0,2,5} = 8g' <45465> = s' 15 {15,19,0,4,10} = 15s' <23233>=g' 9 {9,11,1,3,6} = 9g' <45456> = s 17 {17,21,2,6,11} = 17s <23233>=g' 10 {10,12,2,4,7}=10g' <45456> = s 19 {19,23,4,8,13} = 19s <23233>=g' 11 {11,0,3,5,8} =11g' <36456> = r' 21 {21,0,6,10,15} = 21r' <23233>=g' 12 {12,1,4,6,9} =12g' <36366> = t 23 {23,2,8,11,17} = 23t [7.4] We will not give the 13X24 interval matrix MINT(h') here, but we will note the ic-mapping it generates for RD(2): j-in-C13 k-in-C24 1 --> 1,2 2 --> 3,4 3 --> 5,6 4 --> 7,8 5 --> 9,10 6 --> 11,12 7 --> 12,13 8 --> 14,15 9 --> 16,17 10 --> 18,19 11 --> 20,21 12 --> 22,23 13(=0)--> 24(=0) [7.5] Illustrating the situation for G-COV in RD(2), the partition vectors produce the following (where a=10, b=11, c=12, d=13): U(h') = [2b496785a3c1 1c3a587694b2d] U'(h') = [2+b;4+9;6+7;8+5;a+3;c+1; 1+c;3+a;5+8;7+6;9+4;b+2;d] = [ddddddddddddd] = U(J') V(h') = [2b496785a3c1] V'(h') = [2+b;4+9;6+7;8+5;a+3;c+1] = [dddddd] = V'(J') W' contains three unique strings, r (r'), s (s'), and t, for which V(r) = V(r') = [001112003110], V(s) = V(s') = [000221003110], V(t) = [002003004001]. Thus V'(r) = V'(r') = [0+0;1+1;1+2;0+0;3+1;1+0] = V'(s) = V'(s') = [0+0;0+2;2+1;0+0;3+1;1+0] = V'(t) = [0+0;2+0;0+3;0+0;4+0;0+1] = = [023041] = V(g'). [7.6] For ic "voice leading" in RD(2) we have /5046082\ |0732715| |2354344| AVLIC(Z') = |3246163| |0731905| |4146082| \1543525/ By S-COV we can then determine that, for example, when we move from the chord 8r' to the chord 17s, with a span of 5 generic ic steps between "roots," that V(8r',17s) corresponds to V(pg',(p%5)g') = [4146082], which means that between 8r' and 17s there are available 4 ic0 connections, 1 ic1/2, 4 ic3/4, ..., 2 ic11/12. Leaving out the trivial case of the progression pg'-->pg', there are a total of 6X13=78 possible triad progressions in RD(2). This is in contrast to 3X7=21 possible triad progressions in RD(1). In RD(1) there are 10 distinct spanning vectors; in RD(2) there are 30. All of this is summarized in detail in Table 1 for RD(1) and Table 2 for RD(2). *** Table 1 *** *** Table 2 *** [7.7] That RD(2) is indeed a Riemann diatonic system can now be demonstrated by investigating its C-COV relationships. The C13 chromatic scale Y' can be minimally covered by three pentachords from Z' in two ways. Following RD(1), and our preference for maximal symmetry, we will select COVER(Z') = {pg', (p+6)g', (p-6)g'}. This in turn discloses the following partition of the chords in K': R1(Z') = {0r,11r,13r} R1'(Z') = {21r',8r',10r'} R2(Z') = {6s,17s,19s} R2'(Z') = {15s',2s',4s'} R3(Z') = {23t}. It is easily verified from [6.14] that R1, R1', R2, and R2' are Riemann covers. [7.8] We may now see the characteristic triangular pattern for RD(2) alluded to in [6.16]. If we plot the roots of each of the four Riemann covers as sets of vertices on the C24 circle, (0,11,13), (21,8,6), (6,17,19), and (15,2,4), we note again that these four (congruent) triangles all cross one another in a characteristic "RD pattern" first suggested in [6.16] (see Figure 2). *** FIGURE 2 *** [7.9] We now return to finding a general expression for any Riemann Diatonic system RD(n). First note that both generic strings <223> = <3;7> for RD(1) and <23233> = <5;13> for RD(2), which are not themselves diatonic, can be derived from the diatonic strings <112> = <3;4> and <12122> = <5;8>, respectively, by simply adding 1 to each entry in the strings. Thus <223> = <1+1,1+1,2+1> = <3;4+3> = <3;7> and <23233> = <1+1,2+1,1+1,2+1,2+1> = <5;8+5> = <5;13>. Generally, *any* ME string can be derived by writing out the ME string and then adding k to each entry in the string. But apparently only k=1 will produce a generic string which can be used as a basis for the type of RD string we have been looking at. [7.10] In any RD WARPSET ||x;y;z|| there is a "hidden" diatonic string such that the generic = , and since (by [5.9]) y' = 2(x-1), any RD WARPSET can be expressed in the form ||x;3x-2;6(x- 1)|| for odd x > 1. [7.11] = <2,j,2,k> (where j is a substring of (x-3)/2 3's and k is a substring of (x-1)/2 3's) will be called a Riemann generic string. Thus RD(3)'s generic string is <2332333> (whose "hidden" diatonic string is, incidentally, also the usual diatonic scale string <1221222>). [7.12] RD(n). We may also express any higher RD system in terms of RD(1) as its generator. Thus any RD WARPSET can also be expressed as ||3+2n;7+6n;12+12n|| where n >= 0. By simple algebraic manipulation, we may then define a generalized RD system as RD(n) = (A,B,C), where A = ||2n+1;6n+1;12n|| for n>0. 8. RIEMANN NON-DIATONIC SYSTEMS. [8.1] Riemann covers, which we have seen are a significant characteristic of RD systems, may also be associated with non-diatonic systems. The following general string set formulae assume that x is odd and greater than 1, y=3x-2, and k >= 0. Other variations beyond those given here are possible and finding them is a fruitful exercise. [8.2] The simplest case is ||x;y;(k+1)y|| which represents a series of "smoothly" expanding string sets. CHORDSET(,J), where J= is a string of y 1's, will trivially generate y Riemann covers of the form {pq,(p+z)q,(p-z)q}, where p is a pitch class in Cy, q is some stipulated string in , and z = [y/2]. We already know that this triple will be a cover, but it is also a Riemann cover since all three chords share the string q. then simply enlarges all intervals in the scale string by the same amount which concomitantly enlarges all intervals in q by the same amount, keeping the Riemann cover relationship for any k. [8.3] ||x;y;6(x-1)+ky|| represents an expansion of RD(n)'s scale string by adding multiples of y. ||x;y;6(x-1)|| is the basic formula for RD(n) given above in [7-10]. Adding k to each entry in a diatonic string expands the string into another ME necklace form, keeping the original ME pattern. Thus <7;12> = <2212221> and <7;12+7> = <7;19> = <3323332> retains the basic ME pattern. When this happens, the initial composite WARPSET's resultant strings are uniformly increased by successively adding the (constant) generic string to each of those resultant strings. To continue the example, stipulating <3;7> = <223>, we have ||3;7;12|| = {<435>,<345>,...,<336>}, so (by adding <223> to each of these strings) ||3;7;12+7|| = ||3;7;19|| = {<4+2,3+2,5+3>,<3+2,4+2,5+3>,...,<3+2,3+2,6+3>} = {<658>,<568>,...,<559>}. Since the relative positions of identical strings are retained, the Riemann cover is likewise retained. [8.4] Perhaps the most interesting Riemann non-diatonic system is based on what might be termed the "conjugate-diatonic" WARPSET, ||x;y;3x||. While the generic string is again retained, the values of the elements of the diatonic scale string are reversed; so the diatonic <2212221> becomes the "conjugate-diatonic" <1121112>. [8.5] Two ME strings s = and t = are conjugates of one another if b+b' = x. Thus <5;4X5+3> = <5;23> = <45455> and <5;4X5+2> = <5;22> = <54544> are conjugates. To find the conjugate of the general scale string in RD(n) we first note that, through simple manipulation, <3x-2;6(x-1)> = <3x-2;(3x-2)+(3x-4)>. Since (3x-2)-(3x- 4) = 2, the conjugate-diatonic scale string will be of the form <3x- 2;(3x-2)+2> = <3x-2;3x>. [8.6] Swapping the diatonic scale string for its conjugate has the effect of changing the string's values while retaining its basic ME pattern, thereby retaining the Riemann cover as well. For example, the string set ||5;13;15|| is the basis for the conjugate of RD(2). Its basic scale string is <1111121111112> and, using <5;13> = <23233> as the generic string, the members of the WARPSET can easily be calculated: {<23334>, <24234>, ..., <33333>}. Presence and location of the two pairs of Riemann covers can now easily be determined. 9. EXTENSION OF DAVID LEWIN'S RIEMANN SYSTEMS. [9.1] Returning to Riemann diatonic systems, we now procede to reconcile our "topological" approach with David Lewin's "tonal function" approach. Consider first Lewin's definition which we have been studiously avoiding until now: "By a Riemann System (RS) we shall understand an ordered triple (T,d,m), where T is a pitch class and d and m are intervals, subject to the restrictions that [neither d nor m is 0 and m does not equal d]."(10) He then procedes to define the tonic triad as the unordered set {T,T+m,T+d}. This, and the rest of the relationships investigated by Lewin, can be transported to RD(1) since, for example, his RS (T,7,4) produces the triad {0,0+4,0+7} = {0,4,7} which coincides with 0t in RD(1). But can the Lewin-Riemann concept of chord construction (and concomitant relationships) be modified to fit *any* RD system? Using 0r = {0,4,10,13,19} as a test chord in RD(2) we guess that (T,13,m) might be an irredundant RS since int13 seems to fulfill a "dominant" function. But what do we make of the quality-determining "mediant interval" m? And how do we generate the other three chord members? The answers to these questions will lead us, at the end of our study, to some bizarre (but nevertheless plausible) conclusions about diatonic systems. ============= 10. Lewin, op. cit., p.26. ============= [9.2] Interestingly, any of the four (apex) pentachords (privileged as "tonic" by the definition of a Riemann cover) in RD(2) can be constructed from the RS triple (T,d=13,m=9) as follows: red: {T, T+d,T+d-m,T+d-2m,T+d-3m} green: {T,T+m, T+d,T+d-m,T+d-2m } yellow:{T,T+m,T+2m, T+d,T+d-m } blue: {T,T+m,T+2m,T+3m,T+d } The spacing in each set is used to draw attention to the grouping of elements. The colors on the left are randomly assigned "shape" or "chord quality" or "mode" designations analogous to "major" and "minor." Note that each set contains both T and T+d, as we would expect. But whereas in the simpler triadic system the only other element is T+m, here there is a combination of three additional elements, each with the form T+km or T+d-km (k=0,1,2,3); that is, T and T+d are "anchor points" to which positive and negative integral multiples of m are added. [9.3] Setting T=0,15,6,21, we may now calculate the four basic Lewin- Riemann tonic pentachords in the scale {0,2,4,6,8,10,11,13,15,17,19,21,23}. red: set T=0 {0,0+13,0+13-9,0+13-18,0+13-27} mod 24 = {0,13,4,19,10} (= 0r) green: set T=15 {15,15+9,15+13,15+13-9,15+13-18} mod 24 = {15,0,4,19,10} (= 15s') yellow: set T=6 {6,6+9,6+18,6+13,6+13-9} mod 24 = {6,15,0,19,10} (= 6s) blue: set T=21 {21,21+9,21+18,21+27,21+13} mod 24 = {21,6,15,0,10} (= 21r') [9.4] "Dominant" and "subdominant" pentachords related to each of the four basic pentachords can be found by adding 13 and -13 (=11), respectively, to each T-value in [9.3]. Thus there are four sets of primary pentachords in this extended RS. Lewin's secondary chords can similarly be transported, but we will concentrate here on the primary chords. [9.5] A Lewin-Riemann System (LRS) may be found in any RD system by generalizing [9.2] in the following way. If ||x;y;z|| is an RD WARPSET (where x is odd and > 1, y = 3x-2, and z = 6(x-1)), then an embedded LRS can be identified as the ordered triple (T,d,m) where T is a pitch class (mod z), d=y, and m=y-4. A tonic x-ad of the RS (T,d,m) is the unordered set TON = {T+fm,T+d-gm}, a dominant x-ad is DOM = {T+d+fm,T+2d-gm}, and a subdominant x-ad is SUB = {T-d+fm,T-gm}, where f = 0,...,a and g = 0,...,b are related by a+b = x-2. [9.6] The triple (TON,DOM,SUB) generated by the RS (T,7,4) can be traditionally interpreted as defining a chord-generated "key" in relationship to the pitch class T. Thus the RS (T=3,d=7,m=4) implies the "key" KEY(E ,+) DEF {(E ,+).&.(B ,+).&.(A ,+)} with (E ,+) stipulated as "the harmonic goal". This in turn implies the "relative key" KEY(C,-) DEF {(C,-),&.(G,-).&.(F,-)} with (C,-) stipulated as "the harmonic goal". Looking back at the four basic (T,13,9) chords listed in [9.3] and generating their respective dominants and subdominants, using string notation for clarity we can create the following modal key relationships ("/" here denotes "with"). KEY(0,red) DEF [{0r.&.11r.&.13r} / 0r DEF "goal" KEY0] KEY(15,green) DEF [{15s'.&.2s'.&.4s'} / 15s' DEF "goal" KEY1] KEY(6,yellow) DEF [{6s.&.17s.&.19s} / 6s DEF "goal" KEY2] KEY(21,blue) DEF [{21r',.&.8r'.&.10r'} / 21r' DEF "goal" KEY3] Note that each tonic ("goal" KEYk) is generated by our original choice for the pitch class T = 0 by running through the values of a (see [9.5]) a = 0, KEY0 = T - (0 X m) = T - 0 = 0 a = 1, KEY1 = T - (1 X m) = T - 9 = 15 a = 2, KEY2 = T - (2 X m) = T - 18 = 6 a = 3, KEY3 = T - (3 X m) = T - 27 = -3 (mod24) = 21 This may all be generalized as follows. [9.7] HYPERKEYS. Given the variables stipulated in [9.5], (1) a "key stipulation" generated by the LRS (T,d,m) is defined as KEYa = T-am (mod z) (2) a hyperkey structure KEY(KEYa,name) is defined as [{TON.&.DOM.&.SUB} / TON DEF "goal" KEYa], where name is purely referential and can be chosen at random. (3) the "relative" of (KEYa,name1) is (KEYb,name2), where b = x- 2-a from [9.5]. [9.8] NB: [9.5] makes a significant modification to the original Lewin definition quoted in [9.1]. Whereas RS (tri)chords are always oriented toward T as a "monopole," in order to extend this system into higher order RDs we have been forced to define the generalized LRS chord as bipolar, i.e., the x-2 mediants are added to and/or subtracted from either T or T+d. The effect of this is to destroy the uniformly one-directional nature of Riemann's original concept where the entire chord is described as "up" or "down" from a root/tonic. However it is possible to "save the appearances" with respect to up- ness and down-ness in higher RD systems. [9.9] OPERATIONS IN LRS. In this section we have thus far been concentrating on definitions in order to transport RS structures into higher RD systems as LRS structures. But the heart of Lewin's Riemann System is the family of operations IDENT (identity) CONJ (conjugate) TDINV (tonic-dominant inversion) RET (retrograde) collectively called the "serial group" of operations (GSER).(11) These operations on (T,d,m) consist essentially of alternations of three elements: location (whether the root is T or T+d) polarity (whether d and m are positive or negative) mode (whether the mediant element is m or m'=d-m). So GSER consists of IDENT: change nothing, CONJ: keep T and change mode, TDINV: add d to T and change polarity (of d and m), RET: add d to T and change both polarity (of d and m) and mode. Thus for RS (0,7,4), if the original triad is X = (0,4,7) = C major, IDENT(X) = (0,4,7) = C major CONJ(X) = (0,3,7) = C minor TDINV(X) = (7,3,0) = dual G minor RET(X) = (7,4,0) = dual G major. But our revised definition for an LRS keeps the mode constant to accomodate multiple mediant elements, centering instead on the separate polarity alterations of d and m, a "+" value being measured from T and a "-" value being measured from T+d. Thus the revised family of operations, GSER*, can be described IDENT: change nothing, CONJ: change polarity of m, TDINV: add d to T and change polarity of both d and m, RET: add d to T and change polarity of d. ============= 11. Lewin, op. cit., p.37-39. ============= [9.10] The reader may verify that GSER* produces the same set of chords as GSER in the previous example. But to illustrate that GSER* generalizes to higher RD systems, consider the LRS (T=0,d=13,m=9) and generate a "green" set as defined in [9.3]: X = (T,T+m; T+d-2m,T+d- m,T+d) = (0,9; 19,4,13). Here we have reversed the order of elements on the right to illustrate the pentachord's bipolar structure, (T)-->(T+m) (T+d-2m)<--(T+d-m)<--(T+d), \ / \ / \--------------->---------------/ a short right arrow indicating +9, a short left arrow indicating -9, and the long right arrow indicating +13 (all mod 24). GSER* then yields: IDENT(X) = (0,9; 19,4,13) = 0-green CONJ(X) = (0,9,18; 4,13) = 0-yellow TDINV(X) = (13,4; 18,9,0) = dual 13-yellow RET(X) = (13,4,19; 9,0) = dual 13-green. [9.11] The arrangement which places T on the far left and T+d on the far right with the set of mediant elements in between will be called the canonical arrangement of an LRS chord. In the above example, the intervals between the elements of the canonically ordered X, read left to right, form a substring /9A99/, where A=10 (just why this is called a substring here will be evident shortly). Since the "subdominant" and "dominant" pentachords which join X to form the primary chords of the system each share a common (polar) tone with X, the substring of the canonical (sub)string form of the entire structure (11,20,6,15,0,9,19,4,13,22,8,17,2) is /9A999A999A99/. [9.12] THE SHIFT OPERATION. If we now clone the canonical substring /9t99/ an indefinite number of times we have the infinite repeating string Q = <...9A999A999A999A999A99...>. We may then directly apply Lewin's definition of the SHIFT operation: "Given an integer N ... we will define a formal operation SHIFT(N) which operates on any given [L]RS to produce a transformed [L]RS whose canonical listing is 'shifted N places' from that of the given system."(12) ============= 12. Lewin, op. cit., p.48. ============= [9.13] For a triadic system such as (T,7,4) in C12, K is an alternation of m and d-m, <...343434...>. When paired with appropriate pitch classes, e.g., ( ...g Bb d F a C e G b D f# A ...), SHIFT in effect produces modulations. But even more, it describes a functional relationship between virtually any pair of diatonic chords. For instance, SHIFT(+2) applied to segment (B d F a C e G) modulates to (F a C e G b D), i.e., from F major to C major (or from a B -13th chord to an F-13th chord). In RD(2), SHIFT produces analogous pairing relationships. [9.14] Returning to numerical notation for chord elements (mod 24 for clarity) and assigning 0 to reflect the example in [9.3], the string Q = <...9A999A999A999A999...> produces the canonically ordered structure (...11,20,6,15,0,9,19,4,13,22,8,17,2,11,21,6,15,0,...). Again using red, green, yellow, and blue from [9.3] as mode designations, 0-green indicates the canonic structure (11,20,6,15,0,9,19,4,13,22,8,17,2) with the substring /9A999A999A99/ which can be rearranged to disclose the "0-green scale" {0,2,4,6,8,9,11,13,15,17,19,20,22} with the C24 string <2222122222122>. [9.15] SHIFT(+1) applied to 0-green produces SHIFT(+1)(0-green) = (20,6,15,0,9,19,4,13,22,8,17,2,11) = 9-yellow with the substring /A999A999A999/. The "9-yellow scale" {9,11,13,15,17,19,20,22,0,2,4,6,8} with the string <2222212222221> shows that SHIFT(+1) here has kept all of 0-green's pcs but shifted the "tonic" from pc0 to pc9 and rotated the string, i.e., produced a "modal modulation." [9.16] On the other hand, SHIFT(+2)(0-green) = SHIFT(+1)(9-yellow) = 19-blue = (6,15,0,9,19,4,13,22,8,17,2,11,21) has the substring /999A999A999A/ and represents a "chromatic-modal modulation" with respect to both 0-green and 9-yellow. The "19-blue scale" is {19,21,22,0,2,4,6,8,9,11,13,15,17} with string <2122222122222>; its string is not only a different rotation of <13;24> than either 0-green or 9-yellow, but it also adds pc21 which neither of the other two systems (keys) contains. [9.17] As we have seen, by modifying Lewin's original definitions for Riemann Systems, both the group of operations GSER (as GSER*) and the operation SHIFT(N) are preserved in the hyperdiatonic system RD(2). Extending to larger hyperdiatonic systems, the following progression is easily verified: RD(1) <--> (T,7,3) in C12 RD(2) <--> (T,13,9) in C24 RD(3) <--> (T,19,15) in C36 ... ... RD(n) <--> (T,7+6(n-1),3+6(n-1)) in C12n It is left as an exercise to determine the LRS canonical form of the substring supporting any basic chord in RD(n), i.e., to complete the following: (T,7,3) --> /43/; (T,13,9) --> /A999/; (T,19,15) --> /?/; (T,?,?) --> /?/. *************** INSTEAD OF A CONCLUSION. There is no truth beyond magic.... One, when you've discovered the truth ... it does have the most extraordinary magical quality about it. It's the payoff, to recognize the deep order ..., you feel you are in touch with something fundamental. But there's also a poetic sense in it: reality is strange. Many people think reality is prosaic. I don't. We don't explain things away.... We get closer to the mystery. Brian Goodwin, theoretical biologist, quoted in Roger Lewin, Complexity: life at the edge of chaos (Macmillan, 1992) Despite the promise made at the end of Part I, I must break off the development at this point solely for reasons of space, leaving the promise only partially fulfilled. This study grew over the past two years from a simple premise, the development of which I foolishly believed would be at least short if not sweet. (I have now learned a valuable lesson about simple premises and promises.) Though I had not planned it this way, I will have to publish the conclusion to this tonal fantasy in the future as Part III. But I will take my time with it, perhaps to savor it. Part III begins as a study in hyperdiatonic voice leading based on Richard Cohn's parsimonious chord pairs and Eytan Agmon's efficient linear transformations. These voice-leading considerations then force some startling, even bizarre, conclusions about the nature of higher order hyperdiatonic systems. While maintaining much of the usual diatonic's salient features, a fourth-order hyperdiatonic system contains "hypertones," sets which behave much like single tones in the usual diatonic (this was first hinted at in [9.1] with the "mediant problem"). This behavior then implies a nascent theory of "counterset" which might arise through compositional praxis. But, even without an existing body of hyperdiatonic works, by re-examining Schenker's "axioms" it is possible to devise a "hyper-Schenkerian conjecture" which asserts that counterpoints generally arise as more or less natural products of white note systems, rather than magically as the result of a fortuitous history. Examination of this idea will, finally, conclude Part III of this particular fantasy. But there is more; much more, I think. While examining the "simple premise" in relation to tonal theory, it has become increasingly obvious to me that the WARP function, which effectively transforms any musical structure from one "space" to another, can be useful in the study of (hyper)atonal structures. This idea is now a work-in- progress and has already provided some startling connections and pointed to unsolved problems. But for now I am convinced enough of WARP's power to flush out invariants, that I am willing to make the following statement, not because I think it will necessarily turn out to be "true," but because I think it is the right goal for speculative theory. Just as there are abstract geometries which can only be reached by studying their various models, there are abstract musics which can only be reached by studying their various models. It may be that we will ultimately learn that there is only one abstract music; and, at least in this sense if no other, distinctions melt away: There is only ONE music. ====================== 2. Reviews AUTHOR: Luchese, Diane TITLE: Review of Anthony Pople's *Messiaen: Quatuor pour la fin du Temps* (Cambridge: Cambridge University Press, 1998) KEYWORDS: Messiaen, Quatuor, Quartet, Pople. Diane Luchese Ohio State University Department of Music Theory and Composition 110 Weigel Hall 1866 College Road Columbus, OH 43210-1170 Luchese.1@osu.edu [1] Anthony Pople's *Messiaen: Quatuor pour la fin du Temps* is a book you might rightly judge by its cover: a volume in concise format, with serious design, and careful craftsmanship. Pople's work is precisely that, proving itself to be an excellent analysis of one of the twentieth century's musical masterpieces. This book goes beyond most other writings on this composition, writings that often accomplish little more than identifying Messiaen's signature techniques in the same superficial way that a field guide might identify birds in a forest. [2] The 115 pages of *Messiaen: Quatuor pour la fin du Temps* include an introduction, individual chapters devoted to each of the eight movements, and a concluding chapter, followed by an appendix of Messiaen's seven modes of limited transposition, endnotes, and a select bibliography. Throughout the text, short musical examples illustrate passages under discussion. [3] Pople demonstrates extensive knowledge of the composer's style and works. As he progresses through individual movements, he carefully identifies and explains many of the techniques that Messiaen wrote about in his 1944 treatise, *The Technique of My Musical Language.* Notable among them are nonretrogradable rhythms, modes of limited transposition, rhythms with added values, inexact augmentation and diminution, rhythmic pedals, chords on the dominant, and chords of resonance. Pople compares several passages from the quartet with excerpts from other Messiaen compositions that display similar thematic material and compositional procedures. For example, he shows a passage from the sixth movement ("Danse de la fureur") as a derivation of the opening bars of "L'Ange aux parfums" from *Les corps glorieux* (1939), highlighting motives identical in contour and rhythm, although different in mode and tempo. He identifies the fifth and eighth movements as borrowed transcriptions of sections from two earlier compositions, *Fete des belles eaux* (1937) and *Diptyque* (1930). [4] Pople has not only an appreciation of the historical circumstances surrounding the composition's genesis but also a deep understanding of its significant theological program. He recounts the story of the quartet's composition while Messiaen was incarcerated during World War II, and explains how the circumstances of his internment with three other musicians in the same camp led to its instrumentation. From Messiaen's accounts, recollections of the cellist who first played it, and comparisons of the movements, Pople proposes a hypothetical order in which the movements may have been composed. He discusses the theological issues underlying the *Quatuor pour la fin du Temps,* an integral part of the quartet's expression, and explains (p. 14) that some movements contemplate the qualities of eternity while others are concerned with the events of the apocalypse ("the end of time") as described in the Bible's tenth chapter of the book of Revelation. Pople also gives the dramatic account of the work's first performance in January of 1941, for some five thousand prisoners assembled in a freezing building. [5] Pople's writing shows true craftsmanship. It is usually clear and concise. Often, it is poetic. For example, after citing Messiaen's description of the fifth movement's melody as a song sentence, he writes: Though arguably no more than a description of the melody's formal outline, this lends new meaning to the association of the music with the Word: if this is a 'song' then it is surely a song-without-words, but it is not Wordless. And it may be that the transfer of this melody from the ondes Martenot to the tangibly physical medium of the cello's upper register--in which, for example, the motions of the player's left hand on the neck of the instrument are frequently audible alongside the musical notes--was comparable for Messiaen with the theological fact of the Word made flesh" (p. 55). [6] Pople's analysis is straightforward, direct, and insightful. He thoroughly points out the thematic, tonal, textural, and formal relationships found within and between movements. He uses short musical examples effectively to illustrate compositional processes, melodic structures, and harmonic progressions. He distinguishes chords that serve as harmonizations of melodies from those independent of melody having strictly coloristic functions. Citing Messiaen's words about the colors that are depicted--a result of his rare and individual condition of synaesthesia--he admirably handles the difficulties that sometimes arise from the composer's detailed color descriptions. Pople can be commended for placing the lighthearted character of the 'Intermede' in context; few scholars convincingly address such lightheartedness in Messiaen's music. [7] Pople further illustrates some of Messiaen's innovative techniques by way of comparison with fabricated hypothetical traditional Western models. This kind of illustrative stylistic comparison is instructive. For example, the opening five bars of 'Abime des oiseaux'--an application of one of Messiaen's preferred melodic contours(1) using his second mode of limited transposition, added values, and inexact diminution--are shown as a derivation of a hypothetical, yet conceivable, four-bar tonal model in 4/4 (p. 42). While both musical examples are given for comparison, Pople is careful to present Messiaen's music above the fabrication in order to stress that the derivation is hypothetical and to emphasize that "there is no suggestion that Messiaen actually worked in this way, let alone that he worked with the actual substance of this example in mind" (p. 42). ========================================= 1. Messiaen identifies this pattern with Musorgsky's *Boris Godunov.* ========================================= [8] If there is any substantial fault to this book, it is that it is sometimes too concise. For example, the analysis of the first movement lacks detailed discussion of the principal theme, the clarinet part. Instead, Pople focuses on the rigorous organization of the panisorhythmic piano and cello parts, undoubtedly because these parts also can emphasize several of Messiaen's innovations. He shows the five motives that are chained together to form the violin part and then states that "the clarinet's music proceeds similarly" (p. 27). This is not entirely true. Although both parts are a kind of stylized birdsong, the more subordinate violin plays nothing more than its five motives (with some repetitions and order changes) while the clarinet's initial theme goes through more interesting developmental variations. [9] Some confusion may arise from Pople's initial description of the solo clarinet movement's form. After asserting that the sections are defined by changes of tempo (p. 41), he lists the measure corresponding to the second powerful crescendo on a sustained E as a separate section, "C," because of the changed metronome marking needed to indicate the desired length of the note. Because later in his discussion Pople interprets this note as an introduction to the "presque vif" section that follows it (p. 44), it seems that the chart below the initial assertion that tempo changes determine form gives misleading or at least confusing information. [10] I recommend this book especially to musicians wanting to learn more about the "Quatuor pour la fin du Temps" or Messiaen's style in general. Anthony Pople conveys a sincere appreciation of both the composer and his great work. As his last sentence so eloquently states, the Quartet "remains a unique document of a great composer at the height of his powers responding to extraordinary circumstances with sustained and magnificent invention" (p. 95). AUTHOR: Raschke, Peter, J. TITLE: Review of Music-Theory Web Sites for the Beginner KEYWORDS: WWW review, beginner music theory Peter J. Raschke Northwestern University School of Music 711 Elgin Road Evanston, IL 60201 raschke@nwu.edu [1] Since the advent of the personal computer in the late 1970's and early 80's, music theory instruction has been at the forefront of technology, using a wide variety of CAI (computer aided instruction) programs to supplement classroom instruction. Today, CIA is in a state of transition, with the Internet continuously creating new ways to access and communicate information in a manner not possible a few years ago. The World Wide Web is transforming the study of music theory, expanding the source of learning beyond the traditional classroom. With technological advancements, it is possible to now create a learning environment that incorporates text, narration, graphics, animation, sound, and interactivity into a single multimedia experience that engages the user in cognitive thought processes that exceed the capabilities of written text. [2] This review will examine the effectiveness of existing beginning music theory Web sites intended for beginners. The sites were selected from the Beginners Theory resource page at the Society of Music Theory [Music Theory Resource Page] (http://boethius.music.ucsb.edu/smt-list/docs/beginners-theory.html). These sites reflect the Web's instant access to the world, with their physical locations in Puerto Rico, Nova Scotia, New York, and Illinois. Because this review is online, there will be links to the various Web sites in order to demonstrate features that serve to enhance or detract from the learning process. [3] The most important feature of any curriculum is the content of the material considered. But the presentation of that content is nearly as important. For an instructional Web site multimedia and interactivity are crucial features since they can involve the user as an active participant in the learning process. A hypermedia design allows a user to follow a non-linear approach adding flexibility to the way that the user approaches the material. In this regard, the organization of the Web site is key, for the user must be able to follow a specific order of presentation, or take a nonlinear approach and inquire about specific topics with ease. A Web site designer must allow the user easy and immediate access to the main index from any page within the site. If specific set-up requirements exist for the browser (certain plug-ins, applications), the site must clearly explain which are needed and how the proper support is acquired. The degree to which the Web site incorporates these various features can determine the effectiveness of the learning environment. [4] A great site to start with is "Easy Music Theory" (http://www.musictheory.halifax.ns.ca/) music theory lessons online created by Gary Ewer. Eighteen lessons are available with topics on the grand staff, note names, the piano keyboard, note durations, measures, intervals, scales, key signatures, time signatures, triads, Roman numerals, and key identification. A section on musical terms and definitions supplements the eighteen main topics. Each lesson includes a quiz that may be printed by the student, allowing him or her first to answer the questions and then to check the answers by clicking on a quiz-answer link. [5] Ewer has done an outstanding job of combining text with supporting notation graphics, and the inclusion of MIDI files helps the user to "synthesize" the musical concepts [Example in Chapter 17, Triads and Roman Numerals] (http://www.musictheory.halifax.ns.ca/17triads.html). The explanations are concise and written at a level that a beginning student can understand. Many of the examples have a step-by-step process that challenges the user to utilize critical thinking skills [See Chapter 14, Time Signatures- Measure Completion] (http://www.musictheory.halifax.ns.ca/14tsmc.html). Preceding each lesson Ewer places a list of concepts from previous lessons necessary for mastering the new lesson. There are frequent hyperlinks to previous lessons during the new lesson allowing the user easy access to material for review. [6] Navigation at this site is well organized and consistent. At the bottom of each lesson the user has the option of returning to the main index or clicking on a link to take the quiz for that lesson. At the quiz page, the user is instructed to print the page, complete the material, and then click on a link for the quiz answers. The user may also link back to the lesson for a better understanding of the material before attempting the quiz. At the end of the answer page links to the next lesson or back to the main index are present. The consistent pattern of navigation allows the user to find the exact location of any topic. The site even includes a forum where users may post questions and receive feedback from the author or participants that use this site. [7] Ken Fansler's "Online Music Instruction Page" (http://orathost.cfa.ilstu.edu/~kwfansle/onlinemusicpage.htm) was created in connection with a graduate-level project in music education, and is a good example of using the Web to supplement a music education program. It begins with a welcome page, followed by helpful instructions on how to set-up the browser, a main index (http://orathost.cfa.ilstu.edu/~kwfansle/project/projecthome.htm) that allows the user to choose a skill level, and ultimately proceeds to instruction on selected topics. While this site includes some helpful information on certain music theory concepts, and the author's use of sound and graphics supports the material well, there are certain deficiencies in navigation and content. An exciting feature of hyperlinks is that they do not force the user into a linear path of instruction. Navigation at this site unfortunately does force the user to use a linear sequence of subjects. If a user is in the intermediate section and wishes to review the section "Notation", he or she is forced to follow a linear path that leads through "Beamed notes," "Articulation (Note Markings)," "Endings and Repeats," and "Ledger Lines." Similarly, the portions of the quiz addressing ledger lines are problematic, since the user must return to the section on beamed notes before reaching the section on ledger lines. Such a system is neither flexible nor intuitive [Link to "Section One: Notation"] (http://orathost.cfa.ilstu.edu/~kwfansle/project/IntermediateInstr.htm). A similar example arises for the intermediate topic "Listen and Learn," with sections on triads and percussion instruments. In order to learn about percussion instruments, one must first review the lesson on triads, even though the two topics are not closely related. There are also problems with the content, such as incomplete information. The section on dynamics includes an explanation with sound examples of loud (f) and soft (p). Rather than completing the lesson by continuing with listings and explanations of the remaining dynamic marks pp, mp, mf, ff, Fansler diverges into a section on musical instruments [Link to "Listen and Learn" - Dynamics] (http://orathost.cfa.ilstu.edu/~kwfansle/project/dynamics.htm). [8] An exciting feature of using a Web site in a learning environment is the availability of sound examples that reinforce graphic and textual information. The Online Music Theory Site augments concepts in musical notation by using digital audio files that are accessed by clicking on the actual notation [Example of Audio File] (http://orathost.cfa.ilstu.edu/~kwfansle/project/articulation.htm). Included in the site's "Question and Answer" section are sounds for positive and negative feedback, though these can get annoying after hearing the same sounds with each answer. Feedback sounds are not generally needed, except with very young users. If feedback is included, there should be four or five different positive and negative response sounds so that the user does not become bored with the sound. One technical recommendation is to embed the audio feedback sound into the html document as a QuickTime movie, thereby avoiding the delay in waiting for the plug-in to turn on for each response when the answer page is loaded in the browser. [9] One of the best interactive music theory Web sites is "Java Music Theory" (http://academics.hamilton.edu/music/spellman/JavaMusic/), maintained by Rob Whelan. This is an ideal site for the beginning user who needs drill and practice opportunities in basic music concepts. There are eight main categories, with a choice for sound or no sound with each Java applet. Each applet contains a section that explains how to use the program and provides options for selecting experience levels. The Java applets available include: 1) Note Reading (http://academics.hamilton.edu/music/spellman/JavaMusic/NoteReading. html) Staff note reading tests the user by identifying notes on the entire grand staff or the treble or bass clef. 2) Piano Key Finder (http://academics.hamilton.edu/music/spellman/JavaMusic/PianoKeyFinder. html) While similar to the Note Reading applet, it has the added dimension of matching the notes on a piano keyboard with the notes on the grand staff. 3) Music Speed Reading (http://academics.hamilton.edu/music/spellman/JavaMusic/SpeedReading. html) Challenges the user to identify notes as they move across the staff. An user option allows varying the speed with which the notes move across the screen. 4) C-Clef Note Reading (http://academics.hamilton.edu/music/spellman/JavaMusic/CReading.html) Comparable to the Note Reading applet, but the user works within four possible C clefs, instead of the treble and bass clef. 5) Key Signature Drill (http://academics.hamilton.edu/music/spellman/JavaMusic/KeySigDrill. html) An interactive technique for drill on key signatures, it also has an option for hearing the major or minor tonic chord or the scale. The program may also be set up to ask for the relative key. 6) Scale Building (http://academics.hamilton.edu/music/spellman/JavaMusic/ScaleBuilding. html) An interactive design that allows the user to create major or minor scales. 7) Interval Drills (http://academics.hamilton.edu/music/spellman/JavaMusic/IntervalDrills. html) Gives the user a choice of identifying the interval on the screen or building new intervals based on the note presented. 8) Chord Drills (http://academics.hamilton.edu/music/spellman/JavaMusic/ChordDrills. html) Similar to the interval drill applet, but the user may identify or build triads or 7th chords. [10] The main focus of each page is the Java applet. The size of the applets are designed to fit any monitor, with the directions for using the applet available immediately below the applet. Each page includes a consistent bottom footer that gives the user complete access to any applet on the Web site. The only problem that I encountered with this site is that the main page link for the applet Key Signature Drill is not working, though the footer links on the bottom of each page do connect to the applet. For a beginning theory user to utilize this site, it needs to be supplemented with a beginning theory class, textbook, or another basic online theory site, such as "Easy Music Theory." Once a basic understanding of music theory concepts has been acquired, this site could provide invaluable in reinforcing an understanding of this material. [11] Music instruction and interactive Java applets are also included in another top-rated site, "Practical Music Theory" (http://www.teoria.com/), a bilingual Web site created by José Rodríguez Alvira and dedicated to the study of music theory. In addition to Java applets on identification and construction exercises for intervals, chords, and scales, there is an online music theory book called Teoría's Books (http://www.teoria.com/ba/index.htm), that includes instruction on intervals, chords, and scales. The combination of instruction and interactive learning makes this site a comprehensive source for the beginning theory user, yet there is sufficiently challenging material to make it equally valuable to the intermediate or advanced user. Each applet includes instructions on how to use the applet and allows users to select options based on their ability level. [12] The interval-construction applet (http://www.teoria.com/java/eng/ICTest.htm) allows the user to assemble intervals, while the interval-identification applet (http://www.teoria.com/java/eng/IITest.htm) displays an interval and asks the user to identify the distance. The chord-construction-tool applet allows the user to see any type of chord, as well as the inversions of the chord. Not only does the applet display major, minor, diminished, and augmented triads, the user may select 7th, 9th, and augmented-6th chords. The chord-construction-exercise applet (http://www.teoria.com/java/eng/CCTest.htm) challenges the user to take the next step by having him or her build new chords that include all of the variations from the chord-construction-tool applet. The chord-identification-exercise applet (http://www.teoria.com/java/eng/CITest.htm) has the user identify the listed chord and provides options for levels of difficulty and choices from major and minor triads, 7th, 9th, and augmented-6th chords. The scale-construction-tool applet (http://www.teoria.com/java/eng/SCTool.htm) displays any imaginable type of scale; besides major and minor scales, the user may view various modes and scales. Finally, the scale-identification applet (http://www.teoria.com/java/eng/SITest.htm) presents various scales for recognition. This Web site contains a wealth of information on the elements of music theory and challenges the user to expand his or her knowledge of the elements of music through interactive exercises. This site is unique in that all of the information is available in English and Spanish. [13] The purpose of this review has been to promote the unlimited potential for music theory instruction available through the World Wide Web. Multimedia tools continue to improve and it is important for music sites to remain current with the latest technology. Digital sound files incorporate large amounts of memory and take time to load across the Internet. Alternative technologies include MIDI files or Real Audio files that greatly reduce the size of the file while still preserving the integrity of the sound. The addition of Java applets adds interactive features to a Web site, drawing the student into an engaging learning experience. As a supplement to a music theory class, an online music class, or a learning site available to individuals with an interest in music theory, the Internet is evolving into a new and dynamic place to learn about the elements of music. [14] Information on the author: Peter Raschke is currently at Northwestern University pursuing a Ph.D. in Music Technology. He completed the Masters of Music Technology degree in June, 1997. As a member of the Northwestern University School of Music Web design team, Mr. Raschke helped to create its Web pages and is currently the webmaster of the music site. He has taught a multimedia software development class, Web Authoring (http://www.nwu.edu/musicschool/classes/webAuthoring/index.html), at Northwestern University, and was an instructor and music laboratory technician at Santa Barbara City College prior to beginning his graduate studies. Web sites created by Peter Raschke are located on his home page at Northwestern University (http://pubweb.nwu.edu/~pjr981/). ====================== 3. Announcements Toronto 2000: Open Call for Proposals for Joint Sessions Call for Papers: Don't Stop Till You Get Enough: Consuming Popular Music Call for papers: Arnold Schoenberg Center College Music Society Summer 1999 Opportunities for Professional Development: (1) Center for Professional Development in Music Technology at Illinois State University (2) Center for Professional Development in World Music at New England Conservatory of Music (3) Weekend Workshop on Teaching Women and Gender in Popular Music at the University of Wisconsin, Madison (4) CMS International Conference in Kyoto, Japan New England Conference of Music Theorists: Program Schedule Call for Papers: International Conference on Jean Sibelius, Helsinki 2000 West Coast Conference for Music Theory and Analysis and Rocky Mountain Society for Music Theory Music Theory Society of New York State 1999 Program _______________ TORONTO 2000: MUSICAL INTERSECTIONS Open Call for Proposals for Joint Sessions (*Proposal deadline: June 1, 1999*) The Society for Music Theory will hold its annual meeting November 1-5, 2000 in Toronto, Canada, together with fourteen sister societies engaged in music research and the teaching of music in U.S. and Canadian colleges and universities. Entitled *Toronto 2000: Musical Intersections*, the conference will bring together The American Musical Instrument Society (AMIS); the American Musicological Society (AMS); the Association for Technology in Music Instruction (ATMI); the Canadian Association of Music Libraries, Archives, and Documentation Centres (CAML); the Canadian Society for Traditional Music (CSTM); The College Music Society (CMS); the Canadian University Music Society (CUMS); The Historic Brass Society (HBS); the Canadian and U.S. chapters of the International Association for the Study of Popular Music (IASPM); the Lyrica Society for Word-Music Relationships; the Society for Ethnomusicology (SEM); the Society for Music Perception and Cognition (SMPC); and The Sonneck Society for American Music. The Steering Committee for this joint meeting invites proposals from members of the participating societies for sessions that focus on interdisciplinary topics in the scholarly study, teaching, or creation of music (including performance), in an effective session format involving members from two or more of these societies. A proposal for a joint session may be coordinated with a separate evening concert. Presentations in these sessions may be given in English, French, and Spanish. Proposals for joint sessions must describe the topic and state the purpose of the session in fewer than 1000 words, give contact information for the session coordinator (valid for all of 1999), and provide a one-page resume for each committed participant. The Steering Committee encourages proposals that include participants from many disciplines; it is expected, however, that scholars in the field of music be members in good standing of at least one of the participating societies; membership should be indicated on the resume. All participants must register for the conference. Six copies of each proposal should be sent no later than June 1, 1999 to Dr. Leslie Hall, Department of Philosophy and Music, Ryerson Polytechnic University, 350 Victoria Street, Toronto M5B 2K3, Canada. Proposals may also be sent before June 1, 1999 by electronic mail to Dr. Hall at Facsimile transmissions will not be accepted. Joint sessions for the Toronto 2000 meeting will be selected by the fifteen-member Steering Committee by December 1, 1999, before the SMT deadline for regular proposals for the meeting. Individuals participating in these special joint sessions may also appear on any one other session on the formal Toronto program. _______________________________________________ For further information, feel free to contact me at the e-mail address above (jschmalf@emerald.tufts.edu). Janet Schmalfeldt SMT President Tufts University home: 3 Cliff Street Arlington, MA 02476 (new zip) (781) 641-3317 _______________ Don't Stop Till You Get Enough: Consuming Popular Music CONFERENCE ANN0UNCEMENT/CALL FOR PAPERS DON'T STOP TILL YOU GET ENOUGH: CONSUMING POPULAR MUSIC The 1999 National Meeting of IAPSM-US (International Association for the Study of Popular Music, United States Branch) WHEN: Sept. 30-Oct. 2, 1999 WHERE: Middle Tennessee State University (MTSU), Murfreesboro, TN The 1999 IASPM/U.S. conference welcomes papers on the cultural roles of music and musicians; the means by which music gets to its audiences; and the ways in which music is interpreted and used by listeners in a variety of contexts. Within this broad frame, the conference will focus especially on consumption practices. In the study of popular music, attention is sometimes focused on producers at the expense of consumers: we still understand and investigate very little about who listens to popular music, how they hear it, and how that music affects their lives. Thus we encourage papers on this topic. In addition, we welcome disciplinary and interdisciplinary examinations of (among other topics): * various histories and traditions in popular music * institutions, politics, and popular music * race and popular music * the dominant discourses of popular music/popular music studies * gender studies and its relation to popular music studies * technology and new media * authorship issues in popular music * performance theory and performance styles * new ways of understanding both "popular" and "music" GRAD STUDENT AWARDS: IASPM-US will offer three awards of $200 each to the three best papers presented by graduate students. ABOUT THE LOCATION: Murfreesboro is located approximately 35 miles from Nashville. We will plan several panels, speakers, and recreational activities around music-making activities in the Nashville area. Deadline for proposals: May 15, 1999 Please send all proposals (submissions by e-mail are strongly encouraged) to: Professor Thomas Swiss Chair, Program Committee e-mail: thomas.swiss@drake.edu 1514 Buresh Ave Iowa City IA 52245 For more info, contact: Professor Paul Fischer Dept. of Recording Industry Box 21 Middle Tennessee State University Murfreesboro, TN 37132 Phone: (615) 898-5470 FAX (615) 898 5682 e-mail: pfischer@frank.mtsu.edu conference info is also available at: _______________ Arnold Schoenberg Center EVENT: Call for papers HOST: Arnold Schoenberg Center DATE: September 1999 DESCRIPTION: In September 1999, on the occasion of Arnold Schoenberg's 125th birthday, the Arnold Schoenberg Center and the Arnold-Schoenberg-Institute of the University of Music and Dramatic Arts in Vienna will jointly host a musicological symposium devoted to the topic "Arnold Schoenberg's Viennese Circle" and herewith extend an invitation for papers. The topic embraces Schoenberg and his Viennese pupils, the concept "school" with respect to the Viennese School, and the "Society for Private Musical Performances." Each section will include several papers. Applications should be submitted with a brief abstract to the Arnold Schoenberg Center, attention of Dr. Christian Meyer (Secretary-General) Schwarzenbergplatz 6 A-1030 Vienna Austria e-mail: For more information, contact the Arnold Schoenberg Center. CONTACT: Dr. Christian Meyer Arnold Schoenberg Center Meyer@schoenberg.at _______________ College Music Society Summer 1999 Opportunities for Professional Development Offered by The College Music Society This message contains information and updates on the following Summer 1999 events: (1) Center for Professional Development in Music Technology at Illinois State University, (2) Center for Professional Development in World Music at New England Conservatory of Music, (3) Weekend Workshop on Teaching Women and Gender in Popular Music at the University of Wisconsin, Madison, and (4) CMS International Conference in Kyoto, Japan ******************************************************* Center for Professional Development in Music Technology June 11-16, 1999 The Office of Research in Arts Technology (ORAT) Illinois State University, Normal, Illinois This year's Center for Professional Development in Music Technology will provide beginning to intermediate levels of training with three tracks of Web development with a special emphasis on music tools, Macromedia Director training for music software development and notation and sequencing tools to teach orchestration and arranging. The five-day experience will give participants the opportunity to explore these possibilities, seek answers to questions related to music technology, and work in a cross-platform environment with the large resources of music software, hardware, and well-qualified professional expertise on hand in the arts technology program at Illinois State. Special events and presentations are also planned for each day including a night at the Shakespeare Festival. The three tracks this summer provide enough new areas of study that previous attendees to the workshop should consider returning to the summer Institute. Instruction will consist of lecture and demonstration, followed by hands-on experiences in the four Macintosh and Windows labs. Registration is available for "Internet Observers" who would like private access to RealAudio broadcasts of the lectures over the Internet and access to the Web-based teaching materials. We have made many changes and improvements that include: * New G3 Macintosh systems have been purchased this year for the Mac multimedia lab * Upgraded software (e.g. Finale 98, Cakewalk, QuickTime 3.0, and more) * New high-tech lecture room for morning open sessions * Internet observer delivery will be expanded to provide RealVideo as well as RealAudio support * New staff additions with Henry Panion and Joe Bernert * Motel as well as dorm options for housing Three nationally known music technology faculty will provide the primary instruction for the Center: Peter Webster, Henry Panion, and David Williams. Henry has unique talents, as arranger for Stevie Wonder, in teaching the use of MIDI software for arranging and orchestration and would provide new talent to the instructional mix. Webster and Williams, authors of Experiencing Music Technology, bring a broad range of experience with multimedia, web, and classroom applications. Additional Illinois State ORAT staff support will be provided by James Bohn, Jody DeCremer, David Kuntz and Joe Bernert. For more information, see, Tuition: Before April 30: CMS members, $450. Non-CMS members, $525. Internet Observer, $200. After May 1: CMS members, $550. Non-CMS members, $625. Internet Observer, $25 ****************************************************** Center for Professional Development in World Music New England Conservatory of Music Boston, Massachusetts Again offered in collaboration with the New England Conservatory Summer Intercultural Institute, which is now in its sixth year. The Institute is an immersion experience emphasizing oral learning through close contact with master performers and scholars, integration of performance with cultural study, and an open environment of cross-cultural inquiry. Session I: July 6-11, 1999 East Africa and Haiti. Baganda music from Uganda features drums and xylophones and will be taught by James Makubuya of the Massachusetts Institute of Technology and Andrew Mangeni of the Smithfield, Rhode Island schools. They will also offer a separate course of instruction in teaching the music of East Africa in the K-12 classroom. Drum ensembles, songs, and dances of Haitian Vodun will be taught by Gerdes Fleurant of Wellesley College, Patric LaCroix of the Patric LaCroix Dance Company, and Fritz ("JuJu") Joseph of Boston. Session II: July 12-17, 1999 North India and Turkey. Improvisation and composition in classical Hindustani raga and tala will be taught for Indian and Western instruments and voice by Peter Row of New England Conservatory (sitar), George Ruckert of the Massachusetts Institute of Technology (sarod), and Jerry Leake. Improvisation and composition in classical Ottoman makam and usul will be taught for Turkish and Western instruments and voice by Ihsan Ozgen of Istanbul Conservatory (kemence, tanbur, bendir, voice) and Center/Institute Director Robert Labaree of the New England Conservatory. Session III: July 12-17, 1999 Klezmer: Jewish Folk Instrumentalists and Their Music. A rare opportunity to learn the klezmer style and repertoire directly from master musicians of Moldova and Bessarabia traditions: Yosef Kagansky from Toronto (accordion), Gershon Goldenshteyn from New York (clarinet), and Hankus Netsky of the New England Conservatory. ****************************************************** Weekend Workshop on Teaching Women and Gender in Popular Music June 11-13, 1999 University of Wisconsin, Madison The teaching of subject matter concerning women and gender in music has burgeoned in the past several years, supported in part by constantly expanding research in a variety of disciplines. To enhance professional development for teachers of women and gender in music, The College Music Society sponsors a variety of activities. Its weekend workshops are modeled on week-long summer institutes on women and music held in 1993 and 1996, and designed in part for participants who are not able to invest in a week-long activity. The workshops are of relevance to persons new to teaching women and gender in music, as well as to those seeking a short refresher course, the latest in teaching materials, and new contacts with colleagues around the country involved in this subject matter. The workshops should appeal to graduate students and junior faculty new to teaching, seasoned teachers new to women and gender courses, and veterans of women's studies. The first weekend workshop on women and gender in music was held January 1998 at the University of Texas-Austin, the second in February 1999 at Agnes Scott and Spelman Colleges. The workshop in Madison will be devoted to teaching women and gender in popular music. Workshop formats include large group sessions, smaller breakout discussion groups, and unstructured time for individual work. Some reading materials may be assigned in advance, and participants may be asked to bring some of their own resources to share. Participants may present reports on their research and participate in informal concerts and reading sessions of repertoire. The faculty facilitator is Susan Cook, Associate Professor, University of Wisconsin, Madison, and well-known author of a variety of women and gender studies in music. ****************************************************** CMS International Conference in Kyoto, Japan Thursday and Friday, June 24 and 25 Kanazawa, Japan--Pre-Conference Workshop: "An Introduction to Japanese Culture I" Visit Nishida Family Garden, adjoining Kenrokuen, one of Japan's three most beautiful gardens, for an Urasenke-school tea ceremony, "bento" box dinner with concert featuring hand drum, flute, and koto. Also Noh master class, traditional and modernist flower arranging, and more. Sunday and Monday, June 27 and 28 Kyoto, Japan--Pre-Conference Workshop: "An Introduction to Japanese Culture II" Sabie house--located alongside Kyoto's famous Philosopher's Walk--will provide a priest-led Buddhist temple architecture tour, instruction in the tea ceremony (Urasenke school), including philosophy, teahouse architecture, the use of incense and flowers, and more. Also receive a lesson in Japanese phrases and greetings, with a few words about the language's relationship to the people and culture and learn some traditional Yokyoku songs with an experienced Yokyoku practitioner, who will prepare his teaching selections in Western notation. And enjoy a visit to a Japanese home (in small groups) for an informal lesson in Japanese cooking and table etiquette with the hostess. Monday evening-Thursday, June 28-July 1 1999 CMS International Conference Monday evening, June 28--Conference Opening Reception Tuesday, June 29--Issues in the Transmission of Musical Knowledge in Japan. Plenary addresses and discussions with: Yoshimi Tagahagi (Tokyo Gakugei University) and Robert Werner (University of Cincinnati) (both past presidents of the International Society for Music Education): "Professional Education of Musicians in the United States and Japan." Silvain Guignard (Doshisha Women's College of Liberal Arts, Kyoto): "Fifteen Years of Study with a Living National Treasure," a discussion of his fifteen-year apprenticeship to Madame Yamazaki Kyokusui, considered to be the foremost biwa player in Japan. Kimiko Ohtani (Kochi University): "Non-Western Musics in Schools and Universities in Japan," focusing on the problems and difficulties faced by music educators as they consider the future of music education in Japan at the elementary, high school, and university levels. Akeo Okada (Kobe University): "About the Reception of European Classical Music in Japan," covering western music in Japan as a symbol of social status, its use as "official" music, and traditional Japanese elements "hidden" in the education system of European classical music in Japan. Tuesday will conclude with a concert of biwa music performed by Dr. Guignard, and of gagaku music performed by Tomihisa Hida and his pupils. Guji (Reverend) Hida is priest of the Ichihime Jinja Shinto Shrine in Kyoto and heads a foundation dedicated to teaching Japanese traditional musics to young people. Wednesday and Thursday, June 30 and July 1--A concert, including Works by CMS Composers, and a variety of presentations of interest, covering musics of Japan, Europe, North America, and South America. Friday, July 2--Post-conference day trip to Hiroshima Peace Park and Miya Jima. Miya Jima is considered (along with Mt. Fuji) to be the destination of one of the three most important pilgrimages in any Japanese person's life. Costs (all lodging costs are per person, per night, double occupancy): Kanazawa workshop $245 Kanazawa inn lodging 38 or 45 Kanazawa hotel lodging 44 Kyoto workshop 230 Kyoto inn lodging 55 107 Kyoto hotel lodging 64 78 Conference registration 315 Hiroshima tour 45 (does not include travel--see below) Air travel: the best fares are "consolidators" fares, available from most travel agents. Phone Wide World of Travel (1-800-735-7109) or any travel agent, and ask for a quote. Rail travel: The new Kansai airport at Osaka is 55 minutes by train from Kyoto. Below are sample itineraries and costs, based upon the most economical combination of fare options (US$1 = 110 yen). (1) Kansai, Kanazawa, Kyoto, Hiroshima, Kyoto, Kansai $308. (2) Kansai, Kanazawa, Kyoto, Kansai $108. (3) Kansai, Kyoto, Hiroshima, Kyoto, Kansai $237. (4) Kansai, Kyoto, Kansai $37. Instructions will be provided in the registration packet detailing how the adventurous can easily keep food costs under $20/day. Eating well for $30/day is possible, provided hotel restaurants are avoided! ****************************************************** For more information on these events, including registration materials, please contact: THE COLLEGE MUSIC SOCIETY 202 West Spruce Street Missoula MT 59802 phone: 406-721-9616 fax: 406-721-9419 email: cms@music.org Or see the CMS website at ****************************************************** _______________ New England Conference of Music Theorists FOURTEENTH ANNUAL MEETING MARCH 27-28, 1999 (Sat.-Sun.) Paine Hall, Harvard University Cambridge, Massachusetts PROGRAM Abstracts of presentations may be viewed on the NECMT website, above; follow the Annual Meeting link. Saturday, March 27 9:30-12:30 Music + Drama + Text Deborah Burton, Harvard University, chair "The Strategic Use of Tonality in Twentieth-Century Opera: A Linear-Dramatic Analysis of Debussy's _PellÈas et MÈlisande_" Edward Latham, Yale University (elatham@pantheon.yale.edu) "Schoenberg's 'Vagrant Chords' and Webern's _Dehmel Lieder_" Matthew Shaftel, Yale University (matthew.shaftel@yale.edu) "On Bodily Music, Disembodied Codas, and Beethoven's _Egmont_" Elizabeth Paley, School of Fine Arts, University of Kansas (espaley@falcon.cc.ukans.edu) "The Force of Naming: _Grimes_ and the Operatic Speech Act" Philip Rupprecht, Consrvatory of Music, Brooklyn College, CUNY (PhilipR@brooklyn.cuny.edu) 2:00-3:15 Keynote Address "What Song Cycles Do" Peter Westergaard, Princeton University 3:30-5:00 Schubert's Mirror: Reflecting on Lieder Michael Schiano, The Hartt School, chair "Text, Context, and Conceptions of Distance in Schubert's 'In die Ferne'" Edward Gollin, Harvard University (egollin@fas.harvard.edu) "Intimate Revelation or _Nachtstueck_ of Romantic Irony?: Two Ways of Reading Schubert's _Der Wanderer_, D. 649" James Parsons, Southwest Missouri State University (jap614@mail.smsu.edu) Responses Richard Lalli, Yale School of Music Janet Schmalfeldt, Tufts University 8:30 Keynote Recital Richard Lalli, Yale School of Music, baritone Janet Schmalfeldt, Tufts University, pianist performing Schubert _Sechs Moments musicaux_, a group of Schubert songs, and Schumann _Dichterliebe_ co-sponsored by NECMT and the Harvard Music Department Sunday, March 28 9:30-12:30 Inner and Outer Time: Aspects of Music in the Fourth Dimension Hali Fieldman, University of Missouri at Kansas City, chair "A Marxian Approach to Schubert" Marlon Feld, Columbia University (mbf21@columbia.edu) "Walter Harburger's _Metalogik_: The Rhythmic Theory" Martin Steffen, University of California at Santa Barbara (6500stfn@ucsbuxa.ucsb.edu) "Improvisation as Continually Juggled Priorities: Julian Cannonball Adderley's _Straight, No Chaser_" Karim Al-Zand, Harvard University (alzand@fas.harvard.edu) "The Edge of Intelligibility: Time, Memory, and Analytical Strategies for _Clarinet and String Quartet_ (1983) by Morton Feldman" Mark Janello, School of Music, University of Michigan (mjanello@umich.edu) _______________ International Conference on Jean Sibelius INTERNATIONAL CONFERENCE ON JEAN SIBELIUS IN HELSINKI IN 2000 This is the first announcement and call for papers for the 3rd International Jean Sibelius Conference to be held in Helsinki on December 7-10, 2000. This event belongs to the program celebrating Helsinki as one of the cultural capitals of Europe that year. It will be organized by the Sibelius Academy, Department of Musicology at the University of Helsinki and the Musicological Society of Finland. The main topics of the conference are the life and works of Jean Sibelius, manuscript studies, theater and vocal music, program music and intertextuality, gender and Sibelius, nationality and politics, reception and performance studies. The Honorary Committee of the conference consists of: Professor emeritus Fabian Dahlstrom (Abo Academy), Professor Glenda Dawn Goss (University of Georgia, Athens), Professor James Hepokoski (University of Minnesota), Professor Timothy Jackson (North Texas University), Professor Edward Laufer (University of Toronto), Dr. Robert Layton (London), Professor Tomi Makela (University of Magdeburg), Professor Erkki Salmenhaara (University of Helsinki) and Dr. Marc Vignal (Paris). The organizing committee consists of: Dr. Kari Kilpelainen (Jean Sibelius Gesamtausgabe Project), Ms. Anna Krohn, Secretary (Sibelius Academy), Dr. Eija Kurki (Finnish Cultural Foundation), Professor Veijo Murtomaki (Sibelius Academy), Rector Lassi Rajamaa (Sibelius Academy) and Professor Eero Tarasti, Chair (University of Helsinki). We encourage any music scholar working on Sibelius studies in the world to attend the conference either as an active participant delivering a paper (of 30 minutes, including time for questions) or as a passive one. The deadline for registering for the conference with a paper is December 31, 1999. The abstract (one page) and short CV (half a page) should be sent to the Secretariat of the conference. Participation fee of USD 100 (active participants) or USD 50 (passive participants) should be paid at the conference. The conference is organized in the proximity of the International Jean Sibelius Violin Competition taking place in Helsinki on Nov. 18 - Dec. 2, 2000 and coinciding with the 135th anniversary of the composer on Dec. 8. A visit to the home of Jean Sibelius at Ainola, Jarvenaa (25 kms from Helsinki) will be organized as well. The papers of the conference will be published (the proceedings from the earlier international Sibelius conferences in 1990 and 1995 can be ordered from the Secretariat). Helsinki, January 21, 1999 Eero Tarasti Professor, Chair Anna Krohn Secretary of the Conference All registrations and inquiries should be addressed to: Anna Krohn, Sibelius Academy, P.O.Box 86, 00251 Helsinki, Finland tel. +358-9-405 4645, fax. +358-9-405 4603 e-mail: anna.krohn@siba.fi _______________ West Coast Conference for Music Theory and Analysis Rocky Mountain Society for Music Theory The following information, as well as registration and travel information, is also available on the web at the RMSMT web site: West Coast Conference for Music Theory and Analysis and Rocky Mountain Society for Music Theory Joint Meeting, April 16-18, 1999 Stanford University, Stanford, CA THURSDAY, APRIL 15 2:00-6:00 Pre-conference workshop Introduction to Humdrum David Huron [Enrollees are welcome to attend the graduate seminar on music representation at which David will be a guest speaker on Thursday, 11-1] FRIDAY, APRIL 16 9:30-9:45 Opening Remarks Stephen Hinton, Chair, Music Department, Stanford Jonathan Berger, Acting Head, CCRMA Eleanor Selfridge-Field, CCARH 9:45-12:00 Session I Preferential Strategies in Elliott Carter's Second Quartet (1959) Beth Crafton, University of North Texas Coherence in Prokofiev's 'Wrong-Note' Music: Tonal and Motivic Structures Deborah Rifkin, Eastman School of Music 'Music is an Inexhaustible Sea, No Amount of Paper can Contain its Rules!': The Concept of Tonordnung in Joseph Riepel's Anfangsgruenden Stefan Eckert, SUNY Stony Brook 1:30-3:45 Session II Interstitial Music Tom Baker, University of Washington The Edge of Intelligibility: Time, Memory, and Analytical Strategies for "Clarinet and String Quartet" (1983) by Morton Feldman Mark Janello, University of Michigan "Quartal" Pitch-Class Set Theory and Prokofiev's "There are Other Planets" Daniel Bertram, Yale University Seven Steps to Heaven: A New Two-Part Species Counterpoint Henry Martin, Rutgers University 4:00-5:00 Keynote Address: Bach's Parallel-Section Constructions Joel Lester, Dean, Mannes College of Music 5:15-5:45 Tour and demo: Archive of Recorded Sound, w/ Richard Koprowski 5:30-6:30 Reception and lab demos: CCARH SATURDAY, APRIL 17 9:00-11:30 Session III Schoenberg in Stravinsky's Ears: A Theoretical Approach Christoph Neidhoefer, Harvard University Polyphonic Adjustments to Meter in Torke's "Adjustable Wrench" John Roeder, University of British Columbia Musical Agency and the Communal Web Roger Graybill, University of Texas at Austin Mozart 'In Medias Res' Poundie Burstein, Hunter College 11:40-12:00 Business Meetings 12:15-1:15 Lunch [price included with early registration] 1:15-2:00 Demos and Tours of CCRMA 2:00-5:15 Session IV Compositional Algorithms and Composers' Creative Thought: Towards an Understanding of the Implications of Brian Ferneyhough's Process of Composition Pamela Madsen, UC San Diego Counterpoint Assistant (CPA) David Evan Jones, UC Santa Cruz Issues of Integrated Schematic Memory and Context in a Neural Network Model of Cognition of Music Jonathan Berger, Dan Gang, Stanford University Categorical Perception, Ordering Effect, and Interval Boundaries Leigh VanHandel, Stanford University A Computational System for Metrical Analysis David Temperley (Ohio State University) and Daniel Sleator (Carnegie Mellon University) Discussion: David Cope, University of California, Santa Cruz 5:30-6:30 Music Department Reception 7:00-10:00 Banquet [pre-registration required] Swagat Indian Restaurant, 2700 W. El Camino Real, Mountain View Dinner entertainment and short commentary Parag Chordia, sarod; Dan Schmidt, tabla SUNDAY, APRIL 18 9:00-12:45 Session V Chick Corea's "Crystal Silence": Tonal, Modal, or Post-Tonal? Richard Hermann, University of New Mexico Subverting the Dominant Paradigm? Shifting Concepts of V in Influential 19th Century Theories and Some Implications for Today David Kopp, University of Washington French Connections Anton Vishio, William Paterson University The Mono Mix of Sgt. Pepper Michael Hicks, Brigham Young University Metrical Dissonance in the Music of Chopin Harald Krebs, University of Victoria Program Committee: Steve Larson, Chair; Jack Boss; Jonathan Berger; Jonathan Bernard; Lisa Derry; Stephan Lindeman Local Arrangements: Eleanor Selfridge-Field, Chair; Leigh VanHandel; Craig Sapp; Fred Spitz ______________ Music Theory Society of New York State The program for the 1999 meeting of MTSNYS at Ithaca College on 10-11 April is available on the MTSNYS home page at The MTSNYS home page also contains all relevant conference information: registration form, travel directions, and housing. If you would like additional information, please contact me at the address below. Mary I. Arlin, President MTSNYS arlin@ithaca.edu Office: (607) 274-3350 ====================== 4. Employment Ohio State University: Post-Doctoral Fellowship in Music Cognition Lancaster University, Music Department Lectureships University of Massachusetts at Amherst, Music Theory The University of Dublin (Trinity College, School of Music), Chair of Music Texas Tech University School of Music, Music Theory Ithaca College School of Music, Music Technology Kansas State University, Theory/Applied Music (horn preferred) _______________ Ohio State University The School of Music at the Ohio State University is pleased to offer a Post-doctoral Fellowship in Music Cognition. The fellowship provides one year of support for full-time music research. Candidates choose their own program of research, although preference is given to studies in listening, performance, analysis, modeling and cross-cultural pheno-mena. The fellowship is designed to further a candidate's training and research experience in music cognition and systematic approaches to music theory. The stipend for a twelve-month period is $25,000 plus health benefits. Candidates must have completed a doctoral degree at the time the fellowship starts. The deadline for applications is May 1st, 1999. For further information contact Prof. David Huron or visit _______________ Lancaster University Music Department We are advertising for two lectureships in the Music Department (not CTI!) to start in the autumn. Applications are invited for two full-time posts commencing 1 September 1999. Applicants must be high-quality researchers with a demonstrable commitment to teaching. No research specialisation is precluded, but preference may be given to those with an interest in the eighteenth or nineteenth century, computer applications, or music since 1940. Details can be found on the Web at: Please pass this call on to any colleagues you feel may be interested. _______________ University of Massachusetts at Amherst The University of Massachusetts at Amherst announces two Visiting Appointments in Music Theory (non-tenure-track) for the 1999-2000 academic year. Core responsibilities include teaching undergraduate courses in theory and analysis. One or both positions will involve teaching aural skills and graduate courses. Requirements include a Ph.D. or ABD in Music Theory and a record of excellence in college or university teaching. Desirable qualifications include background and interest in the pedagogy of theory and/or aural skills, and current research activity Rank and salary dependent on qualifications. Review of applications begins February 26, 1999; the process will remain open until the position is filled. Applicants should send a current curriculum vitae, cover letter, representative samples of scholarship, evidence of excellence in teaching, and a minimum of three letters of reference to: Prof. Gary S. Karpinski, Chair, Theory Search Committee, Department of Music & Dance, University of Massachusetts, Amherst, MA 01003. The University of Massachusetts is an Affirmative Action/Equal Opportunity Employer. Women and minorities are encouraged to apply. _______________ University of Dublin Trinity College School of Music Trinity College, Dublin, is seeking outstanding candidates, with an international reputation, for the following appointment in the School of Music, tenable from 1 October 1999 (or as soon as possible thereafter): Chair of Music (1764) Candidates should have a distinguished record of achievement in research and a strong commitment to teaching. The person appointed will serve as Head of Department in accordance with College regulations concerning headship. Appointment will be made at an appropriate point of the professorial salary scale, currently IR£48,175 - IR£62,250. Further particulars of the appointment, including details of salary and other benefits, may be obtained from Michael Gleeson Secretary to the College West Theatre Trinity College Dublin 2 Telephone: +353 1 608 2197/1722 Fax: +353 1 671 0037 e-mail: elmesk@tcd.ie to whom formal application may be sent to arrive by the preferred closing date of Monday, 15 March 1999. Further details regarding the Department may be obtained on the website: Trinity College is an equal opportunities employer Publications in which advertisement will be placed: The Irish Times The Times Higher Educational Supplement The Chronicle of Higher Education (US) The Guardian _______________ Texas Tech University POSITION/RANK: Music Theory; full time, tenure track position at the Assistant Professor rank INSTITUTION: Texas Tech University School of Music, Lubbock, Texas 79409 QUALIFICATIONS: Doctorate required. Must demonstrate promise of scholarly achievement in music theory and excellence in teaching undergraduate and graduate music theory. JOB DESCRIPTION/RESPONSIBILITIES: Responsibilities include teaching graduate and undergraduate music theory, serving on graduate committees, advising graduate theses and dissertations, and some administrative duties within the theory/composition division. Continuing scholarly productivity and service will be expected in order to qualify for tenure and promotion. SALARY RANGE: Salary and benefits are competitive. ITEMS TO SEND: Send detailed application letter, curriculum vitae and 3 current letters of recommendation to: Robert Walzel, Interim Director; TTU School of Music; P.O. Box 42033; Lubbock, TX 79409-2033 DEADLINE: 03/01/99 CONTACT: Robert Walzel, Interim Director; TTU School of Music; P.O. Box 42033; Lubbock, Texas 79409-2033 Phone: 806-742-2270 FAX: 806-742-8284 e-mail: rwalzel@ttu.edu _______________ Ithaca College The Ithaca College School of Music announces a full-time, tenure-eligible position in music technology at the rank of assistant professor, beginning Fall 1999 pending funding. Responsibilities include: developing and teaching music technology courses at introductory and advanced levels, administering two music computer facilities and additional smart classrooms, and assisting faculty in the development of CAI skills. Additional duties include coordinating repair, maintenance, upgrade, and overall technology initiatives for the School of Music. Duties may include teaching courses within individual's music specialty field. Qualifications: 1. Masters degree required, completed doctorate in music preferred. Preference may be given to individuals who are experienced in the pedagogy of music technology. 2. College teaching experience and administrative experience preferred. 3. Candidates must have a firm commitment to providing comprehensive music technology skills for undergraduate music majors and to training future teachers in the area of music technology. The School of Music is a Macintosh-based facility. Applicants should send a letter of application, resume, and supporting credentials to Chair, Music Technology Search Committee School of Music Ithaca College Ithaca, New York 14850-7240 Review of applications will begin on April 1 1999 and will continue until position is filled. Ithaca College is an Equal Opportunity/Affirmative Action College. Members of underrepresented groups (including people of color, persons with disabilities, Vietnam veterans and women are encourage to apply. _______________ Kansas State University Position: Theory/Applied Music (horn preferred) Duties: A full-time, tenure track, nine-month appointment. Teach courses in department's Comprehensive Musicianship sequence and coordinate graduate assistants assigned to courses in ear-training and sight singing. Graduate course assignments possible depending on candidate's strengths. Work closely with other theory faculty in curriculum review/development. Recruit and maintain an applied studio, perform in appropriate faculty ensembles. Other duties as assigned by department head. Qualifications: Completed doctorate preferred, work beyond the Master's required. Successful studio and classroom teaching and performing experience required. Rank and salary: Commensurate with experience and qualifications. Starting Date: 8 August 1999 Application procedure: Send letter of interest, curriculum vitae, three letters of recommendation, transcripts, sample publications, and performance tape (audio cassette or videos of live performance) to: Dr. Gary Mortenson Chair, Theory/Applied Music Search Committee Department of Music 109 McCain Auditorium Kansas State University Manhattan, KS 66506-4702 Inquiries are welcome: 785/532-5740 e-mail: garym@ksu.edu Review of materials begins 15 March 1999. Kansas State University, founded in 1860, is the first and one of the leading land-grant universities in the United States. Kansas State is ranked first in the nation among public universities in producing Marshall, Rhodes, Truman, and Goldwater Scholars and was recently named one of America's best buys in university education by MONEY MAGAZINE. The university is composed of nine colleges and has an enrollment of 20,000 students with more than 200 majors and options available to its students. KSU's mission is rooted in the land-grant principles of teaching, research, and service to people. The Manhattan campus is unique with its native limestone buildings located on a 668-acre area in the heart of the rolling Flint Hills of Kansas. The Department of Music is located administratively in the College of Arts and Sciences, the largest of the nine university colleges. It has 28 faculty members and a student population of over 150 majors. The department offers the Bachelor of Music, Bachelor of Arts in Music, Bachelor of Music Education, and the Master of Music degrees. Music programs service well over 15% of the entire university population. Manhattan (population 38,000) is located in northeastern Kansas, 115 miles west of Kansas Ciety on Interstate 70. Fort Riley military reservation is only nine miles away. KANSAS STATE UNIVERSITY IS AN EQUAL OPPORTUNITY EMPLOYER. KSU ACTIVELY SEEKS DIVERSITY AMONG ITS EMPLOYEES. ====================== 5. New Dissertations Konstantinou, Elena. "Nikos Skalkottas: The Piano Music." University of Reading, 2001. Nelson, Thomas K. "The Fantasy of Absolute Music." University of Minnesota, 1998. Samplaski, Arthur G. "A Comparison of Perceived Chord Similarity and Predictions of Selected Twentieth-Century Chord-Classification Schemes, Using Multidmensional Scaling and Clustering Techniques." Indiana University, 2000. Santa, Matthew S. "Studies in Post-Tonal Diatonicism: A Mod7 Perspective." City University of New York, 1999. _______________ AUTHOR: Konstantinou, Elena TITLE: Nikos Skalkottas: The Piano Music INSTITUTION: University of Reading, Reading, U.K. BEGUN: October 1998 COMPLETION: October 2001 ABSTRACT: My research is concerned with the keyboard music of Nikos Skalkottas. Most of it is unpublished and unperformed, and I propose to assess it with the assistance of supporting analytical methods, addressing the primary sources. Problems to be examined include those surrounding the validity of the texts of the composer currently available and the general appraisal of these in the context of the output of Skalkottas, and his contribution to twentieth-century compositional technique, especially in relation to the structural ideals of his teacher, Schoenberg. Significantly, Skalkottas' idiosyncratic use of serial and developmental techniques is of great interest, particularly viewed in conjunction with the elaborate aesthetic, as opposed to purely technical, concepts with which the majority of Skalkottas' writing is concerned. KEYWORDS: Skalkottas, keyboard music, analytical, primary sources, serial, structural, developmental techniques, Schoenberg, aesthetic concepts, writings. TOC: CONTACT: elenak@zetnet.co.uk Voice:+44(0)181 948 6663 Fax: +44(0)181 948 6663 _______________ AUTHOR: Nelson, Thomas K. TITLE: The Fantasy of Absolute Music INSTITUTION: University of Minnesota BEGUN: COMPLETED: June 1998 ABSTRACT: This dissertation addresses the genealogy of the fantasy of absolute music. It begins with the pastoral of reconciliation in a prelapsarian alternative world compensating for the dysfunctions of the social world. It concludes with the dissolution of the musical means to support that fantasy. The Lieder of Schubert comprise the primary repertory of this investigation of Austro-Germanic art music. The central chapters, 3 and 4, develop a theory of romantic tonality based on Schubert's own poetics of the bVI complex as manifested in his songs. Two preliminary chapters provide a wider cultural-historical context of Schubert's practice. The first chapter explores the literary and artistic figurations of the pastoral, the socio-psychological motivations for fantasy, and Schiller's philosophical theorization of the elegiac idyll as an allegorical idealization of the absolute. Chapter 2 discusses the poetics of 18th-century Galant-Classical musical discourse. The legacy of the fantasy of absolute music in the 19th century coincides with the confusions and mystifications of aesthetic ideology. The concluding chapters discuss how the allegorical approach to fantasy, cultivated in Early German Romanticism as a collaboration of philosophy and poetics, succumbed to the desire for a purely symbolic certainty in an age marked by growing pessimism. By the end of the century, the desire for the musical absolute had driven the musico-poetic language of common practice tonality toward its own absolution. Chapter 6 includes a detailed interpretation of two songs composed in the 1880s that illustrate the full potential of bVI musical poetics. The methodological premise of the dissertation rests on an Early Romantic form of dialectical mediation based on the metaphor of Schweben (hovering or fluctuation) as a means of transcendence. Schweben yields a fundamental concept of the romantic fantasy of absolute music itself and the key to its understanding. Similarly, the bVI provides an allegory for German music history in which the aesthetic experience of tonality is itself subject to a temporal fate of disillusionment. Works examined include art by Klinger, Poussin and Watteau; essays by Nietzsche, Schiller, Schenker and Wackenroder; music by Beethoven, Brahms, Mahler, Marenzio, Mozart, Schubert, and Wagner. KEYWORDS: submediant, lieder, harmony, effect, pastoral, galant, aesthetics, ideology, Arcadia TOC: Introduction: Accorde, or The Fantasy of Absolute Music 1 Chapter 1: Pastoral Reconciliation of Modern Estrangement 1. Introduction 44 2. Pastoral Origins 52 a. The Golden Age Pastoral in Myth and Bible b. Arcadia: Home of the Pastoral Fantasy c. Nature as a Pastoral Alternative to Arcadia 3. Pastoral Motivation 83 a. The Dysfunctions of Order b. Surplus Order Pastorals: Royal and Romantic c. The King's Court as Pastoral d. Literature as Aesthetic Compensation e. Pastoral of Nature: Aristocratic Romanticism 4. Ut Poesis Pictura: the Painted Pastoral 126 a. The Sister Arts b. Romantic Absolutism c. Et in Arcadia Ego f. FÍte Galante 5. Schiller's Naive and Sentimental: the Elegiac Idyll 164 a. Introduction b. Sentimental man c. Toward the elegiac idyll d. Beyond the elegiac idyll g. Schiller's legacy for pastoral thought Chapter 2: The Romanticism of Galant Music 206 1. The Galant Compromise a. Envy and Resentment b. French Court to German Bourgeoisie 2. The Figural Language of Galant Musical Discourse 227 a. Marked Correlations b. Battle of the Pastorals c. Toward a Dictionary of Musical Figuration 3. A Fantasy of Absolute Music: The Pastoral Replete 261 a. Topological Inventory b. Scholarship and the Syntactical Fallacy c. A Pastoral of Galant Courtship 4. Questions of Reception 304 a. The Noncontemporaneous b. Alternative Autonomies 5. Assaulting the Galant 322 a. The Origins of the Sturm und Drang b. From the Storm-Style to Sturm und Drang c. Mozart's Opera of Storms 6. A Second, Romantic Practice 358 a. Toward the bVI complex b. Conclusion Chapter 3: Theory of the bVI Complex: The Logic of its Arcadian Poetics 1. Introduction 379 2. The Arcadian Pastoral 383 3. Why the bVI for Arcadia? 388 4. The bVI Complex 401 a. Progressions by Third b. bVI Effect c. Submerged bVIs d. More Members of the bVI Family e. The Rogue bVI f. An Alternative Route to Distant Parts 5. The Early bVI: A Subconscious Metaphor? 433 6. Musical Scholarship and the Romantic bVI 451 7. The Arcadian bVI: Elegiac Idyll of Romantic Music 475 a. On the Value of the Ideal Type b. Initial Setting c. Entry into bVI Fantasy d. Residence: Illusion e. The Exit: Dis-illusionment of the Fantasy f. Final Reality Chapter 4: Schubert bVI Song Studies Part I: Schubert Studies 502 a. Introduction b. Approaches to Lieder c. The bVI and Schubert's Dysfunctional World d. General Observations on Schubert's bVIs Part II: bVI Songs 539 a. An den Mond, D.193 b. Schaefers Klagelied, D.121 c. Ihr Bild, D.957 #9 d. Nacht und Traeume, D.827 e. Die Goetter Griechenlands, D.677 h. The bVI as a Sign of Mental Clarity (1) Erstarrung, D.911 #4 (2) Fahrt zum Hades, D.526 (3) Aus Heliopolis II, D.754 i. Ihr Grab, D.736 j. Tonic as bVI (1) Geistes-Gruss, D.142 (2) Der Alpenjaeger, D.588 (3) Grenzen der Menschheit, D.716 (4) Selige Welt, D.743 (5) Am Fenster, D.878 (6) Laube, D.214 (7) Der Fluss, D.693 (8) Der Hirt auf dem Felsen, D.965 (9) Der Musensohn, D.764 (10) Bie dir allein, D.866 (11) Staendchen, D.889 (12) Mein!, D.795 #11 k. Meeres Stille, D.216 l. bVI = V as pivot to bII (1) Gruppe aus dem Tartarus, D.583 (2) Prometheus, D.674 (3) Szene aus Goethes Faust, D.126 (4) Wehmuth, D.772 (5) Suleika I, D.720 (6) Ganymed, D544 (7) Der Zwerg, D.771 m. Auf dem Flusse, D.911 #7 n. The song cycles as tonal 'whole' (1) Winterreise, D.911 (2) Schwanengesang, D.957 o. Kennst du das Land, D.321 (1) Beethoven (2) Schubert p. Conclusion Chapter 5: The Poetics of Absolute Music, or Schweben and its Ideological Discontents 1. Introduction: Song and Absolute Music 657 2. Allegory and Symbol as Philosophy and Ideology 664 3. Words and Music: Uneasy Accord 677 4. The Rebirth of Spirit in the Music of Allegory 690 5. As if a Presence in Music 700 6. The Foaming Chalice of Romantic Music 707 7. German Music History: The Long, Hard Line 721 Chapter 6: The Absolution and Dissolution of Pastoral Fantasy 1. Schenker as Arch-allegorist 740 2. Brahms: "Wie melodien zieht es" 755 3. Mahler: "Wenn mein Schatz Hochzeit macht" 782 4. Symptoms of a Fatal Condition 810 List of Works Cited 866 Appendices Appendix # 1: Concordance of bVIs in Schubert's Lieder 903 Appendix # 2: Longer German Quotations 947 Appendix # 3: Outline of Pastoral Types in Western Culture 959 Appendix # 4: Examples of music and art 969 CONTACT: Thomas K. Nelson 2733 40th Ave. South Minneapolis, MN 55406 (612) 724-1651 tknlsn@earthlink.net _______________ AUTHOR: Samplaski, Arthur G. TITLE: A Comparison of Perceived Chord Similarity and Predictions of Selected Twentieth-Century Chord-Classification Schemes, Using Multidmensional Scaling and Clustering Techniques INSTITUTION: Indiana University BEGUN: November 1998 COMPLETED: May 2000 ABSTRACT: There seems to be an implicit consensus among adherents of several classification systems for the chord-types of twentieth-century Western art music that in some sense they reflect listeners' perceptions. This dissertation will undertake one perceptual study to test whether there is support for such a view of these theories. Subjects will listen to pairs of chords under several different experimental conditions as played by a computer program, which will collect their ratings of the chords' similarities. Two different pools of subjects will be recruited, to assess the effects of experience in listening to non-tonal music. Subjects' responses will be pooled and analyzed using multidimensional scaling and cluster analysis. The derived configurations will be compared to the (qualitative) clustering predictions of several chord-classification systems, to see if there is any perceptual support for their grouping criteria. Emphasis will be given to testing perceptual support for theories by Forte and Hindemith, but the method is also applicable to other classification systems. KEYWORDS: music cognition, music perception, atonal analysis, pcset theory, Hindemith, multidimensional scaling, cluster analysis TOC: CONTACT: Art Samplaski Music Theory Dept. IU School of Music Bloomington, IN 47405 _______________ AUTHOR: Santa, Matthew S. TITLE: Studies in Post-Tonal Diatonicism: A Mod7 Perspective INSTITUTION: City University of New York BEGUN: February 1998 COMPLETED: May 1999 ABSTRACT: There is a substantial body of music written in the 20th century in which the notes of a diatonic scale predominate, but which often lacks one or more of the other basic requirements necessary to be considered tonal: 1) a centricity around a single tone p erceived as tonic; 2) a harmonic organization based on triads and seventh chords; 3) a hierarchical organization of functional harmonies; and 4) a contrapuntal substructure based on the laws of species counterpoint. Such music, by the likes of Barber, Copland, Prokofiev, and Stravinsky, has always posed a problem for music theorists, since neither traditional tonal analysis nor pc-set analysis yields satisfying analytic results. This dissertation argues that the problems inherent in analyzing post-tonal diatonic music can be solved by a careful application of set theory modulo 7, in interaction with the more familiar mod12 set theory. The first chapter outlines a system of mod7 set theory designed specifically for the analysis of post-tonal diatonic music . Chapter 2 then utilizes that system to analyze a range of post-tonal diatonic works in order to demonstrate the system's validity, its flexibility, and its explanatory power. Chapter 3 rigorously examines chordal tone centers in post-tonal diatonic music, an aspect of centricity that has thus far only been discussed in the vaguest of terms. Chapter 4 deals with structural levels in post-tonal diatonic music, presenting an approach that considers both the salience of individual pitches, and their place in the work's formal and motivic structure, in determining their structural weight. The final chapter explores how diatonic partitionings of the octave interact with pentatonic, whole-tone, octatonic, and chromatic partitionings in much music of the 20th c entury, and addresses the analytic problems posed by such interactions. KEYWORDS: post-tonal, mod7, centricity, diatonic, set theory, Prokofiev, Stravinsky, Bartok, Copland, Barber TOC: Chapter 1: Set Theory, Mod7 Chapter 2: Motivic Analysis, Mod7 Chapter 3: Chordal Tone Centers Chapter 4: Structural Levels Chapter 5: Beyond Mod7: Relating Diatonic and Nondiatonic Materials CONTACT: Matthew Santa 120 W. 44th St., Apt. 914 New York, NY 10036 (212) 921-2074 ====================== 6. New Books Boydell & Brewer Richard Rastall, The Heaven Singing: Music in Early English Religious Drama Peter Pears (ed. Philip Reed), The Travel Diaries of Peter Pears, 1936-1978 _______________ *The Heaven Singing: Music in Early English Religious Drama* Richard Rastall "Its scope is impressive. Rastall's task has been to explore the wide musical spectrum of early English drama... a formidable achievement, indispensable for any serious and comprehensive study of early English drama." _Medium aevum_ Where should there be music in an anomymous English religious play of the fifteenth or sixteenth century? What sort of music should it be, and by what forces should it be performed? This volume shows how music was used at the time of the plays' production, both through a close examination of individual texts, and of the place of music in the intellectual and artistic life of the Middle Ages. 1 color illus -, 10 b/w illus., 61 line illus.; 454pp, 234 X 156, 0-85991550-6, L19.99 $36.00 c.April 1999 Boydell & Brewer PO Box 9, Woodbridge, Suffolk IP12 3DF Tel: 01394-411320; Fax: 01394-411477 PO Box 41026, Rochester, NY 14604-4126 _______________ *The Travel Diaries of Peter Pears, 1936-1978* Peter Pears Edited by Philip Reed "A valuable source of material on the musical development of both Pears and Benjamin Britten ... a 'must' for those interested in either." _Opera Journal_ This volume brings together all the travel diaries of Peter Pears (1910-1986). The first diary dates from 1936, the year before Pears's friendship with Britten began, when he went on tour in North America with the New English Singers. Other diaries record the five-month tour of the Far East and important encounters (especially for Britten) with the gamelan music of Bali and the Japanese Noh theatre; visits to Russia as guests of Mstistav Rostropovich and his wife Galina Vishnevskaya; attendance at the Ansbach Bach festival when Pears was at the height of his career; holidays in the Caribbean and Italy, a concert tour of the north of England, and accounts of the rehearsals and performances of the New York premieres of 'Billy Budd' and 'Death in Venice'. The diaries, rendered in Pears's highly individual prose, reveal much of his cultivated personality and add significantly to knowledge of Britten. They have been scrupulously annotated by Philip Reed, formerly at the Britten-Pears Library, now at English National Opera. 16 b/w illus.; 272pp, 234 x 156, 0-85115-741-6, c. $31.00 c.May 1999 US: Boydell & Brewer, Inc. PO Box 41026, Rochester, NY 14604-4126 ====================== 7. Communications Editor's Message With this issue, production of Music Theory Online moves fully to Indiana University.  I am pleased to welcome Brent Yorgason, Art Samplaski, Michael Toler, and Elisabeth Honn as Editorial Assistants.  For their willingness to assume these new responsibilities I am grateful.  Physically, MTO will continue to reside on the Boethius server at the University of California--Santa Barbara. 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