[Smt-talk] Symphonia, etc.

[Ildar Khannanov]

Dear David,
 
thank you very much for your informative reponse. I actually have read your 1993 article and many other texts. I agree that this is not the place to discuss these fine matters. On the other hand, does it bother you that other theorists (including Schenker himself) do not care for the Greek theory? And what is the better place to make the discussion of Greek theory decisive and categorical than the place where all men come together to discuss important news? The list is an exact model of Agora for me. If my colleagues decide that what I am writing is OK, then it will turn into cata-agora. Othewise it will remain something which everybody mixes by himself (idiosyncrasy).
 
Yes, synphonos interval blends two notes, and  diaphonos does not. But how the diaphonos is related to synphonos?
 
I wonder if there is anything going to be published or worked on together in Greek field? I would like to participate to the best of my abilities.
 
 
Best,
 
 
Ildar Khannanov 
Peabody Conservatory
ikhanna1 at jhmi.edu
 


--- On Sun, 4/5/09, dec2101 at columbia.edu <dec2101 at columbia.edu> wrote:


From: dec2101 at columbia.edu <dec2101 at columbia.edu>
Subject: Symphonia, etc.
To: "Ildar Khannanov" <solfeggio7 at yahoo.com>
Cc: smt-talk at societymusictheory.org
Date: Sunday, April 5, 2009, 3:16 PM


Dear Ildar (and anyone else interested),

I do indeed understand your point re. interpretation; I cite Barker because his interpretations are exceptionally insightful, in my view and in the view of others knowledgeable about ancient Greek theory. And, as it happens, I have some knowledge of Greek, as well.

"Blend" translates "krasis" (from "kerannumi"); the word is often used to characterize the result of mixing wine with water or honey. It's also used in grammar, to denote contractions like "thanropou" (from "tou anthropou").

The Euclidean _Sectio canonis_ includes the following passage, which although not strictly speaking a definition of "symphonia," is nonetheless clear as to the present point:

"We also recognize that some [combinations of] notes (pthongous) are symphonic (symph?nous), others diaphonic (diaph?nous), the symphonic making a single blend (mian krasin) out of the two, while the diaphonic do not" (_Sectio canonis_, Introduction; ed. Jan, _Musici Scriptores Graeci_, 149:17-20; new edn. by Andre Barbera, _The Euclidean Division of the Canon: Greek and Latin Sources_ [Univ. of Nebraska Pr., 1991], at 116:6-8; cf. Barker, _Greek Musical Writings_, II, 193; also, on "krasis" as opposed to "mixis" or "migma," see Thomas J. Mathiesen, "Euclid's Division of a Monochord," JMT 1975, p. 254, note. 13).

(See also Cleonides, Eisagoge, 5 (ed. Jan, _MSG_, 187:19ff; trans. in Strunk/Treitler, _Source Readings_, 39; Bacchius, Eisagoge, 1 (Jan 293:8ff.), trans. Otto Steinmayer, ?Bachius Geron?s Introduction to the Art of Music,? JMT 29 (1985): 271-298, p. 274 (cf. also ibid, p. 286 with n. 16); Gaudentius, Eisagoge, 8 (Jan 337:8ff).

The idea that _symphonia_ consists in a "blend" of two pitches also recurs prominently in most of the definitions of "consonantia" in Boethius, _De institutione musica_, e.g., this one from I.28:

"For whenever two strings, one being lower [in pitch than the other], are stretched and, having been struck at the same time, produce a sound that is, in a certain way, mixed and sweet, and the two pitches blend as if conjoined into one (in unum quasi coniunctae), then there comes to be that which is called consonance" ("Quotiens enim duo nervi uno graviore intenduntur simulque pulsi reddunt permixtum quodammodo et suavem sonum, duaeque voces in unum quasi coniunctae coalescunt; tunc fit ea quae dicitur consonantia") (_De inst. mus._, I.28; Friedlein, 220:3-7; cf. also the translation by Bower, _Fundamentals of Music_, p. 47).

(See also _De inst. mus._, I.8, IV.1, and V.7. Boethius asserts the synonymity of "symphonia" with "consonantia" in _De institutione arithmetica_, II.48, ed. Friedlein, 155:14-15).

The notion that the sound resulting from this "blend" is unified ("one" sound), is the leading idea of the first of Boethius's various definitions of consonance, at the end of _De Inst. mus._, I.3:

"Consonance (consonantia) ... is the unified harmony (in unum redacta concordia) of notes different from each other" ("Est enim consonantia dissimilium inter se vocum in unum redacta concordia") (_De inst. mus., I.3; ed. Friedlein, 191:3-4; cf. Bower, _Fundamentals of Music_, p. 12).

This last-quoted passage also alludes (obliquely) to the concept of _harmonia_ (expressed here with the Latin word "concordia"), which you also brought up. The basic understanding of _harmonia_ in antiquity seems to have been that expressed in a fragment of Philolaos:

"_Harmonia_ comes to be in all respects out of opposites: for _harmonia_ is a unification [henosis] of things multiply mixed, and an agreement of things that disagree" (quoted in Nicomachus, _Eisogoge arithmetike_, II.19, p. 115:2; also in Diels & Kranz, _Fragmente der Vorsokratiker_, #44 B 10; trans. Barker, _GMW_ II, p. 38).

This is not the place for a serious discussion of the questions and issues you raise. Let me just note instead that there are indeed knotty and interesting problems of interpretation connected with all these concepts and their relations to each other, and suggest that you have a look at the following studies:

Thomas Mathiesen, "Problems in Ancient Greek Terminology: _HAPMONIA_," in _Festival Essays for Pauline Aldermine_, ed. Burton L. Karson (Provo, Utah: Brigham Young University Press, 1976): 3-18.

David E. Cohen, "Metaphysics, Ideology, Discipline: Consonance, Dissonance, and the Foundations of Western Polyphony," _Theoria_ 7 (1993): 1-86. And for fuller discussion of many of these points, my dissertation, "Boethius and the Enchiriadis Theory: The Metaphysics of Consonance and the Concept of Organum" (Ph.D. diss., Brandeis University, 1993).

Best,

-David
-------------------
David E. Cohen
Associate Professor of Music
Columbia University
New York, NY 10027

Quoting Ildar Khannanov <solfeggio7 at yahoo.com>:

> Dear David,
>  
> thank you very much for your suggestion to read the books. I hope  that you understand that the book you have suggested is an  interpretation of events of the past and not the required literature  for an UG student. I happen to be able to read Aristoxenus in the   original language. There were other translations and intepretations  into other languages which I find very interesting and helpful. I  would suggest that you read them too.
>  
> As for the terms, could you elaborate what do you mean by  "blending," and how it is different from my interpretation of  synphona and diaphona? Was there any relationship between these two  groups? If yes, was it related to the concept of harmonia? What is  harmonia? I keep hearing recently that harmony is a "vertical  structure." Then, I assume that counterpoint is defined as a "linear  structure." Both are wrong! Harmony, a universal signifier of music,  cannot be explained by visual metaphors of verticality and  horizonatlity. Harmony is the relationship of  the opposites. It can  be the relationship between darkness and light, but also between the  wasp and the orchid, or even the car and the traffic light. In music  it is diaphona and symphona.
>  
> Latin translations and later English translations present the  problem and it is not only the problem of musical terminology. All  terms, including Being and Nature, were translated into Latin from  Greek with great loss of meaning. There is much written on  this topic  by Heidegger. For example, the Greek preposition dia-  does not mean the same thing as Latin diss-. The fact that we are  having a dialogue on the list is a clear proof of it.
>  
> Today, we can only reconstruct the meanings of Greek terms and the  intentions of Greek authors by deconstructing our prevalent views  and formulations. We've changed and in need of developing a  different organ to see the past events. When I read in Aristoxenus  that all intervals smaller than the diatessaron are diaphona, I ask  myself, what does this mean? And what can be gained by reaching the  diatessaron after passing through the smaller intervals? How this  can be translated into a more modern language? Is not this a clear  case of tension and resolution? Of polemon ending with synousia?  When the voice passes through ho tonos, we do not control two  "pitches" simultaneaously. We are taken off guard by the power of  melodic motion. We are moving through (dia) something which does not  have the beginning and the end.. In this case, even "the path up and  the path down are the same." Only when we reach the diatessaron, the  skies
 are cleared and we start seeing
>  the horizon. This is the junction, connection (syn-) of the  begining and the end of our travel, and the resting point  "Ruhepunkt." The quantity of motion turned into a new quality.
>   In general, we should see the forest behind the trees: harmony in  Greek understanding(s) means the opposition of Chaos and Cosmos, the  reconciliation of the irreconcilables. Music since Greeks has been  always operating with this definition of harmony. It has been  realized in different ways, but it was present at all times. Not to  see this evidence is strange, to say the least!
>  
> The idea that tonoi are the "transposition levels of complete  background scale system" seems too revisionist to me. For imagining  that, a Greek theorist must have had an idea of pitch collection,  pitch class, transposition levels, background structure, etc. Try to  translate these terms back into ancient Greek language! And by the  way, try to translate the word "pitch" into any modern language. I  have tried to translate it in into Russian, my native language, and  I am at loss. There is such a degree of polysemy and such a rich  folkloric etymology that it is very difficult to operate with this  word on a reflective  terminological level.  Systhema teleion  (magnon ou pyknon) is the greatest achievement of Greek theory. It  is a result of a purely theoretical effort to see the invisible  (Platonic idea). It is obvious that early in Greek music history  only shorter melodic patterns were used and they were limited to  small
 number of notes (mostly four).
>  The similar layers of folk music elsewhere have similar oligotonic  character. IN Greek theory, the two genuine melodic patterns were  either connected (synemmenon) or placed next to each other  (diezeugmenon). The functional complexity of this system does not  allow to treat it as a "collection" or a "set." Music is open for  higher levels of abstraction (since it has been introduced in the  West together with theory and philosophy), but harmony seems  to remain an ultimate irreducible prerequisite. Collection and set  are exactly the mathermatical tools which are intended for  disregarding functional differentiation of the elements. Sets are  internally a-systematic. In mathematics itsels, the category of set  is used selectively. (See the reaction of Poincare to Georg Cantor's  idea of transfinite sets). Schenker himself would take my side: for  him a group of notes could not be a "set" of "collection" and  harmonic prerequisite
 would never be negleted.
>  
>  Dynameis  (FUNCTION!) creates a problem. Should we, then, lable it  as "obscure"?
>  
> In general, I suggest  reconsidering our approach to history of  music theory. It is not something that we can "criticize" at  present. It is like a 25-centuries-old cathedral. I suggest walking  inside in soft shoes  and enjoying the beauty of harmony.
>  
>  
> Best,
>  
>  
>  
> Ildar Khannanov
> Peabody Conservatory
> solfeggio7 at yahoo.com
>  
>  
>  
>  
>  
>  
>  
> 
> 
> --- On Sat, 4/4/09, dec2101 at columbia.edu <dec2101 at columbia.edu> wrote:
> 
> 
> From: dec2101 at columbia.edu <dec2101 at columbia.edu>
> Subject: Re: [Smt-talk] Classical Form and Recursion
> To: smt-talk at societymusictheory.org
> Date: Saturday, April 4, 2009, 1:32 PM
> 
> 
> Dear Ildar,
> 
> In your recent post (below) you wrote:
> 
> "A product of real musical intuition is the sense of tension and
> resolution. Musicians started talking about it in the 6th century
> B.C. Diaphona, synphona, ho tonos, dynameis,--these are the terms of
> western music theory of 25 centuries ago."
> 
> There is, however, no evidence that any of these was conceptualized  in terms of "tension and resolution."
> 
> "Diaphonia" and "symphonia" (equivalent, more or less, to our  "dissonance" and "consonance") were usually explained in terms of  thelack or presence of blend and "unity" between two pitches.  ("Diaphonia" means "sounding apart"; "symphonia," "sounding with";  our English terms come from the literal Latin translations of these,  "dissonantia" and "consonantia," introduced probably by Boethius.  Adjectival forms of all four words are often found as well, e.g.,  "diaphona" and "symphona" [though not, of course, "synphona"], and  in Latin "dissona" and "consona.")
> 
> "Tonos," indeed, alludes to "tension," since it derives from  "teino," "to stretch, tighten" but the allusion is simply to the  action of tightening a string to raise its pitch. In ancient Greek  music-theoretical parlance, "tonos" normally denotes either (1) the  interval of the whole tone (usually defined as the "difference"  between a P5th and a P4th, and/or in terms of its ratio, 9:8), or  (2) one of the "tonoi," which for most ancient writers seem to be  simply transposition levels of the complete background scale system  (the "greater perfect system"); hence the oblique reference to  "tension," i..e., pitch. (Ptolemy, though, understands the "tonoi"  in a way that makes the allusion to pitch level irrelevant.) See  also Aristoxenus's discussion of pitch and changes of pitch in  _Elementa harmonica_, Bk. I, sections 10-13 (trans. Andrew Barker,  _Greek Musical Writers_, vol. 2, pp. 133-35): although he's thinking  primarily of the
 singing voice, all his vocabulary
>  concerning pitch alludes linguistically to "tension" ("tasis," also  derived, like "tonos," from "teino"); "tasis" in fact is the word  that actually denotes "pitch," per se, for him.
> 
> Finally, "dynamis," meaning basically "power" or "capacity/ability"  to *do* something, is a term introduced into Harmonics by  Aristoxenus (almost certainly borrowed from his teacher Aristotle,  for whom it is a basic concept of his metaphysics, opposed to  "energeia"/"entelecheia"). It's usually translated as "function" in  English versions or discussions of Aristoxenus, but the precise  sense that he intended has always been obscure. (But see the  interpretation by Andrew Barker in his recent book, _The Science of  Harmonics in Classical Greece_ [2007], pp. 183-92, which I think  goes a long way toward answering this question.)
> 
> Best,
> 
> -David
> ---------------
> David E. Cohen
> Associate Professor of Music
> Columbia University
> New York, NY 10027
> 
> 
> 
> Quoting Ildar Khannanov <solfeggio7 at yahoo.com>:
> 
>> Dear Olli,
>>  
>> sorry to interfere in your exchange with Dmitri.
>>  
>> What makes you think that "closure" and its synonim "prolongation"   are the norms of music, and that they come directly out of musical   intuition?
>>  
>> Or, maybe it is something which was common in   music history? Kirnberger writes about the progression "comming to  a  close," but that means that progression arrives at the cadence.   Cadence is an important device, but is it the goal and essence of   music?  Of course, there is a sense of closure at the end of any   progression, but this is not  a product of  specifically musical   intuition. Rather, it comes from the intuition of a lawyer. The  case  is closed. The relatives of a victim receive the sense of  closure  after the death penalty has been administered. Whatever  happened in  the middle should be forgotten.
>>  
>> A product of real musical intuition is the sense of tension and   resolution. Musicians started talking about it in the 6th century   B.C. Diaphona, synphona, ho tonos, dynameis,--these are the terms  of  western music theory of 25 centuries ago. However, in your   "prolongation" the role of the chord which creates tension and   requires resolution is reduced to almost nothing. It looses its   harmonic function, becomes a "contrapuntal chord" or Nebenakkord.    The most important agency is being reduced, the most important   event--overlooked. By the way, you cannot not notice it while   listening to it, but it is possible to "reduce" it in visual  analysis.
>>  
>> Let me through my 2 cents into the analysis of the Three Blid Mice   motive (3^  2^  1^). A very common example, which is used to   demonstrate the validty of "prolongation," is the voice exchange   progression. And you would say that it has a "passing 6/4 chord in   the middle." What is the function of this middle chord:   "Passing."   How about passing Dominant 6/4? Or the fact that it is  the Dominant  is unimportant?
>>  
>> But then your students will have a surprise for you. They will  write  a ii5/3 in the middle. They do this  very often.  They are  not that  stupid: they are just following the recommendations  concerning  adjacency, "voice-leading" and contrapuntal, passing  function of the  middle chord. Indeed, why not to harmonize all the  notes in a melody  with parallel triads: for 3^ 2^ 1^ to use  iii5/3  ii5/3 and  I5/3? Tell me that this progression does not  create ultimate  parsimony, ultimate voice-leading economy and  ultimate adjacency,   true Nebenakkorden!
>>  
>> Why, then should we bother with  root motion on the fifth, all  this  basso fondamentale influence, a French disease (according to  Oswald  Jonas's introduction to Harmony)?
>>  
>> That is why we discuss the heterogeneous character of music in   general and harmony in particular. And I cannot agree more with   Nicolas when he mentioned basso fondamentale as another example of   parsimony, or economy and laconicity of musical expression.
>>  
>> I do not see the musical intuitive basis for "reduction" of the   middle element.
>> As in  ABA= A. That is exactly what Dmitri has said, which tells  me  that he is a post-Schenkerian.
>>  
>> Resolution of the Dominant is not only and never only   "concatenational.." Plase, read Riemann's analyses and notice the   discussion of large-scale dominants. The Dominant function is   capable of stretching its resolution power over a great nunber of   measures.
>>  
>> As for the phrase Americans care only about Americans, it is an   excellent example of recursion. It does it on all levels, from   syntactic to rhetoric. And how naive is to try to separate them,  or  to reduce one to another!
>>  
>> Best wishes,
>>  
>>  
>> Ildar Khannanov
>> Peabody Conservatory
>> solfeggio7 at yahoo.com
>>  
>> 
>> 
>> --- On Wed, 4/1/09, Olli Väisälä <ovaisala at siba.fi> wrote:
>> 
>> 
>> From: Olli Väisälä <ovaisala at siba.fi>
>> Subject: Re: [Smt-talk] Classical Form and Recursion
>> To: "Dmitri Tymoczko" <dmitri at Princeton.EDU>
>> Cc: "smt-talk Talk" <smt-talk at societymusictheory.org>
>> Date: Wednesday, April 1, 2009, 3:57 AM
>> 
>> 
>> 
>> 
>> 
>> 
>> First, on music versus language:
>> 
>> 
>> 
>> 
>> There were really a pair of issues.  One is grouping -- getting  from  ABAB... to (ABA) ...  But the other is reduction -- getting  from  (ABA) to A.  The point of the "Americans care only about  Americans"  example was that this latter process is also  problematic: the mere  presence of ABA (as in "Americans care ...")  does not automatically  license or motivate a reduction to A  ("Americans").
>> 
>> 
>> 
>> 
>> Dmitri, your analogy between music and language fails in an   illuminative way.  Beginning and ending the sentence with the same   word plays no role for syntactic closure in language. In your   example sentence, the subject happens to be the same as the  object,  but this coincidence has no significance for syntax (only  for  semantics and rhetoric). In tonal music, by contrast, there is  a  norm that closed harmonic progressions begin and end with I (I  hope  you will agree that there is such a norm). If a phrase starts  on I  and proceeds to other harmonies, we are expecting a  convincing  return to I until this happens. (If our expectations  are not  fulfilled and the phrase does not return to I, we do not  hear it as  closed phrase, but await continuation.) This  demonstrates that the  referential status of a single element  (tonic chord in this case)  may have significance for musical  syntax in a way that differs 
 fundamentally from that of a
>  single word for linguistic
>>   syntax. The perception of the syntax in a tonal progression may  be  governed by an element in that progression in a sense for  which  there is no linguistic counterpart. (Closed tonic-to-tonic   progressions are by no means the only way to acheive such  governing  status, but they are a prime example.)
>> 
>> 
>> Owing to this property, music has, in my view, much stronger   potential for extensive recursive (prolongational) structuring  than  has language. Hence, when I received the first mail in this  thread,  I was surprised to see that someone had claimed just the  opposite.  Of course, the existence of this recursive potential  does not mean  that composers have actually utilized it. For  studying this  question, we need empirical research of their music,  and I have  tried to present some ideas how this issue may be  approached.
>> 
>> 
>> Next, let us return to this example:
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> (3^) ? V (2^) ? I (3^) quarter rest / V (2^) ? I (1^) ? V (2^)  q.r.  / I (1^) ? V (7^) ? I (1^) q.r.
>> 
>> 
>> 
>> 
>> As an additional feature, let us suppose that the bass line is   C2?G2?C2, G2?C3?G2, C2?G2?C2, thus further weakening the I in m. 2   and reinforcing the perceptual analogy between bars 1 and 2.
>> 
>> 
>> A crucial difference between a prolongational and concatenational   perception of this progression is as follows. Under prolongational   perception (= I (3^) ? V (2^) ? I (1^), the I in m. 3 offers  closure  for the entire progression; under concatenational  perception, it  only offers closure for the I?V?I succession  starting from bar 2,  beat 2. Frankly speaking, I find the latter  alternative utterly  unintuitive. (I am not sure whether you agree,  Dmitri, but sometimes  I almost cannot avoid the impression that,  whereas you suspect that  I or other analysts may claim to hear  something that we do not  actually hear, you might be claiming not  to hear something that you  actually hear.)
>> 
>> 
>> If we accept the prolongational interpretation, this example   illustrates that I is not the only harmony that can be prolonged.  If  we hear tonal closure only in bar 3, the I in bar 2 prolongs  the  surrounding V. The V at the downbeat of bar 2 creates the   expectation of I, but there are stong perceptual reasons why the   immediately following I fails to fulfill these expecations in a   convincing way. Not only is it rhythmically and registrally weak  and  surrounded by stronger dominants, but the similarity between  mm. 1  and 2 guides the listener to perceive this I in a way  analogous to  the V in m. 1.
>> 
>> 
>> For testing whether a listener actually perceives tonal closure in   m. 3, one might consider the following experiment, though it has a   deficiency. Listen to the progression (1) as written above and (2)   as a truncated version, breaking of after bar 2, beat 2. If one   finds (1) embodying more convincing closure than (2), this speaks  to  prolongational perception. The deficiency in this experiment is  that  (2) does not include all the information that supports  perceiving  bar 2, beat 2 as subordinate to the surrounding  dominant, since part  of this information comes retrospectively  through the return of V  (2^) at beat 3.. Nevertheless, even without  this retrospective  information, I find (2) less satisfactory than  (1) in terms of  closure.
>> 
>> 
>> (The case is different if we break off after bar 3, beat 1. The  last  V (7^) and I (1^) are actually superfluous for the sense of  closure.  In fact, one might say that the sense of closure is  enhanced if the  goal status of the last I (1^) is marked by the  cessation of the  sequential model.)
>> 
>> 
>> In order to overcome the "I hear this ? I hear that ? No, you only   claim so" type of discussion, I have tried to focus on the   compositional evidence that there may be for prolongational   structuring. I suggested that if a composer had written the above   progression, there would be a certain amount of such evidence. The   prolongational model would explain the emergence of several   compositional features, including the feature that the composer  has  stopped the top-voice sequence on 1^?if we suppose that the   progression occurs in circumstances that support its perception as  a  closed entity. (A crucial feature in the explanatory power of  the  Schenkerian approach to sequences concerns the participation  of the  framing points in the larger context; in this case,  however, we have  not identified a larger context.)
>> 
>> 
>> I did not claim that the evidence "proves" the prolongation   hypothesis.. There might be alternative explanations, but at the  very  least the facts are well concordant with that hypothesis.  For  strengthening the case for the hypothesis, we would have to  allow  for the larger context and for the composer's general  practices, but  this, of course, is impossible for this artificial  example.
>> 
>> 
>> Instead, I presented some observations of the descriptive and   predictive power of the prolongation hypothesis for Bach's music.  I  discussed how a passage in G Major Invention involves several   features of design, register, emphasis, and meter that can be   elegantly explained on the basis of the hypothesis that Bach had  in  mind a prolongational pattern II (4^) ? V7 (4^) ? I (3^). (I do  not  mean he was consciously aware of that pattern; one does not  have to  be aware of syntactic or quasi-syntactic rules for  following them.)  I also related this 4^?3^ pattern to the piece as  a whole and to  Bach's general practices (referring to "the  predictive power of the  Urlinie"). My point was that there are  objectively identifiable  compositional features in Bach's music  that can be explained on the  basis of the hypothesis that  prolongational (=Schenkerian) patterns  affected his composition  and for which it is not
 easy to see what  would be
>  equally satisfactory
>>   theories. While this cannot "prove" the hypothesis, it justifies   and motivates it in a way that is largely comparable to any   scientific hypothesis.
>> 
>> 
>> (Incidentally, I do not think that my approach to empirical  evidence  repeats arguments overly familiar from previous  Schenkerian  literature, although the significance of register and  design has  certainly been focused on by authors such as Oster and  Rothgeb. For  example, I am not aware of precursors for my  systematic study of the  predictive power of the Urlinie for the  corpus of 15 Inventions.)
>> 
>> 
>> Olli Väisälä 
>> Sibelius Academy
>> ovaisala at siba.fi
>> 
>> -----Inline Attachment Follows-----
>> 
>> 
>> _______________________________________________
>> Smt-talk mailing list
>> Smt-talk at societymusictheory.org
>> http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org
>> 
>> 
>> 
>> 
> 
> 
> _______________________________________________
> Smt-talk mailing list
> Smt-talk at societymusictheory.org
> http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org
> 
> 
> 
> 





      
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.societymusictheory.org/pipermail/smt-talk-societymusictheory.org/attachments/20090405/4d46d283/attachment-0004.htm>