[Smt-talk] Symphonia, etc.

dec2101 at columbia.edu dec2101 at columbia.edu
Sun Apr 5 13:16:23 PDT 2009

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).


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-----
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