[Smt-talk] Classical Form and Recursion

[Ildar Khannanov]

Dear Nicolas,
 
I have been following your very interesting and useful discourse on tonal-harmonic functions. I appreciate your statement on vi as being a S substitute (this information is missing in our textbooks, as many other things related to functions). Hower, I have a problem with this statement:
 
"It is true that, at an elementary level, my theory does not take the mode of the chords into account. This, in turn, contradicts the dual view of harmony. Riemann, the dualist, would have categorially opposed, say, V-I to v-i (he would have written V–>I and v<–i, in my conventions). At an elementary level, I consider X–>Y, x–>y, X–>y and x–>Y to be equivalent. This has to do with the nature of the diatonic scale in a pre-dodecaphonic conception, in which sharpening or flattening a tone did not essentially modify it. These differences in "mode" make little difference in the voice leading, anyway."
 
This may lead to  some dangerous pedagogical innovations, such as the idea that ii and II function the same way before V. I have heard this from some other teachers of harmony. 
 
Sii is subdominant. Before V it functions as a part of non-modulating progression, in the key. The DD before V functions as a sign for us to  leave the key, as a pointer to a possible modulation into the sphere outside. In this case the fact that the two chords are situated on the same scale step does not make them mutually replaceable. What is extremely important is that they belong to different functions. That is why I mentioned earlier that function is function because it is function. 
 
Scale steps by themself are not functions yet. There is a mysterious cognitive mechanism (which, I hope, will be studied one day by Carol and Fred) behind functions. It is not merely psychological or culturally predetermined. It is psycho-somatic, because many listeners perceive Dominant the same way (and this is a secret advantage of "common practice music" before the "20th-century music"). The cognitive mechanism which is responsible for Dominant may choose certain scale stepts to represent the Dominant.
 
How about this theorem of Dominant:
 
Dominant is function, i.e. relationship* as such
 
Dominant is commonly represented by scale step five in the context of both major and minor tonality*
 
Dominant must be a major triad
 
Corollarium 1: tonality is not the diatonic collection of pitch classes;
tonality is the set of relationships, for which the seven scale steps play the same role as the acustic basic scale plays for the set of modes. 
 
Corollarium2: relationship  is the basic organizational principle of function; it cannot be visualized or reduced to concatenation of scale steps..
 
 
 
Best,
 
Ildar Khananov
Peabody Conservatory
solfeggio7 at yahoo.com
 
 
 
 
 
 
 
 



--- On Mon, 4/13/09, Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr> wrote:


From: Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr>
Subject: Re: [Smt-talk] Classical Form and Recursion
To: "smt-talk Talk" <smt-talk at societymusictheory.org>
Date: Monday, April 13, 2009, 5:34 AM


I wrote

my old harmony teachers gave us rules (mainly, a formal ban on vi-V) that I interpret now, after many years, as meaning that I-vi can only be T––>S<.
This is elliptic to the point of unintelligibility, excuse me. 

What I mean is that my old teacher would have rejected reading, say, vi-V-I as Tp<–D–>T (a pendular movement). I think that Simon Sechter also would have considered vi-V as implying an understood ii in between, with the result that vi would appear as IV< in a chain of dominant vectors: I–>IV< (–>ii–>) V – a reading that ressembles the double emploi, but implies sort of a double substitution, from S< to Sp, which furiously resembles a dominant vector, S< –> Sp. It is difficult to disentangle such cases without their context.

Yours,

Nicolas Meeùs
nicolas.meeus at paris-sorbonne.fr
http://www.plm.paris-sorbonne.fr

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