[Smt-talk] Theory textbooks

Ildar Khannanov solfeggio7 at yahoo.com
Tue May 1 14:57:06 PDT 2012

Dear Nicolas and the List,

I agree that it is very difficult to get the relationship between syntax
 and TSDT cycle in some RIemann's writings. I have been rereading his 
Musikalische Syntaxis (Lepzig 1877). He runs circles around the topic, 
but on page 75 he explains how harmony is working together with the 
meter and creates syntax. He brings an example from Schumann's 
Kreisleriana, Piece 5, an intermediary theme. It goes like this: S - D -
 T, while the meter is anapest (weak, stronger, strong). I read between 
the lines that this is one of the most interesting examples of genesis 
of tonal functions. Riemann comments that it is ultimately important 
where the dissonance is placed in a measure. Here, in Schumann, it is 
subdominant on the weak, dominant on the stronger, and tonic on the 
strongest beat. I assume that not geometry, but interaction with meter 
assigns the tonal-harmonic function to a chord. Terminal dominant in 
measure 7 and terminal tonic in measure 8, for example, are the 
prototypes for all other dominants and tonics in a progression.

I was trying to save Rieamann's theory from well-deserved critique by 
chanelling its pathos in a different field, the field of interaction 
between harmony, meter and form. 

As for the problem of S - D connection, it remains a geometrical 
problem, but not the problem of syntax. By the way, I quoted your 
article on harmonic vectors in my book Music of Sergei Rachmaninof: 
Seven Musical-Theoretical Etudes (Moscow 2011, in Russian). I think than
 you are making an invaluable contribution to the transformational 
theory by adding the idea of directionality to geometry of voice 
leading. You are making musically dead geometry more alive.

I studied harmony by Brigade Texbook (Moscow, 1937), which is a version 
of Louis and Thuille (the same outline and similar use of concepts). 
These textbooks did not hesitate to mix what you call scale-step theory 
with Rameau and Riemann. The most important ingredients are:

1) to teach students hearing intervals in key and out of key. If there 
is a slightest problem with that, it has to be corrected right away, 
otherwise studens will fail to measure the root motions

2) to teach hearning the structure of the chord--finding its root by ear and determining its function in relationship to tonic

3) using the aural skills to place the chords in syntactic cycle of TSDT.

I think that seven tonal functions will not work. There are three, but 
they self-replicate at different levels of transposition, including at 
the fifth, which generates Quintenzug. Still, T S D are not vectors, but
 the forces which generate vectors and attractions. There are only three
metric-harmonic-syntactic forces. Static energy of dwelling (T), its opposite, stirring energy of
 motion (D) and the third agency which makes the progression working 
only clockwise and blocks the counterclockwise motion (S). The S allows a progression to move ahead and not in reverse or back and forth. Probably, there is a weakness in Riemann's theory, or rather, its unfinished character. I hope that I am thinking in the right direction, continuing his ideas.

I do not know how to attribute this: whether it is function or 
scale-degree concept. But it seems to work for the music of the 19th 


Ildar Khannanov

Peabody Conservatory

Johns Hopkins University

--- On Tue, 5/1/12, Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr> wrote:

From: Nicolas Meeùs <nicolas.meeus at paris-sorbonne.fr>
Subject: Re: [Smt-talk] Theory textbooks
To: "Ildar Khannanov" <solfeggio7 at yahoo.com>
Cc: smt-talk at lists.societymusictheory.org
Date: Tuesday, May 1, 2012, 1:00 PM


    Dear Ildar and the list,


      I did not mention Schenker in this context (and I agree with you
      that Schenkerian theory probably would not be much help for
      teaching elementary tonal writing). My question concerned the  root progression theory of the Sechter/Bruckner tradition, of which another
      important representative is Schœnberg. 

          I feel that the problem with German Funktionstheorie is its
      dualism: the function is viewed as a relation between two chords
      (say, between dominant and tonic, or between subdominant and
      tonic), but the theory has little to say of the direction of the
      relation: Riemann makes little difference between I–V and V–I (or
      between I–IV and IV–I) and, above all, does not see the relation
      of similitude between V–I and I–IV, for instance. (This problem
      exists also in neo-Riemannian theory.)

          The cycle TSDT that you describe seems to me much better
      accounted for in root progression theory. Besides, Riemann himself
      seems to have had some problems with it, especially with the
      progression from S to D.

          I must confess that while I have read a lot of Riemann, I am
      less informed about later forms of the theory, e.g. Louis and
      Thuille or, more recently, Diether de la Motte. The question that
      I have, to put it otherwise, is about the point of keeping to
      three functions only, if dualism is abandoned. It has been said
      that root progression theory is a theory of six or seven
      functions: why not?


    Nicolas Meeùs

    Université Paris-Sorbonne





    Le 1/05/2012 19:19, Ildar Khannanov a écrit :
              Dear Nicolas and the List,
              I have studied both (German Funktionstheorie in
                Russia and Schenkerian theory of scale-degrees in the
                United States). Both sides propose statements but they
                do not necessarily adequately  translate into pedagogic
              I noticed that when students realize figured bass,
                they count notes from each given bass up. I have seen
                some of them using fingres to count. So, practically, on
                the undergraduate level, realization of a figured bass
                presents calculating of the notes of each chord from a
                bass up and adjustments made in response to schoolbook
                requirements of voce leading (such as "resolve the
                seventh by step down). Ears may not participate in this
              I do not know of any compositional technique for
                building harmonic progression using Schenkerian theory.
                Analysis--yes, actual composing of a 4-part
                progression--no. There are some suggestions concerning
                prolongation but they refer mostly to analysis of a
                given score. As such, Schenkerian fundamtenal line is
                inaudible. It is purely graphic phenomenon. If to
                reconstruct a harmonic progression from a given
                fundamental line, we will receive one and the same
                harmonic progression, a standard school-book harmony
                which has nothing to do with actual endless variety of
                harmonic progressions in music.
              When a student builds a harmonic progression using
                functional theory, he or she must hear the functions
                underlying an unfigured melody or unfigured bass. It is
                impossible to simply calculate the possible chords under
                a given note: this will not lead to a meaningful
                progression. The only way to harmonize a given melody in
                functional style is to hear the flow of functions in
                cycles of TSDT. This method cannot promise a student the
                understanding of the structure of the whole Beethoven' s
                symphony in one grasp, but can lead to knowledge of
                shorter chord progressions, cycles, phrases, breathing
                curves of harmony.
              Tonal-harmonic function is a quality of a chord which
                connects it to other chords and places it in a syntactic
                whole. Functional hearing, based upon congnitive
                mechanisms of tension, attraction and resolution,
                regulates horizontal dimension of a harmonic
              Tonal-hamonic function is used not to separate chords
                into pure verticalities, but to connect them in
                horizontal dimension. The only agency which makes
                harmonic progression meaningful is its coordination with
                the tonal-harmonic functional syntax. Of course, threre
                are exeptions and licences which composers take, but
                they only make the rule more meaningful and useful.
              Ildar Khannanov
              Peabody Conservatory
              Johns Hopkins University
              solfeggio7 at yahoo.com



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