[Smt-talk] Theory Textbooks (Musical Syntax)

[Ninov, Dimitar N]

Dear Nicholas,

I agree with much of what you say; it is a matter of personal choice at some point, and I will tell you what I have based my personal choice on. But I wonder why there should be a big fuss about a non-existing minor, when the minor triad physically exists between the 10th, 12th, and 15th harmonic tones (mi-sol-si) with the ratio of 10:12:15, and I do not know why Riemann had to copy Zarlino in his procedure of obtaining the minor chord through a mirror inversion of the major (through non-existing undertones). Maybe their idea was to establish a minor chord whose root is an imaginary fundamental? Otherwise, the minor triad is as old as the major one, only that it resides remotely from the fundamental, which gives rise to a major triad. But acoustically, all those tones have been in existence forever.

I know about Schoenberg's theory, but, in his usual style, he begins a concept in very simple terms, and then he develops it into a labyrinth of complexity with many symbols and terms that I eventually relinquish. For example his strong, super strong progressions, and other types of relationship are based on descent or ascend, but do not reflect openly an element I am more attracted to.

I am talking about about stability and instability in the virtual sense of the word. If we accept that the only stable chord in the mode is T, then all of the rest will be unstable. The degree of their instability will vary according to their structure and distance from the tonic. If we talk about root position chords, the mediants exhibit the smallest degree of instability towards the tonic, for they share two common tones with it, and are physically closer to it than S and D. Next comes the subdominant, which shares one common tone with T (the tonic note itself) and is remote. Next comes the dominant, which, besides the fact that in its most typical form contains the leading tone, is built on the fifth degree which, when serving as a root, becomes the utmost harmonically unstable tone available in tonality - a potential overtone of T, which wants to resolve not by a step, but by a leap directly into the tonal center.

The remaining chords: II and VII, are close to T but do no share any common tones with it. They share two common tones with IV and V, respectively, and are very easily regarded as substitutions for them. Within the general S function, II will come after IV, because it is less stable (contains auxiliary pitches only, while IV contains the tonic note) and IV-II increases the instability. On the contrary, within the general D function V will come after VII, because its root bears the greatest harmonic instability as a potential overtone of the center. Paradoxically, out of context, a diminished triad  is acoustically more unstable than a major triad, but within the functional realm V exhibits greater instability than VII for these reasons.

At first glance, a certain discrepancy may be observed in this logic, though. If V7 contains all the tones of VII, and therefore V is the genuine representative of the D function, we may claim that II7, which contains the tones of IV, should be the genuine representative of the general S function. Indeed, in the standard jazz idiom II7 has much greater wight and exploration than IV, which is explained as a substitute for II. In in Baroque, Classicism and (to a great degree, but not exclusively), Romanticism, it is IV which prevails, even if it be II6. It is true that II has a greater drive toward V, because it is a potential dominant of the latter. On the other hand, the bass note which has  a stronger relationship to the tonic is the fourth scale degree. Thus the classical composers wanted to hear 4 as bass departing from the tonic, while jazz musicians want to hear 2 as a bass driving towards the dominant. Since I and II, both in root position, do not connect very impressively, jazz musicians replace I with VI. Thus the once prevailing mode I-IV-V is giving way to VI-II-V in jazz. But the two modes, as our colleagues from Barcelona pointed out, are basically the same functional orders: I is replaced by VI, and IV is replaced by II. 

Therefore, I base my functional evaluations on the relationships of the diatonic triads with the tonal center, and think of this system as a simple and comprehensible one.

Thank you,

Dimitar

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
________________________________________
From: Nicolas Meeùs [nicolas.meeus at paris-sorbonne.fr]
Sent: Thursday, May 03, 2012 12:06 PM
To: Ninov, Dimitar N
Cc: smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Theory Textbooks (Musical Syntax)

Le 2/05/2012 20:27, Ninov, Dimitar N a écrit :
> [...]
> We should also keep into account that the harmonic syntax of the common practice period [...] is as much a reflection of acoustic realities inherent in the harmonic tone series, as a  psychological reaction related to style. For example, we may agree that the proper order of chords in the common practice period is governed by the principle of progressing, that is - increasing the degree of instability between two points of stability as represented by the tonic.
> [...]
There certainly is a privileged direction in common practice tonality,
but I'd hesitate to qualify it as increasing instability, or as
reflecting an acoustic reality. Schoenberg, at least, described the
usual progressions as "descending", by which he meant that the roots
descended the harmonic series (say, from V to I, harmonic 3 to 2,
possibly also from V to III, harmonic 6 to 5, or III to I, harmonic 5 to
4). He would probably have described such movements as increasing
stability (or decreasing instability). Yet, the reference to the
harmonic series is possible only in major and remains, I think,
metaphoric at best.

Or else the increasing instability must be viewed as a move away from T
(the tonic), either "upwards" toward D (the dominant) or "downwards"
toward S (the subdominant), followed by a return: this, I think, would
reflect how Riemann himself understood tonal functions – but such a view
does not account for the privileged direction.

The privileged direction, in my opinion, can only be described as
statistical, as being the most frequent, without recourse to acoustic
considerations that do not resist close scrutiny. Some of my younger
colleagues in the Sorbonne have evidenced that one reason of the
privileged direction is that it allows resolution of the dissonances.
But that simply (or not as simply as that) displaces the problem to
determining why dissonances must be resolved in descending. I think that
this has been discussed already on SMT-Talk.

Recognizing that the privileged direction cannot be rooted in acoustics
(because of the problem of the minor) leads one to admit that the only
possibility is to offer theoretical explanations that are more or less
arbitrary – and to admit that several theories may include some of the
"truth" (whatever that is). Ildar's suggestion that we should clearly
identify our theoretical paradigms at the beginning of our classes
therefore is important. But I see little possibility to decide that one
theory is better than another.

Nicolas Meeùs
Université Paris-Sorbonne