[Smt-talk] Diatonic Meaning and Other Considerations

[Andrew Milne]

Perhaps a demonstration of the logic of Dimitar’s scale names (harmonic, melodic and double harmonic as applied to both major and minor) is that I—quite independently—came up with precisely these terms for my site www.tonalcentre.org, which I wrote over 1997–1998. I had no knowledge of Russian music theory at that time (I would also hasten to add that I would now revise the site to include proper citations and perhaps temper some of the more speculative claims—but this was written many years before starting my academic career).

It seems to me that each of these eight scales: the Ionian and Aeolian modes of the diatonic, the harmonic major, harmonic minor, major and minor modes of the melodic scale, and major and minor modes of the double harmonic cohere tonally in a way that other scales do not. In this way each forms a self-sufficient tonal construct and, it is for this reason, that they are a useful means for understanding tonal music and chromaticism as a system which switches (often in a parallel fashion) between these scales. The importance of the minor iv in major is that it so strongly exemplifies the subdominant function, which mirrors that of the dominant but is weaker because the downwards leading tone of b6 moves to the fifth of the tonic whereas in the dominant the leading tone (7) leads to the tonic’s root.

—

Dr Andrew Milne
Postdoctoral Research Fellow
Music Cognition & Action Group
MARCS Institute
University of Western Sydney
Australia

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On 4 Dec 2013, at 8:05 am, Ninov, Dimitar N <dn16 at txstate.edu> wrote:

> Dear Colleagues,
> 
> I would like to address several points as follows.
> 
> 1. Nicholas, I called the whole-tone tetrachord "Lydian" only to refer to the fact that Lydian mode begins with it.  I prefer the "whole-tone" name and do not assign any "original" title to it. However, the terms "Ionian-, Dorian-, and Phrygian tetrachords I encountered when I was 15 years old,  in two elementary theory of music books written between 1950-70, and I liked this differentiation.
> 
> 2. No one can claim a true historical platform for our notion of modes and scales today. Firstly, it is widely suggested that Heinrich Glarean copied the original Greek scales wrongly, and our contemporary theory assumed the official  names and modal arrangements from him, rather than directly from the Greeks. What we call Dorian today  (starting on Re) is not the Greek Dorian, which starts on a different tone (was it mi?). Therefore, I am not trying to do back two thousand years to justify some practical methods which have a supposed connection to the past but have been modified. For me it is a simple and nice method to imagine the diatonic scales as combinations of four different diatonic tetrachords. Someone else may explain their structure differently.
> 
> 3. I was very intrigued by Ildar's reflections on reaching the end of the first tetrachord and creating  a threshold - this for me is a great angle to explain melodic and harmonic events from another perspective, especially the critical role of the fourth degree and the S function. I also praise Ildar for not insisting that the S function "denies" the Tonic, as was customary explained in Soviet theory (Ildar, you remember, I had a little argument with our colleague Daniel Shutko in St. Petersburg, who is a strong proponent of this notion and insists that S is neutral and does not know where it is going, because it is a potential fundamental to T, as T is its potential overtone). I am convinced that if there is a tonal center, there is a force of gravity and vice versa, and S represents a level of instability which is greater than that of M, but weaker than that of D. Furthermore, one can tonicize a secondary tonic by using a secondary S alone (IV of or II of, IVm and II half-
> diminished 7 being the strongest secondary S) which happens more rarely than the combination II and V of... or IV and V of...
> I proposed to Daniel to play a major triad out of the blue (no tuning, no, context), then make it minor and add a major sixth on top of it. Then see if he would be directed to resolve it somehow. The immediate aural suggestion (expectation) is to resolve it a perfect fourth down. This procedure reveals the nature of the Plagal relationship S-T, theoretically justified bu J. Ph. Rameau under the name of "Irregular Cadence". Of course, you can resolve the half-diminished in a variety of ways, but there are some expectations related to it as well as to the Mm7 chord. 
> 
> I also recognize that I give a definition of a pure diatonic system by different examples, for instance: seven different tones that could be arranged in perfect fifths. The scalar arrangement of those tones yeilds a natural scale which is the embodiment/host of the old modes. Of course, these perfect fifths are a part of the well-tempered system.
> 
> 4. On another note. Jazz departments and theory books use the term "harmonic major", and for melodic major they use "major flat six and flat seven" which is a true explanation of the structure, but is too long to pronounce and misses the logic behind the "melodic" label in general: 1) melodic minor and melodic major are the same scale, started on different degrees, and 2) the upper tetrachord of melodic minor is borrowed from natural major, while the upper tetrachord of melodic major is borrowed from natural minor. The double harmonic versions of major and minor are also the same scale started on different degrees. The harmonic versions, on the other hand, have identical upper tetrachords. All this logic is simple and clear for me (as I have not invented it but I was taught in it in the past) to use it in the explanation of the "expanded diatonic system" which includes not only pure diatonic, but also some chromatic scales, intervals and chords. One familiar example of a real
> ly altered chord is the fully diminished seventh chord, which resides outside of the pure diatonic system. It is so much domesticated that many teachers think of it as diatonic, and that in major it is borrowed from minor. It does not exist in either - it is a unique structure which is obtained through 50-50 modal interaction between both modes: major gave the raised 7th to minor, and minor gave the lowered 6th to major.
> 
> Thanks,
> 
> Dimitar
> 
> 
> Dr. Dimitar Ninov, Lecturer
> School of Music
> Texas State University
> 601 University Drive
> San Marcos, Texas 78666
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