Techniques of Polytempic Polymicrotonal Composition: Division of the Whole Tone, part VII

 What is a Whole Tone, and Why Divide It?

Anaximander

Anaximander believed in a concept called "unity," wherein infinite divisions were possible, and apparently, this philosophy included divisions of musical intervals, such as the tone. Aristoxenus was also an advocate of this philosophical standpoint. "All and innumerable worlds are infinite in possible harmonies." 

Conventional wisdom states that a whole tone is composed of two semitones that range from ratios 11:10, at 165 cents, all the way through 8:7, at 234 cents. Generally, the ratio 9/8 is the most accepted version at 204 cents. If we are not speaking about rational tunings or string lengths from the monochord, then we are referring to 12tet, where the whole tone is simply 200 cents. 

Although I went through a bit of the history of tuning in my thesis, Polytempic Polymicrotonal Music: the road less traveled, 2012, I just want to discuss my personal thoughts on pitch. 

I am not a tuning/temperament math theorist. I just use the intervals for my music. Scala has a portfolio of over 5000 tunings and temperaments, and I really do not care if I never add another scale to this massive folder. I just want to USE them in my music. That is all. I also really do not care about the retuned, continued, neotonal use of common practice harmony disguised as microtonal music. The fundamental chosen for a just intoned tuning essentially remains an extended drone for the duration of that music, at least until a second fundamental is employed. I understand that this is an outgrowth of minimalism, and that's great. I simply do not make music this way, and so far, it has cost me. 

Frankly, I like harsh dissonances. I like wolf fifths. I like how the quartertone is the most dissonant interval at 50 cents, which is the furthest shade of pitch color away from our standard 12tet in use today. And if you use the overtone series tuning, or any limit of just intonation, as long as we measure in cents, 50 cents away from your desired set tuning per note is the most dissonance you can achieve, because at 49, or 51 cents, you are going back, or forward, to the next consonant destination. So, if you love 386-cent major thirds, and you assign a quartertone at 436, or 336 cents, that just major third will sound horrible to you, just as 450, or 350 cents for a major third sounds horrible to someone using 12tet. That's it. Changing one cent fore or aft from that quartertone and one is on their way back to intervallic safety. This, for me, is the ultimate power of the quartertone.

The good news about composing polymicrotonal music is that the composer can use any tuning/temperament they wish. This is an open system. If Schönberg was climbing "up" the overtone series (not quite microtonal) by equalizing semitones, then my non-system polymicrotonal approach is related to that climb. Well, I say non-system, but this is why I am writing this blog: to find a system. 

Why divide the whole tone? Parity. Nothing more. The division of the whole note needs an allegorical "other." I see both the whole note and whole tone as a couple of eggs that needed to be broken open for that delicious polymicrotonal yoke. 

Figure 1. Flow chart of divisions of the whole tone with cents values

So why stop the division of the whole tone at two semitones? Why not continue? By continuing to divide the whole tone, systems similar to the divisions of the whole note arise: quartertones, third tones, sixth tones, eighth tones, etc. How about prime divisions? 5th tones at 40 cents, and 7th tones at 28.6 cents. In fact, Julian Carrillo and Alois Haba had already used third and sixth tones in their music early last century. Nothing is new, except how it is used. This approach is new. 

To dispel confusion, the divisions of the whole tone would not be equivalent to equal divisions of the octave. For example, a 13th tone, at 15.4 cents, would obviously not be equivalent to 13tet, at 92.3 cents per interval. 

Generally, knowing some basic math is helpful, and having access to a calculator on your phone should suffice for operations of division while exploring tunings. Microtonal scales, such as these, if not already created in Scala, can be created with Scala. As far as MIDI playback, as long as MPE is a feature of the software, any tuning program, such as Entonal, can be used for realization. 

Nevertheless, I thought that pairing the tuning with the same tempo would be a novel idea. If it is not an actual literal relationship, based on similar numbers pertaining to similar physical phenomena, then perhaps it becomes a conceptual relationship —that of fusing a related tempo number to its concomitant tuning, per part. 

Figure 2. Polymicrotonal pre-compositional sketch planning, using 13, 17, 19, and 22tet. 2009

To be continued...