Techniques of Polytempic Polymicrotonal Composition: Myriad Microtonal Systems, part IX

 5000 Microtonal Scales

Myriad intervals from a plethora of microtonal scales. Considering the wealth of information about this on the internet, this will oddly be my shortest blog entry. As I write these, I am trying not to recreate my own book, Polytempic Polymicrotonal Music, or start another survey of sorts. I would rather just get down to it, but I have to consider whether things are extraneous or redundant. 

Ultimately, we are still at the precipice of the eternal argument between Pythagoras and Aristoxenus. Will we use rational unequal tunings, or equal divisions with or without octave equivalence into infinity? Answer: BOTH. I prefer to forget the position of either/or in consideration of a stance that embraces both of these paradigms.

So, with precision and concision, I will adroitly say this: 

There are choices to be made in polymicrotonal composition (you may use dice for this decision). If we consider the historical, theoretical, and cultural microtonal scales in Scala or other repositories, choices must be made. Will this music be performed by humans, or realized on the computer, or simply remain for posterity? I suppose this part should have come before the division of the whole tone, but each successive blog forces me to consider things ex post facto. 

When I indicated that any microtonal systems can be combined in this music, I meant it. We can, therefore, have: 

Octave Equivalent scales, like EDOs, or Just intonation. We can have non-octave equivalence, like Bohlen-Pierce scales, that stretch well past the octave. We can have extended untempered Pythagorean tuning, keeping and building on the comma. In fact, new simultaneities and verticalities are absolutely assured to be surprising with non-octave scales. 

We can have equal divisions of the whole tone, or octave, or even inharmonic equal divisions of microtones that bypass the octave altogether. For example, we can build microtonal scales using e or pi, like Nancarrow did with tempi, extending into infinity without octave equivalence. 

We can even have x < 12 macrotones, which sound even weirder than microtones. 

How about one scale with 1200 cents to the octave? The Gamut. 

But, for me and for now, until more performers learn more microtonal scales, I maintain a compromised, smallish set of microtonal systems for performance. For computer realization, the sky's the limit. 

Up until now, I have used: 7 8 10 12 13 14 15 16 17 18 19 20 21 22  23 24 31 36 48 50 53 72 84 96 and 128 tones to the octave, plus extended just intonation up to the 17th limit, and higher. They are all beautiful. They are all ear colors. They are paintings for the ears. As for specifically divisions of the whole tone, I have used quarter tones, third tones, sixth tones, and eighth tones. 

For those who want to argue that some equal divisions contain other systems, I say yes and no. The effect of total compression of the interval size is a huge factor and a tremendous sound. Therefore, quarter tones and eighth tones, though overlapping, do NOT sound the same when a single line of ultrachromatic voice leading precludes leaps and jumps, and simply compresses, like the weight of a Blue Whale on top of the staves. 

But this particular minute, tiny ultrachromatic voice leading is a feature of my style. Xenakis and Jean-Etienne Marie also used this technique. In fact, Bartok may be the first composer to literally compress equal division sound structures in his Music for Strings, Percussion and Celesta, by compressing whole tones to chromatic tones in symmetrical order. My idea would be to compress them further by going to third tones, quartertones, sixth tones, and lastly, to eighth tones. This intervallic compression idea has always fascinated me. It is a texture mixing sound mass and intervallic voice-leading. 

Rather than retuning to extant classic intervals, I would rather like to focus on the microchromatic, or polymicrochromatic sound of minuscule voice leading. 

 

to be continued...