72 thoughts and more from Anton

Dear Joseph,

Your thoughts on the symmetrical quality of 72-tET make a lot of
sense. It is probably a logical thing to do to divide 12-tones into
another 6 parts, since that shows the continuation of the same
symmetry. One of your observations made me realize something very
important that I completely forgot, which I wrote down myself. I am
ashamed to say, but I forgot one important point. I remembered it
when you mentioned Just Intonation. The reason that Murzin decided to
invent the ANS synthesizer was that Murzin wanted to continue
Scriabin's aspiration toward not only intervals smaller than the
semitone, but also "natural" intervals, i.e. those pertaining to
Just Intonation. In the interview that I did with Stanislav Kreichi,
he mentions that Murzin wanted to incorporate pure intervals,
pertaining to Just Intonation, and not merely to double or triple
standard 12-tone equal temperament intervals with quarter-tones or
eighth-tones. Very silly of me to forget. Protopopoff, on the other
hand, never got that far in his thinking (nor did he get as far in
his book as 72-tET. He merely made a dive into the nearest microtonal
temperaments available at his disposal - namely quarter-tones, third-
tones and sixth-tones - to prove that Yavorsky's system is universal
and can be applied to all music, from the "music of the past", i.e.
folk music, to the "music of the future" i.e. microtonal music. If he
instinctively paved the way towards 72-tET, I think that this was done
irrationally, without any conscious thought of 72-tET or the Just
Intonation harmonies that are derived from it. It might show
the "inherently dominant" qualities of 72-tET, to which composers and
theorists aspire without even realizing it consciously.

You can post this response on the Tuning List. I will really try to
get back to it as soon as possible.

Best,

Anton