Re: Paul H. Ehlich

To: internet:tuning@onelist.com
Date: 03-05-99

>>Though, the "comma pump" chord sequence you mention
>>can't be easily resolved in any ET that "supports a comma" (which, it
>>appears, 22TET DOES, and 31TET, oddly, does NOT).

>Not odd at all -- that is why 31-tET is so popular for diatonic music.
>22-tET is HORRIBLE for diatonic music. I've found 10-tone scales that
>function "diatonically' in 22-tET and give you rich 7-limit harmonic
>resources (tetrads instead of triads):

Yes, my use of the word "odd" was off the mark. Looking at some ET
scales, it would seem that:

19-tET, 26-tET, 31-tET, and 43-tET are meantone scales: they narrow
the fifth, eat the syntonic comma, and take the resulting thirds. All
have only a single major second interval: four fifths "equal" a major
third.

22-tET, 34-tET, 41-tET, and 53-tET all widen the fifth compared to
12-tone, and compared to just (except 53TET, which is ALMOST exactly
right!). All support the syntonic comma (i.e., show net microtonal
motion) in the progression I-vi-ii-V-I. All have two major second
intervals: four fifths do NOT equal a major third.

(I have long considered 53-tET to be a beautiful thing, since its base
microtonal interval falls nicely between a Pythagorean comma and a
syntonic comma, but I've never written music in it...)

As for your 22-tET to adaptive JI challenge (if I may call it that),
can you tell me where I might find a 22-tET sequence to work with? What
file format is used?

Implicit in the pitch-bending method of tuning is a sharp limitation on
the number of voices that can be sounding simultaneously, since each
note, except for octave intervals, needs its own channel. A single
voice (piano?) is comfortable; two may work when 16 MIDI channels are
available (as they are with General MIDI - well, 15 are, anyway...).

JdL