Carrillo continued

Carrillo wrote that he considered the number of notes per octave analogous to altitude records and that therefore because he had gone to 96-EDO, he should also be credited with using all lower numbers of tones above 12. As far as I know, he never composed in anything but a subset of those tunings divisible by 6 (18, 24, 30?, 24, 48, 96). However, he had pianos built to play 36, 42, 54, 60, 66, 72, 78, 84 and 90-EDO as well. His daughter made a demo tape of each of them, but that's the only use I know of the the other divisions.

While his numerical notation would easily handle 19, 31, etc., I don't know if he ever proposed using these tunings or his notation for them. Lolita told me that he favored those divisible by 6 in order to retain the whole-tone and our familiarity with it as an interval. Most of his music uses 12, 24, 48 and 96, though there is at least one concerto for 18 (piano) and 12 (orchestra) together. I believe there is a short piece in 30-edo, but I don't have access to my files today to check.

Ironically, his insistence on zero-modulo-6 tunings just misses the most harmonically and melodically interesting systems -17,19, 25, 29, 31, 41, 43, 46, 50, 53, 55, 65 etc., by one or two degrees.

Novaro, btw, was much more catholic and built instruments for 53, 15 and possibly 16 as well, IIRC. He also proposed a form of polymicrotonality involving the simultaneous use of 15 and 12, essentially a subset of 60-tet. He also discussed other non-zero-modulo-6 tunings.

--John

Thanks for filling in some much needed details.
It seems odd he would have missed 72 being 12 times 6.
Novaro system being analogous to Pascals triangle is uncanny
(i pointed this one out to Erv)

-----Original Message-----
From: John Chalmers [mailto:JHCHALMERS@...]
Sent: Monday, January 14, 2008 02:26 PM
To: 'Tuning', 'tuning math', MakeMicroMusic@yahoogroups.com
Subject: [MMM] Carrillo continued

Carrillo wrote that he considered the number of notes per octave
analogous to altitude records and that therefore because he had gone
to 96-EDO, he should also be credited with using all lower numbers of
tones above 12. As far as I know, he never composed in anything but a
subset of those tunings divisible by 6 (18, 24, 30?, 24, 48, 96).
However, he had pianos built to play 36, 42, 54, 60, 66, 72, 78, 84
and 90-EDO as well. His daughter made a demo tape of each of them, but
that's the only use I know of the the other divisions.

While his numerical notation would easily handle 19, 31, etc., I don't
know if he ever proposed using these tunings or his notation for
them. Lolita told me that he favored those divisible by 6 in order to
retain the whole-tone and our familiarity with it as an interval. Most
of his music uses 12, 24, 48 and 96, though there is at least one
concerto for 18 (piano) and 12 (orchestra) together. I believe there
is a short piece in 30-edo, but I don't have access to my files today
to check.

Ironically, his insistence on zero-modulo-6 tunings just misses the
most harmonically and melodically interesting systems -17,19, 25, 29,
31, 41, 43, 46, 50, 53, 55, 65 etc., by one or two degrees.

Novaro, btw, was much more catholic and built instruments for 53, 15
and possibly 16 as well, IIRC. He also proposed a form of
polymicrotonality involving the simultaneous use of 15 and 12,
essentially a subset of 60-tet. He also discussed other non-zero-
modulo-6 tunings.

--John

[Non-text portions of this message have been removed]