Partch progressions

Adam et al. in re Partch: I don't think anyone should take his
statements on the "magnetic" tendencies of prime identities too
literally, but only as a general guide. HP often separated his theory
from his practice. One might imagine upon reading about Monophony that
it would be applied to sustained tones with harmonic spectra and
vocal texts, however, HP used plucked string and inharmonic percussion
timbres primarily and except in Oedipus and some other early works, seldom
wrote extended lyrical vocal lines, instead preferring short aphoristic phrases, nonsense syllables, interjections, etc.

So, I think we can justifiably divorce his chordal progressions from
his theoretical 43-tone scale and even add extra tones whenever
necessary to make the harmony less static.

For the benefit of those without access to a copy of _Genesis of a Music_,
I've translated some of HP's progressions into ratios which show the
voicing better: (The page #'s are from the first edition of Genesis.)
The O's and U's refer to Otonality and Utonality, HP's terms for harmonic
and subharmonic as applied to chords. O and U come from Over and Under.

p185: 3/1 -> 3/1
21/8 -> 5/2
9/4 -> 2/1
15/8 -> 2/1
3/2 -> 1/1

3/2 O 1/1 O (V7 to I)

p.186, Diagram 13:
11/8 -> 11/8 (both voices to 11/8)
27/20 ->

33/32 -> 11/10
-> 11/12 (11/6 in lower octave)

11/8 O? 11/8 U (HP admits that the first chord is
not easily analysed and not very tonal.)

p. 186:
33/16 -> 2/1

27/16 -> 7/4
21/16 -> 5/4
9/8 -> 9/8

15/16 -> 1/1
3/4 -> 3/4 (3/2 in lowest octave)

3/2 O 1/1 O

p. 187:
8/3 -> 8/3
32/15 -> 2/1

16/9 -> 16/9
32/31 -> 8/5
32/27 -> 8/7

32/33 -> 1/1 (64/32 in lowest octave)

4/3 U 1/1 U (plagal cadence)

p. 188, Diagram 14:
12/7 -> 7/4
10/7 -> 7/5
8/7 -> 7/6

8/7 O 7/4 U (example of "tonality flux"

p. 188, Diagram 15:
11/5 -> 24/11

11/6 -> 20/11
11/8 -> 16/11

11/8 U 16/11 O (the other example)

My class notes state that the homework for the Nov 9, 1967 class was
to choose any two hexads which resolve by small intervals and to also
write 3 lines of counterpoint in any scale that can be played on the
Chromelodeon. The progression HP gave us in class was from 11/8 U to
8/5 O in which the 11/6 moved to 8/5 in the bass, 11/9 to 6/5, 11/7
to 9/5, 2/1 and 11/5 were held, and 11/4 resolved to 14/5.

Other examples I have in my notes are 5/4 U to 1/1 O, 8/7 O
to 4/3 O, and 8/5 O to 4/3 O. I suspect these were my own
solutions.

What I can't seem to find are any examples of the strongly beating
progressions that I recall HP played for us, unless the second
one from the top (above) is one of them one. My question to Allen about
the class notes was partly rhetorical and partly because mine are
very incomplete, especially about the chordal sequences we studied.
Most of what HP taught us was in Genesis, save for the beating
progressions. I'm sure I've seen a score of them somewhere, but I can't
find it now, even though I am back in Texas in my own house at the
moment.

--John


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Aha! 3:5:7:9 harmonies for Pierce-Bohlen. Excellent. I've been wondering
for a long time, but never had the time to sit down and crank out, what ratio
approximations Pierce-Bohlen makes available. Thanks for pointing that out,
John.

That makes sense in light of Brian M's observation that Pierce-Bohlen is
essentially every fifth step of 41TET, and that 88CET is essentially every third
step. That of course means that 3 PB steps ~= 5 88CET steps, which is a pretty
good approximation to 9:7 (checko). And 6 PB steps ~= 10 88CET steps, which is
a good approximation to 5:3 (checko again).

Oh, by the way, the corresponding harmonic series fragment for 88CET is
4:6:7:9:10:11:15. And as with Pierce-Bohlen's 3:5:7:9 fragment John mentioned,
it can be taken in retrograde to form a subharmonic series fragment.

One very valuable difference that falls out of those two harmonic series
fragments is that 88CET has a 10:7 tritone, whereas Pierce-Bohlen has a 7:5
tritone. I personally have always liked 7:5 better than 10:7, although that's
kind of like saying that I carrots more than potatoes. They both have value in
their own right.

Sorry to keep prattling on about 88CET, or even more importantly, to relate
an observation about Pierce-Bohlen, to 88CET as though 88CET were some sort of
universal tuning reference. I blabber about 88CET because it's my current
"thing". But anyway, a number of you have experimented with both tunings, so I
thought some of you might find that relationship interesting.


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