w.a. mathieu's _harmonic experience_

just to follow-up on yesterday's recommendation:

i studied with allaudin mathieu last year and so have some hands on
experience with his theories of tonal harmony, as well as conceptual
approaches to just intonation composition, based on the 5-limit lattice
(although i forced him to work with me on 7-limit as well). i'd be happy
to answer anyone's questions re: his book and will provide his address to
any seious parties, as he would appreciate the feedback. he seems to be an
unrecognized contemporary of la monte young and terry riley and was a
long-time student of pandit pran nath. . .

also: you folks _must_ check out his lattices; they incorporate staff
notation into the pitch-space graph--fascinating!

-f.c.
~'~~'~~~'~~~~~'~~~~~~~~'~~~~~~~~~~~~~'~~~~~~~~~~~~~~~~~~~~~
Flynn Cohen
Mills College

snailmail: email:
p.o. box 9312
oakland, california
94613
u.s.a. tel.(510) 649-1728

~'~~'~~~'~~~~~'~~~~~~~~'~~~~~~~~~~~~~'~~~~~~~~~~~~~~~~~~~~~
~'~~'~~~'~~~~~'~~~~~~~~'~~~~~~~~~~~~~'~~~~~~~~~~~~~~~~~~~~~
~'~~'~~~'~~~~~'~~~~~~~~'~~~~~~~~~~~~~'~~~~~~~~~~~~~~~~~~~~~



SMTPOriginator: tuning@eartha.mills.edu
From: kukula@synopsys.com
Subject: Blackwood's proof
PostedDate: 25-09-97 20:32:59
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Mark Nowitzky writes:
---
It was something about Helmholtz' and Ellis' attempt to use just
intonation to get better harmony than equal temperament being proved
impossible by Easley Blackwood in "The Structure of Recognizable
Diatonic Tunings".
---

James Kukula writes:
---
Before I read Blackwood I had tried taking a couple of Bach harmonized
chorales and figuring out how they should be played in j.t.[...]
Basically the problem is just to figure out which of a set of nearby
pitches to use for each note, the pitches differing by the 80/81 comma.
[...] the exercise really opened up for me the structure of the Bach
pieces, or seemed to anyway. I found, though, that the pieces seemed to
turn on a kind of musical pun, to take advantage of the blurring of
harmonic distinctions provided by temperament.

As I read Blackwood, the point is not so much that e.t. or any
temperament is so much better than j.t. in any universal or absolute
sense, but that mainstream European musical practise at least in the
18th & 19th Centuries was really structured around temperament, and you
can't just slide j.t. into the classics and make them better. A
different kind of music based on j.t. might be better in some sense, but
the structure of composition is strongly connected to tuning, so you
can't change one without some adjustment in the other.
---

After 10 months or so of research on the subject, I have come to the
exact same conclusions as Mr. Kukula, and he has phrased them very
nicely above. For a different phrasing, though, I must once again
shamelessly plug my thesis, available in various forms (including HTML)
at

http://theremin.media.mit.edu/~bdenckla/thesis/main.html

I believe my thesis' tuning theory is an improvement upon Blackwood's,
although Blackwood's musical examples are very instructive and are the
real strength of his book. On this particular subject, my thesis frames
these "puns" (a nice metaphor) as reliance on what I call A1_1
enharmony, which is analogous to d2 (diminished second) enharmony, i.e.
enharmony between notes like G# and Ab.

Ben


SMTPOriginator: tuning@eartha.mills.edu
From: Carl Lumma
Subject: Re:deployment
PostedDate: 30-09-97 21:02:38
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>As I read Blackwood, the point is not so much that e.t. or any
>temperament is so much better than j.t.

Strictly as a minor aside, it's probably wise to point out that "Just
Temperament" (which is what I presume you mean by "j.t.") is an oxymoron.
By definition Just Intonation is untempered.


SMTPOriginator: tuning@eartha.mills.edu
From: "Collins, Gordon"
Subject: RE: What Is Microtonal Music?
PostedDate: 09-10-97 16:09:51
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