source file: mills2.txt
Date: Thu, 3 Jul 1997 21:02:40 +0200

Subject: Muddy waters

From: Mckyyy@aol.com

Hi Paul E,

>Let those of us who don't understand Partch's work not accuse
>him of muddy thinking!!!

How about muddy writing?

>As for priority, I seriously doubt the claim that the
>prime-limit concept predated Partch's work; in fact, it is often
>merely the result of misunderstanding Partch.

Gosh, I thought Pythagorus started the whole thing (at least in
the west) with his famous 3 limit.  I certainly was working with
prime limits before I ever heard of Partch.

>There are those who subscribe to a rectangular
>matrix/ROHS/LCM/Tenney harmonic distance idea.  According to any
>of these philosophies, 15:1 is "the same" as 5:3,...

They produce patterns of the same length, but the patterns are
quite different.  The picture frames are the same size, but the
pictures they contain are not the same.  But you can use LCMs to
both determine the size of the picture frame and the contents of
the picture.

Actually, the 15:1 ratio, assuming it is truly phase-locked,
would be heard as a single tone, since it can be assumed that a
substantial amount of the acoustical energy is in the
fundamental.  However, if we decompose the sum of 5:3, into its
component sine waves from the viewpoint of the 15 unit length of
the repeated pattern, we find that it has no energy in the
fundamental, and therefore would be heard as two distinct,
harmonious tones.

>i.e., a major seventh is just as dissonant/complex as a major
>sixth.

I must be missing something here.  I thought a major seventh was
15:8, and a major sixth was 5:3.  The last time I checked the LCM
of 5:3 was 15 and the LCM of 15:8 was 120.

In your discussion, you talk of the consonance of intervals,
which I presume means you are discussing only the consonance of
diads.  How does your theory handle triads?

As a programmer, I find it more comfortable to deal with these
questions in terms of the sorting and searching of lists.  All
these geometrical approaches seem to me to be only introducing
unnecessary complications.  The geometry relevant to music is the
geometry of the sound waves produced, and perhaps the geometry of
the ear.  JI music theory is a very quantum kind of thing, and
analyzing it in terms of lines and spaces with their infinite
numbers of points seems to me to drag in lots of irrelevant
information which just has to be filtered out later.

Using octave equivalence, there would seem to be 1320 possible
chords in a 12-tone scale.  Making a list of these chords and
sorting them according to their LCMs is simple and easy on a
computer, and gives a good starting point for a discussion of
relative consonance.  Certainly, the list could be reordered in
many ways, but I believe that most of these orderings would have
a high correlation with an LCM ordering.

If we want to discard octave equivalence and use instead just the
list of all notes in a multi-octave scale, or if we want to use
more notes per octave, the problem is still quite manageable.

I don't see that picking certain diads out of a scale and
analyzing them geometrically gives as full a picture as analyzing
every possible triad the scale can produce.

I believe it is good that there are many points of view, but if I
am obliged to understand Partch, does that also mean you are
obliged to understand me?

Marion

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