source file: m1413.txt
Date: Mon, 11 May 1998 19:59:51 -0400

Subject: Odd vs. Prime; the blues

From: monz@juno.com (Joseph L Monzo)

Carl Lumma:
> As Gary Morrison points out...

>>Admittedly, 2 is a very special prime number,
>>in that it is the only one which is even (not odd), so
>>most likely, this fact can go a long way to explain
>>why we hear these similarities.

It was I who wrote that.

> Now you might say that we can just as well have
> music with 7's and no 5's, creating an ill-defined
> prime limit.  And true, we can have such a music,
> but we don't.

As I stated in a recent posting, La Monte Young's
"Well-Tuned Piano" is a 5-hour-long JI piece using
intervals with factors of only 3 and 7 -- no 5's.
 
> The reason, I suspect, that Paul Erlich fights for
> odd limits: He is a man of equal temperaments :~)

I suspect that you're correct about this.  After
composing, theorizing, performing, and listening
in JI for a few years, it's quite easy to hear the
prime factors in the music (if it's perfomed in tune,
and if it's not  _really_  high primes like La Monte
Young's sound-installation pieces).

When I hear composite odd identites, like 9, 15, 21,
etc., in quickly-moving real music, I don't get any
particular sense of their particular odd-integer
quality, but I  _do_  hear the qualities of the prime
factors.  Under different conditions, such as
listening to experiments at home, the qualities of
individual odd identities can be isolated.

This simply can't be heard correctly in  _any_
equal-tempered music with a reasonable number
of degrees (say, under 100), because, although it
may represent ratios of certain prime factors well
(or even very well), a tempered scale will  _never
give the ratios exactly_  except for the generating
one of the octave (or other interval if not an octave),
and thus will never produce the _precise_  effect/affect
of the primes in the ratio being implied.

>  The idea that 9's do not become harmonically
> significan't until we have 7's does not hold in
> my experience.

I  _know_  you're correct about this.  3-limit music
can be written in which 9 and 27, and probably
even 81, have harmonic significance.  27 and
especially 81 sound pretty dissonant, but that
doesn't mean they can't be used as chord
members. ( Who wants chords that are always
consonant?)

This variety is exactly what makes JI so
compositionally useful.  One of the reasons why
working in JI is so wonderful is because there
are so many different ways to combine the
prime qualities and compare identities which are
very close in frequency but have different prime
factors (for example, chord tones an 81/80 apart).

This is indeed exactly what makes good blues
singing so expressive -- Robert Johnson could
sing a "blue note" that starts at one pitch and
then slides ever-so-slgihtly to another one very
close by in frequency.  But this tiny change in
pitch produces a shattering emotional effect,
which I believe is due to a smoothly-executed
but radical change in prime factors.  The only
reason it comes off so strikingly is because
Johnson's aural and vocal abilities allow him
to perform it so precisely.

As I've stated many times before, I believe we
_do_  perform prime factorization on music
_as we listen_.  Perhaps this is so because
it is the fastest way to understand the harmonic
relationships occuring in the music as it flies
past our ears in real time.  I will argue that
harmonic relationships are _always_  implied,
whether implied well or badly.

   Joseph L. Monzo
    monz@juno.com

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