prime/ odd limits

> I personally am pretty much a fence-sitter on the
> prime vs. odd question, but perhaps it's worth
> asking: Do you perceive that there's any mechanism
> in our auditory system for detecting powers of two
> (i.e.,octaves)? If so, then why not powers of three or five?

As anyone who reads this digest knows by now, I am
someone who certainly believes that our ears/ brains
calculate prime factorization as we listen to music.

I think Gary Morrison's second sentence here gives
the best perceptual evidence that it occurs: under
normal circumstances (i.e., instruments with basically
harmonic spectra), no-one will deny being able to
hear the similarity of tones one or several octaves
apart. 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. But I still maintain
that each prime factor in the music is like a separate
dimension in sound and feeling.

I personally feel that most of those who either deny
or fence-sit on prime-factorization do so simply
because we are largely unfamiliar with the sounds
and feelings created by most higher-prime ratios,
i.e., those other than straight harmonics of the 1/1.
Even today among JI microtonalists, I would say
that 7 is the highest prime that's generally used
in a systematic way (Partch is the big exception,
along with a few others) -- higher primes are
generally used only as "overtones" of the 1/1.
For example, 17/8 or 19/8 may be corralled for use
as the "flat 9" or "sharp 9", but most other 17- and
19-limit ratios will not be used. Following Partch's
lead, I would say that the only way to decide
beyond a doubt on the questions regarding higher
primes in music, is to hear lots of high-prime music.

As I've said before, in my theory, the sonance
continuum tends to increasing dissonance as
the numbers of *both* the primes *and* their
exponents increase. I tend to agree with most
of what's been posted here in the last week
about perceptual limitations and dissonance:
dissonance increases linearly as the size of
the odd numbers increases, and at some point
around 19, 21, or 23 our perceptual ability
falters.

According to my theory, intervals which are
similar in size (cents) will have different
"flavors" based on the prime numbers involved.

The jury is still out on whether these "flavors"
can be perceived in individual dyads. I tend to
feel that they become more evident in more
complex chords and in other situations where
the context provides more to compare to.

This is the essence of the matter to me. Our
mental apparatus will try to simplify everything
we hear (and remember -- ultimately, harmony
is rhythm too, just speeded up a great deal) into
its most basic components. In my opinion, if
we are scrutinizing a particular dyad with a
more complex ratio, it is very easy to hear it as
something else which lies close by in frequency
but has much simpler relationships -- simpler
meaning basically lower prime numbers, or just
smaller numbers period. If other surrounding
musical events are present, they will help us
pinpoint what that particular interval is if it is a
larger-number relationship.

In my "Hendrix Chord" piece, the 12-eq chord is
played and then all pitches are "bent" until they form
a JI chord. This JI chord is transposed slightly higher
in each successive measure. Even where these
"roots" are less than 1 cent apart, I hear clearly
audible differences in beating. The ratios in the
JI chord are always the same, so the only thing to
which I can ascribe these differences is the
relationship of the transposition (a high-prime ratio)
to the *memory* of the original 1/1, plucked at the
start of the chord before the notes slide upward.

Joseph L. Monzo
monz@juno.com
4940 Rubicam St., Philadelphia, PA 19144-1809, USA
phone 215 849 6723

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