Yahoo Tuning Groups Ultimate Backup mills-tuning-list Primes or Odds

> > But for whatever it's worth, I don't think that 9 would be considered a
> > limit on the grounds that it's not prime.
> I, for one, completely disagree. I would define the limit as the largest
odd
> number that occurs in ratios that are considered consonant.

I certainly agree with Dan Wolf that we ought to use the definition from
the person who coined the term, that being Harry Partch. I was under the
apparently false impression that he defined it in terms of primes rather
than odds. I confess that I have only read Genesis of a Music in
fragments, so I have every reason to believe that Dan Wolf must be correct
and I'm not.

But regardless of the definition of "limit", there are definitely two
different schools of thought here. The premise that odd numbers rather
than primes outline various classes of harmony is based on the
well-accepted fact that octaves, or stacks of octaves, produce a sensation
of duplication, like that of a major tenth being practically the same
harmony as a major third.

Clearly then even whole numbers, all of which produce "octave
duplicates" of an odd number's harmonics, can have no
practically-meaningful effect on harmony. Or to put it another way,
putting a single two into the product forming a numerator or denominator is
as good as putting in as many as you'd like.

The case for prime numbers rather than odds outlining new harmonies is
based on the idea that stacks of ANY small whole number produce similar
effects. That is to say that, multiplying in one of three, for example, is
"as good" as adding in any number of threes.

That is not, however, in the sense that threes create a sense of
duplication like an octave, but that they create another characteristic
sensation. As I understand it anyway, the more or less accepted
characteristic for three is that of a cold, logical simplicity, as
evidenced in the character of P4s and P5s.

Based upon this premise, then clearly the elements of sort of
classification are primes. That in the sense that multiplying by a
composite is the same as multiplying by a product of primes, bringing in
each of their effects into the soup.

And the idea continues from there, again, as I understand it:
2: Duplication (i.e., pitch classing)
3: Cold, logical simplicity
5: Sweetness
7: A kind of Bluesy "Zap"
11: Ambiguity, lost-in-space sensation

My own personal opinion is that the prime approach is correct at its
root, but vastly oversimplified, and even still the biggest factor
determining the character of a chord is its width. By that I mean that,
for example, M3s of ANY formulation are going to have a more similar
musical effect than any of them will have to a m7 for example. I base that
statement partly on comparing the sensation of 27:16 and 5:3 M6s. 5:3
definitely has a sweetness that I don't hear in 27:16, regardless of their
similar size.

The oversimplification in the prime idea appears to be this: The
ability to stack up an arbitrary number of any particular prime without
fundamentally changing the basic nature of the harmony, decreases rapidly
as you go up the series of primes.

By that I mean that you can stack up plenty of octaves before you break
two's characteristic sensation of duplication, but you can only stack a
handful of threes before you lose three's sensation of cold logic. You can
probably only stack two or so fives before you lose its sense of sweetness.
You can only do one 7 or 11 best I can tell, meaning that 49 and 121 don't
carry on the sensation of 7 and 11 (respectively) at all. I personally
have very little feel for 13, although certain Mayumi and Johnny Reinhard
to.

I suspect that this case of (more or less) diminishing returns is a
consequence of the size of the numbers in the ratio. Generally speaking,
the larger the size of the numbers, the more difficult it is to associate a
characteristic feel to that harmony, and the greater the chances that
they'll be viewed instead as an out-of-tune rendition of a simpler pitch
relationship.

From what I've seen, to find a distinct character to a ratio whose
numbers are larger than somewhere around 50 starts to become limited to
very specialized circumstances, like long sustained notes, harmonic or
melodic (but not both) presentation, carefully-chosen pitch ranges, pure
timbres, very little vibrato or other forms of fluctuation, and such. I
can recall at least one episode where I could not attribute a character to
an interval - curiously I don't recall the interval other than that it was
fairly complex - wherein I had to resort to something like five minutes of
side-by-side comparison to the simpler interval that it sounded like an
out-of-tune rendition of. That's obviously far beyond any realistic
expectation of an audience get excited about in a truly musical performance
situation!

That ease also depends on how wide in the big sense the interval is. I
find it much more difficult to attribute a clear musical sensation to
intervals between a triple- and quadruple-octave than those between a
unison and an octave.

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Primes or Odds

🔗Gary Morrison <71670.2576@...>

🔗Gary Morrison <71670.2576@...>