Re: [tuning] Subject: Re: 11/8 vs 11/9 and 10/9 vs 7/5

Subject: Re: 11/8 vs 11/9 and 10/9 vs 7/5

During an earlier round of discussions, I did a lot of listening to dyads
created with DSP and came to the conclusion that,

in mid-range*,
with a fixed lower pitch*,
at middling amplitudes,
and with harmonic timbres,

with all ratios reduced to simplest form,
excluding dyads falling within a margin* of tolerance of previously encountered
ratios,

sensory consonance decreases as the size of the denominator increases.

(* these ranges and the fixed pitch left, diplomatically, undefined)

Thus, I was observing an apparently equal sensory consonance for each dyad in
each row, and decreasing sensory consonance from one row to the next:

2/1, 3/1, 4/1, 5/1, 6/1 ...
3/2, 5/2, 7/2, 9/2, 11/2 ...
4/3, 5/3, 7/3, 8/3, 10/3 ...
5/4, 7/4, 9/4, 11/4, 13/4 ...
6/5, 7/5, 8/5, 9/5, 11/5 ...
7/6, 11/6, 13/6, 17/6, 19/6 ...
8/7, 9/7, 10/7, 11/7, 12/7 ...
9/8, 11/8, 13/8, 15/8, 17/8 ...
10/9, 11/9, 13/9, 14/9, 16/9 ...
11/10, 13/10, 17/10, 19/10, 21/10 ...

This result was startling to me, as someone who had invested a lot in the
musical identity of particular factors. Could I suddenly accept 13/6 or 17/6 as
more consonant that 10/7, or 11/7 as more consonant than 11/8? Were the dyads
in each row really of equal consonance? Listening to the intervals was a
convincing exercise, and then looking at the spectra redoubled my conviction.

However, this experiment also made it more clear to me that _contextual_
consonance will often be independent from the sensory. For example, the
interjection of an augmented fourth or diminished fifth of whatever ratio into a
collection of otherwise perfect fourths or fifths might create a more jarring
effect then the presence of a neutral third. Or, in a texture of only ratios
composed of factors of 3 and 7, the introduction of 5:4 Major third might be
jarring. In this way, the issue of limits and factoring (prime, odd etc.) was
identified as a compositional or stylistic concern rather than an immediately
perceptual one.

Daniel Wolf
Budapest
http://home.snafu.de/djwolf/