TUNING digest 1414

Paul Erlich wrote:

> Ratio Prime Limit Cents
> 34/27 17 399.1

> (SWEEP THRU FROM ONE TO THE OTHER)

> 89/70 89 415.7

> If you have a way of tuning intervals with 0.1 cent precision, hold one
> note constant and sweep the other one through this range. Without
> looking, stop the sweep where you hear 3-ness. Do the same for 7-ness,
> and, if you believe in such things, 13-ness, 17-ness, 19-ness, 23-ness,
> 29-ness, 31-ness, etc.

When I attempt this (sweep thru 399-416) on an acoustic instrument
the notion of identifying _and_ correlating a variety of qualitative
shadings (consonance?) to ratios seems ludicrous. OK.

To my ear there are shadings of character pertaining within
this tiny interval which are of musical consequence, but they
are:

1) not dependent on 3/5/7 - ness etc
2) nor do they appear to depend purely on interval (which
is my point).

Unfortunately I can't do the experiment to Paul's satisfaction (?)
on my sampler since it tunes nominally to 1 cent. However,
to the extent that I can, it seems that to describe the experiment
independently of describing the _sounds_ which are being used is
misleading. But I'll assume you are assuming complex harmonic tones.

I would therefore ask Paul whether, when he does the experiment using
timbres as different from each other as a french horn or an oboe or a
guitar or cello, this gives differing results? _It does for me_ .
(I mean of course combinations off _both_ same and different
sounds). The cause is what? Partial frequency amplitudes? or
something to do with the way each individual timbre is 'processed'
and 'co-created' by the ear?

And what about when others try the same?

In my (forthcoming) paper I use the concept of an "intervallic zone",
or even "primary intervallic zones". The reason I adopt this is for
a similar reason as that implied by Paul E's experiment. But
I'm still unclear as yet exactly how an 'intervallic zone' might be
defined. It clearly can't be defined purely in terms of a 'limit' in
either prime or odd incarnation.

Carl: the idea that consonance is not important in serialism is very
odd. Sorry, can't let that one pass!

Patrick O-L