Bearsley vs. Sethares

David Beardsley wrote,

>A sine tone is perfect for JI because there are no harmonics
>to interfere with the special stuff that happens when you
>have an interval in tune by ratios. All you hear is the relationship
>between
>two notes without all the beating from overtones of a timbre - just
>the beating of the notes..

Clearly there is a vast gulf between this point of view and the one
presented by Sethares. Although it is true that only intervals near 1:1
can create beating in the absence of harmonics, there are many
psychoacoustical effects that both create harmonics for sine waves and
create fundamentals for the sine waves to be harmonics of. This effects
must explain what David Beadsley is hearing, but these effects must be
subtle enough to have been unnoticed in the classic Plomp & Levelt
experiment, except for the case of 2:1 (two sine waves at a near-2:1
ratio do create beating -- this is called second-order beating). I would
have to side with Sethares that JI (and, I would add, utonal harmony in
particular) really works best when the tones are fairly rich in harmonic
partials. Inharmonic timbres often demand that JI not be used and non-JI
tunings are clearly more consonant. Sine waves alone are fairly amenable
to any kind of tuning, although many sine waves in a harmonic-series
(otonal) relationship produce the special effect of a single tone with a
rich, harmonic timbre. This is the effect that LaMonte Young exploits
and is very different from the considerations that lead many to suggest
JI for performances of common-practice music on conventional
flexible-pitched instruments.

From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

>Clearly there is a vast gulf between this point of view and the one
>presented by Sethares. Although it is true that only intervals near 1:1

>can create beating in the absence of harmonics, there are many
>psychoacoustical effects that both create harmonics for sine waves and
>create fundamentals for the sine waves to be harmonics of. This effects

>must explain what David Beadsley is hearing, but these effects must be
>subtle enough to have been unnoticed in the classic Plomp & Levelt
>experiment, except for the case of 2:1 (two sine waves at a near-2:1
>ratio do create beating -- this is called second-order beating). I
would
>have to side with Sethares that JI (and, I would add, utonal harmony in

>particular) really works best when the tones are fairly rich in
harmonic
>partials. Inharmonic timbres often demand that JI not be used and
non-JI
>tunings are clearly more consonant. Sine waves alone are fairly
amenable
>to any kind of tuning, although many sine waves in a harmonic-series
>(otonal) relationship produce the special effect of a single tone with
a
>rich, harmonic timbre. This is the effect that LaMonte Young exploits
>and is very different from the considerations that lead many to suggest

>JI for performances of common-practice music on conventional
>flexible-pitched instruments.

I should point out that I was refering to sine tones with no harmonics.

Nice thread title, it sounds like a WWF event.

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