Re: [tuning] Digest Number 1107

Message: 19
Date: Tue, 13 Feb 2001 16:13:25 -0500
< From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
<Subject: RE: Re: Digest Number 1106
<
<Daniel Wolf wrote,
<
<>What about 6:5 and 32:27? Okay, I can buy 32:[2]7 as
<>an out-of-tune 6:5.
<
<But you've skipped over 13:11, which is closer. So perhaps things start
<getting a bit fuzzy around 11?

That's reasonable. But after sleeping over it, I find myself a bit uncomfortable
with hearing 32:27 as an out of tune 6:5. The differences in the listening tests
for the various minor thirds were really quite vivid

And you're also right. Characterizing 32:21 as a small minor sixth was
misleading. I should have characterized it simply as 32:21.

In any case, the limit model based on instrumental spectra suggests 16 to 24 as
the range where "fuzziness" enters. Perhaps instead of your "fuzziness" or my
"out-of-tuneness" we could start talking about interval classes.

It's nice that both of these models start to parallel critical band width in
that they reach a plateau where the width gets no narrower.

<
<I think they do, in some listeners and in some registers. Witness Dan
<Stearns' opinion that 11:9 is more concordant than 9:7 or 11:8. And <harmonic
entropy, my little model of "fuzziness", seems to predict this <quite clearly.

I have no doubt that one can create musical contexts where the denominator rule
is overridden (that's in my original post), especially when the denominators are
so close. Conditioning is a strong form of contextualization. But repeated
tests comparing randoming selected dyads from neighboring denominator classes
have really convinced me that 9:7 will have more sensory consonance than 11:8,
which is, in turn, more consonant than 11:9, provided the intervals are voiced
sufficiently high up (i.e. above the harmonic series scaffolding).

As I wrote in the initial posting, accepting this outcome required a heavy
revision of my investment in factoring.

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

I wrote,

><I think they do, in some listeners and in some registers. Witness Dan
><Stearns' opinion that 11:9 is more concordant than 9:7 or 11:8. And
<harmonic
>entropy, my little model of "fuzziness", seems to predict this <quite
clearly.

Daniel Wolf wrote,

>I have no doubt that one can create musical contexts where the denominator
rule
>is overridden (that's in my original post), especially when the
denominators are
>so close. Conditioning is a strong form of contextualization. But repeated
>tests comparing randoming selected dyads from neighboring denominator
classes
>have really convinced me that 9:7 will have more sensory consonance than
11:8,
>which is, in turn, more consonant than 11:9, provided the intervals are
voiced
>sufficiently high up (i.e. above the harmonic series scaffolding).

But Daniel, Dan Stearns and I were talking about a case where this intervals
are not voiced particularly high. In a high register, the central pitch
processor has less uncertainty, and the harmonic entropy model predicts, as
you say, that 9:7 is more concordant than 11:8 which is a bit more
concordant than 11:9 -- and this agrees with my perceptions too. But in a
lower register, a greater uncertainty is in effect, and Dan Stearns' and my
perceptions, as well as the harmonic entropy model, predict that 11:9 is the
most concordant of these three intervals. Care to comment?

>As I wrote in the initial posting, accepting this outcome required a heavy
>revision of my investment in factoring.

Well, let me breathe a great big sigh of relief for that! I'm glad we can
agree on that.