Fwd: [tuning-math] Re: from the realms of private correspondence

The question of span is an important one in considering
intervals larger than 2:1, but it draws in the matter
of timbre. For some insight on this, you might want to
look at Gregory Danner's work in MUSIC PERCEPTION
(a quarterly journal) using mathematical models of
dissonance in 12tet and timbres in which amplitude of
hamonics is in inverse proportion to their distance from
the fundamental.(2:1 has 1/2 the amplitude of 1, etc.)

What he found was that the correlation between mathematical
estimates and listener estimates of dissonance was VERY
weak. One issue is that the further apart two tones are,
the more their consonance/dissonance will be affected
by the fletcher-munson curve, which can vary a good deal
from listener to listener.

It is my hypothesis that this is one of the complications of
dissonance that led to pitch grammars in which some intervals
are understood to be dissonant, even if they are not
especially rough, or lacking a strongly defined tone of
reference/precedence.

(In case you're wondering, I did my thesis on the conditions
of dissonance of the augmented triad).

---- Original message ----
>Date: Thu, 07 Nov 2002 15:18:03 -0000
>From: "gdsecor" <gdsecor@yahoo.com>
>Subject: [tuning-math] Re: from the realms of private
correspondence
>To: tuning-math@yahoogroups.com
>
>--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
>> [Paul wrote...]
>> >>>...with 5:3 v. 6:5, doesn't it seem wrong that adding
span
>> >>>should be able to change the relative concordance
(10:3 v.
>> >>>6:5)?
>> >>
>> >>not to me. we're not just adding span, we're also adding
>> >>complexity. ask george secor what he thinks.
>>
>> Heya George... out there? Do you find 5:3 or 6:5 more
concordant?
>
>I say 5:3 is more consonant; my experience has indicated
that
>consonance of intervals between 1:1 and 2:1 can be ordered
by the
>size of the product of the integers in their ratio -- up to
a point:
>as long as the numbers are small enough that the identity
of an
>interval isn't subject to confusion, such that it is more
likely to
>be interpreted as a tempered approximation of another (more
>consonant) interval (which gets us into the study of
harmonic
>entropy, but I digress).
>
>> Howabout 10:3 and 6:5?
>
>This one's a tougher call. The product is the same, but
the span is
>so different that we're beginning to compare apples with
oranges.
>Are we talking about comparing these with the lower tones
being the
>same pitch, or the same upper tones, or an average of the
two? You
>could even compare a 6:5 (with lower tone on middle C) with
a 6:5 two
>octaves lower, and I think you would agree that the lower
one is more
>muddy, i.e., less consonant, so range of pitch also enters
into the
>picture.
>
>Now to answer your question, I think I would judge them to
be equally
>consonant if the average pitch for each of the two
intervals were the
>same. (Just my present opinion -- subject to change with
persuading
>new evidence.)
>
>--George
>

> It is my hypothesis that this is one of the complications of
> dissonance that led to pitch grammars in which some intervals
> are understood to be dissonant, even if they are not
> especially rough, or lacking a strongly defined tone of
> reference/precedence.

Your hypothesis is that because psychoacoustic dissonance
varies from listener to listener, music had to develop a
grammar to make the perception of dissonance more... uniform?

-Carl

I don't recall saying that it "has to", or even that
to whatever extent it "ought to", that variation in
perception of dissonance would be the only reason.

Music doesn't "have to" do anything, unless you
want it to be generally intelligible :P

---- Original message ----
>Date: Thu, 07 Nov 2002 21:44:21 -0000
>From: "Carl Lumma" <clumma@yahoo.com>
>Subject: Fwd: [tuning-math] Re: from the realms of private
correspondence
>To: tuning-math@yahoogroups.com
>
>> It is my hypothesis that this is one of the complications
of
>> dissonance that led to pitch grammars in which some
intervals
>> are understood to be dissonant, even if they are not
>> especially rough, or lacking a strongly defined tone of
>> reference/precedence.
>
>Your hypothesis is that because psychoacoustic dissonance
>varies from listener to listener, music had to develop a
>grammar to make the perception of dissonance more...
uniform?
>
>-Carl

>>Your hypothesis is that because psychoacoustic dissonance
>>varies from listener to listener, music had to develop a
>>grammar to make the perception of dissonance more...
>>uniform?
>
>I don't recall saying that it "has to", or even that
>to whatever extent it "ought to", that variation in
>perception of dissonance would be the only reason.

Not sure how this answers my question...

-Carl

How are we defining "octave"?

---- Original message ----
>Date: Fri, 08 Nov 2002 21:50:29 -0000
>From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
>Subject: [tuning-math] Re: from the realms of private
correspondence
>To: tuning-math@yahoogroups.com
>
>--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
>> >I don't understand how the term "limit" got into your
question,
>> >or is this what others have called it?
>>
>> It comes from that it can be used as an alternative to
odd limit.
>> Interestingly, IIRC Paul showed odd-limit is as close to
the
>> product thing as we can get in an octave-equivalent
measure. Is
>> that right, Paul?
>
>in a certain sense dealing with harmonic entropy, yes.
>
>
>To unsubscribe from this group, send an email to:
>tuning-math-unsubscribe@yahoogroups.com
>
>
>
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http://docs.yahoo.com/info/terms/
>
>

2:1

--- In tuning-math@y..., <Josh@o...> wrote:
> How are we defining "octave"?
>
> ---- Original message ----
> >Date: Fri, 08 Nov 2002 21:50:29 -0000
> >From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> >Subject: [tuning-math] Re: from the realms of private
> correspondence
> >To: tuning-math@y...
> >
> >--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
> >> >I don't understand how the term "limit" got into your
> question,
> >> >or is this what others have called it?
> >>
> >> It comes from that it can be used as an alternative to
> odd limit.
> >> Interestingly, IIRC Paul showed odd-limit is as close to
> the
> >> product thing as we can get in an octave-equivalent
> measure. Is
> >> that right, Paul?
> >
> >in a certain sense dealing with harmonic entropy, yes.
> >
> >
> >To unsubscribe from this group, send an email to:
> >tuning-math-unsubscribe@y...
> >
> >
> >
> >Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
> >
> >

Try it with clarinet timbre, piano timbre and oboe timbre,
and I can practically guarantee that you'll each get an
inconsistent result across timbres.

---- Original message ----
>Date: Fri, 08 Nov 2002 16:43:59 -0000
>From: "gdsecor" <gdsecor@yahoo.com>
>Subject: [tuning-math] Re: from the realms of private
correspondence
>To: tuning-math@yahoogroups.com
>
>--- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:
>> >>That's my interpretation of span -- it dilutes
concordance
>> >>without adding discordance. But according to the
product limit,
>> >>we've just added discordance to 5:3 by stretching it by
an
>> >>octave.
>> > [GS:]
>> >Depends on which direction you stretch it. Transpose
the bottom
>> >tone downward and you'll add discordance, but transpose
it upward
>> >and you won't add nearly as much
>> [CL:]
>> Transposing the bottom tone upward flips the ratio.
Perhaps you
>> meant the top tone upward?
>
>Yes.
>
>> Listening just now (in two registers), I find 10:3 less
concordant
>> than 5:3, and 12:5 more concordant than 6:5. 6:5 suffers
unfairly
>> perhaps from too little span.
>
>I don't think that I would agree, but perhaps the timbres
that we're
>hearing these in might have something to do with it:
>
>/tuning-math/message/4945
>
>I haven't had any desire to delve too deeply into the all
of the
>variables that would be considered in a scientific
treatment of the
>subject (too many other things to do) and am happy to leave
that to
>others to pursue. I gave my opinion only because you asked
for
>it. :)
>
>--George
>
>
>
>To unsubscribe from this group, send an email to:
>tuning-math-unsubscribe@yahoogroups.com
>
>
>
>Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

--- In tuning-math@y..., <Josh@o...> wrote:
> Try it with clarinet timbre, piano timbre and oboe timbre,
> and I can practically guarantee that you'll each get an
> inconsistent result across timbres.

I have, and I don't. Have you?

-Carl

For what it's worth, the Danner thing I mentioned before
deals mostly with trichords.

MUSIC PERCEPTION also has some articles on subjective
trichord similarity, which might also help gauge
"normal" interpretation of comparative dissonance.
Also some good work on scale construction as resolution
of inharmonic partials in Indian music, and in piano tuning
(!).
Have you guys seen this journal?

---- Original message ----
>Date: Fri, 08 Nov 2002 20:19:07 -0000
>From: "Carl Lumma" <clumma@yahoo.com>
>Subject: [tuning-math] Re: from the realms of private
correspondence
>To: tuning-math@yahoogroups.com
>
>> Tenney Harmonic Distance. Note that it is only defined
for
>> dyads. I attempted to extend it to triads. Paul claims
that
>> in so doing, I removed its metric status.
>
>I also don't see how Tenney HD meets property 4... take
>dyads 33:26 and 39:22 (Paul's example).
>
>-Carl
>
>
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--- In tuning-math@y..., <Josh@o...> wrote:
> For what it's worth, the Danner thing I mentioned before
> deals mostly with trichords.
>
> MUSIC PERCEPTION also has some articles on subjective
> trichord similarity, which might also help gauge
> "normal" interpretation of comparative dissonance.
> Also some good work on scale construction as resolution
> of inharmonic partials in Indian music, and in piano tuning
> (!).
> Have you guys seen this journal?

i've seen a little bit. what's this inharmonicity article? i might
try to check it out if i can, if only to poke holes in it . . .

Definition of "diminished second":
two oboes playing in unison.

---- Original message ----
>Date: Fri, 08 Nov 2002 21:59:02 -0000
>From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
...
property 4 only says that if
>the distance between two points is *zero*, they have to be
the same
>point.

Always?

---- Original message ----
>Date: Fri, 08 Nov 2002 22:42:21 -0000
>From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
>Subject: Fwd: [tuning-math] Re: from the realms of private
correspondence
>To: tuning-math@yahoogroups.com
>
>2:1
>
>--- In tuning-math@y..., <Josh@o...> wrote:
>> How are we defining "octave"?
>>
>> ---- Original message ----
>> >Date: Fri, 08 Nov 2002 21:50:29 -0000
>> >From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
>> >Subject: [tuning-math] Re: from the realms of private
>> correspondence
>> >To: tuning-math@y...
>> >
>> >--- In tuning-math@y..., "Carl Lumma" <clumma@y...>
wrote:
>> >> >I don't understand how the term "limit" got into your
>> question,
>> >> >or is this what others have called it?
>> >>
>> >> It comes from that it can be used as an alternative to
>> odd limit.
>> >> Interestingly, IIRC Paul showed odd-limit is as close
to
>> the
>> >> product thing as we can get in an octave-equivalent
>> measure. Is
>> >> that right, Paul?
>> >
>> >in a certain sense dealing with harmonic entropy, yes.
>> >
>> >
>> >To unsubscribe from this group, send an email to:
>> >tuning-math-unsubscribe@y...
>> >
>> >
>> >
>> >Your use of Yahoo! Groups is subject to
>> http://docs.yahoo.com/info/terms/
>> >
>> >
>
>
>To unsubscribe from this group, send an email to:
>tuning-math-unsubscribe@yahoogroups.com
>
>
>
>Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

With the synthetic versions of these timbres I've played
with in JI, I've yet to find any reliable way of projecting
comparative dissonances of ic3 and ic4 across all three,
and the clarinet seems to present a lot of extra
uncertainties on the extreme ends of audible space.
Your ears may differ, but I several other people who
have experienced similar phenomena, although not necessarily
as mapping onto my own experience.

I may have mentioned this before, but in my thesis work
I was conditioning mostly non-musicians to hear either
either 12tet augmented triads or various forms of 12tet
major & minor triads as more "stable" in synthetic clarinet
timbre. The conditioning not only had no significant effect,
between these two groups, but both groups actually
significantly preferred the augmented triad as MORE stable
than a first inversion major triad.
Since then, a lot of things have started to sound different
to me. In particular, clarinets playing in parallel major
ninths have come to sound quite consonant to me; I seem to
be "unlearning" tonal grammar.

---- Original message ----
>Date: Fri, 08 Nov 2002 23:09:53 -0000
>From: "Carl Lumma" <clumma@yahoo.com>
>Subject: Fwd: [tuning-math] Re: from the realms of private
correspondence
>To: tuning-math@yahoogroups.com
>
>--- In tuning-math@y..., <Josh@o...> wrote:
>> Try it with clarinet timbre, piano timbre and oboe timbre,
>> and I can practically guarantee that you'll each get an
>> inconsistent result across timbres.
>
>I have, and I don't. Have you?
>
>-Carl

Neither of the specific inharmonicity articles I'm
thinking of is dogmatic enough to require much hole-poking.
Sorry I can't remember the authors' names right now.
One article basically shows that inharmonic partials
produced by putting threads under the ends of strings on
Indian string instruments (standard technique) were
well-correlated with intonation variances of some scale
degrees; that at least some good performers intone
with at least implicit reference to inharmonics.
The piano tuning article, if I remember correctly, shows
that the extent to which piano tuners stretch the octave
on a piano correlates with the degree of stretching of
the harmonic series on piano strings.
I only remember the piano article at all because it
also showed that piano tuning makes ic4 sound like shit,
which was an important point in my thesis; it may explain
why pianists hate the augmented triad so much, and why
piano-oriented theorists are so quick to consider it
a dissonance in practically any timbral context.

---- Original message ----
>Date: Fri, 08 Nov 2002 23:58:25 -0000
>From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
>Subject: Fwd: [tuning-math] Re: from the realms of private
correspondence
>To: tuning-math@yahoogroups.com
>
>--- In tuning-math@y..., <Josh@o...> wrote:
>> For what it's worth, the Danner thing I mentioned before
>> deals mostly with trichords.
>>
>> MUSIC PERCEPTION also has some articles on subjective
>> trichord similarity, which might also help gauge
>> "normal" interpretation of comparative dissonance.
>> Also some good work on scale construction as resolution
>> of inharmonic partials in Indian music, and in piano
tuning
>> (!).
>> Have you guys seen this journal?
>
>i've seen a little bit. what's this inharmonicity article?
i might
>try to check it out if i can, if only to poke holes in
it . . .
>
>
>To unsubscribe from this group, send an email to:
>tuning-math-unsubscribe@yahoogroups.com
>
>
>
>Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

i'm not sure what you're asking. if it's about harmonic entropy,
perhaps it's better asked on that list.

--- In tuning-math@y..., <Josh@o...> wrote:
> Always?
>
> ---- Original message ----
> >Date: Fri, 08 Nov 2002 22:42:21 -0000
> >From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> >Subject: Fwd: [tuning-math] Re: from the realms of private
> correspondence
> >To: tuning-math@y...
> >
> >2:1
> >
> >--- In tuning-math@y..., <Josh@o...> wrote:
> >> How are we defining "octave"?
> >>
> >> ---- Original message ----
> >> >Date: Fri, 08 Nov 2002 21:50:29 -0000
> >> >From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> >> >Subject: [tuning-math] Re: from the realms of private
> >> correspondence
> >> >To: tuning-math@y...
> >> >
> >> >--- In tuning-math@y..., "Carl Lumma" <clumma@y...>
> wrote:
> >> >> >I don't understand how the term "limit" got into your
> >> question,
> >> >> >or is this what others have called it?
> >> >>
> >> >> It comes from that it can be used as an alternative to
> >> odd limit.
> >> >> Interestingly, IIRC Paul showed odd-limit is as close
> to
> >> the
> >> >> product thing as we can get in an octave-equivalent
> >> measure. Is
> >> >> that right, Paul?
> >> >
> >> >in a certain sense dealing with harmonic entropy, yes.
> >> >
> >> >
> >> >To unsubscribe from this group, send an email to:
> >> >tuning-math-unsubscribe@y...
> >> >
> >> >
> >> >
> >> >Your use of Yahoo! Groups is subject to
> >> http://docs.yahoo.com/info/terms/
> >> >
> >> >
> >
> >
> >To unsubscribe from this group, send an email to:
> >tuning-math-unsubscribe@y...
> >
> >
> >
> >Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
> >
> >

--- In tuning-math@y..., <Josh@o...> wrote:
> Neither of the specific inharmonicity articles I'm
> thinking of is dogmatic enough to require much hole-poking.
> Sorry I can't remember the authors' names right now.
> One article basically shows that inharmonic partials
> produced by putting threads under the ends of strings on
> Indian string instruments (standard technique) were
> well-correlated with intonation variances of some scale
> degrees; that at least some good performers intone
> with at least implicit reference to inharmonics.

this is sensible.

> The piano tuning article, if I remember correctly, shows
> that the extent to which piano tuners stretch the octave
> on a piano correlates with the degree of stretching of
> the harmonic series on piano strings.

this is well-known (see Hall, _Musical Acoustics_).