The high note

It seems intuitive that, when any chord is played, in any inversion,
the note of highest pitch strikes the ear much more clearly than the
others. It seems to follow that this note has more compelling need to
be tuned as expected in order not to be flagged as sour.

As anecdotal reinforcement, Paul E's points of displeasure in some of my
retuned files tend to focus on melody (== highest) notes. The Bach
Chaconne, for example, does have a note moving by 20 cents where he
identifies it, but there is also an earlier note, at about 1:58, which
moves by about same amount. That earlier note is not the HIGHEST note,
however, whereas the one Paul identifies IS.

My question: does anyone know of studies that attempt to document this
effect, and perhaps even quantify it?

JdL

John deLaubenfels wrote,

>It seems intuitive that, when any chord is played, in any inversion,
>the note of highest pitch strikes the ear much more clearly than the
>others. It seems to follow that this note has more compelling need to
>be tuned as expected in order not to be flagged as sour.

>As anecdotal reinforcement, Paul E's points of displeasure in some of my
>retuned files tend to focus on melody (== highest) notes. The Bach
>Chaconne, for example, does have a note moving by 20 cents where he
>identifies it, but there is also an earlier note, at about 1:58, which
>moves by about same amount. That earlier note is not the HIGHEST note,
>however, whereas the one Paul identifies IS.

>My question: does anyone know of studies that attempt to document this
>effect, and perhaps even quantify it?

John Starrett had pointed to some research indicating that in Barbershop
singing, the melody (highest part) tends to be tuned pretty much in 12-tET
and the other voices tune in JI relative to that note. That would, of
course, be a type of adaptive JI, one that has near-zero tolerance for
drifts/shifts in the upper voice but doesn't care about them at all in lower
voices.

>From: "John A. deLaubenfels" <jadl@idcomm.com>
>
>It seems intuitive that, when any chord is played, in any inversion,
>the note of highest pitch strikes the ear much more clearly than the
>others. It seems to follow that this note has more compelling need to
>be tuned as expected in order not to be flagged as sour.
>
[clip]
>
>My question: does anyone know of studies that attempt to document this
>effect, and perhaps even quantify it?

I believe the phenomenon goes by the name "masking".

John Link

****************************************************************************

Watch for the CD "Live at Saint Peter's" by the JOHN LINK VOCAL QUINTET,
featuring original compositions as well as arrangements of instrumental
music by Brahe and Taylor, Chick Corea, Miles Davis, Claude Debussy, Bill
Evans, Ennio and Andrea Morricone, Modeste Mussorgsky, Erik Satie, and Earl
Zindars.

****************************************************************************

Check out WWW.DUESBERG.COM for information that could make the difference
between life and death for you or someone you know.

****************************************************************************

>I believe the phenomenon goes by the name "masking".

Masking is actually the phenomenon in which the lowest note is heard clearly
while it creates an apparent reduction in volume in higher notes.

Daniel Wolf wrote,

>In
>early polyphonic music the uppermost melodic line is not necessarily the
most
>important one (_Hauptstimme_). (The same, may I add, is true for most
gamelan
>genres and for "barbershop" arrangements).

It would seem unusual for a barbershop arrangement not to put the main
melody in the top voice. Do you have any examples?

>The "lead" voice in "barbershop" arrangements is the 2nd tenor.

Thanks for pointing that out. I wonder, in regard to the research John
Starrett brought up, if it is in fact the "lead" voice rather than the
highest voice which supposedly approximates 12-tET.

>>The "lead" voice in "barbershop" arrangements is the 2nd tenor.
>
>Thanks for pointing that out. I wonder, in regard to the research John
>Starrett brought up, if it is in fact the "lead" voice rather than the
>highest voice which supposedly approximates 12-tET.

The Lead voice is what John Starrett was talking about. It is usually the
2nd highest voice, but the tenor may often be lower, and the baritone may
even be higher in some voicings.

And BTW, the Lead most certainly does _not_ approximate 12-tET. It may
approximate open-ended pythagorean tuning. But I'll eat an item of
clothing if anyone can show a recording with fifths centered around 700 cents.

>John Starrett had pointed to some research indicating that in Barbershop
>singing, the melody (highest part) tends to be tuned pretty much in 12-tET
>and the other voices tune in JI relative to that note. That would, of
>course, be a type of adaptive JI, one that has near-zero tolerance for
>drifts/shifts in the upper voice but doesn't care about them at all in
>lower voices.

That wasn't research, it was the consensus of a usenet discussion. One
which hardly inspires confidence, if you read it.

>> [Carl]
>> Blasted California school!
>
>Presuming myself to be a sort-of member of the
>California microtonal 'scene', I'm mystified by
>references to this 'California school'.

I think Paul meant the 'American Gamelan' school (Harrison and Doty).
Interestingly, both of these composers have also worked with
extended-reference-like JI (Harrison's free JI and several of Doty's
efforts on _Uncommon Practice_). Perhaps less interesting, but worth
noting, is that I find Other Music's (14-tone) fixed JI sublime...

-Carl

>And BTW, the Lead most certainly does _not_ approximate 12-tET. It may
>approximate open-ended pythagorean tuning.

Well that would still be far closer to 12-tET than the result of most strict
or adaptive JI schemes.

>But I'll eat an item of
>clothing if anyone can show a recording with fifths centered around 700
cents.

I think you'll have trouble making a statistically significant distinction
between 700� and 702� melodic fifths in the Lead line. You might have a
better chance with 800� vs. 794� melodic minor sixths. I don't see any good
reason why the latter would be preferred. Again, I believe that, with the
possible exception of octaves, fifths, and fourths, _melodic_ (though not
harmonic) intervals are mainly learned through cultural conditioning -- just
look at the wide variety of melodic minor sixths found in the scales of the
world's melodic traditions.

>>Presuming myself to be a sort-of member of the
>>California microtonal 'scene', I'm mystified by
>>references to this 'California school'.

>I think Paul meant the 'American Gamelan' school (Harrison and Doty).
>Interestingly, both of these composers have also worked with
>extended-reference-like JI (Harrison's free JI and several of Doty's
>efforts on _Uncommon Practice_). Perhaps less interesting, but worth
>noting, is that I find Other Music's (14-tone) fixed JI sublime...

Those are still strict JI, as opposed to adaptive JI.

I wrote,

>You might have a
>better chance with 800� vs. 794� melodic minor sixths.

Oops -- 794 should be 792.

>
>>The "lead" voice in "barbershop" arrangements is the 2nd tenor.
>
> Thanks for pointing that out. I wonder, in regard to the research John
> Starrett brought up, if it is in fact the "lead" voice rather than the
> highest voice which supposedly approximates 12-tET.

I would think it very much depends on who is singing the 2nd tenor (lead)
and what his tuning habits are. If I were singing it you wouldn't hear much
12-tET.(But then, as a bass-baritone I never had the responsibility :-)

>Well that would still be far closer to 12-tET than the result of most
>strict or adaptive JI schemes.

Absolutely. But I think it's a mistake to say 12-tET unless you can show
that the performers have a way to, and reason for, making the small and
very precise adjustments that define the temperament. This is a
temperament that could not be tuned on a fixed-pitch instrument with any
accuracy much before the 20th century. And the number of Barbershop tunes
that depend on the vanishing of the pythagorean comma are very few indeed.

>>But I'll eat an item of clothing if anyone can show a recording with
>>fifths centered around 700 cents.
>
>I think you'll have trouble making a statistically significant distinction
>between 700� and 702� melodic fifths in the Lead line.

Okay, but that's not evidence for 12-tET.

>You might have a better chance with 800� vs. 794� melodic minor sixths.

Or, maybe even better with... the majors thirds!

>I don't see any good reason why the latter would be preferred. Again, I
>believe that, with the possible exception of octaves, fifths, and fourths,
>_melodic_ (though not harmonic) intervals are mainly learned through
>cultural conditioning -- just look at the wide variety of melodic minor
>sixths found in the scales of the world's melodic traditions.

I don't believe that any cultural conditioning could specify 12-tET over
pythagorean in a melody (or anywhere else, for that matter). I'd be
surprised to meet a performer who could switch between them at will. My
only problem with calling either 12-tET is that while just intervals have
been shown to be attractors for performance data of all types all over the
world, I've never seen believable evidence that any 12-tET interval was
attracting performance data of any type anywhere.

>>I think Paul meant the 'American Gamelan' school (Harrison and Doty).
>>Interestingly, both of these composers have also worked with
>>extended-reference-like JI (Harrison's free JI and several of Doty's
>>efforts on _Uncommon Practice_). Perhaps less interesting, but worth
>>noting, is that I find Other Music's (14-tone) fixed JI sublime...
>
>Those are still strict JI, as opposed to adaptive JI.

Yup.

-Carl

Carl Lumma wrote,

>My
>only problem with calling either 12-tET is that while just intervals have
>been shown to be attractors for performance data of all types all over the
>world, I've never seen believable evidence that any 12-tET interval was
>attracting performance data of any type anywhere.

On the contrary, I've only ever seen studies of Western performances that
show _no_ evidence for leaning toward just intervals in melody, and at best
represent evidence for a _stretched_ 12-tET standard.

>Absolutely. But I think it's a mistake to say 12-tET unless you can show
>that the performers have a way to, and reason for, making the small and
>very precise adjustments that define the temperament. This is a
>temperament that could not be tuned on a fixed-pitch instrument with any
>accuracy much before the 20th century. And the number of Barbershop tunes
>that depend on the vanishing of the pythagorean comma are very few indeed.

My intent was quite the opposite -- I meant that the precise intervals that
define Pythagorean tuning would have to be sung quite accurately to be
statistically distinguishable from a null hypothesis of 12-tET with random
errors. You took it the other way around.

>On the contrary, I've only ever seen studies of Western performances that
>show _no_ evidence for leaning toward just intervals in melody, and at best
>represent evidence for a _stretched_ 12-tET standard.

On what basis do you claim the 3:2 works to select "tetrachordal" scales?
Anyway, this statement is not contrary to mine; I suspect that's a very
active "at best", and I don't necessarily believe 12-tET has anything to do
with "stretched 12-tET".

>>Absolutely. But I think it's a mistake to say 12-tET unless you can show
>>that the performers have a way to, and reason for, making the small and
>>very precise adjustments that define the temperament. This is a
>>temperament that could not be tuned on a fixed-pitch instrument with any
>>accuracy much before the 20th century. And the number of Barbershop tunes
>>that depend on the vanishing of the pythagorean comma are very few indeed.
>
>My intent was quite the opposite -- I meant that the precise intervals that
>define Pythagorean tuning would have to be sung quite accurately to be
>statistically distinguishable from a null hypothesis of 12-tET with random
>errors. You took it the other way around.

I was responding to the "consensus" of the e-mail discussion mentioned by
John Starrett, that Lead's sing their melodies in 12-tET. That means
12-tET is not the null hypothesis. Which is all I was trying to say above.

-Carl

Carl Lumma wrote,

>On what basis do you claim the 3:2 works to select "tetrachordal" scales?

Acoustics.

>I don't necessarily believe 12-tET has anything to do
>with "stretched 12-tET".

Well, Pythagorean intervals are larger than their 12-tET cousins half the
time, and smaller the other half.

>I was responding to the "consensus" of the e-mail discussion mentioned by
>John Starrett, that Lead's sing their melodies in 12-tET. That means
>12-tET is not the null hypothesis. Which is all I was trying to say above.

What is or is not the null hypothesis depends solely on the intent of the
investigator. The "consensus" may simply have reflected a perception that
the deviations from 12-tET in the lead line were not systematically in the
direction of one or another pre-specified tuning system to say that one of
the latter was being used instead of 12-tET.

[Carl Lumma:]
>I don't necessarily believe 12-tET has anything to do with "stretched
12-tET".

[Paul Erlich:]
>Well, Pythagorean intervals are larger than their 12-tET cousins half
the time, and smaller the other half.

[Carl Lumma:]
>I was responding to the "consensus" of the e-mail discussion
mentioned by John Starrett, that Lead's sing their melodies in 12-tET.

Actually the very first html (Thread 1) under the heading "CONCLUSION
FIRST" reads quite a bit differently than that:

"So the lead uses Pythagorean or Equal-Tempered or even some
compromise between the two -- it probably doesn't even matter, as long
as his melody sounds like a melody."

Dan

Dan wrote,

>Actually the very first html (Thread 1) under the heading "CONCLUSION
>FIRST" reads quite a bit differently than that:

>"So the lead uses Pythagorean or Equal-Tempered or even some
>compromise between the two -- it probably doesn't even matter, as long
>as his melody sounds like a melody."

Thanks Dan. That is how John Starrett reported it. The important point, in
the context of the adaptive tuning discussion in which this arose, is that
given the 5- or 7-limit JI verticalities that occur in barbershop harmony,
this "conclusion first" implies that the other three voices would be forced
to make nearly full syntonic and septimal comma adjustments quite often,
while the lead line would stick quite close to a fixed, Pythagorean/12-tET
set of intervals. Given our recent observations that comma adjustements tend
to be more disturbing when in the melody than when in other voices,
"Conclusion first" does not seem unreasonable to me.

>>On what basis do you claim the 3:2 works to select "tetrachordal" scales?
>
>Acoustics.

But you've never seen a study that suggested leaning toward just intervals
in melody?

>>I don't necessarily believe 12-tET has anything to do
>>with "stretched 12-tET".
>
>Well, Pythagorean intervals are larger than their 12-tET cousins half the
>time, and smaller the other half.

Sure, but how does that relate to the quoted statement?

>What is or is not the null hypothesis depends solely on the intent of the
>investigator.

That's right! And the intent of the "investigator" in this thread was to
show that 12-tET was the basis of Barbershop melody. While another
investigator may choose the reverse, I hope to show that he would be
mis-guided. What Leads sing may be statistically indistinguishable from
any number of crazy tuning schemes. I hope to show there's no reason to
single out 12. Barbershopers do not train with tempered instruments.

>The "consensus" may simply have reflected a perception that the deviations
>from 12-tET in the lead line were not systematically in the direction of
>one or another pre-specified tuning system to say that one of the latter
>was being used instead of 12-tET.

If you read the discussion, you'll see that about half of the authors
claimed Pythagorean, and about half 12-tET. What I'm saying is, there's
absolutely no reason to involve 12-tET, and that means it _shouldn't_ be
involved.

>Thanks Dan. That is how John Starrett reported it. The important point, in
>the context of the adaptive tuning discussion in which this arose, is that
>given the 5- or 7-limit JI verticalities that occur in barbershop harmony,
>this "conclusion first" implies that the other three voices would be forced
>to make nearly full syntonic and septimal comma adjustments quite often,
>while the lead line would stick quite close to a fixed, Pythagorean/12-tET
>set of intervals. Given our recent observations that comma adjustements
>tend to be more disturbing when in the melody than when in other voices,
>"Conclusion first" does not seem unreasonable to me.

I'd like to quote from a discussion that took place here over two years ago...

[me, Carl Lumma]
>This concept is very important in Barbershop, which is, by definition,
>melody being backed up with chords. The melody is usually sung in
>something roughly close to 12-tone Pythagorean (3-limit), while the notes
>used for the chords fit almost exactly in the 7-limit.

[Paul Erlich]
>The 7-limit harmony in barbershop is not merely "stuck on" to the diatonic
>scale; it consists of dominant seventh chords which are diatonic in
>function and origin, and the 27-cent adjustments required to achieve JI are
>not large enough to disturb the essential diatonicity of the music.

...Barbershop uses the 4:5:6:7 as a functional harmony far more often than
as a dominant chord...

[Paul Erlich]
>As for the pitch sets being different for melody and harmony, don't tell me
>that the sevenths of these dominant seventh chords never occur in the
>melody!

[me]
>They do, but not often. If the lead is singing the 7, then usually the
>tenor has the melody. There are many songs where the melody contains no
>pitches outside the 3-limit. What is important is that the melody is not
>really part of the voice leading in the traditional sense, except in the
>case of sustained notes. Chords are built _on_ it.

-Carl