defining just intonation (barbershop)

It seems clear to me that Vicentino's proposed adaptive JI, my own work
with adaptive JI (and/or quasi-JI), and barbershop singing, should all
fall into the same category, with many possible synonymous names:

adaptive JI
vertical (but not horizontal) JI
harmonic (but not scale) JI

(substitute HI (Harmonic Intonation) for JI as desired).

No one has brought forth figures of cents values used by skilled
barbershop singers, but I'm guessing they may deviate from exact
integer ratios by several cents, especially when singing 4:5:6:7 or
other complex chords. I typically keep vertical deviations to within
a few cents of theoretical as well, but not to within +-0.5 cents as
proposed by Dave Keenan for a true JI label.

JdL

--- In tuning@egroups.com, "John A. deLaubenfels" <jdl@a...> wrote:

> http://www.egroups.com/message/tuning/16506
>
> No one has brought forth figures of cents values used by
> skilled barbershop singers, but I'm guessing they may
> deviate from exact integer ratios by several cents,
> especially when singing 4:5:6:7 or other complex chords.
> I typically keep vertical deviations to within a few cents
> of theoretical as well, but not to within +-0.5 cents as
> proposed by Dave Keenan for a true JI label.

For the record, note that I agree pretty much with Dave
Keenan's restriction to "within +-0.5 cents" for a true
JI label. I've always contended that differences of
1 cent or less are negligible under most circumstances,
excluding only such particular cases as La Monte Young
sound installations.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> --- In tuning@egroups.com, "John A. deLaubenfels" <jdl@a...> wrote:
>
> > http://www.egroups.com/message/tuning/16506
> >
> > No one has brought forth figures of cents values used by
> > skilled barbershop singers, but I'm guessing they may
> > deviate from exact integer ratios by several cents,
> > especially when singing 4:5:6:7 or other complex chords.
> > I typically keep vertical deviations to within a few cents
> > of theoretical as well, but not to within +-0.5 cents as
> > proposed by Dave Keenan for a true JI label.
>
>
> For the record, note that I agree pretty much with Dave
> Keenan's restriction to "within +-0.5 cents" for a true
> JI label. I've always contended that differences of
> 1 cent or less are negligible under most circumstances,
> excluding only such particular cases as La Monte Young
> sound installations.
>
> -monz

Folks,

Show me any Barbershop Quartet singer, or any singer that can
deliberately sing "within +-0.5 cents" of Just Intonation, and
sustain this degree of "mechanical" accuracy over the course of
entire compositions, and I will dub him "Man Machine". Before I can
further swallow this - hook, line and sinker - I would like to
request that those using this analogy, come forth with measured proof
that singers are working with this degree of accuracy. My imagination
is stretched like a monochord string on this one! Especially since
I'm very accustomed to listening closely to, and analyzing the
realities and results of harmony singing in my own music, I will be
extremely interested to learn of artists with this kind of talent. I
would conjecture that if you analyze the individual parts of a four
part Barbershop Quartet harmony, you would find that each singer is
constantly subtly wavering in their pitch to match that of the rest
of the group and is likely not singing with this kind of imagined
accuracy for significant amounts of time.

In light of the above challenge, can it truly be shown that
Barbershop Quartet singing is really the ironclad and unshakeable
proof we need of the definition of JI? To clarify my point here: If
indeed a "beatlessness" is perceived in the chords of this music, and
yet we are saying also that there must be "within +-0.5 cents"
accuracy for it to truly be considered JI, then which am I to
understand is correct; an audible quality of beatlessness, or
the "within +-0.5 cents" rendered accuracy of the performance?

Come on through me a rope here! Rescue me from this sea of
ambiguities!

In eternal gratitude,

Jacky Ligon

[Jacky Ligon wrote:]
>Folks,
>
>Show me any Barbershop Quartet singer, or any singer that can
>deliberately sing "within +-0.5 cents" of Just Intonation, and
>sustain this degree of "mechanical" accuracy over the course of
>entire compositions, and I will dub him "Man Machine".

Jacky, I think you misinterpreted what was being said. Monz and I
agree that singers DON'T stay within +-0.5 cents. I'm still looking
for numbers, but I'd guess that the best barbershop singers stray
outside +-5 cents fairly regularly, but still achieve an excellent
harmony in intervals compared to 12-tET.

The only question is whether +-5 cents qualifies as "true JI" vs.
"quasi-JI". Yes?

JdL

--- In tuning@egroups.com, "John A. deLaubenfels" <jdl@a...> wrote:
> [Jacky Ligon wrote:]
> >Folks,
> >
> >Show me any Barbershop Quartet singer, or any singer that can
> >deliberately sing "within +-0.5 cents" of Just Intonation, and
> >sustain this degree of "mechanical" accuracy over the course of
> >entire compositions, and I will dub him "Man Machine".
>
> Jacky, I think you misinterpreted what was being said. Monz and I
> agree that singers DON'T stay within +-0.5 cents. I'm still looking
> for numbers, but I'd guess that the best barbershop singers stray
> outside +-5 cents fairly regularly, but still achieve an excellent
> harmony in intervals compared to 12-tET.
>
> The only question is whether +-5 cents qualifies as "true JI" vs.
> "quasi-JI". Yes?
>
> JdL

John,

Hello!

No, I did understand you and Monz, and was merely challenging the
idea of this degree of accuracy. And to illustrate the problem in
front of us all in pursuance of this topic, when a singer deviates "+-
5 cents" whilst singing a 3/2 or 2/1 in a harmony, what do you get?
Beats showering down like raindrops in a hurricane! Although with
thirds (or other intervals, according to the chord voicing) this
might be less perceptible.

This prompts the further question of; To what subjective (audible
quality) or mathematical degree will we allow the rapidity of beats
to determine or disqualify the "justness" of a chord's intoning?
Obviously there is a point at which an interval would be distuned
sharp or flat, when it would begin to slowly beat, and as it's tuned
further away, more defined and rapid beating is perceived. To
clarify: If certain chord tones are slightly distuned to where there
is only very slow beating, would we not generally tend to perceive
this as also being justly intoned? Especially if one were to hear it
without having first tuned the interval themselves. Would this slight
phasing make any difference in qualifying a chord as being justly
intoned? Perhaps there is a larger average tolerance of deviation for
the perception of justness, than the stated ""within +-0.5 cents" of
Just Intonation"", dependent upon the timbres under consideration. My
experience is that the human voice has the wonderful quality of
somewhat masking these kinds of deviations, likely because it's such
a "continuously variable" sort of sound and its harmonic structure.

I'm sure these are constant considerations in your adaptive work
(btw, I really enjoyed your recent midi files, which played
wonderfully on my system - preferring the 7 limit versions.).

To answer your question, in light of the Keenanian/OED definition,
being an audible quality, likely it would be construed as "true
JI".

Thanks,

Jacky Ligon

[I wrote:]
>>Jacky, I think you misinterpreted what was being said. Monz and I
>>agree that singers DON'T stay within +-0.5 cents. I'm still looking
>>for numbers, but I'd guess that the best barbershop singers stray
>>outside +-5 cents fairly regularly, but still achieve an excellent
>>harmony in intervals compared to 12-tET.

[Jacky:]
>No, I did understand you and Monz, and was merely challenging the
>idea of this degree of accuracy.

Oops, my bad. Thanks for the clarification!

[Jacky:]
>I'm sure these are constant considerations in your adaptive work
>(btw, I really enjoyed your recent midi files, which played
>wonderfully on my system - preferring the 7 limit versions.).

Kyool!! I really love this old stuff, and these are by far the richest
sequences I've tuned to date. I sent one of the premier swing
sequencers a sample of "A String of Pearls" in 7-limit, with rigid
vertical springs just like the one you downloaded, and he wrote back to
say he couldn't tell any difference! I guess the positive spin would be
that I didn't shock him, but to my ear the passage beginning at about
0:54, containing tonic seventh and subdominant seventh chords, is SO
much smoother and lovelier in 7-limit! Maybe he didn't get that far...

Paul E, is there any chance I could entice you into listening to this
file? You once spoke of tonic sevenths being used in blues. Well,
swing has them too! I'd be VERY curious to know if you think this is a
legitimate use of 7-limit tuning, especially since every example I've
thrown at you so far seems to get a thumbs-down in that regard!

JdL

--- In tuning@egroups.com, ligonj@n... wrote:
>
> Show me any Barbershop Quartet singer, or any singer that
> can deliberately sing "within +-0.5 cents" of Just Intonation,
> and sustain this degree of "mechanical" accuracy over the
> course of entire compositions, and I will dub him "Man Machine".

Jacky,

Most of us engaged in this debate (on this list) concur that
Barbershop should be labelled "adaptive JI". That's certainly
what I'd call it, and there's no way I ever intended to
imply that real humans could sing within the +-0.5 cents
accuracy I'd stipulate for the label of "true JI".

Additionally, since Barbershop style is permeated with
7-limit ratios and also makes use a great deal of the
10:12:15:17 chord, I'd hesitate to call it "true JI" anyway,
given my inclination to restrict that label to 5-limit music.

> To clarify my point here: If indeed a "beatlessness" is
> perceived in the chords of this music, and yet we are saying
> also that there must be "within +-0.5 cents" accuracy for
> it to truly be considered JI, then which am I to understand
> is correct; an audible quality of beatlessness, or the
> "within +-0.5 cents" rendered accuracy of the performance?
>
> Come on through [_sic_: you did mean "throw", correct?]
> me a rope here! Rescue me from this sea of ambiguities!

I would tend to go along with Dave Keenan and emphasize the
*audible* aspect. The fact that relatively beatless music
can usually be modelled mathematically by low-whole-number
ratios, regardless of its actual tuning, is something that
I think ties into my concept of finity:

http://www.ixpres.com/interval/dict/finity.htm

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, ligonj@n... wrote:
> ...Would this slight phasing make any difference in
> qualifying a chord as being justly intoned? Perhaps there
> is a larger average tolerance of deviation for the
> perception of justness, than the stated ""within +-0.5
> cents" of Just Intonation"", dependent upon the timbres
> under consideration. My experience is that the human
> voice has the wonderful quality of somewhat masking these
> kinds of deviations, likely because it's such a
> "continuously variable" sort of sound and its harmonic
> structure.

Jacky,

As we on this list know, Bill Sethares has done a great
deal of work on the interaction between timbre and tuning.
And you make the additional interesting point that perhaps
it is *because* the human voice is so easily adaptable as
regards tuning that listeners are much more "lenient" in
their peception of tuning for _a cappella_ voices.

But another very important consideration is the tempo of
the music. There has been quite a bit of argument that
the reason musical tempi became so much more rapid after
the Renaissance was *because* of the "fudging" of JI harmonies
in the meantone and, even more so, well- and equal-temperaments
which became the predominant tunings during the Baroque and
Classical periods.

Barbershop style generally has a slow enough pace that
listeners can get a real appreciation of the beatless JI
vertical sonorities. This is certainly another aspect to
its labelling as JI ... whether it's "adaptive" or "true".

-monz

[I wrote:]
>>to my ear the passage beginning at about
>>0:54, containing tonic seventh and subdominant seventh chords, is SO
>>much smoother and lovelier in 7-limit!

Oops again! The passage in question comes after the piece modulates
from C major to G major; the chords in question are G6 (G, B, D, E) and
C7 (G, Bb, C, E). So, one of the two is nicely 7-limit; the other is
the same in 5 or 7-limit. A "tonic seventh" exists only technically,
not in the modulated key.

JdL

[Carl Lumma:]
>Accuracy of barbershop? Their singers are
>capable of sustained chords tuned beatless to the limit of the timbres.
>See my post, "Barbershop Spectrogram", circa Dec. '98 (the files for
>the post are temp. off line, but I will provide them upon request).

I would very much like to see this!

[JdL]
>>The only question is whether +-5 cents qualifies as "true JI" vs.
>>"quasi-JI". Yes?

[Carl:]
>No! That question is meaningless. Shame on you all for entertaining
>it under the guise of good scholarship. If anyone disagrees, then
>he should provide the criteria that were used to arrive at these
>numbers, and why a binary distinction around them is warranted.

Dang, Carl - what's this upset about? I thought you were the guy who
wants infinitely rigid vertical springs (i.e. exact vertical JI) in his
tunings! Yet, am I understanding you correctly here as saying that an
unqualified "JI" should apply to +-5 cents? Or you saying that any
attempt to quantify a limit of true JI in cents is misguided?

(as I've said, I routinely tolerate vertical deviations of around +-5
cents in my adaptive work, and don't care, except to achieve some
convention for clear communication, whether this is called "adaptive JI"
or "adaptive quasi-JI")

[Carl:]
>I must be crazy.

I'm missing something. Please explain.

JdL

John deLaubenfels wrote,

>The only question is whether +-5 cents qualifies as "true JI" vs.
>"quasi-JI". Yes?

It's quasi-JI. If ±5.38 cents were the criterion, then 1/4-comma meantone
would be JI -- totally unacceptable given the vast literature contrasting
the two.

However, a ±0.5 cent critetion would be liberal enough to include schismatic
temperament, and composers like Eivind Groven did refer to schismatic
temperament as JI.

>Paul E, is there any chance I could entice you into listening to this
>file? You once spoke of tonic sevenths being used in blues. Well,
>swing has them too! I'd be VERY curious to know if you think this is a
>legitimate use of 7-limit tuning, especially since every example I've
>thrown at you so far seems to get a thumbs-down in that regard!

I listened to this when you first posted it, and I liked it. There were a
couple of questionable harmonic intervals that really stuck out from the
preponderantly beatless context . . . but for the most part I found it an
enjoyable "xenharmonization" of the tune.