Yahoo Tuning Groups Ultimate Backup tuning High third demo revealed!!!

I took a few hours to carefully examine the Jerry's high third demo (the
first example from Jerry's site). Results are surprising but eventually make
sense. First, I should state that computer analysis is not good at all to
isolate a single voice from a group (it is not possible, contrarily to the
human ear, to focus on a single instrument or singer). Nevertheless, if some
care are taken, and if I know what to look for, it is possible to asses
quite reliably the average pitch, overall pitch pattern. Further, eyeball
examination of spectrum and sonogram is void of any psychoaccoustic effect
affecting (possibly differently) trained or naive ears. "Quite reliably",
does not mean within 0,01 cent accuracy. I think that a precision is within
5 cents: sometime better when singer are really self assured in stable
unison, occasionally worse, when singers "fiddle around" and the signal is
not stable over long sufficiently long window.

First remark, as noted by Carl:

> Indeed, on the first check the piano seems sharp, and not on the second.

As far as I can see from the initial C3, the piano is around 30-32 cents
sharp. Is it intentional? Is it a the effect of bad A/D conversion
(sampling frequency slightly below 44100)? I doubt that it has anything to
do with mp3 encoding, but how to be sure?. Anyway, as it is consistent
throughout the recording it has no effect on relative results.

Another general remark is that every voice entry starts 70-80 cents below: a
sort of micro-portamento that settle after around 100 ms. That is quite
normal for vowel that are not preceded by a consonant and is due to the
build up of the sub-glottal pressure. Those transient part are discarded
from the measures.

OK boys (and girls!) here we go!

After the piano C3 cues, bass settle to a stable C3 that is the same as the
piano +- 1cents.

Soprano entry (after the micro-portamento) reach a rather large third wrt
the initial C3, around 393 cents (+- 5 cents) then goes down to finish at a
more stable value some 7 cents below its initial value. So naturally it is
ends down some 13 cents below piano E4.

What every body seem to have missed is that while the soprano was getting
down, bass was getting up, moving from 133.3 Hz to around 135.0 Hz some 20
cents up!! The "final" third is very small 365 cents, more than 20 cents
short of 4/5!! seems that soprano and bass missed their rendezvous.

But at this point, nobody seems to be very self assured and harmonics are
blunt (some "giggling" takes place).

Then the piano give the E4 and the soprano readjust to a much more precise
value that is the same as the piano +- 2 cents.
In the while, bass goes down again to settle to a very pure 4/5 third around
383 cents (+ 1200 of course) below soprano/piano E4.

Then the tenor enter and quickly settle to a fairly good fifth around 700
wrt to bass. but to get to this interval, the bass has get down a little
down and finish nearer (some 7 cents above) the piano C3 than in has been
when it was alone with the soprano. In the while, after tenor entry, soprano
raise her pitch by some 5 cents or so. The final chords look very much like
a 12 ET chord, but 5-7 cents sharp wrt the piano (accuracy +-5 cents at
best):

C3/G3 696
C3/E4 402

So it is not the soprano which is high, it is all voices in the chord.

---------------------- that is all for the "facts" ---------------------

I put "facts" between quotes because I am sure that not everybody will be
convinced, even though I provide fairly large error margins.

My interpretation (my out-of-the-blue theory) is:

Before soprano enter, they build up a 12ET mental image of the tenth. That
is the initial utterance of soprano, then both soprano and bass try to
readjust to 4/5 but overdone it and missed the point (perhaps they would
have succeed with some more time to settle).

Then with the help of the piano, soprano get reassured, produced a higher,
clearer E4 and the bass was able to produce a fairly good 4/5 third.

Afterward the tenor entered and both tenor and bass quickly adjust to
produce a good fifth with a root nearer to the piano pitch than it was just
before, but a little high (7 cents). That exemplify how a cappella singer
trade-off to move from chord to chord in order to keep both relative and
absolute justness (there is no such thing as the pitch drift as described in
http://www.medieval.org/emfaq/zarlino/article1.html "The myth of drifting
pitch")

Soprano readjusted to 12ET sixth wrt to tenor (who are, I suppose physically
nearer than bass).

BTW the interpretation still hold even if the soprano and bass produced a
correct naked tenth at the beginning.

any comments?

Franï¿½ois Laferriï¿½re

🔗emotionaljourney22 <paul@stretch-music.com>

🔗Gerald Eskelin <stg3music@earthlink.net>

On 4/3/02 7:18 AM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

> Message: 23
> Date: Wed, 3 Apr 2002 12:06:01 +0200
> From: LAFERRIERE François <francois.laferriere@cegetel.fr>
> Subject: High third demo revealed!!!
>
> I took a few hours to carefully examine the Jerry's high third demo (the
> first example from Jerry's site).

Many thanks for taking the time, François. I wish the recording and the
"performance" had been better. Had I known at the time that we would be
examining it with this kind of precision, I would have taken more time with
it. It was done primarily to demonstrate what I was reporting on the list at
the time. Unfortunately, it doesn't do that very well, particularly when
examined as closely as you have done. Nevertheless, your findings are
interesting here.

> Results are surprising but eventually make
> sense. First, I should state that computer analysis is not good at all to
> isolate a single voice from a group (it is not possible, contrarily to the
> human ear, to focus on a single instrument or singer). Nevertheless, if some
> care are taken, and if I know what to look for, it is possible to asses
> quite reliably the average pitch, overall pitch pattern.

I would think that's all we would need here.

> Further, eyeball
> examination of spectrum and sonogram is void of any psychoaccoustic effect
> affecting (possibly differently) trained or naive ears. "Quite reliably",
> does not mean within 0,01 cent accuracy. I think that a precision is within
> 5 cents: sometime better when singer are really self assured in stable
> unison, occasionally worse, when singers "fiddle around" and the signal is
> not stable over long sufficiently long window.

Lots of fiddling going on here, unfortunately.
>
> First remark, as noted by Carl:
>
>> Indeed, on the first check the piano seems sharp, and not on the second.
>
> As far as I can see from the initial C3, the piano is around 30-32 cents
> sharp. Is it intentional? Is it a the effect of bad A/D conversion
> (sampling frequency slightly below 44100)? I doubt that it has anything to
> do with mp3 encoding, but how to be sure?. Anyway, as it is consistent
> throughout the recording it has no effect on relative results.

I think Carl's "first check" and "second" are referring to the E the piano
plays to "check" on the current position of the sung third.

Since the school pianos are tuned quite regularly, I have to think the
sharpness of the initial C must be due to recording transfers. I agree that
it would have little or no effect on the relative results. Unfortunately,
the basses settle on a pitch that is audibly higher than the piano's C,
making the two "check" pitches (E) somewhat less valid than they should have
been.
>
> Another general remark is that every voice entry starts 70-80 cents below: a
> sort of micro-portamento that settle after around 100 ms. That is quite
> normal for vowel that are not preceded by a consonant and is due to the
> build up of the sub-glottal pressure. Those transient part are discarded
> from the measures.

Too bad the basses overcooked their portamento and made it "macro-".
>
> OK boys (and girls!) here we go!
>
> After the piano C3 cues, bass settle to a stable C3 that is the same as the
> piano +- 1cents.

That is surprising to to me. Both Bob and I hear the basses settle on pitch
much higher (many cents) than the piano's initial C. Skipping back and forth
from any later spot in the recording and the initial C verifies this.

However, skipping around after the basses settle seems to show that the
fundamental pitch holds firmly to a single pitch. There is no "bump" as I
skip. Whatever changes exist in the fundamental pitch once the basses
settle are imperceptible to my ear.

Since Paul will be quick to point out the difference between my "ear" and
objective truth, I will request that others do the same check.
>
> Soprano entry (after the micro-portamento) reach a rather large third wrt
> the initial C3, around 393 cents (+- 5 cents) then goes down to finish at a
> more stable value some 7 cents below its initial value. So naturally it is
> ends down some 13 cents below piano E4.
>
> What every body seem to have missed is that while the soprano was getting
> down, bass was getting up, moving from 133.3 Hz to around 135.0 Hz some 20
> cents up!! The "final" third is very small 365 cents, more than 20 cents
> short of 4/5!! seems that soprano and bass missed their rendezvous.

What "everybody" are you referring to? Were there earlier aural judgments on
this besides Bob's?

By "short of" do you mean "smaller than"? Yes, it would seem that JI was
missed somewhat by the basses and sopranos. (It still seems strange to me
that the basses moved much from their established pitch.
>
> But at this point, nobody seems to be very self assured and harmonics are
> blunt (some "giggling" takes place).

Believe me, there is considerable lack of self assurance here. This group
had only sung together for a few classes. In a sense, that was the idea: to
demonstrate that the "high third" effect occurred even among novice ears.
Looks like this recording doesn't represent that very well. By the same
token, it doesn't *disprove* the effect either. Since I no longer have a
choir to do a better job. We're (I'm) hoping Bob will recreate the
experiment using his seasoned singers.
>
> Then the piano give the E4 and the soprano readjust to a much more precise
> value that is the same as the piano +- 2 cents.
> In the while, bass goes down again to settle to a very pure 4/5 third around
> 383 cents (+ 1200 of course) below soprano/piano E4.

As Carl pointed out, it would have been smarter to have not played the
"check" pitch during the recording, but to add it later for comparison.
Clearly, the singers were influenced by hearing what some of them may have
heard as a "correction" of their pitch. I didn't instruct the singers to do
anything other than to sing what they felt is the "best" pitch throughout
the exercise.
>
> Then the tenor enter and quickly settle to a fairly good fifth around 700
> wrt to bass. but to get to this interval, the bass has get down a little
> down and finish nearer (some 7 cents above) the piano C3 than in has been
> when it was alone with the soprano. In the while, after tenor entry, soprano
> raise her pitch by some 5 cents or so. The final chords look very much like
> a 12 ET chord, but 5-7 cents sharp wrt the piano (accuracy +-5 cents at
> best):
>
> C3/G3 696
> C3/E4 402
>
> So it is not the soprano which is high, it is all voices in the chord.

Apparently true, particularly in view of the basses high start. However, if
all the voices are high we have learned very little here about the relative
difference between the dyad third and the triad third. Too bad. Hopefully a
better performance and recording will yield more reliable evidence one way
or the other.

> ---------------------- that is all for the "facts" ---------------------
>
> I put "facts" between quotes because I am sure that not everybody will be
> convinced, even though I provide fairly large error margins.
>
> My interpretation (my out-of-the-blue theory) is:
>
> Before soprano enter, they build up a 12ET mental image of the tenth. That
> is the initial utterance of soprano, then both soprano and bass try to
> readjust to 4/5 but overdone it and missed the point (perhaps they would
> have succeed with some more time to settle).

Sounds right.
>
> Then with the help of the piano, soprano get reassured, produced a higher,
> clearer E4 and the bass was able to produce a fairly good 4/5 third.

"Reassured" in the context of this experiment should unfortunately read
"influenced by."

Perhaps the basses as well may have been influenced by hearing the pianos
"check" pitch, although I don't hear them moving much. The soprano move to
the piano's pitch is disturbingly audible. Since the basses are already
sharp to the given C, it's not surprising that this third is closer to 4:5
than to ET.

By redoing the experiment following Carl's suggestion to not sound the E
should help in this regard, whether the singers be novice or experienced.
>
> Afterward the tenor entered and both tenor and bass quickly adjust to
> produce a good fifth with a root nearer to the piano pitch than it was just
> before, but a little high (7 cents). That exemplify how a cappella singer
> trade-off to move from chord to chord in order to keep both relative and
> absolute justness

My thoughts exactly.

> (there is no such thing as the pitch drift as described in
> http://www.medieval.org/emfaq/zarlino/article1.html "The myth of drifting
> pitch")

I'll have to check this out. Maybe I'll try to find some time during the
next decade. In the meantime, I'll take your word for it.
>
> Soprano readjusted to 12ET sixth wrt to tenor (who are, I suppose physically
> nearer than bass).

Yes, they are. Perhaps this factor could be minimized by mixing the singers
next time.
>
> BTW the interpretation still hold even if the soprano and bass produced a
> correct naked tenth at the beginning.

I'm not sure what a "correct" naked tenth is. Do you mean a JI 3:5?
>
> any comments?

Thanks again for the effort, François. This was interesting and helpful,
particularly in showing why we could use a better example to study next
time. :-)
>
Jerry

🔗emotionaljourney22 <paul@stretch-music.com>

🔗jpehrson2 <jpehrson@rcn.com>

🔗LAFERRIERE François <francois.laferriere@cegetel.fr>

Paul wrote:
> > actually, this sixth is 6 cents sharper than an ET major sixth, by
> > the numbers above. well, it sure seems that this example confirms
> > jerry's claim, despite its 'giggles'!

I would not be that confident about this 6 cents above 12ET sixth value. The
errors in cents add to each other when comparing voices. Considering the
signal in the recording, 3 cents of accuracy for each voice is quite
optimistic, so 6 cents could be just an "experimental error". What is sure
is that this sixth (~906 cents) is much more "like" ET sixth (900 cents)
than JI 5/3 (884 cents). It is also quite sure that the whole chord is above
the piano by 6-7 cents (this value is more reliable because it compares
voices to the piano, not voice to voice).

In this single experiment, I would say that the dominant effect is the rise
of triad mainly due to the fact that the bass has been pulled up some 15
cents (to be 5/2 below soprano) when the soprano reajusted itself to the
piano E4.

> ***So does *this* "prove" that Jerry's "high third" is a
> scientifically verifiable phenomenon??

The third (tenth) is definitely higher than 5/4 (5/2) but is it sure that it
is higher than ET third? My measurement on a single sample can not prove
(nor disprove) it for sure (but perhaps am I over cautious?)

> perhaps francois could post a picture of the sonogram so that we can
> see more clearly what happens as a function of time.

I will try to do something about it, but it is not that easy to illustrate
this because to get those results, I had to produce many spectrograms with
various window size, in order to localize stable segment from which I could
"slice" of usable spectrum. I will make an effort to work out something
illustrative, but remember that I do that as a hobby....

yours truly

François Laferrière

🔗robert_wendell <rwendell@cangelic.org>

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., LAFERRIERE François <fran
cois.laferriere@c...>
> wrote:
>
> > The final chords look very much like
> > a 12 ET chord, but 5-7 cents sharp wrt the piano (accuracy +-5
> cents at
> > best):
> >
> > C3/G3 696
> > C3/E4 402
> >
> > So it is not the soprano which is high, it is all voices in the
> chord.
>
> hi francois, thanks for your good work. as a matter of fact, this
402
> cent interval *does* bespeak the soprano singing a high third,
> according to jerry. the high third, he says, is higher than equal
> temperament, but lower than pythagorean tuning. 402 cents certainly
> qualifies, doesn't it?

Bob Wendell:
With a margin of error of +-5 cents on both the root and the tenth,
how can we say 2 cents above ET qualifies, Paul? If the root is 5
cents higher than measured and the tenth 5 cents lower, that yields
a 392 cent third which, since dissonance is roughly an exponential
function of pitch deviation from JI, sounds in relation to ET almost
just. I personally doubt it is likely that both measurements were at
these extremes of the stated tolerance, but the final "near just"
tenth I describe in my initial response was brief in the middle and
very brief at the very end. Francois has made it clear that such
brief excursions are outside the scope of his setup to measure,and
even for +-5 cent tolerances require some length of time to measure.
>
> > Soprano readjusted to 12ET sixth wrt to tenor (who are, I suppose
> physically
> > nearer than bass).
>
> actually, this sixth is 6 cents sharper than an ET major sixth, by
> the numbers above. well, it sure seems that this example confirms
> jerry's claim, despite its 'giggles'!

Bob Wendell:
Both this information and my ear find it very hard to buy that, Paul.
First the soprano tenth is slighty sharp tending away from JI from
the outset. This is slight but aurally detectable. Then when the
piano sounds the ET tenth for reference the first time, there is a
very brief excursion of the soprano to the ET third (a naturally
stronger attraction to adjust to a near unison) and then very briefly
beyond it just BEFORE the tenors add the fifth. This eliminates out
of hand any possibility for an adequate demonstration of upward
pressure on the pitch when the tenor part enters.

In fact, the soprano very briefly moves down in the direction of a JI
relationship to the tenor right after it enters, demonstrating an
initial tendency quite the opposite of the intended purpose of the
demo, but then moves back up. These excursion are brief enough so
they would be difficult to detect within the limitations described by
Francois.

Briefly at the very end, the bass and tenor have moved far enough up
that even though the soprano remains sharp to the piano tenth, it is
on the bottom side of ET to my ear in terms of the triad formed with
the other voices. First the voice goes sharper each time the piano
sounds the tenth, then moves back toward JI briefly once the tenor is
there. I hear this both upon the initial tenor entry and again later.
There is not a whole lot of steadiness in the soprono voice in the
first place pitch-wise. The relative justness of the final triad I
referred to in my initial post on this demo is at the very end and is
quite brief.

Further, even if the experiment demonstrated exactly what it purports
to demontrate, the whole thing is ill-conceived, since the basses
have only the initial reference for the root, and then are cut loose
to drift, which they indeed do. Secondly, the piano references the
tenth while they are singing instead of being mixed in later, which
again clearly influences the pitch to the sharp side before the tenor
part enters on the fifth, destroying any possible legitimate
demonstration of the phenomenon as described.

All these points considered, I can't possibly see how anyone can
legitimately conclude on the basis of Francois's information that
this demo in any way serves its stated intention.

> thanks again francois for spending the hours necessary to do this
> analysis.

Bob:
Yes, thank you, Francois, for what I know must have been a valiant
effort. None of my remarks above diminish in any way my appreciation
for your efforts.
>
> peace,
> paul

🔗emotionaljourney22 <paul@stretch-music.com>

🔗LAFERRIERE François <francois.laferriere@cegetel.fr>

Robert Wendell wrote:
> > All these points considered, I can't possibly see how anyone can
> > legitimately conclude on the basis of Francois's information that
> > this demo in any way serves its stated intention.

Robert is correct to said that what can be conclude from what I mesured on
this single instance is scarce

Paul replied:
> isn't it true, though, that on average, the major tenth in the dyad
> is narrower than the major tenth in the triad? this is what jerry
> reported observing in doing the experiment with all kinds of choirs
> (hundreds of times?) . . . that observation does seem to be borne out
> in this instance, doesn't it?

Nevertheless if this is one thing that is (mostly?) sure, it is that.

I not really had time to do more than consider to post some commented
spectrogram (Perhaps I should consider having a website of my own). I looked
back at my data, reread some posts, become doubtful, check it again and I
can confirm the results that I posted before.

When I looked at "large" bandwith spectrum I can see some giggle, but cannot
be sure of the central value. To get a resolution of the order of 5 cents, I
must use longer window that smooth out giggling to get only overall pattern.
On those small bandwith window sonogram, the peak spectrum value moves only
a few pixel (at most), so that the thresholds of the greyscale and
preemphasis MUST be set to make the peak frequency represented by a single
pixel everywhere on the same sonogram. That is no easy task but I do not
give up yet.

I will have to get back to the study of one-voice-per-part ensemble to
understand more clearly some aspect of JI for a cappella music before
spending more time on chorus sample. There are some very peculiar phenomena
out there for which I need more measurement with various sample before
concluding anything.

yours truly.

François Laferrière

François

🔗francois_laferriere <francois.laferriere@cegetel.fr>

🔗emotionaljourney22 <paul@stretch-music.com>

🔗LAFERRIERE François <francois.laferriere@cegetel.fr>

Matter of factly I missed the "Next" button: I tought I was done with it
whenever I got a "No matches found". This interface is not very convenient
for huge archive such as Tuning. By the way, searching newsgroup archive on
google is much more convenient.

thank for your patience and your help.

François Laferrière

> -----Message d'origine-----
> De: emotionaljourney22 [mailto:paul@stretch-music.com]
> Date: mardi 9 avril 2002 16:56
> À: tuning@yahoogroups.com
> Objet: [tuning] Re: searching yahoo archive
>
>
> --- In tuning@y..., "francois_laferriere" <francois.laferriere@c...>
> wrote:
> > I just discovered a "feature" of yahoo groups. Seemingly, the search
> > is limited in the past to the date of my sign in to the group. Is
> that
> > right? Is there a workaround (beside asking to an "old timer" to
> > perform the research)? Is there a an help desk on yahoo where to
> post
> > this kind of questions?
> >
> > yours truly.
> >
> > François Laferrière
>
> dear françois,
>
> you should be able to keep clicking on "Next" after typing a search
> query and seeing the first screen of results (or lack thereof). this
> will result in the program searching earlier and earlier slices of
> the archives, until finally you come to the very beginning of the
> archives.
>
> i know this works because i belong to other yahoo groups and have had
> no difficulty searching archives from before i joined those groups.
>
> probably you just didn't notice the "Next" thingy.
>
> peace,
> paul
>
>
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