[tuning] a cappella major triad big surprise

When discussing the jerries, Gerald made a quite interesting remark:

Gerald Eskelin wrote:

> Sounds like a hypothesis worth discussing sometime. Actually, it has
nothing
> to do with the high third we're talking about here. Here's the set up:

> Play a low C and ask the basses to match it. Then ask the women to tune
> a tenth above it. Once tuned, compare it to the piano's E and notice that
it
> is as one would think--slightly below. No surprise.

> Then play a low C and ask the basses to match it and ask the tenors to
> tune a perfect fifth above it. When the perfect fifth is in evidence,
again
> ask the women to tune a tenth above the bass. Note that their "third" will
> be higher than the piano's third. *Big* surprise!

> It works *every* time. I've demonstrated it with my choirs, other people's
> choirs, and on the road with choral festival choirs I've never met.

> No 7ths, 9ths and 13ths. No 6-9 chords. Just a simple major triad. Just
like
> in Renaissance endings.

That is extremely interesting and altogether disturbing!! I had not the
chance to propose this experiment to our choir master yet but I can't wait
to do so!

I have no explanation but only a few cues from my observation of a cappella
ensemble sonogram. It seems that when a chord take place, the outer voices
(i.e. soprano and bass) settle first while inner voices "fiddle around"
their notes. Then after a very short while (order of tenths of second) inner
voices find their place in the chord. I cannot claim to have a statistically
representative sample but that seems to match subjective experience of
chorus singing. Then intonation of various inversion of the same chord may
be different, and furthermore, the order of entry of the voices may be quite
significant as proved by Gerald experiment.

I have another remark, If we look at the placement of the partial in the
chord, with emphasis on the common partial (assuming JI) for soprano-bass
and soprano-tenor pair

soprano...........1..........2.........3.........4
tenor..........1.....2.....3.....4.....5.....6....
bass.........1...2...3...4...5...6...7...8...9...0
S/Bcommon....................X...................X
S/Tcommon..............................X..........

In the first case (B,S then T entry ) sopranos can rely on the beat of their
F2 with bass F5.
In the second case (B,T, then S) depending of the physical disposal of the
choir, the bass F5 may be more or less masked by tenor F3 which is normally
much louder. Then instead of relying solely on bass F5, soprano may now rely
also on the beat of their F3 with tenor's F5. Unfortunately, as I stated I a
previous message, human voice is not produce by a string stretched on a
wooden box and higher harmonics are not as sharp (in term of narrowness of
spectral peak) as lowers ones, thus using soprano's F3 instead of F2 for
beating cues for justness may be less reliable. If it is the case, sopranos
may then rely on more subtle cues than beat adjustment (as well as on their
musical subjective experience), subtle cues that may more subject to
psychoacoustic affect such as octave stretching (but I do not know how).

Anybody has ideas on the subject?

François Laferrière