Musings on Vocal Tunings

Paul H. Erlich has been as kind as he has been generous in helping me
through a number of important tuning concepts. It seems that our
discussion (actually, more his pedagogy of me) has reached a level where
some reader's of this list might find it helpful as well. With that, I'm
including our last post:

On 24 Apr 00, at 15:00, Paul H. Erlich wrote:

[Me:]
> >When someone is singing a tune by himself, how does he proceed? Is it
> >not by incrementing off of the previous note? So, if I'm singing a 'C'
> >at, say, 256 Hz, then I would increment this frequency by 1+1/9, at
> >arrive at my 'D' of 288 Hz (to the best of my ability). Others, when
> >singing a tune to the Ptolemaic syntonon diatonic, we'll increment up;
> >1+1/10; and if singing to the Zalzal's intonation, we'll go up 1+1/11.
>
> >Clearly someone can sing a tune without harmony.
>
> Yes, but most of the world's melodic tunings do not conform to your logic
> above.

It would seem that someone can arrive at a tuning mathematically, divide a
monochord accordingly, and then sing to it. And someone may be able to
learn the tuning by heart.

But singing unaccompanied presents an entirely different challenge the
vocalist. After intoning the fundamental (tonic) note, 1/1, (which in most
cultures, and in most people, will be a relative note, not an absolute Hz
frequency), he then must proceed by gauging his movement against the
fundamental. So, if he wants to sing a song to Al Sibn (sp?) tuning, (1/1,
9/8, 27/22, 4/3). While theoretically, he would proceed by 1/1, 1+1/8,
1+1/11, 1+7/81; this is not within the realm of unaccompanied human
performance. Rather, he may very well proceed by 1/1, 1+1/8, 1+1/11,
1+1/12 (i.e., 1/1, 9/8, 12/11, 13/12) for either 493c to the tetrachord.

As I mentioned, actually tuning recordings of chanters shows variances well
above 7+/- cents, even by the same performer and another time. So, again,
it seems that their are a number of "virtual tetrachords", i.e.,
tetrachords that aurally are complete, but mathematically are not.

It still seems to me that this notion is related to the concept of "unison
vectors."

> >Thank you much. Would you find the following a plausible hypothesis.
> >Someone may sing the sequence 1/1, 9/8, 99/80 monophonically; but with
> >the accompaniment of a drone, would sing 1/1, 9/8, 11/9; his attempt to
> >increment 9/8 by 1+1/10 being attracted into the harmonic 11/9?
>
> Very plausible. I see no need to reference 99/80 or 1+1/10, though.
>
> >Hmm. This then supports the hypothesis I just stated above, i.e., in
> >trying to navigate an interval smaller than the minor tone 10/9 (yielding
> >a 3rd of 5/4 = 386c) yet larger than the semi-tone 16/15 (yielding a 3rd of
> > 6/5 = 316), his only harmonic harbor would be found at 11/7 (=347c).
>
> You mean 11/9. Yes, that would be the only harmonic harbor.
>
> >Hmm, again. So, it appears that 21:17 (=366c) might also be a harmonic
> >point for our now throughly struggling chanter.
>
> For a slightly superhuman ear, yes.
>
> >Paul, I greatly appreciate your helping me along in this discussion. Do
> >you think that this post would be of some interest to the Tuning list, or
> > is too elementary?
>
> It's not too elementary -- in fact, nothing could be.
>
> >PS. Just thinking. The Ptolemaic Diatonic Hemilion yields thirds of
> >6/5, 11/9, 27/22, 5/4, and 40/33. Then, it would seem, that the 11/9 and
> >and 27/22 would wind up, in unaccompanied vocals, as 11/9.
>
> Only if there were a drone.
>
> >Not sure what would
> >happen to the 40/33, perhaps taken as 6/5?
>
> According to my harmonic entropy model, a _harmonic_ interval of 40:33
> would be heard as 17:14 by an oustanding ear, and 6:5 by an average to
> very good ear.

The harmonic entropy model sounds very interesting. I'll try to follow-up
later.

Best regards,

Polychroni

the question of tuning in unaccompanied melody has been a topic of
discussion the past few days and I'm wondering to what degree people on the
list feel that rational intervals matter in contexts where no harmony is
present. On the cello and other bowed strings, notes played at least mf
audibly reverberate in the resonating bodies of the instrument for a
considerable while, and so in Bach's solo suites, where the melodies tend
to be more compound than staightforwardly stepwise, and the motion rapid, I
could see rational harmony potentially playing a role. In unaccompanied
singing without a drone, is the difference even between 9/8 and 10/9 going
to effect the experience of the music? According to A H Benade, the
unaccompanied singer tunes his/her pitches on the basis of reverberations
of previous pitches, and in, say, an anechoic chamber or outdoors, would
have no basis for a precise tuning this way or that. According to La Monte
Young reverberations in the form of firing neurons (correct me if I'm
wrong) continue in the nervous system after a pitch is heard and account
for pitch memory. Could we possibly percieve tuning in remembered pitches?
How can tuning happen linearly? Any feelings?

jason yust

Jason!

Jason_Yust wrote:

> the question of tuning in unaccompanied melody has been a topic of
> discussion the past few days and I'm wondering to what degree people on the
> list feel that rational intervals matter in contexts where no harmony is
> present.

there are quite a few cultures where this appears india and persia both with drones and
without.

> On the cello and other bowed strings, notes played at least mf
> audibly reverberate in the resonating bodies of the instrument for a
> considerable while, and so in Bach's solo suites, where the melodies tend
> to be more compound than staightforwardly stepwise, and the motion rapid, I
> could see rational harmony potentially playing a role.

I have always thought that bach heard/played the music more resonant rooms than dead ones
which has always thought he expected these "blurring" into chords

> In unaccompanied
> singing without a drone, is the difference even between 9/8 and 10/9 going
> to effect the experience of the music?

yes

> According to A H Benade, the
> unaccompanied singer tunes his/her pitches on the basis of reverberations
> of previous pitches, and in, say, an anechoic chamber or outdoors, would
> have no basis for a precise tuning this way or that.

it should be tested, but the reverberations can occur also in the musical mind as well like
the Big L says below. boomsliter and Creel did testing that showed that even in a single
melody a "modulation" can/does occur. They referred to these temporary shifts as extended
references.

> According to La Monte
> Young reverberations in the form of firing neurons (correct me if I'm
> wrong) continue in the nervous system after a pitch is heard and account
> for pitch memory. Could we possibly percieve tuning in remembered pitches?
> How can tuning happen linearly? Any feelings?
>
> jason yust
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Jason,

My strong belief, based on my knowledge of world musics and my own searching
investigations as a musician, is that for unaccompanied melody, any
intervals are equally valid, with only the very simplest ratios such as 2:1,
3:2, and 4:3 having any "pull". 9:8 and 10:9 certainly have no "pull" as
melodic seconds (though 9:8 is often a by-product of stacking two 4:3s under
a 2:1) -- even in the West the mean tone was easily accepted after centuries
of Pythagorean tuning -- and even for thirds 6:5 and 5:4 only seem to be of
importance as harmonic intervals, not melodic ones.

-Paul