RE: [tuning] high third sound examples

Gerald Eskelin wrote,

>Evidently so. It's also interesting to consider that the ear, while hearing
>two related pitches whose wave patterns are not likely to physically line
up
>their common vibrations at exactly the same time, in effect "slides them
>into focus" for comparison. Pretty impressive!!!

Hold on. Are you talking about phase differences or slight mistunings?

Jerry wrote,

>>>Evidently so. It's also interesting to consider that the ear, while
hearing
>>>two related pitches whose wave patterns are not likely to physically line
>> up
>>>their common vibrations at exactly the same time, in effect "slides them
>>>into focus" for comparison. Pretty impressive!!!

I wrote,
>
>> Hold on. Are you talking about phase differences or slight mistunings?

>Phase differences. Thanks for the appropriate terminology, Paul.

Jerry, I suspect you're operating under a serious misconception here. Our
ears and brains are remarkably oblivious to phase, and the kind of "lining
up" you're talking about, even if you could come up with a mathematical
definition of such a thing (there's a challenge), would have virtually no
effect on any audible characteristics of the sound. So I believe it's
meaningless to say that the ear does anything like what you describe above.
I'm not sure of the source of your misconception, but it reminds me of
Robert Asmussen's web page:
http://www.leeds.ac.uk/music/Studio/rproj_swss/tuning/tuning.htm. Here he
makes the error of picturing all tones as sine waves (a very unmusical
timbre); that makes "lining up" easy to define, but leads to the false
conclusion that the consonance of simple ratios is somehow enhanced when
this lining up is done correctly. Though framed as a computer music project,
Asmussen probably never carried out a comparison with different phases; if
he did, he surely would have heard no differences.

It may sound like I'm actually supporting your point, Jerry, because if you
don't hear a difference, it would seem that the ear must be "lining things
up" so that no difference arises. But it is simpler, and more in keeping
with how we understand hearing, to assume that there is no difference
because we are essentially picking up only the frequencies, and not the
relative phases of the different frequencies, in the sounds we hear.

I wrote,

>> Anyway, it sure seems like you're saying Jerry was able to "lock" the low
>> third much more accurately than he was the high third. A few cents
variation
>> around 5:4 is really the best you could hope for from a human vocalist.

Jerry wrote,

>I suspect the reason for the "security" on the low third was the " quiet
>rumbling" of the fundamental assuring me that I was close. With the high
>third, no such rumbling occurs, therefore there is likely more flexibility
>as to the optimum placement.

So Jerry, what is your current theory as to what defines the "locking" or
the "optimum placement" of the high third?

>However, a phenomenally fine children's choir of about 70 voices
>often agreed on very high thirds.

Note the word "very". Are you giving up your notion that the high third (in
the specific context of the major triad) is an interval of fixed size, like
the low third which we all agree is 5:4?

Graham wrote,

>As I said in the original message, there's a wide variation in pitch
>over small periods of time. I think this is from 6:5 (definitely this
>time) to 9:7. But, if you do the Fourier transform over a longer
>period of time, you see a constant but blurred trace. The most
>intense frequencies in that blur are colored differently, and fairly
>consistently correspond to a 5:4. Which is what we would have
>expected. Looks like the ear does a similar thing.

I don't think the ear does a similar thing.

>The "blurring" would presumably be interpreted by the ear similarly to
>vibrato.

Naah, I definitely heard Jerry's low third example as spending most of its
time within a few cents of 5:4, with occasional rapid departures and
returns. I did not hear it as a consistent 5:4, "blurred" or otherwise. Of
course, my ear may be performing Fourier transforms over different periods
than yours, maybe as a result of too much time figuring out fast guitar
licks :)

>However, it is qualitatively different. It looks like a
>fractal trace, rather than a sine wave. I'd like to hotwire a synth
>to emulate this. Maybe over the weekend. It must come from some
>feature of the vocal chords

I think it happens as a result of the feedback interaction between the vocal
chords and the ear, mediated by the brain, in the effort to sing a steady
pitch. You can see a similar effect by trying to hold a heavy object up at a
certain level, lining it up with a reference point in the background. The
vocal chords alone would do no such thing. A better singer than Jerry or I,
say Sheila Chandra, is able to sing a steady tone with almost none of these
effects, due to the level of perfection she has achieved in this feedback
mechanism.