Oh.......it's Graham Breed

I know him! :-)

Thanks for your post, Graham. Here are a few responses to your thoughts:

> Well, I don't have a good enough ear to know a high third when I hear it,
> and don't have experience of choral singing. So there's not really much I
> can say, but it would be interesting if you could put numbers on this.

That was my original intention, but I'm not sure it can be done. I'm
beginning to think there is another answer.

-----------------
>
>> > As the human ear is more sensitive to
>> > flatness than sharpness,
>>
>> Really? Tell me more. I don't know about this.
>
> I can't give a reference off hand, but physics of music books tend to
> cover this sort of thing. It also agrees with anecdotal evidence: I've
> heard more singers criticised for being flat than sharp.

Tuning is often more affected by poor singing technique than poor ears.
Badly resonated or unsupported vocal tone tends to succumb to a kind of
"gravity" that pulls is under pitch. The exuberant singer that pushes sharp
is a rarer animal. So, you are correct.

-------------
>
>> Consider that the "demo" I described has been tested many dozens of
>> times
>> with groups of singers who never met the others. Are you suggesting that
>> _every group had an overexuberant singer? I doubt that.
>
> No, but it's a possibility that the most confident singer will always be
> the one with the best memory of what the "real" chord should sound like.
> This could be tested: take randomly selected newbies, and get them to sing
> individually against a tape playing the root and fifth.

I'll add this good idea to my list and see if I can get to it.

-------------
>
>> > If the chord "locks" it probably means an interval from this list is
>> > being
>> > chosen.
>>
>> That was my initial hope--to find such a simple explanation. However,
>> look
>> at the size of those numbers. I don't _think_ so.
>
> You mean the size of the cent-intervals or the size of the ratios? I'm
> open to the possibility that 24:19 could be perceived as such. If you can
> show people consistently hitting this, it would be good proof.

The size of the ratios. That, I believe, is the basis for "locking." My
concern about 24:19 and the others is the question of why singers would give
up the comfort of 4:5 for 24:19 or the like. It just doesn't make much
sense.

----------------
>
> I saw a post on Usenet recently where somebody said that parallel major
> thirds increase the tension. I presume he meant bare thirds (parallel
> fifths mean something else in voice leading, but again I'm no expert).
> That went against my experience, so I tried it, and it is the case --
> provided they're tuned to 12-equal. So it's the out-of-tuneness that
> gives the tension, not the third-ness. However, the remark went by
> without comment, so I took it to be generally agreed that bare thirds
> (which most know only in their Equal Tempered form) are essentially
> dissonances. Maybe he did mean voices moving in parallel thirds, I dunno.

I suspect that your source was referring to the fact that parallel major
thirds creates a melodic cross relation of a tritone (C-e, d-F#). Most
composers in the common practice period _love thirds, particularly Brahms.
>
---------------
>
> Now, if I were singing a major third, I don't know if I'd get it
> accurately to say if it were a 5:4, 7:9 or even 9:11. I should really try
> these things.

Sustain a low pitch on your synth and sing or hum (match timbre) a tenth
above. Move it _very slowly upwards and downwards until it finds a position
of optimum agreement. Now play the synth's tenth and note the difference.

(Commercial: get my "Natural Ear Training" for additional suggestions.) :-)
>
----------------
>
> Well, try for half an hour and see if it makes a difference. Or even tune
> a keyboard to JI, hit a major chord and say "sing this". Or -- now here's
> an idea -- play a JI chord on a string patch, and get them to sing along.
> Then remove notes one by one, and see if the third changes as the keyboard
> loses it. Try the same thing with the meantone fifth.

I really like this one.

> One other thing I was thinking about. You were saying
> before about how Sheila Chandra sang a high E with a low F. It's also an
> article of faith (with some experimental backing) that minor seconds in
> melody tend to be narrowed, whereas larger intervals tend to be widened.
> The whole subject of melodic intonation tends to be ignored relative to
> vertical harmony. I think the reason is that harmony can be easily
> explained with reference to the harmonic series, but nobody really
> understands pure melody in terms of anything more fundamental. So, if you
> think you have something to say about melody, the field's wide open.

I plan to do so in my next book--if I ever get off this Tuning List
addiction.
>
> But more specifically, the idea (which I agree with) that E# should be
> lower than F is entirely based on tuning to low-integer-ratio intervals.
> It has nothing to do with how scales will most likely be tuned
> melodically. So you may find a melodic F appearing where a harmonic E#
> should be. This is why I think it may be better to assume E# and F are
> the same pitch class, outside of an explicit meantone context. If the
> harmonic and melodic rules lead to a different order of pitches, neither
> can be relied upon as a standard.

Yes. There is no doubt that any musician will notate Sheila's F as "F," a
diatonic member of the prevailing scale. Tuning it is a different matter.
Calling it E# simply complicates understanding, in my opinion. (The key here
is your phrase "outside of meantone.")
>
> Another thread: the measured values for C, E and G in "Can't Buy Me Love"
> (see earlier in the month) are 262, 337 and 405 Hz. That's consistent
> with the melodic intervals being stretched. 405/337, the measured minor
> third, is close to just, and so wider than ET. A just major third would
> be narrower than ET, and so has to be stretched. I wonder if the
> approximations to 9/7 and 6/5 are a coincidence.

I wonder. I haven't been able to find it (with small effort) to listen to.
>
Thanks for your input, Graham. Every bit is important to me. Never can tell
what thought will break it open.

Jerry