"Listener's preference"

T0 Robert C Valentine

It was I, Gerald Eskelin, who wrote:

>> Understanding the "high third" is my burning passion at the moment. I'm very
>> interested in seeing responses to John Link's 9/7 "solution." If that turns
>> out to be valid, it raises the question as to WHY the "high third" would be
>> "preferred" over the 4:5:6 tuning of the major triad, which is clearly more
>> "consonant" by JI standards. Also, it raises considerable concern as to the
>> "root" occurring as partial 7. Perhaps roots are beside the point in this
>> regard and are only important to writers of harmony books. Maybe we are
>> looking in all the wrong places.

In order to understand the issue, you would have to dig up a number of posts
over the past few weeks in which I and others have been looking for a
mathematical basis for the observation that singers (and presumably string
players) seem to "prefer" a third (when both root and fifth are sounding)
that is considerably higher than 12j-tET. I will attempt to clarify in
response to your questions.

>Is the "high third" on a I chord, a V chord (etc...) and where is it
>going melodically?

Function is not at issue.

Despite your paragraph here, I think you have
>been looking in the right places, those being what is appropriate for
>the melody and harmony of the moment.

I agree that tuning is modified by context. What we are discussing has no
context other than a major triad.

>9/7, even for a leading tone, seems a bit more sharp than I would expect.
>I'd be more inclined to think pythagorean, which is only 8 cents sharper
>from just than 12tet. Heres a few different leading tones, the first is
>based on 9/7, the second is pythagorean, for those who like primes and
>overtones then "the 11/8 of the 11/8" is almost deadon to 12tet, and
>the last two are a pair of "next overtone" from 15/8.
>
>ratio 27/14 243/128 121/64 61/32 31/16
>cents 1137 1110 1103 1117 1145
>
>of course, 36/19 is also a nice leading tone at 1106 cents (and comes
>from the classic 38:48:57 triad...) Beats me, as Charlie Parker said,
>its "still gone music."

Here's the crux of the problem. Singers seem to agree on a single specific
tuning of the major third when root and fifth are sounding, apparently
because it "locks" in tune. The questions are: what? and why?

Your five leading tones are probably very lovely, but we are looking for a
very specific one.

Thanks for your interest.

G. Eskelin