RE: [tuning] Re: Hypermeantones [...]

George Kahrimanis wrote,

>A third, more perplexing approach would be to assume both approaches
>(whole-sonorities and interval-networks) as valid in this case,
>therefore a transistion from tuning "9:12:16" to the tempered one
>(which moves the outer ratio closer to 7/4) would effect a change
>of function, therefore a more serious matter. I do not think that
>this is the case (imho, should I add).

You do not think that both approaches can be valid? Well, I do.

Anyway, it sounds like you're talking about my observation:

> > Certainly in the case of 9:12:16, I would say that, for most
> > musically useful timbres and registers, the 16:9 minor seventh is
> > already too complex a ratio to be perceptibly worsened by
> > mistuning. Instead, bringing it any distance (in this case, halfway)
> > towards 7:4 only improves its concordance. Meanwhile, the two
> > perfect fourths are only tempered by 1/4 of a septimal comma. As a
> > result, this two-stacked-fourths chord (and for similar reasons,
> > chords of three stacked fourths) sounds very pleasant in "pure 9:7
> > hypermeantone tuning", or the virtually identical 22-tET.

I was thinking of the cases where D-G-C is used as a D7sus4 (no 3rd) chord,
i.e., D is clearly the root (say it's doubled an octave or two lower by the
bass). Your theory may not allow this interpretation but believe me, as a
musician I know it is real. In this case, bringing the seventh down toward
7/4 is helpful both in terms of making the 16:9 more consonant, and in terms
of chord function.

I wrote,

>> You do not think that both approaches can be valid? Well, I do.

George Kahrimanis wrote,

>I only had this particular case in mind, not postulating a general rule.
>To test this matter in earnest, show me a short progression to try
>out by ear, such that you think sounds better in that temperament.

Go 3/4 of the way down
http://artists.mp3s.com/artists/72/the_tuning_punks.html and listen to my
piece TIBIA. 8 second into the piece, you have this chord (with a "fifth"
added). Essentially, the previous chord is 1/1:7/6:7/4. Then, holding these
notes, the root moves down a "fifth." The temperament is essential since it
allows the 7/4 to function as a smooth suspended "fourth" over the new root,
while remaining consonant with the 7/6 which is a smooth "seventh" over the
new root.

>> I was thinking of the cases where D-G-C is used as a D7sus4 (no 3rd)
chord,
>> i.e., D is clearly the root (say it's doubled an octave or two lower by
the
>> bass). Your theory may not allow this interpretation but believe me, as a
>> musician I know it is real.

>"D", you say? "My" theory (Partch would agree, I think) says that D is
>one of the two alternate roots (an incomplete Gm with added 4th,
>common overtone D). (Of course you do know this
>sort of calculus, only you do not apply it. BTW, I am still
>grateful for catching a silly mistake of mine once.)

By emphasizing the low bass note, I'm clearly implying a normal, otonal
root, rather than a high-pitched common overtone which would be the utonal
"root".

>> In this case, bringing the seventh down toward
>> 7/4 is helpful both in terms of making the 16:9 more
>> consonant, and in terms of chord function.

>I repeat, it might be so in certain progressions but I remain
>to be convinced with an example. In the static case my ears simply do
>not perceive the advantage, not yet in any case.

I certainly don't disagree with you -- from the point of view of roughness,
the fourths will probably suffer more from being mistuned by 1/4 septimal
comma than the seventh gains by its mistuning being reduced from 1 septimal
comma to 1/2 septimal comma. However, the chord gains a certain quality
having to do with the seventh approaching a 7:4, thus strengthening the root
feeling of the bass note, despite the apparent contradiction that the
fourths, still heard as 4:3s, would mathematically imply a 16:9 seventh.

>(The stack of
>three fourths is another story.)

Why?

I think in that case the consonance of using a 7:3 for the outer interval is
a strong motivation to use this temperament.

>I joined the list to look for
>suggestions on a certain subject but I got distracted by the
>argument on the ideal tuning of stacked fourths.

That not really what this exchange was about -- I think you took my remarks
out of context. I did not say that 22-tET or a similar hypermeantone was
"the ideal tuning of stacked fourths." I was simply responding to Margo's
note that for a 4:6:9, 6:8:9, 8:9:12, or 9:12:16 chord, the tempering would
disturb the 9-limit interval twice as much as it disturbs the 3-limit
intervals. My response was that, particularly in the case of the 9:12:16,
the disturbance of the 9-limit interval could be more than offset by
bringing it closer to a simpler 7-limit interval. However, the disturbance
of the 3-limit intervals remains unmitigated.