Replies to Ed Dotson, Gary Morrison, Pat

Gary: Yes, I was taking these chords out of musical context. Even a triad
can be a dissonance when the prevailing harmonic texture is dyadic, as in
Medieval music which is based on the "perfect" consonances. I was trying to
use naive, conservatory definitions of consonance and dissonance to keep the
discussion brief. In jazz, the seventh chord is consonant, especially in the
mixolydian mode, where the "dominant" seventh is the tonic. Resolutions are
easy to create, but finding appropriate ones within a coherent pitch system
is more difficult and very important. Too many different pitches without
simple relationships and within too short a period of time, and music
becomes unlistenable to my ears. Unless we're talking about sliding pitches
motivically used or something like that.

You wrote,

> Now understand that I don't doubt for a moment that tuning the seventh
>sharper produces a MORE satisfying resolution. But 7:4 provides a
completely
satisfying resolution to my ears, and many others'.

The first sentence here seems to contradict everything else you're saying.
Do you want to modify this statement?


Ed: I'm not sure what you're disagreeing with, but I'll guess. I'll grant
you that in barbershop singing, all chords are tuned as justly as possible.
I will also grant you that a skillful vocal quartet can reduce the perceived
difference between a 16/9 and a 7/4 by sliding, subtly shifting the 1/1,
etc. The difference between a 10/9 and a 9/8 may be imperceptible
melodically (one does not notice that two D's are used in the progression
C-F-Dm-G-C), but the difference between 16/9 and 7/4 (in the progression
C-F-G7-C) is noticeable and requires other means to cover it up. To my ears,
anyway. Try playing Mozart with dominant sevenths tuned 4:5:6:7, and you'll
get some angry scowls from the audience.


Pat: More recent studies than Helmholtz have found that although violinists
prefer sharpened major thirds and major sixths, which was thought to be due
to a preference towards Pythagorean intonation, they also prefer sharpened
minor thirds, fouths, and fifths, so the preference seems to be towards
larger intervals in general. All of these studies, by the way, are concerned
with these intervals in a melodic, not harmonic, context.


Brian: Your assertion that 99+% of psychoacoustic research supports the
conclusion that the fifth perceived as most pure is larger than 702 cents,
is ridiculous, unless you meant to add, "in a melodic context."
Harmonically, there is nothing which distinguishes a 709 cent fifth (with
which I am very familiar) from a 702 cent fifth, except that the latter does
not beat. If the lack of beating is not a criteria for "purity," then I
can't imagine what is.


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