RE: More Meantones

From: PAULE

John Chalmers wrote,

>It seems to me that the 5/3 and 6/5 are not independent of the 5/4
>and 3/2 and not really necessary

As a result of this assumption, most of the tunings that John derives have
significantly worse major sixths and minor thirds than the ones I derived.
If one wants these intervals to be smooth just as much as one wants the
major third and minor sixth to be smooth, including them certainly is
necessary!

I would like to propose a test so that anyone can decide for themselves
whether I or John Chalmers have better specified the problem of finding a
tuning with the best triads. Compare major and minor triads in 15-equal to
those in 10-equal. The perfect fifth is identical in both tunings. The major
third is 14 cents sharp in 15-equal, and 16 cents flat in 10-equal. So John
Chalmers would rate the two tunings as equally good. However, the minor
third is 4 cents sharp in 15-equal and 44 cents sharp in 10-equal. So I
would rate 15-equal as much better than 10-equal. Listen for yourself and
decide!

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I'm finally back on line since my address was changed to reinhard@idt.net

I've been teaching music composition and theory at C.W. Post, Long Island
University so that list member Howard Rovics can take a sabatical. Prof.
Rovics is composing for bassoon and flute in eighthtones, along with
synthesizer in the mean time.

Thursday, March 6th I am lecturing at Post on Ives' Universe Symphony, now
studio mixed to CD, non-commercial.

I have been reading the list, however, and would like to add 2 cents.

For Beethoven to declare his ability to distinguish between and C# and Db
would coincide with Johann Nepomuk Hummel, Beethoven's contemporary and
pianistic rival. Humel writes in 1850 in his piano treatise that though
the piano erases the distinctions between enharmonic relationships, they
are important for composition. And that this needn't concern the pianist.

It also is interesting that there seems a Dutch propensity to keeping JS
Bach in the 12ET corral. When Rudolf Rasch published his Musicalische
Temperatur edition from plates, untranslaed, he added a lengthy prologue
regardings his conjectures on Bach's tuning. This, though, there is nary
a mention of 12ET. I am in possession of a translation of this _still_
untranslated cornerstone of tuning history thanks to Mark Lindley, by way
of one Elizabeth Hehr.

In my paper _Bach's Tuning_ published in PITCH I:2 I challenged
Professor Rasch - a good friend and always Rudolf to me. There are those
that do not recognize either the aesthetic virtue of variegated keys, or
its historical likelihood.

Johnny Reinhard
American Festival of Microtonal Music
reinhard@idt.com



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