tempered and just

I think of this as a very important aesthetic issue, and one quite aside from
questions of adequate approximation or tolerance. When I compose the chord
16:20:24:27, I wish to hear the 27/20 interval as itself, not tempered to
better approximate a 4/3. Similarly, when I compose in a temperament onto
which the nearest approximate of 27/20 and 4/3 is the same interval, I wish
to hear this interval as tempered.* I consider the problem of making these
interval audible as themselves to be a compositional problem, not a
psychoacoustical one. Psychoacoustics tells us a lot, but, operating within
very narrow parameters within which music is construed, precious little about
our potential for hearing.

It was Nicholas of Cusa (1401-1464) who described the difference between
logic and faith or knowing and truth in terms of a circle and an n-sided
polygon inscribed within the circle. Logic, or knowing, is like the polygon:
the more sides you add, the more complexities, the closer the polygon
approaches the circle. But at the same time, it gets farther away from the
circle. For the the circle is a single, seamless line, while the polygon is
formed of ever more line segments and angles, broken up into ever more parts.
No matter how large n may become, no matter how closely the polygon
approximates the circle, it never reaches the circle. Nicholas described the
leap from tangent to arc, from endlessly compounded multiplicity to
singleness in terms of _grace_.

Personally, I find it more interesting, elegant, beautiful to see -- and to
make audible -- the difference between the simple form and the complex
approximation than to ignore their differences as a sign of grace. _Grace_,
I'll save for a desperate hour.

Daniel Wolf
Frankfurt-am-Main

_________
* This is not unrelated to the discussion on possible just tunings for the
'augmented triad' . The discussion was framed in terms of the sonority as it
is found in a given temperament, not in terms of the compositional contexts
in which it is used within that temperament. For example, (0,4,8) may be the
best mapping in 12tet of the 7:9:11 triad, I know of no 12tet repertoire
where such a just interpretation could unambiguously be made. On the other
hand, an interpretation of Eb G B (natural) in c minor in terms of two 5/4
thirds, or even a 5/4 with an 81/64 above seems not only reasonable, but the
implied 'bitonality' of the sonority, has a certain amount of interpretive
power for familiar repertoire.

Greetings all,
Daniel Wolf writes:
>It was Nicholas of Cusa (1401-1464) who described the difference between
>logic and faith or knowing and truth in terms of a circle and an n-sided
>polygon inscribed within the circle.

What a great post! Thanks.

I have only the regret that I didn't read this post earlier. I have just
returned from the Piano Technician's Guild's National Covention in Kansas
City, where I would have found SOME place to have used it in my talk. While
there, I presented two classes about unequal tunings on modern acoustic
pianos, and got a good reception. This is great news to many of us, since
the subject of temperament variety is easily the most controversial in the
Guild and while the bickering was going on between small minorities, the
large body of potential converts began to lose interest in even hearing about
them. Hopefully my class, and one from Dave Lameroux ,(who often maintains
the pianos at the Smithsonian) have begun to reverse that trend.
A very interesting item I learned was from Dr. Al Sanderson, inventor of
the Sanderson Accu-Tuner. He said that pianists in the northeast region
where he is are increasingly requesting various temperaments on the pianos
for perfomances. This is a strong sign that the temperament revival is
healthy and growing.
Though this may be of limited interest to the microtonalist "math
monsters" ( to quote H'stick, I think), next year there is a "Piano 300"
program shared by many major museums. There will be much made of the early
historical instruments, and hence, there will be something of a pulpit for
the early guys to tout their tunings.
Under this legitimizing aura of respectibility that comes from big names
getting involved, the public awareness may be more accessible to the wide
variety of tuning enthusiasts. I know many of us see teaching as important a
part of what we are doing as perfoming, and the inequalites of the past may,
in demonstration, suggest a new avenue of investigation in the future. To
this end, I am concerning myself with the use of a variety of temperaments on
the grand pianos for modern as well as old music and have found a number of
"Victorian" style tunings that just turn the color on for Jazz as well as
much earlier music.
Anyhow, some may want to keep their ears open for historical events next
year, pianos are still big business.
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.

A440A@aol.com wrote:

> Though this may be of limited interest to the microtonalist "math
> monsters" ( to quote H'stick, I think), next year there is a "Piano 300"
> program shared by many major museums. There will be much made of the early
> historical instruments, and hence, there will be something of a pulpit for
> the early guys to tout their tunings.
> Under this legitimizing aura of respectibility that comes from big names
> getting involved,

The organizers should cough up the big bucks for a series
of performances of The Well Tuned Piano by La Monte Young.

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* xouoxno@virtulink.com
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