chestnuts

>The Bach "chestnut," as Reinhard said, is rather enduring, it seems.

Somewhere, in a cyber-corner of space, a motley crew of harmonic
hobos gather around the warm ,glowing list with the low flames and alluring
coals. They begin to hammer once again on the chestnut..............

Neil starts it: (:)}}
>It
>also seems that tunings were in a much less settled state at that time
>than they are now, with well temperaments, meantone, equal temps, >and most
likely others,

I agree. with one obsessive/compulsive flag. It is very difficult to
believe that ET was tuned on a keyboard before 1830. I say this because I
know how hard it is to tune ET today, with all the checks and balances that
were perfected in the late 1800's. According to the research done by Barbour
and Jorgensen, there was no evidence of the tools necessary to tune ET being
used before that time.
I would defy anyone to aurally tune a temperament on a piano,
harpsichord, or clavichordy today that is equal without the use of the thirds
as measurment intervals. I can't do it, and I am real familiar with 12 TET.
You simply cannot tune ET on a strung keyboard using fifths and octaves.
The M3-min3 and M3-sixth tests are needed.
The M3rd/sixth test is also useful for testing the widths of fourths,
( and will actually tune a guitar in very close ET if you know how to count
the beats at the G-B third).
Hipkins tells us that ET was nowhere near practised at the Broadwood
factory in 1848, by the best tuners there !!
>From Jorgensen, we read that Mersenne himself said that the ratios for ET he
is credited with publishing (1635?) could not be used in tuning a clavier.
Organs, which could sustain a long enough tone to count the beats, could be
tuned in ET, but nobody seemed to like it.
Lutes, with linear placement of the frets rendering any mathematically
described temperament possible, were perhaps the first truly equally tempered
Western instrument, along with the viols.

>also know that Handel had a keyboard with, I believe, 16 tones/octave...was
>this a common practice then?
The physical limitations of the human hand seem to have limited the
number of keys for ordinary use. There have been many versions of more than
12 tried, but none seem to have been accepted for long.

> Mself, I believe that Bach, and most likely many others, used various
>tunings, depending on the context of the piece, and the instrumentation.
>Bach was nothing if not very practical, so to think that he would switch
>between systems is not too farfetched. As to what he would have ideally
>preferred, are there any writings on this subject?
I remember reading that he could retune his clavier in 15 minutes, I
suspect that refers to changing the enharmonic notes. Also I remember a
quote from one of Bach's sons, stating that the old man would not have
preferred ET.
This is somewhat hazy, as the smouldering coals get raked, there is a
chestnut in here, I just know it........

Best regards and abcdefghijkmnopqrstuwxyz (No L) to all.
Ed Foote


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From: A440A
Subject: what "well temperament" means
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> I would vote to use Well Temperament to describe the irregular,
>circulating, non-restrictive tunings that seemed to have begun with
>Werckmiester, and found perfection in the Young.

Presumably not Young as in LaMonte Young?

I once defined well temperament, keying off the obviously overvague
definition in the New Harvard Dictionary (and freely admitting that I don't
know how authoritative this definition would be), as a tuning of twelve
steps per octave based upon a circle of fifths, no two of which differ in
size by more than a pythagorean comma.

That seems to match all of the well temperaments that I'm aware of.
Unfortunately it also allows for pythagorean to be called well temperament!
That being the case, it might be better to restrict, instead or
additionally, the difference in size of ADJACENT fifths in the circle, and
to something somewhat smaller. That somewhat smaller allowable difference
would be whatever matches historical Werckmeister, Kirnberger, etc.
temperaments of course.

I noticed that your definition specifically excludes equal temperament
from being a "degenerate" (in the semimathematical sense of "extreme") case
of well temperament. I'm inclined to think that that's probably
appropriate, but I'm not sure.

Ronnie Milsap you say has played with well temperaments?! Interesting.


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From: Polychroni Moniodis
Subject: Arabic Tunings
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