In a message dated 4/13/00 12:09:32 AM Central Daylight Time,
fndango@azstarnet.com (Robert A. Anderson) writes:
<< I have a question. Is there a table or some reference, that says which
HT,
sounds best
with which composer?
How does a person determine which piece of music, sound best in a
particular
HT?
Thank you.
John M. Ross"
I think that's a good question, but I think that there's a better way of
going about it than looking for someone else's notion of what
temperament should be used in which situation. Everyone who's interested
should simply start trying them out, listening, and letting others
listen. >>
Your answer couldn't have been better nor more complete. Only when tuning
for a specific period and for a performance where the tuning will serve only
that performance do you really need to choose a temperament which is specific
for that kind of music. 1/4 Comma Meantone for Baroque music, for example,
Werkmeister for Bach, 1/5 Comma Meantone for Mozart, etc.
Even the recent recommendation by Owen Jorgensen that the Kirnberger, an
early Well-Temperament that would be suitable for Bach, Baroque or Classical
periods to be used for Chopin demonstrates that a temperament may be chosen
for its characteristics more than for the period of music it comes from.
Generally, the earlier the period, the more unequal. The more unequal, the
purer the sound from the simple keys, 0-3 sharps or flats and the more
vibrant or harsh, the remote keys, 4-6 sharps or flats.
This is true for both Meantone and Well-temperament. In Meantone, the larger
the fraction, 1/3, 1/4 or 1/5, the purer the simple keys will sound and the
harsher the remote keys and the stronger the "Wolf". the 1/6 Comma is about
in the middle. The 1/7 Comma begins the kind of Meantone that might be
considered "universal", that is, useful for playing all kinds of music on the
modern piano. This temperament however might be considered at the extreme
end of that spectrum. Some people may find its mild harshness in the remote
and "Wolf" keys to be a bit too strong.
The 1/8 Comma might be considered "Victorian", having plenty of color but not
too much harshness. 1/9 and 1/10 Comma would be in the Quasi-Equal range
("quasi" means "almost"), offering only "pastel" shades of color and finally,
the 1/11 is the virtual equivalent of ET. The value for the Syntonic Comma,
21.5 cents divided by 11 = 1.95 cents, the approximate size of an ET 5th.
It should be said that all of these Meantone temperaments are defined by the
Syntonic Comma, not the Pythagorean Comma which is a different value, 24
cents. Therefore, ET is a 1/12 Pythagorean Comma Meantone and a 1/11
Syntonic Comma Meantone. The Syntonic Comma is the amount short of an octave
that you get when you tune 3 pure contiguous 3rds. That 21.5 cents
(theoretical) difference, gap or shortfall is called the Comma. The
Pythagorean Comma is the amount in excess of an octave that you get when you
tune 12 pure 5ths, 24 cents.
Because any Meantone Temperament is defined as a chain of 5ths (and/or 4ths)
all tuned by the same amount (whichever fraction is chosen), they lend
themselves easily to using an Electronic Tuning Device (ETD) for tuning them.
I do not mean using deviations of an FAC program for this although that is
possible too. It is a very simple idea and you do have to make an adjustment
for inharmonicity.
To me, however, this is a fascinating way of constructing a temperament where
you are playing an active role in directing the ETD what to do rather than
simply accepting the calculation handed to you. You will have to create your
own octaves but this too puts you in charge where you can choose the kind of
compromises you want to make rather than accepting whichever ones are fed to
you. Once you have made your decisions, a programmable ETD such as any of
the SAT's will preserve your work to be used over and over.
If there is interest, I can spell out in another post how you do this and
also how you can make variations of any Meantone temperament such as Tim
Farley has done by inserting 1 pure 5th in the 1/7 Comma Meantone. This
alteration mitigates by just a bit the harshness of the remote keys and the
so-called "Wolf" interval.
Bill Bremmer RPT
Madison, Wisconsin
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