Temperaments (In defense of Bill)

[Billbrpt@aol.com]

In a message dated 98-01-29 20:26:17 EST, you write:

<< Doesn't this amount to an evening out of the very effect you are trying
 create with the 1/7 meantone?   It would seem to me, that if you want the
 full effect of this temperement to be appreciated, you might prefer a low
 inharmonicity instrument, which would also be more consistant with the
 inharmonicity of the more "historical" instrument on which this temperement
 was originally used.
  John McKone, RPT >>

    This is an often asked question so I'm glad you brought it up.  On one
hand, you might well want to preserve the original character of one of the
ancient temperaments, especially when you are playing early music.  At the
Historical Temperament Recital in Dearborne, Owen Jorgensen had me tune two
pianos, each one quite differently, one from the other.  One was to be tuned
in 1/4 comma Meantone, the other in Thomas Young #1 Well-Tempered tuning.  The
1/4 Comma was to have "minimal stretch" and the Well-Temperament was to have
"optimum stretch" by the artist's direction.

    By the way, in my previous post, I misidentified the results of the two
"mitigations" you could use if you found that the 1/7 CMT was too "strong".
They become 1/7 Comma Modified Meantone and 1/7 Comma Victorianized Modified
Meantone.  The Modified Meantones can sound a lot like Well-Temperaments and
can usually be freely substituted for them but they are of different origins
and so they are not one and the same.  A modified Meantone also breaks some of
the basic rules of a Well-Temperament but often the Victorianized type is
mitigated to the point where it is in line with those rules and can thus be
called a Well-Temperament too.

    By choosing the Kawai piano, the one available with the lowest
inharmonicity, I could best preserve the apparent sound of the 9 pure 3rds
that the 1/4 CMT is supposed to have.  I say "apparent" because the Kawai
piano, being a modern piano, does still have inharmonicity.  Just as 3rds in
ET cannot be the 13.6¢ wide of just intonation that is theoretical, they MUST
be widened to some degree to accomodate inharmonicity,  9 absolutely pure 3rds
cannot exist on a modern piano and create an accurately effected 1/4 CMT.
They must be widened but must still sound pure to the ear.  In this case, each
3rd was 0.8¢ wide, an amount that was imperceptible to the ear and
consistently and accurately provided for by the SAT. 

    It would be very difficult indeed to do the same thing aurally because
there is no aural check for a pure 3rd.  All you can do is tune it so that it
has no apparent beat.  Just as when attempting an ET by ear, the cummulative
effects of the cummulative errors you make in your estimations of what you
think the interval ought to sound like can result in a puzzling and
perplexing, erroneous end.  Owen confirmed that all of the aural tests he knew
for the temperament checked out.  He was delighted.

    I was also thrilled to see that my idea had worked.  I felt like Dr.
Frankenstein when he saw the Monster's hand move, "It's ALIVE!!!".   The idea
I had of pre-programming the SAT to produce any kind of meantone temperament
was only a hypothesis.  It has never failed, however to produce stunningly
accurate results!

Since I always read my 3rd, 4th & 5th octaves all on the 5th octave, (the same
as is done for the RPT Exam but not the way the SAT is set up to do
automatically) I can have absolute, rational control over my octave
stretching.  To have "minimal" stretch is easier than you could ever want it
to be.  Once you have calculated the figures for the temperament, all you have
to do is enter the same numbers for each note in the 3rd, 4th & 5th octaves
and tune to what ever it says.  Then when you get to the 6th octave, you play
the note an octave below the one you want to tune, stop the lights and tune to
whatever it says and enter that value in the program.  In the bass, you do
similarly, play the note an octave above the one you want to tune, stop the
lights and tune to whatever it says and enter that value in the program.

This resulted in a very still, contracted sound, virtually devoid of the
resonances that we usually expect to hear from the modern piano.  It fit the
music he played on it, however.  It was the way the artist wanted it.

The other piano, a Samick grand with somewhat higher inharmonicity, but still
in the moderate range, was tuned entirely differently.  It was a Well-Tempered
Tuning.  Just as has been recently advocated with ET, to stretch the octave
out very widely and also stretch the outer octaves as much as possible, we can
use the inharmonicity that the piano has to our advantage to play tricks with
the comma.  Here, retaining the sound of tempered 5ths in the outer octaves is
definitely not what I wanted to do.  That just makes the modern piano sound
poorly tuned!  That tempering must be present in the midrange but in the outer
octaves, anything goes!  This is absolutely no different than the way ET is
manipulated contemporarily by skilled, artful technicians.

    Now, with the 1/7 Comma Meantone you have a clear choice you can make.
You can try to preserve an "ancient"-like sound and still have a tuning that
will be very versitile.  Or you can take it and manipulate the outer octaves
and use it as a substitute for a Well-Tempered tuning and play Romantic music,
modern jazz or virtually anything else on it.  The amount of inharmonicity the
piano has need not dictate which bend you give to the outer octaves, you only
need to be aware of what you have to work with and what your goals are.

Bill Bremmer RPT
Madison, Wisconsin