I'm very impressed with how long this discussion of tuning has
continued  and this reply by now is a little late, but I want to write in
reply to David Calhoun's posting of Wed. 11/23.   First though, I will
comment on what may not be a self evident result of unequal temperament.
People have often asked about the root and origin of key colors, observing
that they can hear these same colors in equal temperament.  Why bother with
making the apparent
painfully obvious, they ask?   I do not dispute these observations and they
are not new.   However, I believe that what is happening here is that over
time great composers learned to write in subtle, yet different styles for
different tonalities.  Eventually, both these particular compositional
styles and their corresponding tonal centers became associated with certain
expressions.  Taken all together these styles, with their tonalities,
create the illusion that the keyboard is more harmonic or "in tune" than it
really is.  Naturally, some of these styles overlap and other differences
are very subtle, but we can see differences.  Notice how often C major is
written with bold vertical harmonies and that somewhat more vibrant keys
are more melodious.  Chopin often created his veiled elusive effect in the
remote keys by keeping the larger tenths and thirds to the off beat of the
measure, only rarely on a downbeat and then only when we are well adjusted
to it.  When these pieces are performed in equal and someone recognizes
that Brahms Op.118  No. 6, for example,  sounds a little spooky and other
worldly, it is not a convincing argument that therefore equal is the best
choice since this color is preserved.  If somehow in the future, the color
in all of our modern films was lost, but so that they were otherwise
perfectly preserved,  future generations could still understand the plot,
and even learn something about our time.  But in black and white the
experience could never be the same.  I think that on this list we all would
agree on that point, and I do not mean to waste time by arguing the
obvious.  Someone may have even alluded to these compositional styles
already, and I missed it.  This particular Bach toccata I do not know and
should take a close look at it, but possibly the answer lies in its
compositional style.  If the harmonies are somewhat vertical, which I
really doubt,  than that might support the transposing theory.  My instinct
however,  leads me elsewhere, and I think I can offer a better explanation.
 
         My recent reading is leading me to the conclusion that in the 18th
century mod. meantone was far more prevalent than I had ever previously
thought.   There really are some major differences between a strong,
harmonically balanced well-temperament and a typical mod. meantone, and F#
major is one of those significant differences.  In an 18th century mod
meantone the key colors start with C, G, D. and F major, but than proceed
around the sharp side first before the flats.  In this method F# major
would be considerably less tempered than in a typically more harmonically
balanced well-temperament.  In the Rameau-Rousseau-Hall mod. meantone, for
example, F#-A# is set equal beating to Bb-D.  Kirnberger  lists the major
keys in order of their hardness as follows:  C, G, D, F, A, E, B, F#, Bb,
Eb, Ab, Db.  In this scheme F# is quite a bit less than Pythagorean, but Db
is greater than Pythagorean, and he repeatedly points out that C Maj. and
Ab Maj. are at the opposite poles of purity.  That alone is a very strong
clue supporting  mod. meantone, and does not fit his famous 1/2 ditonic
comma well-temperament that we all know.    Anyway, my recommendation for
this Bach toccata is not Werckmeister, but one of the many 1/5 comma
varieties of Mod. Meantone.  The Rameau-Rousseau-Hall temperament mentioned
earlier is a good example and easy to tune.  It is listed in Owen
Jorgensen's small equal-beating temperament book,  and like all of the
other formulas, it to can be modified.  Try setting C-E not exactly pure
but with 1 or 2 beats/sec.
        In case there is confusion about the Pythagorean thirds, an equal
tempered third is 13.86 cents, a Pythagorean third is 21.5 cents, and the
wolfish diminished fourth of 1/4 syntonic comma meantone is 41.05 cents
(two Syntonic Commas minus a Schisma).  The Pythagorean third is important
because historically it defines the limit of a major third and provides a
convenient boundary between well-temperament and mod. meantone.
Technically, well-temperament cannot have any major third larger than one
syntonic comma, or 21.5 cents.  Equal thirds are tempered only 64% as much
as these Pythagorean thirds.
 
 
 
        David Calhoun brought up a very good question which may not  effect
everyone here but it is very significant and one that I have given
considerable thought:
------------------------
 
David writes:
 
>"My intention was to ask whether
>I should have done just what Joe describes, rotating the
>temperament so that C flat major sounded like C major, or just
>acceded and tuned equal temperament, or should I have tried to
>explained to Very Famous Violinist that C flat major was supposed
>to sound like that"?
 
>We never found a satisfactory answer.
------------------
 
        In the end of course every case is individual. I know that I am
treading on thin ice here, but I have learned, hard as it is, that my best
strategy for now is generally not to talk about the temperament.  The only
few times that I ever did have a problem was when I offered to explain what
I had done, giving it a "label".  In your case I think  there was
disagreement between the performers and probably discussion of temperament
came up even before the tuning.  These combined can be a sure setting for
trouble, and perhaps unavoidable.  But my experience has been to check the
music (as you did), learn what I can about the performer, and than taylor a
tuning as subtle or obvious as "I" see fit.  I do generally tend to error
on the safe side however, I confess, especially if I do not know the
performer.  But I can tell many, many stories of artists who came and
played on my unequal tunings and never knew the difference, but told others
how much they enjoyed the instrument.  These are pianists whom I know
without question would have had a major problem if they knew something was
"unconventional".  Do you think that the Violinist would have had a problem
if nothing was said?   Now,  I can just hear someone jumping on me for the
insubordinate implications of this silence and that is why I avoided this
question before.  I do not like this situation, and look forward to day
when we can openly discuss this important element of interpretation.
Usually, if I do say something it is little like this, and no more unless
asked:  "I took the time here to slightly modify our conventional
temperament and taylored something special for this instrument which I
believe enhances its overall harmonics, I think you'll like it".
        Actually, there are few things going on here.  First, the
keyboardist is allowed the luxury of an unbiased, objective and honest
judgment of the tuning, (without any label).  Second,  the artist is
exposed to a legitimate possibility that they would most likely not have
come to on their own.  Third,  I protect myself.  After someone has been
playing on a particular temperament for some time, and even compliments me
on the beautiful tuning, they can't really jump all over me later if and
when it does come out that this had been something unequal all along.  And
finally,  I, as a concert technician, take some pride in the approval of my
concert pianos and am admittedly a little sensitive to those musicians who
would prefer to minimize the technicians aesthetic involvement in their
performance.  I would never offer musical interpretation to a pianist
unless asked, and I do not expect a pianist to TELL me how to tune.   I see
this as mutual respect. Eventually, as pianists become more familiar with
these temperaments they will seem less daring and we will be able to
discuss these possibilities openly without misunderstanding.  I have
already seen this beginning to happen with some of the faculty at my
College.  One thing that I will not do is set myself up for an argument
over misunderstood terms.   Anyway, I have never yet had a problem with my
choice temperaments for performance.  Even though I am responsible for
every tuning I do, every tuning must also satisfy my own standard of good
taste.  I would never tune a restrictive temperament for performance on my
own whim without it first being requested or discussed.
        In closing,  I have often found it curious that so often when
someone (musician or tuner)  tells me that they did not like some
particular equal tuning it is understood that the tuner must be at fault,
but if they are dissatisfied with a tuning that had been labeled "unequal",
"well" or whatever, than immediately the entire class of unequal
(historical) temperaments are written off as inferior.  Where would we be
if equal temperament was held up to this same standard?
 
        Wow, this did get to be long!
 
 
 
 
Dennis Johnson
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