In a message dated 9/21/00 6:10:51 PM Central Daylight Time,
Richard.Brekne@grieg.uib.no (Richard Brekne) writes:
<< I am sure there is, and perhaps you might take a moment to explain a bit
about a
few things I wonder about from time to time. First,, as long as I am on about
this "chord",,,, I wonder what if any, temperament scheme that might most
closely
fit in.
Then there is this buisness about the colour of keys. One thing that has
troubled
me all along is that key colour must be related to which temperament one
chooses,
and which starting point for each temperament as well. That being the case
the
"colour" of B flat (or any other key) is by no means even close to being
constant. In fact it could feasably vary fairly wildly...>>
This has been explained quite a bit but it is worthwhile finding different
ways to express it. There are some odd kinds of HT's and experimental
tunings/temperaments but I am not interested in them and do not practice
them. I have always been in search of the kind of arrangement that only ET
is supposed to be able to satisfy. That is, a "universal" one which can be
used for any and all kinds of music. It has always been my contention that
ET goes further than it has to in order to be a "universal" temperament. The
earlier, more extreme forms of temperament are not "universal", so I only use
them in specific and special circumstances.
All of the Well-Tempered Tunings (also called Well-Temperaments) have what I
would call a Cycle of 5ths alignment. This is something very simple to bear
in mind. It means that the speed of the Major 3rds will correspond to the
number of sharps or flats in the key signature. The fewer sharps or flats,
the slower the beating, the more sharps of flats, the faster. It's as simple
as that. The range of speeds however can be from Zero (pure) to an amount
that is nearly (but not quite) the same as in ET.
The slower (and more "dead" sounding) the beating at the top, the faster (and
more intolerably harsh) the beating will be at the bottom. The early
Well-Temperaments (WT) used around Bach's time had pure or nearly pure 3rds
at the top and harsh ones at the bottom. Generally speaking, as time went
on, new WT's were designed which gravitated towards ET by making less and
less contrast. All along the way, incidentally, these WT's were often
erroneously referred to as "ET". This fact has caused much confusion.
In the two examples you gave, D Major and Bb Major, both keys have only two
sharps or flats, so in any WT, they would be expected to be mild sounding,
having a slower beat than in ET. This is part of what is meant by "Key
Color" (and the most important feature). The other is whether the 5th is
pure or tempered and if so, by how much.
If only WT's are considered, you really couldn't expect either the key of D
or Bb to sound that much different from one temperament to the other. In
fact, it is the expectation of what a key with only two sharps or flats would
sound like that forms the basis for choosing it. The key of Bb is likely to
have a pure 5th and a gently beating 3rd and the key of D would have a
similar 3rd but probably have a tempered 5th.
The WT's are a combination idea that joins the Meantone idea and the
Pythagorean one. In Meantone, there are always 11 tempered 5ths with the
remaining one being wide and untuned. It is the so-called "Wolf" key. That
widened 5th is almost always left between Ab & Eb (actually, it is
theoretically not a 5th but a diminished 6th between G# & Eb but as a
practical matter, especially if it is one of the milder Meantones, that
diminished 6th is used as a super-energized 5th which can have a striking
amount of "color" to it.)
In Pythagorean tuning, 11 of the 5ths are tuned pure with the remaining one
left untuned and narrow. The WT's take the Pythagorean idea and apply it
mostly to the black keys and mostly to the bottom of the Cycle of 5ths and
leave the other half sounding like a kind of Meantone temperament with
tempered 5ths and slower beating 3rds. There is also a whole class of
temperaments called the Modified Meantones which take the one "Wolf" 5th and
divide it between two or more 5ths, thus mitigating the harshness.
There are also the Quasi-Equal Temperaments ("quasi" means "almost") which
generally have some of the Cycle of 5ths idea behind them but do not
completely conform to a complete set of rules the way the WT's and the
Meantones do. You can have, for example a temperament identical to ET but
where only the note C is sharpened by 1 cent. This makes the key of C sound
a bit gentler and the key of Ab more vibrant. It would work well for any
Romantic era music.
Generally speaking, the earlier the temperament, the purer the 3rds at the
top and the harsher the 3rds at the bottom and if it is a Meantone, the
stronger the Wolf. Composers of those times expected to hear these sounds
and chose to write in a key which reflected the mood of the piece. You see
very little of Mozart written in remote keys and when you do, it is usually
in a minor key. Minor keys in 4 or more flats in early temperaments have a
very dark sound but it is not unpleasant to the ear. Music written in a
minor key is often meant to be sad and that darker sound enhances that
feeling.
Mozart would not have chosen the key of F# Major, for example and written
material similar to his C Major Sonata. Neither would have Bach or any other
composer. Those very harsh keys had fast, flighty, detached notes (not close
harmony) type of music written for them. If you were to transpose any of
that music to a key at the top of the Cycle of 5ths, the music would sound
inappropriately dull.
Unfortunately, today, most musicians and piano technicians have never been
taught any of this. Anything that is purported to be *Unequal* is something
to be afraid of. Anyone can go up to a piano tuned in an HT and *bang* on a
triad in the key of F# right in the middle of the piano and exclaim and
proclaim that it sounds terrible and inappropriate. One may do the same for
the gentle sounding keys. *Bang* on them and announce that they sound "dead".
I have often heard technicians say something to the effect that only ET is
appropriate because "you never know when the pianist might jump into six
flats". If it is modern music, this might well be the case and an early
temperament with lots of contrast might well be inappropriate. However,
music and musicians don't just "jump into" a key for no reason. There has
always been the expectation, even throughout the 20th Century that a
particular key has a "color" to it and that is why it is being chosen. It
reminds me of a statement made by the new local symphony conductor that more
or less sealed the reason why I could not and did not want to work under him.
He said, "We *have* to have the piano tuned in ET because we don't know what
we're doing".
I rarely choose to tune such an extreme and early temperament as the 1/4
Comma Meantone. It is also meant to have as pure (contracted) octaves as
possible. To me, this gives the modern piano an entirely different sound.
It literally "kills" all of the resonance that we are used to hearing from
the modern piano. Nevertheless, it is appropriate for some early music and
if the demand is there, it should be used for that. It really messes up a
piano's tuning, however, about like a 25 cent pitch change might do.
If you are tuning for a program of music that is all early, or you have more
than one piano to use for a concert, it is indeed more appropriate to choose
an early temperament for the early music. It's as simple as that. While I
consider the EBVT to be slightly more appropriate than ET for Mozart, I know
full well that virtually any Mozart would sound better in an early WT or a
1/5 or 1/6 Comma Meantone.
I'm not afraid to use the words "better" and "more appropriate" when
discussing *choices* of temperament. In one sense, it cannot be said that
one temperament is "better" than the other because for every interval that is
"favored", another is "disfavored" in direct proportion. However, not all
music is meant to be smooth and harmonious. Music rightly has emotion to it.
It can and does have clashing dissonance that sometimes is resolved by quiet
harmony. To take away the features that Cycle of 5ths based temperaments
have by neutralizing them into ET only serves to rob the music of the
contrasts and emotion it was meant to have.
I personally believe that there is no music worth listening to or put another
way, that enough people will buy so as to make it worth creating and
producing that *requires* ET. ET produces its own particular sound and
distinctive resonance on the piano and yes, this generation of people have
been raised on it and accept it and even find any other arrangement to be
disagreeable, but that does not mean that I have to like it or that I am
wrong if I actually dislike that sound. I have very good and sound reasons
for the preferences I have developed but in contrast, I'm afraid that most
people who express a preference for ET only simply have no knowledge or real
experience with anything else.
<< Also we keep hearing about the "appropriateness" of certain temperaments
with
certain composers or musical time periods. Now you know me and words like
"appropriate"... grin.. but that aside I am wondering how one makes
intellegent
choices about which temperament to choose (and which arrangement of that
particular temperament) for any given key signature. By this I mean that its
no
point in taking for example a 1/6 meantone that wolfs like crazy in the key
of
say F# if the key signature is F#. (I am just throwing letters and numbers
out
there randomly but you get my meaning I think. >>
Bill Bremmer RPT
Madison, Wisconsin
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