More on keyboard temperament, especially in music by composers named Bach
(my apologies for the length):
 
Unfortunately, much that has been written on this subject is questionable
in its logic or its use of historical evidence.  For example, a number of
books contain recipes for temperaments, some of which are now referred to
by the names of certain theorists.  But I'm not sure how closely these
recipes actually approximate the theorists' prescriptions, nor whether
historical musicians actually followed the latter.  In addition, our
perception of pitches and intervals tends to be mixed up with all sorts of
non-acoustic things--feelings, associations, etc.--that may cause us to
think that the latter are essential parts of the former (e.g., that
dissonances are really "bad").  Thus we need to be careful to avoid
asserting as fact what are actually subjective impressions or products of
convention (e.g., that a particular key is more or less "like" or "related
to" another).
 
It wouldn't hurt to bear in mind that the only evidence that we have
regarding the way Bach tuned his keyboards suggests that he would not have
tolerated any temperament that left any key perceptibly out of tune.
C.P.E. Bach, who presumably learned how to tune from his father,
recommends tuning _all_ thirds wide (he does not say how much or how
equally).
 
Now, _we_ don't have to do what we _think_ Bach did, but I think that we
_should_ have good reasons for _whatever_ we choose to do, and I can't
think of a good reason for using a tuning in either the F-sharp-minor
toccata or the Wuerttemberg Sonatas that leaves wolves or other sour
chords anywhere.  To be sure, there are many circular temperaments that
some ears will accept as "good" for all keys yet sufficiently "unequal" to
give certain keys a distinctive flavor.  Many such temperaments will also
tend to make dissonant chords sound more dissonant and chromatic
voice-leading harsher or more disjunct (because of the unequal half-steps
involved).  But we should recognize that any decision to use such a tuning
in a Bach-circle work reflects a _modern_ preference for the piquant
sonorities and irregularities that it produces; apart from the witness of
Kirnberger (whose own temperament is too dissonant to be used for his
teacher's music) there is no _historical_ basis for associating such
tunings with Bach-circle music.
 
There are several reasons, however, for doubting that anyone in the Bach
circle preferred temperaments that are substantially different from equal
temperament.  First, although C.P.E. Bach does not explicitly advocate the
latter, he says nothing in favor of unequal tunings.  Second, when Bach
(J.S.) transposed pieces from one key to another he did so without
changing anything else substantially--as we might have expected him to do
if certain sonorities would have been significantly affected by the
transposition (as to why he might have transposed them, see below).
Third, temperament does not seem to have been an issue among players of
non-keyboard instruments; there are, of course, the well-known concerns of
wind players about fingering (D-flat vs. C-sharp, etc.), but these are
never referred to specific temperament systems and there is little
indication that different keys were intentionally played differently; a
flutist, for instance, did his or her best to play "in tune" when playing
in C minor, even though that is a difficult key.  Keyboard players had to
play alongside non-keyboard instruments, yet Bach wrote keyboard and
non-keyboard music in pretty much the same style; there is no good
evidence that he exploited temperament effects in writing for either type
of instrument.
 
We tend to assume that the tonality of a keyboard work was chosen because
of the way it would _sound_; but there are many other reasons why an
18th-century composer might have written in a given key.  For instance, D
major tends to be associated with bright, lively music, probably because
of its association with natural brass instruments and with the open
strings of the violin; this association seems to carry over to some of
Bach's keyboard music (the D-major Partita, the prelude in D from WTC2),
but not for reasons of keyboard tuning.  Some composers seem to have had
private associations of certain keys with certain affects--Bach, for
example, seems to have used B minor for particularly profound fugal
movements--but again it is hard to associate these preferences with
temperament (if B minor is "profoundly expressive" for Bach, why not also
E minor, which in most temperaments contains similar intervals?).  In a
few cases, Bach put pieces in certain keys in order to fulfill a
preordained tonal plan (as in the transposed pieces in the WTC and the
Clavieruebung), but again this has no demonstrable relationship to the
actual _sound_ of the music.  So-called internal evidence can be found to
"prove" that a given temperament suits a given piece, but the methods of
proof are invariably subjective (Barnes, for instance, bases his argument
in the cited article [EM 1979] on highly questionable assumptions
concerning the alleged perceptibility of certain intervals in certain
pieces).  A _single_ bad chord resulting from the use of a particular
temperament in a given piece ought to rule out use of that temperament.
 
This is not to say that keyboard temperament shouldn't be an issue for
20th-century players.  But the delight that we derive from hearing a
familiar piece in a new temperament is like that of playing it on a new
instrument; the novelty should not fool us into thinking we've found an
answer to the question of what temperament or instrument is "right" for
the piece.  My own preference is to find an easy-to-tune temperament that
works for all the music I happen to be playing at a given time.  Equal
temperament is good for 20th-century music and usable everywhere;
1/4-comma meantone is good for most pre-1700 music (especially if you have
split accidentals) and bad elsewhere; temperament ordinaire will work for
much but not all 18th-century music, e.g., J.S. Bach or Couperin's 26eme
Ordre in F# minor/major, for which some sort of sophisticated circular
temperament (including equal, but not "Werckmeister" or "Kirnberger")
seems necessary.
 
David Schulenberg
Dept. of Music
Univ. of N. Carolina at Chapel Hill
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