J.S. Bach and contemporaries played around with various temperaments.
Before the equal-tempered scale was widely adopted, a lot of musicians
performed and wrote music for the just-scale or variants of the just
scale. A just scale based upon the key of C will only sound best when
music is written in the key of C. Music written in other keys, but
played on a harpsichord tuned to just-C, will sound dissonant (more
beats). Some key signatures are better, and some worse, in terms of
beats.
The composers of the time knew that when writing music in different
key-signatures they could get different tonal qualities. And, there
were some key-signatures that they strictly avoided because they sounded
really bad.
Some historians have said that Bach nearly invented or at least promoted
the equal-tempered scale. Recent evidence indicates this may not be
true; rather, Bach had his own tuning method that was a compromised just
scale, but not equal-tempered. Remember that when playing different
key-signatures on an equal-tempered instrument, the same composition
transposed into any key will sound equally good, which might also be
described as equally bad. However, if the instrument is tuned just,
then music played in that key sounds wonderful. Bach apparently had a
compromised tuning that sounded wonderful even when using several
different key-signatures, but it did sound worse in a few which he
avoided.
Supposedly, when Bach would interview for a job or a commission, he
would first tune the harpsichord (or organ) to his secret method, then
when he played his music for the jury, which could be transposed into
various keys that he knew were good with his temperament, the jury was
always impressed and gave him the job or commission.
Bach never told anyone (except probably family members) what his tuning
method was. Recently a music professor, Bradley Lehman, has published
papers indicating that he believes he has deciphered Bach's secret code.
Bach frequently scribbled doodles in the margins of his music. Most
people thought there was no significance to these doodles. Lehman has
convinced me, and many others, that these doodles hold the key to Bach's
tuning. Properly decoded, the doodles show which fifths to flatten
(shrink) from just temperament, and how much to flatten them. The final
fifth is sharped (stretched).
Brad Lehman is an acquaintance of some Bluffton professors because he
attended Goshen College, which is a sister college of Bluffton
University (because we have the same church affiliation). Brad went on
to University of Michigan to earn his doctor of arts in music. Last
year he came to Bluffton to explain his decoding of Bach's secret, and
to play some of Bach's harpsichord music on just temperament, equal
temperament, and Bach's temperament.
There is a difference in the sound, and I believe Bach's music does
indeed sound best when played in a harpsichord tuned the way Brad
believes Bach indicated it should be tuned.
Brad has a website where he explains the code and how it signifies that
you start with perfect fifths (2:3 ratio) and then tweak it using Bach's
recipe.
The top of this second website shows Bach's "doodle" the way it appears
on Bach's music. Not counting the beginning squiggle on the left, and
the ending squiggle on the right, the doodle has 11 major loops. I'll
signify this with stacked oh's, but Bach's squiggles are nested.
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0
c
The first three loops are double loops. The next three are single
loops, and the last five are triple loops. Near the triple loop is the
letter C indicating musical note C on the scale. The code is actually
upside down because you actually want to go right to left if you use it
as shown. The loops don't actually indicate the frequencies, but
indicate the intervals between the fifths. Starting on the right would
be F, then C, then G, then D, then A, etc. A single loop means don't
flatten that fifth at all. A double loop (one extra loop) means flatten
it (make the interval narrower) by 1/12 of the musical interval of a
comma. A triple loop (two extra loops) means flatten by 2/12 comma.
0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
f c g d a e b f# c# g# d# a#
To get back to f from a#, that fifth has to be stretched by 1/12 comma.
Consult Brad Lehman's web pages for more details.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu