It was written: I'm finding this discussion of temperaments most
interesting. I wonder if any of you would like to discuss the
relationship of different key signatures to different musical and
emotional effects. I have long recognized that key was not arbitrary,
and that different keys were appropriate to different moods, but have
never understood how this worked, or why. This discussion suggests to
me that temperament must play a role.
Would anyone care to enlighten me, in exceedingly simple-minded terms?
Others have replied - but simple-minded I can do.
You are asking about what's called the theory of "affects..."
that each key must have its own character, deeply involved in
Baroque theory (will an academic help us here?)
A few years ago I met a Canadian harpsichordist who had obtained
a doctorate with her theory that
a) since Bach was a proponent of Equal Temperament, and
b) since we hear the character of music at a' = 440; therefore
3) Bach must have written at a' = 440, or he was WRONG!
I remember as a kid thinking that chords on the piano had
different feelings about them. I suppose the piano was at least a
try at E.T. I have no explanation for that - maybe the CAnadain
But the clues given by unequal temperaments of the Baroque sort
(circulating, or well-temperaments) are an important source of
key meaning. There are two elements (merged, of course) - melodic
The differences among the various "well" temperaments and ET are
small, melodically. It's easiest to hear what happens with an
extreme case, like the standard quarter - comma meantone. A piece
like Sweelinck's "chromatic fantasy", whose theme is jsut a
fourth which descends by half tones, is dull in ET; since there
are big and small semitones in meantone, the motif becomes very
colorful in meantone. Try transposing it up, or down, a semitone!
The harmonic element is easiest thought of as what happens in
major chords. In ET the fifth of the chord is almost clean; the
major third is so wide that it's not only not consonant, but it
blurs so badly as to be beyond dissonance. Ears accustomed to
meantone would have taken it to be one - a diminished fourth.
That's what is being referred to as a "Pythagorean" third.
(not exactly - but close)
The normal way of tuning these "well" systems is to distribute
the available "goodness", or consonance, of the major thirds so
that the "best" third, the least stretched, is in the "home" key
with no accidentals, or C major. In general the major "thirds"
get progressively stretched as they move into more flats or
sharps, until they reach this "phthagorean" nastiness. At the
same time, the impure fifths have been purified: so that in keys
with four sharps or flats the major chord has a screaming major
third and a serene fifth, which contrasts with the serene major
third and wobbly fifth of C major.
On the way around the circle of fifths, the recipe changes
gradually; so that every key has its own combination of
consonance and dissonance in the major triads. The discussion
about Werckburger and Kernmeister and Kellner is an argument
about the recipe.
The same is true for minor triads, and every other interval; and
of course as the music does what it does, all sorts of things
happen. The argument is that the composer is exploiting the shift
of consonance and dissonance, or good and bad; that's what
I think of a couple of good organ pieces in which to hear this -
Bach, of course. The little prelude on "erbarm dich" chugs along
in prayer for forgiveness, ending with the words "try me," or
"scourge me", or "judge me" ... with an F# major triad, the most
agonized chord available in any "well" temperament. A clear
statement about "judgment."
And Bach does the same thing in the three-section "O lamm
Gottes," which is in a relatively sunny A major until in the
third section there is a vivid piece of picture writing with the
crown of thorns, the whipping, the crucifiction - in which the
piece suddenly skids sideways into the same agnoized distant key
- then there is a sudden clearing and the agony is all swept
away. In equal temperament it's still a great piece - but missing
Now, Joseph Spencer reported an adventure with a Bach toccata:
I ended up making a map of the key areas
that dominate that rather peculiar work, and comparing them to common
temperaments of the period. What I noticed was that the predominate
tonal areas were a half-tone sharp of the "good" key areas in
Werckmeister (or any of the usual modified meantones of the time). I
immediately thought "transposing keyboard", and furrowed my brow,
thinking "If only Bach had a transposing keyboard!" I talked with John
Koster at the Shrine to Music Museum about it, and he pointed out that
North Germany and indeed Thuringia seems to have been a center for such
devices, as they appear on some of the earliest instruments there.
So... we tuned the Jacques Germain instrument in Werckmeister transposed
a half step, and the result was magical. I don't know if others have
made this discovery, but it was great fun.
I haven't heard the disk, and I don't play the piece, but ...
Joe - why did Bach write the piece in F#?
Early in this thread I asked about a problem in a Haydn trio with
fortepiano, in which the string players complained they couldn't
find the c flat - e flat interval in a section with five flats,
and asked for equal temperament. 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.
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