Dude -- I know how old this thread is.
Is there any evidence that the two books of the Well-Tempered Clavier (20 years apart in the publication) were written with two different well temperaments in mind?
Reason I ask: I'd be interested in looking more closely at key characteristics and whether the various preludes and fugues for a particular key exhibit similar predilections based on key. I can say that I feel this to be the case just from listening to and glancing at them, but haven't checked more closely. If the answer to the above question is 'yes', then that would save me a lot of trouble and/or 'nguish.
(I realize that 4 pieces is a rather small sample for any significant quasi-scientific investigation)
Is there any extant literature on this topic which experts here can point me to?
I haven't noticed the slightest 'predilection based upon key' in any of the Bach keyboard works - other (that is) than for associating particular keys with particular
affects (which is a rather different matter). The Well Temperaments available at the time all have one thing in common: they can be regarded essentially as equally-tempered systems that retain various colours.
The most common was Werkmeister III, which Werkmeister illustrated by means of a monochord diagram. The trouble with monochords, however, is that they are only capable of indicating mathematical rather than geometric ratios according to string length. So when, say, a tone is divided into 2 semitones (i.e. on the monochord), placing a further mark equidistant from either surrounding tone creates
unequal semitones (since the higher of the two semitones provides a ratio based upon a shorter string than the lower of the pair). All Werkmeister's monochord markings are arrived at by simple string-length ratios, although the fractions used are often non-Pythagorean. So the question should really be: "What is Equal Temperament?".
That fretted instruments required (eventually) an equally-tempered system is obvious, since the frets cross all the strings (thereby becoming unable to differentiate between the large and small semitones normally needed within the diatonic system). But the earliest example of a
keyboard tuned to equal temperament is the instrument normally known as the Arcicemabo (sometimes misspelt with an 'h' before the 'i'), which the 16th-Century composer Guillaume Costeley prescribed - for performing his chanson
Seigneur dieu ta pitie - needed 19 notes per octave. Here (as can be seen from web illustrations) each black note was split into two separate notes, and an extra black note was inserted between B and C, and also between E and F. Costeley demanded that the pitch difference between adjacent notes should be equal to one-third of a tone, and that the diatonic semitone should equal two-thirds of a tone.
So this instrument (as used by Costeley) was an example of 19-tone Equal Temperament. It is not clear how (other than by judgment of ear) this tuning might have been achieved, since to draw it upon a monochord would have needed a geometry capable of generating precisely the 19th-root of 2! But it seems clear that (to Costeley) the ideal would have been an octave in which each degree of the scale was 63 cents higher than its lower neighbour. Indeed the chanson concerned is unusual since it modulates flatwards through all the flats, and then continues modulating further flatwards through all the double-flats as well! Nothing other than some kind of equal tuning could have coped with such a piece.
I have created a sound file of this piece, with exact tunings according to the composer's requirements, and this can be listened to
Most of the melodic semitones are diatonic, but a couple of times a chromatic semitone is required (and indicated), and this (together with a number of false relations in the harmony) has a very
antique effect.
Baz
