The A Minor Fugue from Book Two of the Well-Tempered Klavier.

October 4, 2020

I think of this fugue as being somewhat like someone who takes a new deck of cards and throws them in the air and then picks up the individual cards off the surface they have fallen on.hoping to find the cards thoroughly shuffled.  Only to find out, when he begins picking up the cards lying on the table that the shuffling was not complete.  There are still adjacent groups of cards like a 3, 4, and 5 of clubs followed by a seven and 8 of diamonds, etc..   Substituting rhythmic patterns and motives for cards in a deck, we say: well, I tried to randomize the order of the notes’ rhythmic values throughout the piece but find that there remain smaller but intelligible repeating segments of “DNA”.  And they appear over and over again.

Another analogy would be that we are living two thousand years ago, and are making a mosaic to represent, say, a Roman arcade.  But we are under a lot of rules.  We always have to use certain pieces, tesserae, together with specific other ones.  It can’ be random juxtapositions. In these local groups, we may find that all the tesserae have the same shape, and/or the same color, as the macro object they are attempting to depict.  On the scale of small to medium-sized groups, the groups all have be assembled into a prescribed set of shapes (like triangle, circle, rectangle, etc.).  We want the individual pieces to look somewhat random in this mosaic, but we’ve got some severe restrictions on us that results in local islands of fairly intense order.

In terms of rhythmic patterns.  We will use letters of the alphabet to distinguish among them.

Pattern “A”.  Example: the first four notes of the piece.  Notes of

equal rhythmic value.  They are all quarter notes. The pattern starts

on an offbeat and concludes on the next beat.

If you examine the next four notes in the fugue, which are still in

the same voice, d4 b3 e4 c4, we find that it is the same rhythmic

pattern A only the rhythmic values of the notes have been exactly

halved.  It is the same up and down pitch line as before.  Down a

third, up a fourth, down a third.  To keep the rhythmic pattern the

same, the four notes begin, rather than on an offbeat, on an off

“and”. And concludes on the next strong beat.

And the next four notes do the same thing in terms of pitch shape

and rhythmic values.

This is a somewhat unusual way of beginning a Bach fugue.  Two

different durational versions of the same patterns, one the

“diminished” version of the other, with note values, exactly halved.

We may feel compelled to salvage our standard collection of fugue

rules, or better fugue habits, by saying that the entire fugue theme

is only four notes long, and that the diminutions act as a bridge to

the next voice entrance as much as or more than as statements of the

theme.

Then, in measure 3, we have four thirty-seconds followed by an eighth

note.  I call this rhythmic pattern “B”.  It is different from what

has occurred so far.  It can’t really sound like a fast version of the

main fugue theme although it does involve notes of equal duration.  We

strive to make it sound like its own, unique, structural element.  We

give it what I have elsewhere called a dynamic rhythm.  It is not a

subdivision of something else, it has its rhythmic character of its

own.  And a character that is not bellied in any way, or marred in any

way, or set off its track by anything that is going on at the same time in any of the other voices.

Now, in measure 4, we have a sort of variant on B.  It is different in

certain significant ways, however. It begins with two thirty-second

notes followed by a sixteenth note tied to a third-second and then

fills out the eighth note with three more thirty-second.  We can call

this B-2 or C.  There is also an ambiguity whether it starts with the

last three thirty-second notes in measure 3.

“D” is the pattern that begins in the second half of measure 4. |: .e ts

ts :|.  The .e bears a trill.   As C evolves out of B, so D evolves

out of C.

In m5 the tie is taken away and we have the rhythm of Beethoven’s

Fifth Symphony (rest, short short short long).  This is another

variation on B or C.

Then, occasionally there is a longer pattern of notes of identical

duration.  It too is a variation on C and D.  It is first seen in m9.

starts on the off thirty-second of a beat. and goes to the next beat.

we see it again in m17, m21, 25, 26.

And of these patterns, even the ones that are variations on some of

the others, should be given by us as performers a very distinct

identity as a rhythm.  So that if one played any one of these rhythmic

patterns on a drum, it would immediately stand out for being the one

played and blurred and conflated with any of the others.  This is again what I mean by a ‘dynamic’ rhythm.  No one is any way absorbed into another

variant.  It is too tempting, too philosophically pleasing, to bring

out the similarities between these variations when we play.  Or, to put it in

another way, to conflate cause and effect.

I think the piece succeeds the best when one of these rhythms remain

sounding most different from others similar to it.  I think the similarities between rhythmic patterns will come through, without our trying; our role is to keep the differences apparent.