Saturday, September 23, 2006


JS Bach: WTC I, E Minor Fugue

Hello all,

It will help if you have read the post:

Significance of the number nineteen

We are looking for the dynamic symmetry in JS Bach's WTC I, E Minor Fugue. This is a two-voice fugue, which could have been named an invention, but qualifies as a fugue. The agent defining the symmetry is lengthy consecutive parallel intervals and the number 19. Counting measures, we have the first 19 meassures ending with a measure of consecutive parallel octaves. The second 19 measures also ends with a measure of consecutive parallel octaves. These 38 measures (2x19) lead to a four-measure coda yielding the total 42 measure fugue.

Any odd number has a central number that divides two equal portions. Thus it behooves us to observe the midpoints of our two 19 measure leads. Measure 10 mediates the first 19 with consecutive parallel sixths. Measure 29 mediates the second 19 with consecutive parallel thirds.

Sixths and thirds so highlighted might lead the contrapuntalist to suspect Double Counterpoint at the octave. A simpler understanding might be gained that the combination of a sixth to a third will span an octave. (C up to A = sixth [C,D,E,F,G,A]; continuing A up to C = third [A,B,C]; overall the resulting C up to C is an ocatve [C,D,E,F,G,A,B,C].

The parallelisms are distinguished by length of consecutiveness, minimally nine sixteenths, and the full measure of twelve sixteenths for measures 19 and 38. Thus the two midpoints of the 19 measure portions have combined meaning for the overall middle 38 measure lead to the coda. Indeed, measure 20 continues with four more sixteenths to perfect the middle of the 38 measure lead to the coda.

Thus the fugue is organized by the number 19 with significant intervalic parallelisms yielding dynamic symmetry.


Wednesday, September 20, 2006


Proportions: The Number 19

The number nineteen is a favorite number used by Bach. I will be using analyses of the number 19 in Bach and Beethoven. So first, here are some sites on the number nineteen.

The proportions for the number nineteen are:

3:2:5:7:12:19:31:50 etc.

Beginning with the numbers 3 and 2, adding consecutive numbers yield the next number in the sequence. Maybe the most frequently and maybe least noticed proportions from the series are the seven days of the week, from which we separate two weekend days and five work days; and 12 is used twice to count the number of hours in a day, and 12 months divide a year. Less formally astrology is planned in 19 year cycles.

Cheers, and happy counting

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