ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Friday, August 18, 2006

Duality, quantisation and symmetry in BWV-999





I just love BWV-999, the Dm Prelude to the lute works by Bach. It is relatively simple to get started and there is ample potential to improve. It seems to be written to be played fast. As usual with Bach, it should be played very balanced to make the different parts stand together coherently. Speed and balance in a piece with very difficult chord transitions. A piece for life.

Measure is the most outstanding aspect of a musical piece. BWV-999 has 3/4, with each quarter further divided into 4, giving 12 sixteenths. Bach chooses special numbers with religious and mystical qualities, 2, 3, 4, 12. No surprises here. 2 comes from bass and treble duality.

Measure also happens to be the most outstanding aspect of any physical entity. Life is made of cells. Matter is made of atoms. Light is made of photons.

The first beat of all measures belongs to bass. Although it is the opening shot of the measure, it also closes the previous measure. This linking, or chaining, is very elementary and comes from the scales;
(C,D,E,F,G,A,B,(2C),2D,2E,2F,2G,2A,2B,3C)
When a two octave scale is played, one can hear the dual role of the root C. It is both the ending of the previous and the beginning of the next. This dual property of the root is central to music.

Life also displays this property of ever becoming.

Bass and treble make a 3+3 pattern with bass twice slower. Bass has 2+1 pattern with 2 completing to 3 in the next measure.

Another duality comes from the bass-treble interaction. Chords act as vertical glue to bind bass and treble. The first quartet (D,2D,2F,2A) sets out the dual vertical pattern.
((D,2D),(2F,2A)) and (D,(2D,2F,2A))
The 2+2 pattern arises since D and 2D attract each other, being the same.
The 1+3 pattern is due to bass and treble duality. Treble flock together.

The ambiguity in meaning is what makes the bonding between parts. He then plays with harmony, in the rest of the peace, to explore the interactions between dualities. The quantum, or measure, is the one that carries all these dualities. Reminding the uncertainty principle.

Dual ambiguity gives us depth in our vision and hearing.

There is also a spine of the piece, formed out of 6 alternate 16ths. Bass and treble are bonded to aech other around a spine. When played fast it sounds like a tremelo. As if the whole thing is like a DNA piece, with bass and treble dancing around each other around a spine. Even the numbers of bases match (2+2). We enjoy music because, it seems, the patterns of the mind match that of music.

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