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How exactly is Bach mathematical? Explain, say, how his Organ Fugue in G Minor (my favorite) is mathematical.
The fugue is one of the most mathmatically organic forms in music. You can start with a very short subject (in some cases almost a motif) and the music will 'grow' out of it.
The G Minor fugue is a lovely piece (quite simple in structure but mathmatically interesting nonetheless). The interest lies in the opening leap of a fifth which seems to drive the design of the whole piece.
First subject enters on the 'G' and starts with a leap upwards of a fifth.
The next entry of the subject starts on the 'D' (entering at the fifth). Each entry of the subject thereafter enters alternately on the tonic and the fifth in either g minor or it’s relative major.
The subject is 10 bars long (multiple of five).
In between the entries of the subject there are episodes based on part of the material from the subject moving through the 'Cycle of Fifths' to add interest by moving through different keys.
About two thirds of the way through there is also a long pedal note on the fifth.