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In music, a monad is a single note or pitch.
Just as a tempered tritone bisects the octave such that it has only six non-enharmonically equivalent positions (can be transposed five times, that is), just as the augmented triad trisects the octave and has four positions, just as the diminished seventh chord divides the octave in four and has three positions, just as the whole-tone scale divides the octave in six and has two positions, just as the chromatic scale divides the octave in twelve and has one position, the monad makes of the octave a single sector and has twelve positions. This seemingly trivial property of the monad is in fact an essential part of the arithmetical partitioning of the power set (set of all subsets) of the equally tempered chromatic scale.
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Pitch sets by cardinality |
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