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...Chapter vector analysis of musical intervals the between notes can be regarded as vectors in a space diatonic scale have natural and dimensional representations there are also mappings from to dimensions kernel d mapping is generated by syn tonic comma which equals harmonic heptagon provides compact visualisation all consonant relationships trip once around corresponds one syntonic three dierent when i rst started trying understand on seemed almost too many ways describe pairs this applies however for sake concreteness examples based white e c f g b firstly an interval two described logarithm frequency ratio well tempered integral powers so equivalent simple count semitones example next higher representation possible copyright philip dorrell tervals but it does not take into account structure some steps note tones second formulation number separately would semitone far we yet neither them says anything about most important feature that chords harmony repeating correspond fractional rat...