The use of DFT in music theory really soared after the notion was resuscitated from Lewin’s work by Quinn  in 2005. As we have seen, it bears the tremendous advantage that each coefficient, and moreover each polar coordinate of each coefficient, yields dramatically important musical information (say, the phase of a5 shows which diatonic universe is closest to the pc-set in question). Some musical qualities are immediately visible in Fourier space whereas they require computations in the original musical domain (say, pc-distributions); Fourier space, with this minimised computational complexity, is closest to our perception of music. Indeed, psycho-acoustic experiments on the perception of saliency (and its evil twin, low saliency including nullity of a coefficient) should be enhanced and furthered, since Furier qualities seem to mirror exactly musical features processed by the human brain.
KeywordsFourier Space Music Theory Tonal Music Musical Feature Integer Approximation
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