Some discontinuous properties of the phases of the DFT of pc-sets

Properties related to the discreteness of the phases of the Discrete Fourier Transform (DFT) of pitch-class (pc)-sets in the 12-tone universe were studied. We primarily investigated the conditions where the DFT phases are integer multiples of π/12 for pc-sets of up to six tones (effectively covering all the pc-sets in the 12-tone universe). Pc-sets were classified into five classes according to whether or not each DFT component’s phase was an integer multiple of π/12. It was also found that phases of non-integer multiples of π/12 tend to be associated with larger Fourier components. Additionally, discontinuities associated with pc-sets with indeterminate phases were also investigated by tracking the phase changes in certain chord progressions.