Figure 2
From: Artificial Neural Networks Solve Musical Problems With Fourier Phase Spaces
The six Fourier phase spaces, Ph1, Ph2, and so on used by Yust23. Each space represents the twelve pitch-classes on a clock face. (A) Phase space Ph1. The arrow, pointing at 0 o’clock, indicates a phase of 0. Solid lines denote projections from the pitch-class locations on the clock to the arrow. (B) Distances between each projection in (A) and the center of the phase space. Distances towards the arrowhead are positive. (C,D) Ph2 and its projection distances. (E,F) Ph3 and its projection distances. (G,H) Ph4 and its projection distances. (I,J) Ph5 and its projection distances. (K,L) Ph6 and its projection distances. The projection distance graphs show that each phase space represents a cosine function, and that the difference between phase spaces is the frequency of this function. Ph1 has a frequency of 1, Ph2 has a frequency of 2, and so on. Musical sets can be reconstructed by adjusting the phase of each component, weighting them and summing them together.
