A novel characterization of ME sets

I stumbled by chance on a nice musical interpretation of an esoteric theorem due to Pierre Beauguitte that more clearly demonstrates its perceptual consequences. It is a translation of a statement on Fourier coefficients in terms of the IFunc between two generated pc-sets, and it characterizes the non-periodic maximally even sets, those generalizing pentatonic or diatonic scales. As a simple example, a chromatic pentachord always has three notes in common with any diatonic scale, except for one case when there are only two; and the diatonic and pentatonic scales are the only pc-sets harbouring that relationship with these chromatic spans. A very slightly different and simpler condition characterizes periodic pc-sets.