Of All Interval Tetrachords and Octatonic Scales

Serendipity is another name for method. When order appears unexpectedly in music, the explanation is so often mathematical. Here, a nice feature of a hand-made picture revolves about the Sylow subgroups of the affine group modulo 12 (and of its maximal normal subgroup T / I), explaining the surprise occurrence of octatonic scales when trying to organize all-interval tetrachords by common dyads.