Hierarchy of Truncations (new!) (Patreon)

This is a better version of a diagram I made back in 2016 or so. These are the truncations of modes of limited transposition, described by Messiaen. A truncation is when you remove tones from a scale to produce a subset with preserved rotational symmetry. Solid arrow indicates removal of 2 tones (preserving symmetry of 6 semitones), a dashed arrow indicates removal of 3 tones (preserving symmetry of 4).

It's fun to note scale 1365 can be arrived at from 1 path through 1911, or via two truncations 2015 and 1495.

This diagram is going in the book.