So, a roadmap:
- overtone series and JI to approximations of finite subsets thereof in an equal temperament
- subsets of the overtone series, esp. partially overlapping ones given different starting points in the equal temperament
- from temperaments and JI to chords as subsets of an ET
- from temperaments and JI to MOSes and MODMOSes as subsets of an ET
- chords as subsets of MOSes and MODMOSes
- movements by restricted paths /by step-size or step-type combinations) within and between group-structures of chords within a temperament; the subset of movements that is within a MOS/MODMOS is of special interest
- movements by restricted paths from MOS/MODMOS to rotation of the same MOS/MODMOS as a group operation. movements from one type of MOS/MODMOS to another type as a group operation.
- OTHER thing altogether: Comma pumps. Making comma pumps and the above come together. Using the inter-MOS/MODMOS modulation or extra-MOS/MODMOS modulation to create compelling chord progressions
- embedding MOSes/MODMOSes in larger MOSes/MODMOSes and relating this to the previous set of ideas (i.e. melodies moving in chords moving in scalesmoving in scalesmoving in scales...)
- Question: is there anything analogous to the comma pump in higher-level modulation?
- Question: does any other weird phenomenon happen in modulation that involves multiple levels of modulation, where weird things start happening?
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