Thursday, October 22, 2015

Microtonal Theorizing: A roadmap to my ideas

So, while I am writing these posts I am also kind of developing my own take on the ideas I present – this is why it takes the better part of forever to make new posts. In large parts, this is stuff based on things other xenharmonists and theorists have worked out, but it probably bears some undeniable traces of my own mind as well: I might have misunderstood other theorists' ideas, or maybe I have even introduced some ideas of my own.

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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