18edo/Inthar's approach

From Xenharmonic Wiki
Jump to navigation Jump to search

Notes: I (Inthar) am also taking some of Well-Tempered Fox's ideas how to approach 18edo.

Scales

Chords

Stacked-third chords

Split the major ninth, 1400 cents, into two different fifths, one 666 and one 733. Split each fifth into two thirds. This results in 24 possibilities.

  • 0-467-733-1133-200
  • 0-467-733-1067-200
  • 0-467-733-1000-200
  • 0-400-733-1133-200
  • 0-400-733-1067-200
  • 0-400-733-1000-200
  • 0-333-733-1133-200
  • 0-333-733-1067-200
  • 0-333-733-1000-200
  • 0-267-733-1133-200
  • 0-267-733-1067-200
  • 0-267-733-1000-200
  • 0-400-666-1133-200
  • 0-400-666-1067-200
  • 0-400-666-1000-200
  • 0-400-666-933-200
  • 0-333-666-1133-200
  • 0-333-666-1067-200
  • 0-333-666-1000-200
  • 0-333-666-933-200
  • 0-267-666-1133-200
  • 0-267-666-1067-200
  • 0-267-666-1000-200
  • 0-267-666-933-200

Harmonic syntax

  • resolve the 600 tritone inwards to 467 or outwards to 733 instead of a traditional third

Modulation

Some important modulatory intervals in 18edo:

5ths and 4ths

  • sup5 / sub4, sub5 / sup4

3rds and 6ths

  • maj3 / min6, supmin3 / submaj6, submin3 / supmaj6

2nds

  • maj2 / min7 (maj2 = sup5 + sub5 = 3*sub4 = 3*submaj6) -- these are familiar

Dissonances

  • supmin2 / submaj7, submin2 / supmaj7, tritone

Sup and sub cancel and result in a 12edo (actually 6edo) interval. So do 3 sup's and 3 sub's, as one sup/sub = ±1\36.

sub5/sup4 forms a 9edo subset, maj3 forms 3edo subset, maj2 forms 6edo subset. supmin3 and sub4 form complete cycles