Rastmic chords

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A rastmic chord is an essentially tempered dyadic chord tempered by the rastma, 243/242, in the 2.3.11 subgroup in the 11 odd limit.

The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:

  • There are three rastmic triads: the classic neutral triad 1-11/9-3/2 with steps 11/9-11/9-4/3, and an inversely related pair of triads, 1-9/8-11/6 with steps 9/8-18/11-12/11 and 1-9/8-11/9 with steps 9/8-12/11-18/11.
  • Rastmic tetrads are seven in number: the palindromic classic neutral tetrad 1-11/9-3/2-11/6 with steps 11/9-11/9-11/9-12/11; the palindromic 1-3/2-18/11-11/6 with steps 3/2-12/11-9/8-12/11; the palindromic 1-9/8-11/9-11/8 with steps 9/8-12/11-9/8-16/11; the inverse pair 1-11/9-11/8-3/2 with steps 11/9-9/8-12/11-4/3 and 1-12/11-11/9-3/2 with steps 12/11-9/8-11/9-4/3; and the inverse pair 1-9/8-11/9-3/2 with steps 9/8-12/11-11/9-4/3 and 1-9/8-3/2-11/6 with steps 9/8-4/3-11/9-12/11.
  • There are five rastmic pentads: the palindromic pentad 1-9/8-11/9-3/2-11/6 with steps 9/8-12/11-11/9-11/9-12/11; the pair 1-9/8-11/8-3/2-11/6 with steps 9/8-11/9-12/11-11/9-12/11 and 1-11/9-11/8-3/2-11/6 with steps 11/9-9/8-12/11-11/9-12/11; and the pair 1-9/8-11/9-11/8-3/2 with steps 9/8-12/11-9/8-12/11-4/3 and 1-9/8-3/2-18/11-11/6 with steps 9/8-4/3-12/11-9/8-12/11.
  • There is also a rastmic hexad: 1-9/8-11/9-11/8-3/2-11/6, with steps 9/8-12/11-9/8-12/11-11/9-12/11. This can be extended to the neutral diatonic scale, LsLsLss, which is Neutral[7]. In neutral, with the neutral third (~11/9) as generator, the rastmic hexad is a chain of five neutral thirds rather than the six which give neutral7, which therefore has two rastmic hexads and of course many more smaller rastmic chords.

Equal divisions of the octave with rastmic chords include 10, 17, 24, 31, 41, 58, 72, 130, 202, 736be, 938be, 1075be, 1116be, 1277be, 1318be.

chord by pitches chord by intervals
1 - 11/9 - 3/2 11/9 - 11/9 - 4/3
1 - 9/8 - 11/6 9/8 - 18/11 - 12/11
1 - 9/8 - 11/9 9/8 - 12/11 - 18/11
1 - 11/9 - 3/2 - 11/6 11/9 - 11/9 - 11/9 - 12/11
1 - 3/2 - 18/11 - 11/6 3/2 - 12/11 - 9/8 - 12/11
1 - 9/8 - 11/9 - 11/8 9/8 - 12/11 - 9/8 - 16/11
1 - 11/9 - 11/8 - 3/2 11/9 - 9/8 - 12/11 - 4/3
1 - 12/11 - 11/9 - 3/2 12/11 - 9/8 - 11/9 - 4/3
1 - 9/8 - 11/9 - 3/2 9/8 - 12/11 - 11/9 - 4/3
1 - 9/8 - 3/2 - 11/6 9/8 - 4/3 - 11/9 - 12/11
1 - 9/8 - 11/9 - 3/2 - 11/6 9/8 - 12/11 - 11/9 - 11/9 - 12/11
1 - 9/8 - 11/8 - 3/2 - 11/6 9/8 - 11/9 - 12/11 - 11/9 - 12/11
1 - 11/9 - 11/8 - 3/2 - 11/6 11/9 - 9/8 - 12/11 - 11/9 - 12/11
1 - 9/8 - 11/9 - 11/8 - 3/2 9/8 - 12/11 - 9/8 - 12/11 - 4/3
1 - 9/8 - 3/2 - 18/11 - 11/6 9/8 - 4/3 - 12/11 - 9/8 - 12/11
1 - 9/8 - 11/9 - 11/8 - 3/2 - 11/6 9/8 - 12/11 - 9/8 - 12/11 - 11/9 - 12/11