Ibnsinmic chords

From Xenharmonic Wiki
Jump to navigation Jump to search

Ibnsinmic chords are essentially tempered chords tempered by the ibnsinma, 2080/2079.

There are 12 triads, 36 tetrads and 18 pentads as 21-odd-limit essentially tempered chords.

For triads, there are six pairs of chords in inverse relationship:

  • 1-11/8-13/9 with steps of 11/8-21/20-18/13, and its inverse
  • 1-21/20-13/9 with steps of 21/20-11/8-18/13;
  • 1-21/16-13/9 with steps of 21/16-11/10-18/13, and its inverse
  • 1-11/10-13/9 with steps of 11/10-21/16-18/13;
  • 1-26/21-11/8 with steps of 26/21-10/9-16/11, and its inverse
  • 1-10/9-11/8 with steps of 10/9-26/21-16/11;
  • 1-13/11-21/16 with steps of 13/11-10/9-32/21, and its inverse
  • 1-10/9-21/16 with steps of 10/9-13/11-32/21;
  • 1-9/8-26/21 with steps of 9/8-11/10-21/13, and its inverse
  • 1-11/10-26/21 with steps of 11/10-9/8-21/13;
  • 1-9/8-13/11 with steps of 9/8-21/20-22/13, and its inverse
  • 1-21/20-13/11 with steps of 21/20-9/8-22/13.

For tetrads, there are eighteen pairs of chords in inverse relationship:

  • 1-16/13-16/11-21/13 with steps of 16/13-13/11-10/9-26/21, and its inverse
  • 1-10/9-21/16-21/13 with steps of 10/9-13/11-16/13-26/21;
  • 1-16/13-18/13-32/21 with steps of 16/13-9/8-11/10-21/16, and its inverse
  • 1-11/10-26/21-32/21 with steps of 11/10-9/8-16/13-21/16;
  • 1-16/13-18/13-16/11 with steps of 16/13-9/8-21/20-11/8, and its inverse
  • 1-21/20-13/11-16/11 with steps of 21/20-9/8-16/13-11/8;
  • 1-21/16-11/8-13/9 with steps of 21/16-22/21-21/20-18/13, and its inverse
  • 1-21/20-11/10-13/9 with steps of 21/20-22/21-21/16-18/13;
  • 1-26/21-11/8-13/9 with steps of 26/21-10/9-21/20-18/13, and its inverse
  • 1-21/20-7/6-13/9 with steps of 21/20-10/9-26/21-18/13;
  • 1-11/9-11/8-13/9 with steps of 11/9-9/8-21/20-18/13, and its inverse
  • 1-21/20-13/11-13/9 with steps of 21/20-9/8-11/9-18/13;
  • 1-13/11-21/16-13/9 with steps of 13/11-10/9-11/10-18/13, and its inverse
  • 1-11/10-11/9-13/9 with steps of 11/10-10/9-13/11-18/13;
  • 1-7/6-21/16-13/9 with steps of 7/6-9/8-11/10-18/13, and its inverse
  • 1-11/10-26/21-13/9 with steps of 11/10-9/8-7/6-18/13;
  • 1-10/9-11/8-13/9 with steps of 10/9-26/21-21/20-18/13, and its inverse
  • 1-21/20-13/10-13/9 with steps of 21/20-26/21-10/9-18/13;
  • 1-10/9-21/16-13/9 with steps of 10/9-13/11-11/10-18/13, and its inverse
  • 1-11/10-13/10-13/9 with steps of 11/10-13/11-10/9-18/13;
  • 1-11/10-11/8-13/9 with steps of 11/10-5/4-21/20-18/13, and its inverse
  • 1-21/20-21/16-13/9 with steps of 21/20-5/4-11/10-18/13;
  • 1-9/8-26/21-11/8 with steps of 9/8-11/10-10/9-16/11, and its inverse
  • 1-10/9-11/9-11/8 with steps of 10/9-11/10-9/8-16/11;
  • 1-10/9-21/16-11/8 with steps of 10/9-13/11-22/21-16/11, and its inverse
  • 1-22/21-26/21-11/8 with steps of 22/21-13/11-10/9-16/11;
  • 1-10/9-5/4-11/8 with steps of 10/9-9/8-11/10-16/11, and its inverse
  • 1-11/10-26/21-11/8 with steps of 11/10-9/8-10/9-16/11;
  • 1-9/8-13/11-21/16 with steps of 9/8-21/20-10/9-32/21, and its inverse
  • 1-10/9-7/6-21/16 with steps of 10/9-21/20-9/8-32/21;
  • 1-10/9-5/4-21/16 with steps of 10/9-9/8-21/20-32/21, and its inverse
  • 1-21/20-13/11-21/16 with steps of 21/20-9/8-10/9-32/21;
  • 1-11/10-26/21-13/10 with steps of 11/10-9/8-21/20-20/13, and its inverse
  • 1-21/20-13/11-13/10 with steps of 21/20-9/8-11/10-20/13;
  • 1-9/8-13/11-26/21 with steps of 9/8-21/20-22/21-21/13, and its inverse
  • 1-22/21-11/10-26/21 with steps of 22/21-21/20-9/8-21/13.

For pentads, there are nine pairs of chords in inverse relationship:

  • 1-13/11-21/16-13/9-13/8 with steps of 13/11-10/9-11/10-9/8-16/13, and its inverse
  • 1-9/8-26/21-11/8-13/8 with steps of 9/8-11/10-10/9-13/11-16/13;
  • 1-16/13-18/13-16/11-21/13 with steps of 16/13-9/8-21/20-10/9-26/21, and its inverse
  • 1-10/9-7/6-21/16-21/13 with steps of 10/9-21/20-9/8-16/13-26/21;
  • 1-16/13-18/13-16/11-32/21 with steps of 16/13-9/8-21/20-22/21-21/16, and its inverse
  • 1-22/21-11/10-26/21-32/21 with steps of 22/21-21/20-9/8-16/13-21/16;
  • 1-10/9-7/6-21/16-13/9 with steps of 10/9-21/20-9/8-11/10-18/13, and its inverse
  • 1-11/10-26/21-13/10-13/9 with steps of 11/10-9/8-21/20-10/9-18/13;
  • 1-10/9-21/16-11/8-13/9 with steps of 10/9-13/11-22/21-21/20-18/13, and its inverse
  • 1-21/20-11/10-13/10-13/9 with steps of 21/20-22/21-13/11-10/9-18/13;
  • 1-10/9-11/9-11/8-13/9 with steps of 10/9-11/10-9/8-21/20-18/13, and its inverse
  • 1-21/20-13/11-13/10-13/9 with steps of 21/20-9/8-11/10-10/9-18/13;
  • 1-11/10-26/21-11/8-13/9 with steps of 11/10-9/8-10/9-21/20-18/13, and its inverse
  • 1-21/20-7/6-21/16-13/9 with steps of 21/20-10/9-9/8-11/10-18/13;
  • 1-11/10-11/9-11/8-13/9 with steps of 11/10-10/9-9/8-21/20-18/13, and its inverse
  • 1-21/20-13/11-21/16-13/9 with steps of 21/20-9/8-10/9-11/10-18/13;
  • 1-10/9-5/4-21/16-11/8 with steps of 10/9-9/8-21/20-22/21-16/11, and its inverse
  • 1-22/21-11/10-26/21-11/8 with steps of 22/21-21/20-9/8-10/9-16/11.

Equal temperaments with ibnsinmic chords include 41, 46, 53, 58, 72, 87, 94, 111, 130, 140, 183, 198, 224, 270, 311, 422, 441, 494, 581 and 764.

Retrieved from "https://en.xen.wiki/index.php?title=Ibnsinmic_chords&oldid=127784"