Xenllium: Created page with "'''Neogrendelismic chords''' are essentially tempered chords tempered by the neogrendelisma, 5985/5984. There are 12 triads, 36 tetrads and 18 pentads as..."

2023-12-01T12:42:55Z

Created page with "'''Neogrendelismic chords''' are essentially tempered chords tempered by the neogrendelisma, 5985/5984. There are 12 triads, 36 tetrads and 18 pentads as..."

New page

'''Neogrendelismic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the neogrendelisma, [[5985/5984]].

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:
* 1-21/16-22/15 with steps of 21/16-19/17-15/11, and its inverse
* 1-19/17-22/15 with steps of 19/17-21/16-15/11;
* 1-21/17-22/15 with steps of 21/17-19/16-15/11, and its inverse
* 1-19/16-22/15 with steps of 19/16-21/17-15/11;
* 1-22/19-21/16 with steps of 22/19-17/15-32/21, and its inverse
* 1-17/15-21/16 with steps of 17/15-22/19-32/21;
* 1-22/19-21/17 with steps of 22/19-16/15-34/21, and its inverse
* 1-16/15-21/17 with steps of 16/15-22/19-34/21;
* 1-17/15-19/16 with steps of 17/15-22/21-32/19, and its inverse
* 1-22/21-19/16 with steps of 22/21-17/15-32/19;
* 1-16/15-19/17 with steps of 16/15-22/21-34/19, and its inverse
* 1-22/21-19/17 with steps of 22/21-16/15-34/19.

For tetrads, there are eighteen pairs of chords in inverse relationship:
* 1-21/16-7/5-22/15 with steps of 21/16-16/15-22/21-15/11, and its inverse
* 1-22/21-19/17-22/15 with steps of 22/21-16/15-21/16-15/11;
* 1-21/16-11/8-22/15 with steps of 21/16-22/21-16/15-15/11, and its inverse
* 1-16/15-19/17-22/15 with steps of 16/15-22/21-21/16-15/11;
* 1-21/17-7/5-22/15 with steps of 21/17-17/15-22/21-15/11, and its inverse
* 1-22/21-19/16-22/15 with steps of 22/21-17/15-21/17-15/11;
* 1-21/17-21/16-22/15 with steps of 21/17-17/16-19/17-15/11, and its inverse
* 1-19/17-19/16-22/15 with steps of 19/17-17/16-21/17-15/11;
* 1-21/17-22/17-22/15 with steps of 21/17-22/21-17/15-15/11, and its inverse
* 1-17/15-19/16-22/15 with steps of 17/15-22/21-21/17-15/11;
* 1-19/16-11/8-22/15 with steps of 19/16-22/19-16/15-15/11, and its inverse
* 1-16/15-21/17-22/15 with steps of 16/15-22/19-19/16-15/11;
* 1-19/16-21/16-22/15 with steps of 19/16-21/19-19/17-15/11, and its inverse
* 1-19/17-21/17-22/15 with steps of 19/17-21/19-19/16-15/11;
* 1-19/16-19/15-22/15 with steps of 19/16-16/15-22/19-15/11, and its inverse
* 1-22/19-21/17-22/15 with steps of 22/19-16/15-19/16-15/11;
* 1-22/19-21/16-22/15 with steps of 22/19-17/15-19/17-15/11, and its inverse
* 1-19/17-19/15-22/15 with steps of 19/17-17/15-22/19-15/11;
* 1-17/15-21/16-22/15 with steps of 17/15-22/19-19/17-15/11, and its inverse
* 1-19/17-22/17-22/15 with steps of 19/17-22/19-17/15-15/11;
* 1-17/15-21/16-7/5 with steps of 17/15-22/19-16/15-10/7, and its inverse
* 1-16/15-21/17-7/5 with steps of 16/15-22/19-17/15-10/7;
* 1-22/19-21/16-11/8 with steps of 22/19-17/15-22/21-16/11, and its inverse
* 1-22/21-19/16-11/8 with steps of 22/21-17/15-22/19-16/11;
* 1-22/19-21/17-21/16 with steps of 22/19-16/15-17/16-32/21, and its inverse
* 1-17/16-17/15-21/16 with steps of 17/16-16/15-22/19-32/21;
* 1-17/15-19/16-21/16 with steps of 17/15-22/21-21/19-32/21, and its inverse
* 1-21/19-22/19-21/16 with steps of 21/19-22/21-17/15-32/21;
* 1-22/19-21/17-22/17 with steps of 22/19-16/15-22/21-17/11, and its inverse
* 1-22/21-19/17-22/17 with steps of 22/21-16/15-22/19-17/11;
* 1-17/15-19/16-19/15 with steps of 17/15-22/21-16/15-30/19, and its inverse
* 1-16/15-19/17-19/15 with steps of 16/15-22/21-17/15-30/19;
* 1-21/19-22/19-21/17 with steps of 21/19-22/21-16/15-34/21, and its inverse
* 1-16/15-19/17-21/17 with steps of 16/15-22/21-21/19-34/21;
* 1-17/16-17/15-19/16 with steps of 17/16-16/15-22/21-32/19, and its inverse
* 1-22/21-19/17-19/16 with steps of 22/21-16/15-17/16-32/19.

For pentads, there are nine pairs of chords in inverse relationship:
* 1-21/17-21/16-7/5-22/15 with steps of 21/17-17/16-16/15-22/21-15/11, and its inverse
* 1-22/21-19/17-19/16-22/15 with steps of 22/21-16/15-17/16-21/17-15/11;
* 1-19/16-21/16-11/8-22/15 with steps of 19/16-21/19-22/21-16/15-15/11, and its inverse
* 1-16/15-19/17-21/17-22/15 with steps of 16/15-22/21-21/19-19/16-15/11;
* 1-22/19-21/16-11/8-22/15 with steps of 22/19-17/15-22/21-16/15-15/11, and its inverse
* 1-16/15-19/17-19/15-22/15 with steps of 16/15-22/21-17/15-22/19-15/11;
* 1-22/19-21/17-21/16-22/15 with steps of 22/19-16/15-17/16-19/17-15/11, and its inverse
* 1-19/17-19/16-19/15-22/15 with steps of 19/17-17/16-16/15-22/19-15/11;
* 1-22/19-21/17-22/17-22/15 with steps of 22/19-16/15-22/21-17/15-15/11, and its inverse
* 1-17/15-19/16-19/15-22/15 with steps of 17/15-22/21-16/15-22/19-15/11;
* 1-17/15-21/16-7/5-22/15 with steps of 17/15-22/19-16/15-22/21-15/11, and its inverse
* 1-22/21-19/17-22/17-22/15 with steps of 22/21-16/15-22/19-17/15-15/11;
* 1-17/15-19/16-21/16-22/15 with steps of 17/15-22/21-21/19-19/17-15/11, and its inverse
* 1-19/17-21/17-22/17-22/15 with steps of 19/17-21/19-22/21-17/15-15/11;
* 1-16/15-21/17-7/5-22/15 with steps of 16/15-22/19-17/15-22/21-15/11, and its inverse
* 1-22/21-19/16-11/8-22/15 with steps of 22/21-17/15-22/19-16/15-15/11;
* 1-21/19-22/19-21/17-21/16 with steps of 21/19-22/21-16/15-17/16-32/21, and its inverse
* 1-17/16-17/15-19/16-21/16 with steps of 17/16-16/15-22/21-21/19-32/21.

Equal temperaments with neogrendelismic chords include {{Optimal ET sequence|72, 94, 118, 193, 217, 255, 270, 311, 342, 400, 472, 525, 581, 742, 836, 1053, 1178, 1578 and 1920}}.

[[Category:21-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Neogrendelismic]]

Neogrendelismic chords - Revision history

Xenllium: Created page with "'''Neogrendelismic chords''' are essentially tempered chords tempered by the neogrendelisma, 5985/5984. There are 12 triads, 36 tetrads and 18 pentads as..."