Sextantonismic chords: Difference between revisions
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'''Sextantonismic chords''' are [[essentially tempered | '''Sextantonismic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the sextantonisma, [[2601/2600]]. | ||
Sextantonismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.3.5.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. | Sextantonismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.3.5.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. | ||
The three sextantonismic triads include a palindrome since it identifies [[18/13]] by a stack of two [[20/17]] | The three sextantonismic triads include a palindrome since it identifies [[18/13]] by a stack of two [[20/17]]s: | ||
* 1-20/17-18/13 with steps 20/17-20/17-13/9. | * 1-20/17-18/13 with steps of 20/17-20/17-13/9. | ||
And an inversely related pair: | And an inversely related pair: | ||
* 1-20/17-17/13 with steps 20/17-10/9-26/17, and its inverse | * 1-20/17-17/13 with steps of 20/17-10/9-26/17, and its inverse | ||
* 1-10/9-17/13 with steps 10/9-20/17-26/17. | * 1-10/9-17/13 with steps of 10/9-20/17-26/17. | ||
They can be extended to the following palindromic tetrads: | They can be extended to the following palindromic tetrads: | ||
* 1-10/9-20/17-17/13 with steps 10/9-18/17-10/9-26/17; | * 1-10/9-20/17-17/13 with steps of 10/9-18/17-10/9-26/17; | ||
* 1-20/17-17/13-20/13 with steps 20/17-10/9-20/17-13/10. | * 1-20/17-17/13-20/13 with steps of 20/17-10/9-20/17-13/10. | ||
And inversely related tetrads: | And inversely related tetrads: | ||
* 1-20/17-17/13-18/13 with steps 20/17-10/9-18/17-13/9, and its inverse | * 1-20/17-17/13-18/13 with steps of 20/17-10/9-18/17-13/9, and its inverse | ||
* 1-18/17-20/17-18/13 with steps 18/17-10/9-20/17-13/9; | * 1-18/17-20/17-18/13 with steps of 18/17-10/9-20/17-13/9; | ||
* 1-20/17-18/13-20/13 with steps 20/17-20/17-10/9-13/10, and its inverse | * 1-20/17-18/13-20/13 with steps of 20/17-20/17-10/9-13/10, and its inverse | ||
* 1-20/17-18/13-9/5 with steps 20/17-20/17-13/10-10/9. | * 1-20/17-18/13-9/5 with steps of 20/17-20/17-13/10-10/9. | ||
Then there is an inversely related pair of pentads: | Then there is an inversely related pair of pentads: | ||
* 1-10/9-20/17-17/13-20/13 with steps 10/9-18/17-10/9-20/17-13/10, and its inverse | * 1-10/9-20/17-17/13-20/13 with steps of 10/9-18/17-10/9-20/17-13/10, and its inverse | ||
* 1-10/9-20/17-17/13-17/10 with steps 10/9-18/17-10/9-13/10-20/17. | * 1-10/9-20/17-17/13-17/10 with steps of 10/9-18/17-10/9-13/10-20/17. | ||
Equal temperaments with sextantonismic chords include {{Optimal ET sequence| 34, 46, 60, 72, 77, 106, 111, 137, 140, 171, 183, 217, 243, 277, 354, 388, 460, 494 and 848 }}. | |||
[[Category:17-odd-limit]] | [[Category:17-odd-limit]] | ||
Revision as of 04:38, 26 November 2023
Sextantonismic chords are essentially tempered chords tempered by the sextantonisma, 2601/2600.
Sextantonismic chords are of pattern 1b in the 2.3.5.13.17 subgroup 17-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
The three sextantonismic triads include a palindrome since it identifies 18/13 by a stack of two 20/17s:
- 1-20/17-18/13 with steps of 20/17-20/17-13/9.
And an inversely related pair:
- 1-20/17-17/13 with steps of 20/17-10/9-26/17, and its inverse
- 1-10/9-17/13 with steps of 10/9-20/17-26/17.
They can be extended to the following palindromic tetrads:
- 1-10/9-20/17-17/13 with steps of 10/9-18/17-10/9-26/17;
- 1-20/17-17/13-20/13 with steps of 20/17-10/9-20/17-13/10.
And inversely related tetrads:
- 1-20/17-17/13-18/13 with steps of 20/17-10/9-18/17-13/9, and its inverse
- 1-18/17-20/17-18/13 with steps of 18/17-10/9-20/17-13/9;
- 1-20/17-18/13-20/13 with steps of 20/17-20/17-10/9-13/10, and its inverse
- 1-20/17-18/13-9/5 with steps of 20/17-20/17-13/10-10/9.
Then there is an inversely related pair of pentads:
- 1-10/9-20/17-17/13-20/13 with steps of 10/9-18/17-10/9-20/17-13/10, and its inverse
- 1-10/9-20/17-17/13-17/10 with steps of 10/9-18/17-10/9-13/10-20/17.
Equal temperaments with sextantonismic chords include 34, 46, 60, 72, 77, 106, 111, 137, 140, 171, 183, 217, 243, 277, 354, 388, 460, 494 and 848.