Sextantonismic chords: Difference between revisions
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'''Sextantonismic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the sextantonisma, [[2601/2600]]. | '''Sextantonismic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the sextantonisma, [[2601/2600]]. | ||
Sextantonismic chords are of [[ | 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]]s: | 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 of 20/17, 20/17, 13/9. | ||
And an inversely related pair: | 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: | 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: | 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: | 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 {{Optimal ET sequence| 34, 46, 60, 72, 77, 106, 111, 137, 140, 171, 183, 217, 243, 277, 354, 388, 460, 494 and 848 }}. | 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 chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||