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 [[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]]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.
* 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  
* 1–20/17–17/13 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.
* 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;
* 1–10/9–20/17–17/13 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.
* 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  
* 1–20/17–17/13–18/13 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;
* 1–18/17–20/17–18/13 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  
* 1–20/17–18/13–20/13 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.
* 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  
* 1–10/9–20/17–17/13–20/13 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.
* 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]]