Sextantonismic chords: Difference between revisions

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'''Sextantonismic chords''' are [[essentially tempered ~~dyadic chord~~]]s 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.

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 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:

* 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:

* 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:

* 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:

* 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]]

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-'''Sextantonismic chords''' are [[essentially tempered dyadic chord]]s 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.
-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 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:
-* 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:
-* 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:
-* 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:
-* 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]]