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]].

~~There~~ are ~~three sextantonismic triads~~ in the 2.3.5.13.17 subgroup 17-odd-limit, ~~including~~ a ~~palindromic one~~ since it identifies [[18/13]] by a stack of two [[20/17]]'s:

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.

* ~~1-20~~/~~17-18~~/13 with steps 20/17-20/17-13/9.

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:

* ~~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 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.

~~Then there are two inversely related pentads:~~

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 }}.

* 1-10/9-20/17-17/13-20/13 with ~~steps 10/9-18/17-10/9-20/17-13/10~~, and ~~its inverse~~

* 1-10/9-20/17-17/13-17/10 with steps 10/9-18/17-10/9-13/10-20/17.

[[Category:17-odd-limit]]

[[Category:17-odd-limit chords]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

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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]].
-There are three sextantonismic triads in the 2.3.5.13.17 subgroup 17-odd-limit, including a palindromic one since it identifies [[18/13]] by a stack of two [[20/17]]'s:
+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.
-* 1-20/17-18/13 with steps 20/17-20/17-13/9.
+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:
-* 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 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.
-Then there are two inversely related pentads:
+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 }}.
-* 1-10/9-20/17-17/13-20/13 with steps 10/9-18/17-10/9-20/17-13/10, and its inverse
-* 1-10/9-20/17-17/13-17/10 with steps 10/9-18/17-10/9-13/10-20/17.
-[[Category:17-odd-limit]]
+[[Category:17-odd-limit chords]]
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]