Xenismic chords: Difference between revisions

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'''Xenismic chords''' are [[essentially tempered ~~dyadic chord~~]]s tempered by the xenisma, [[2058/2057]].

'''Xenismic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the xenisma, [[2058/2057]].

~~There~~ are ~~three xenismic triads~~ in the 2.3.7.11.17 subgroup 21-odd-limit, including a ~~palindromic one~~ since it identifies [[34/21]] by a stack of two [[14/11]]'s:

Xenismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.3.7.11.17 [[subgroup]] [[21-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the [[3/2|perfect fifth]] is prioritized.

* 1-21/17-11/7 with steps 21/17-14/11-14/11;

There are three xenismic triads, including a palindrome since it identifies [[34/21]] by a stack of two [[14/11]]s:

* 1-21/17-11/7 with steps of 21/17-14/11-14/11.

And an inversely related pair:

* 1-11/7-21/11 with steps 11/7-17/14-22/21, and its inverse

* 1-11/7-21/11 with steps of 11/7-17/14-22/21, and its inverse

* 1-17/14-21/11 with steps 17/14-11/7-22/21.

* 1-17/14-21/11 with steps of 17/14-11/7-22/21.

They can be extended to the following palindromic tetrads:

* 1-3/2-11/7-21/11 with steps 3/2-22/21-17/14-22/21;

* 1-3/2-11/7-21/11 with steps of 3/2-22/21-17/14-22/21;

* 1-17/14-11/7-21/11 with steps 17/14-22/17-17/14-22/21.

* 1-17/14-11/7-21/11 with steps of 17/14-22/17-17/14-22/21.

And inversely related tetrads:

* 1-21/17-3/2-11/7 with steps 21/17-17/14-22/21-14/11, and its inverse

* 1-21/17-3/2-11/7 with steps of 21/17-17/14-22/21-14/11, and its inverse

* 1-17/14-3/2-21/11 with steps 17/14-21/17-14/11-22/21.

* 1-17/14-3/2-21/11 with steps of 17/14-21/17-14/11-22/21;

* 1-21/17-11/7-21/11 with steps 21/17-14/11-17/14-22/21, and its inverse

* 1-21/17-11/7-21/11 with steps of 21/17-14/11-17/14-22/21, and its inverse

* 1-17/14-17/11-21/11 with steps 17/14-14/11-21/17-22/21;

* 1-17/14-17/11-21/11 with steps of 17/14-14/11-21/17-22/21.

Then there is an inversely related pair of pentads:

* 1-21/17-3/2-11/7-21/11 with steps of 21/17-17/14-22/21-17/14-22/21, and its inverse

* 1-17/14-3/2-11/7-21/11 with steps of 17/14-21/17-22/21-17/14-22/21.

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

Equal temperaments with xenismic chords include {{Optimal ET sequence|46, 58, 63, 72, 89, 104, 118, 135, 193, 207, 253, 342, 400, 446, 535, 607 and 742}}.

* 1-21/17-3/2-11/7-21/11 with ~~steps 21/17-17/14-22/21-17/14-22/21~~, and ~~its inverse~~

* 1-17/14-3/2-11/7-21/11 with steps 17/14-21/17-22/21-17/14-22/21.

[[Category:21-odd-limit]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Xenismic]]

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-'''Xenismic chords''' are [[essentially tempered dyadic chord]]s tempered by the xenisma, [[2058/2057]].
+'''Xenismic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the xenisma, [[2058/2057]].
-There are three xenismic triads in the 2.3.7.11.17 subgroup 21-odd-limit, including a palindromic one since it identifies [[34/21]] by a stack of two [[14/11]]'s:
+Xenismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.3.7.11.17 [[subgroup]] [[21-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the [[3/2|perfect fifth]] is prioritized.
-* 1-21/17-11/7 with steps 21/17-14/11-14/11;
+There are three xenismic triads, including a palindrome since it identifies [[34/21]] by a stack of two [[14/11]]s:
+* 1-21/17-11/7 with steps of 21/17-14/11-14/11.
 And an inversely related pair:
-* 1-11/7-21/11 with steps 11/7-17/14-22/21, and its inverse
+* 1-11/7-21/11 with steps of 11/7-17/14-22/21, and its inverse
-* 1-17/14-21/11 with steps 17/14-11/7-22/21.
+* 1-17/14-21/11 with steps of 17/14-11/7-22/21.
 They can be extended to the following palindromic tetrads:
-* 1-3/2-11/7-21/11 with steps 3/2-22/21-17/14-22/21;
+* 1-3/2-11/7-21/11 with steps of 3/2-22/21-17/14-22/21;
-* 1-17/14-11/7-21/11 with steps 17/14-22/17-17/14-22/21.
+* 1-17/14-11/7-21/11 with steps of 17/14-22/17-17/14-22/21.
 And inversely related tetrads:
-* 1-21/17-3/2-11/7 with steps 21/17-17/14-22/21-14/11, and its inverse
+* 1-21/17-3/2-11/7 with steps of 21/17-17/14-22/21-14/11, and its inverse
-* 1-17/14-3/2-21/11 with steps 17/14-21/17-14/11-22/21.
+* 1-17/14-3/2-21/11 with steps of 17/14-21/17-14/11-22/21;
-* 1-21/17-11/7-21/11 with steps 21/17-14/11-17/14-22/21, and its inverse
+* 1-21/17-11/7-21/11 with steps of 21/17-14/11-17/14-22/21, and its inverse
-* 1-17/14-17/11-21/11 with steps 17/14-14/11-21/17-22/21;
+* 1-17/14-17/11-21/11 with steps of 17/14-14/11-21/17-22/21.
+Then there is an inversely related pair of pentads:
+* 1-21/17-3/2-11/7-21/11 with steps of 21/17-17/14-22/21-17/14-22/21, and its inverse
+* 1-17/14-3/2-11/7-21/11 with steps of 17/14-21/17-22/21-17/14-22/21.
-Then there are two inversely related pentads:
+Equal temperaments with xenismic chords include {{Optimal ET sequence|46, 58, 63, 72, 89, 104, 118, 135, 193, 207, 253, 342, 400, 446, 535, 607 and 742}}.
-* 1-21/17-3/2-11/7-21/11 with steps 21/17-17/14-22/21-17/14-22/21, and its inverse
-* 1-17/14-3/2-11/7-21/11 with steps 17/14-21/17-22/21-17/14-22/21.
 [[Category:21-odd-limit]]
 [[Category:Essentially tempered chords]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
 [[Category:Xenismic]]