Werckismic chords: Difference between revisions

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A '''werckismic chord''' is an [[essentially tempered dyadic chord]] ~~in [[Werckismic temperaments|werckismic]] (~~[[441/440~~]]) tempering in the 2.9.5.7.11 [[Just intonation subgroup|subgroup]] in the [[11-odd-limit~~]].

A '''werckismic chord''' is an [[essentially tempered dyadic chord]] tempered by the werckisma, [[441/440]].

~~The werckismic~~ [[triad]]s consist of three pairs of inversely related chords:

Werckismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 [[triad]]s, 15 [[tetrad]]s and 6 [[pentad]]s, for a total of 27 distinct chord structures.

The werckismic triads consist of three pairs of inversely related chords:

* 1-11/9-7/5 with [[step]]s 11/9-8/7-10/7, and its inverse

* 1-11/9-7/4 with steps 11/9-10/7-8/7;

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* 1-14/11-10/7 with steps 14/11-9/8-7/5.

The werckismic ~~[[tetrad]]s~~ consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are

The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are

* 1-5/4-10/7-7/4 with steps 5/4-8/7-11/9-8/7;

* 1-9/8-10/7-11/7 with steps 9/8-14/11-11/10-14/11;

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* 1-9/8-11/7-7/4 with steps 9/8-7/5-10/9-8/7.

The werckismic ~~[[pentad]]s~~ consist of three pairs of chords in an inverse relationship:

The werckismic pentads consist of three pairs of chords in an inverse relationship:

* 1-9/8-5/4-10/7-7/4 with steps 9/8-10/9-8/7-11/9-8/7, and its inverse

* 1-11/9-7/5-14/9-7/4 with steps 11/9-8/7-10/9-9/8-8/7;

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* 1-9/8-9/7-10/7-11/7 with steps 9/8-8/7-10/9-11/10-14/11, and its inverse

* 1-9/8-10/7-11/7-7/4 with steps 9/8-14/11-11/10-10/9-8/7.

~~The count of chords is therefore triads: 6, tetrads: 15, pentads: 6, for a total of 27.~~

[[Equal temperament]]s with werckismic chords include {{EDOs| 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, and 320 }}, with [[320edo]] giving the [[optimal patent val]].

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-A '''werckismic chord''' is an [[essentially tempered dyadic chord]] in [[Werckismic temperaments|werckismic]] ([[441/440]]) tempering in the 2.9.5.7.11 [[Just intonation subgroup|subgroup]] in the [[11-odd-limit]].
+A '''werckismic chord''' is an [[essentially tempered dyadic chord]] tempered by the werckisma, [[441/440]].
-The werckismic [[triad]]s consist of three pairs of inversely related chords:
+Werckismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 [[triad]]s, 15 [[tetrad]]s and 6 [[pentad]]s, for a total of 27 distinct chord structures.
+The werckismic triads consist of three pairs of inversely related chords:
 * 1-11/9-7/5 with [[step]]s 11/9-8/7-10/7, and its inverse
 * 1-11/9-7/4 with steps 11/9-10/7-8/7;
@@ Line 9: / Line 11: @@
 * 1-14/11-10/7 with steps 14/11-9/8-7/5.
-The werckismic [[tetrad]]s consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are
+The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are
 * 1-5/4-10/7-7/4 with steps 5/4-8/7-11/9-8/7;
 * 1-9/8-10/7-11/7 with steps 9/8-14/11-11/10-14/11;
@@ Line 28: / Line 30: @@
 * 1-9/8-11/7-7/4 with steps 9/8-7/5-10/9-8/7.
-The werckismic [[pentad]]s consist of three pairs of chords in an inverse relationship:
+The werckismic pentads consist of three pairs of chords in an inverse relationship:
 * 1-9/8-5/4-10/7-7/4 with steps 9/8-10/9-8/7-11/9-8/7, and its inverse
 * 1-11/9-7/5-14/9-7/4 with steps 11/9-8/7-10/9-9/8-8/7;
@@ Line 35: / Line 37: @@
 * 1-9/8-9/7-10/7-11/7 with steps 9/8-8/7-10/9-11/10-14/11, and its inverse
 * 1-9/8-10/7-11/7-7/4 with steps 9/8-14/11-11/10-10/9-8/7.
-The count of chords is therefore triads: 6, tetrads: 15, pentads: 6, for a total of 27.
 [[Equal temperament]]s with werckismic chords include {{EDOs| 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, and 320 }}, with [[320edo]] giving the [[optimal patent val]].