Swetismic chords: Difference between revisions

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A '''swetismic chord''' is a swetismic ([[540/539]]) 11-odd-limit [[essentially tempered chord]].

A '''swetismic chord''' is a [[Swetismic temperaments|swetismic]] ([[540/539]]) [[11-odd-limit]], [[essentially tempered chord]].

There are six swetismic triads, consisting of three pairs of chords in inverse relationship:

There are six swetismic [[Triad|triads]], consisting of three pairs of chords in inverse relationship:

* 1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;

* 1-7/5-12/7 with [[Step|steps]] 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;

* 1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;

* and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.

There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:

There are fifteen swetismic [[Tetrad|tetrads]], consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:

* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;

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* and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.

Finally, there are six swetismic pentads coming in three pairs:

Finally, there are six swetismic [[Pentad|pentads]] coming in three pairs:

* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;

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The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.

If we are willing to consider the 15-odd-limit, there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.

If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.

~~Equal temperaments with swetismic chords include {{EDOs|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}~~.

[[Category:11-odd-limit]]

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[[Category:Swetismic]]

[[EDO|Equal temperaments]] with swetismic chords include {{EDOs|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.

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-A '''swetismic chord''' is a swetismic ([[540/539]]) 11-odd-limit [[essentially tempered chord]].
+A '''swetismic chord''' is a [[Swetismic temperaments|swetismic]] ([[540/539]]) [[11-odd-limit]], [[essentially tempered chord]].
-There are six swetismic triads, consisting of three pairs of chords in inverse relationship:
+There are six swetismic [[Triad|triads]], consisting of three pairs of chords in inverse relationship:
-* 1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;
+* 1-7/5-12/7 with [[Step|steps]] 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;
 * 1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;
 * and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.
-There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:
+There are fifteen swetismic [[Tetrad|tetrads]], consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:
 * 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;
@@ Line 22: / Line 22: @@
 * and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.
-Finally, there are six swetismic pentads coming in three pairs:
+Finally, there are six swetismic [[Pentad|pentads]] coming in three pairs:
 * 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;
@@ Line 30: / Line 30: @@
 The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.
-If we are willing to consider the 15-odd-limit, there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.
+If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.
-Equal temperaments with swetismic chords include {{EDOs|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.
 [[Category:11-odd-limit]]
@@ Line 41: / Line 39: @@
 [[Category:Swetismic]]
-{{Todo| add links }}
+[[EDO|Equal temperaments]] with swetismic chords include {{EDOs|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.