Dyadic chord/Pattern of essentially tempered chords: Difference between revisions

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 Pattern 1 turns up for commas of the form (''n''<sub>1</sub><sup>2</sup>''n''<sub>2</sub>)/(''d''<sub>1</sub><sup>2</sup>''d''<sub>2</sub>) up to [[octave equivalence]]. It contains a palindromic triad and an inversely related pair of triads, two palindromic tetrads and two inversely related pairs of tetrads, and an inversely related pair of pentads, for a total of 11 distinct chord structures.
-Pattern 1 has two subpatterns, 1a and 1b, both of whose basic palindromic triads are of the same form, but their final pentad extensions differ. The palindromic triad is
+Pattern 1 has two subpatterns, 1a and 1b, both of whose basic palindromic triads are of the same form, but their final pentad extensions differ. Examples of pattern 1a chords are [[cuthbert chords]] (13-odd-limit), [[aureusmic chords]] (19-odd-limit) and [[palingenetic chords]] (21-odd-limit). Examples of pattern 1b chords are [[lambeth chords]] (13-odd-limit) and [[sextantonismic chords]] (17-odd-limit).
+The palindromic triad is
 * 1-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''d''<sub>2</sub> with steps ''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>2</sub>/''n''<sub>2</sub>.
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 * 1-''n''<sub>1</sub>/''d''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>2</sub> with steps ''n''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>1</sub>-''d''<sub>2</sub>/''n''<sub>2</sub>, and its inverse
 * 1-''n''<sub>2</sub>/''d''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''d''<sub>2</sub> with steps ''n''<sub>2</sub>/''d''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''d''<sub>2</sub>/''n''<sub>2</sub>.
-Examples of pattern 1a chords are [[cuthbert chords]] (13-odd-limit), [[aureusmic chords]] (19-odd-limit) and [[palingenetic chords]] (21-odd-limit).
 === Pattern 1b ===
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 * 1-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''d''<sub>1</sub>/''d''<sub>2</sub> with steps ''d''<sub>1</sub>/''n''<sub>2</sub>-''n''<sub>2</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>, and its inverse
 * 1-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>1</sub> with steps ''d''<sub>1</sub>/''n''<sub>2</sub>-''n''<sub>2</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>.
-Examples of pattern 1b chords are [[lambeth chords]] (13-odd-limit) and [[sextantonismic chords]] (17-odd-limit).
 === Defective ===
 Defective pattern 1 is where some of these chords turn out essentially just. [[Ptolemismic chords]] are of this category, as it only has a palindromic triad, two pairs of inversely related tetrads, and a pair of inversely related pentads.
+== Pattern 2 ==
+Pattern 2 turns up for commas of the form (''n''<sub>1</sub>''n''<sub>2</sub>''n''<sub>3</sub>)/(''d''<sub>1</sub><sup>2</sup>''d''<sub>2</sub>), or (''n''<sub>1</sub>''n''<sub>2</sub><sup>2</sup>)/(''d''<sub>1</sub>''d''<sub>2</sub>''d''<sub>3</sub>) up to [[octave equivalence]]. It contains three inversely related pairs of triads, three palindromic tetrads and six inversely related pairs of tetrads, and three inversely related pair of pentads, for a total of 27 distinct chord structures.
+Notable examples of this pattern are [[keenanismic chords]], [[werckismic chords]], and [[swetismic chords]].