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 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 basic inversely related pair of triads and final pentad extensions differ. Examples of pattern 1a chords are [[sensamagic chords]] (9-odd-limit), [[cuthbert chords]] (13-odd-limit) | Pattern 1 has two subpatterns, 1a and 1b, both of whose basic palindromic triads are of the same form, but their basic inversely related pair of triads and final pentad extensions differ. Examples of pattern 1a chords are [[sensamagic chords]] (9-odd-limit), [[cuthbert chords]] (13-odd-limit) and [[aureusmic chords]] (19-odd-limit). Examples of pattern 1b chords are [[marvel chords]] (9-odd-limit), [[lambeth chords]] (13-odd-limit) and [[sextantonismic chords]] (17-odd-limit). | ||
The palindromic triad is | The palindromic triad is | ||
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== Pattern 2 == | == 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 | 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 pairs of pentads, for a total of 27 distinct chord structures. | ||
Notable examples of this pattern are [[keenanismic chords]] (11-odd-limit), [[werckismic chords]] (11-odd-limit) | Notable examples of this pattern are [[keenanismic chords]] (11-odd-limit), [[werckismic chords]] (11-odd-limit) and [[swetismic chords]] (11-odd-limit). | ||
== Pattern 3 == | == Pattern 3 == | ||
Pattern 3 turns up for commas of the form (''n''<sub>1</sub>''n''<sub>2</sub>''n''<sub>3</sub>)/(''d''<sub>1</sub>''d''<sub>2</sub>''d''<sub>3</sub>) up to octave equivalence. It contains six inversely related pairs of triads, eighteen inversely related pairs of tetrads, and nine inversely related | Pattern 3 turns up for commas of the form (''n''<sub>1</sub>''n''<sub>2</sub>''n''<sub>3</sub>)/(''d''<sub>1</sub>''d''<sub>2</sub>''d''<sub>3</sub>) up to octave equivalence. It contains six inversely related pairs of triads, eighteen inversely related pairs of tetrads, and nine inversely related pairs of pentads, for a total of 66 distinct chord structures. | ||
Notable examples of this pattern are [[neosatanismic chords]] (19-odd-limit) and [[ibnsinmic chords]] (21-odd-limit). | |||