Dyadic chord/Pattern of essentially tempered chords: Difference between revisions
Created page with "This page discusses some common patterns of essentially tempered chords for a given comma and an odd limit. == Pattern 1 == Pattern 1 turns up for commas of the..." |
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== Pattern 1 == | == Pattern 1 == | ||
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 | 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. The palindromic triad is | ||
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Examples of pattern 1b chords are [[lambeth chords]] (13-odd-limit) and [[sextantonismic chords]] (17-odd-limit). | 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. | |||