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

(2 intermediate revisions by 2 users not shown)

Line 1:

This page discusses some common patterns of [[essentially tempered chord]]s for a given [[comma]] and an [[odd limit]].

Line 63:

Line 64:

== Pattern 2 ==

Pattern 2 turns up for commas of the form (''n''1''n''2''n''3)/(''d''12''d''2), or (''n''1''n''2</sub~~>2</sup~~>)/(''d''1''d''2''d''3) 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.

Pattern 2 turns up for commas of the form (''n''1''n''2''n''3)/(''d''12''d''2), or (''n''12''n''2)/(''d''1''d''2''d''3) 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) and [[swetismic chords]] (11-odd-limit).

Line 70:

Line 71:

Pattern 3 turns up for commas of the form (''n''1''n''2''n''3)/(''d''1''d''2''d''3) 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).

Notable examples of this pattern are [[neosatanismic chords]] (19-odd-limit), [[ibnsinmic chords]] (21-odd-limit) and [[neogrendelismic chords]] (21-odd-limit).

[[Category:Essentially tempered chords]]

[[Category:Chords]]

@@ Line 1: / Line 1: @@
+{{breadcrumb}}
 This page discusses some common patterns of [[essentially tempered chord]]s for a given [[comma]] and an [[odd limit]].
@@ Line 63: / Line 64: @@
 == 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 pairs of pentads, for a total of 27 distinct chord structures.
+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><sup>2</sup>''n''<sub>2</sub>)/(''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) and [[swetismic chords]] (11-odd-limit).
@@ Line 70: / Line 71: @@
 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).
+Notable examples of this pattern are [[neosatanismic chords]] (19-odd-limit), [[ibnsinmic chords]] (21-odd-limit) and [[neogrendelismic chords]] (21-odd-limit).
+[[Category:Essentially tempered chords]]
+[[Category:Chords]]