Dyadic chord/Pattern of essentially tempered chords - Revision history

ArrowHead294 at 20:47, 25 November 2024

2024-11-25T20:47:44Z

← Older revision		Revision as of 20:47, 25 November 2024
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			{{breadcrumb}}
	This page discusses some common patterns of [[essentially tempered chord]]s for a given [[comma]] and an [[odd limit]].		This page discusses some common patterns of [[essentially tempered chord]]s for a given [[comma]] and an [[odd limit]].

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	Notable examples of this pattern are [[neosatanismic chords]] (19-odd-limit), [[ibnsinmic chords]] (21-odd-limit) and [[neogrendelismic 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:Essentially tempered chords]]
	[[Category:Chords]]		[[Category:Chords]]

BudjarnLambeth: Categorised this uncategorised page

2023-12-09T12:41:48Z

Categorised this uncategorised page

← Older revision		Revision as of 12:41, 9 December 2023
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	Notable examples of this pattern are [[neosatanismic chords]] (19-odd-limit), [[ibnsinmic chords]] (21-odd-limit) and [[neogrendelismic 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]]

Xenllium at 13:23, 30 November 2023

2023-11-30T13:23:04Z

← Older revision		Revision as of 13:23, 30 November 2023
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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 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).		Notable examples of this pattern are [[keenanismic chords]] (11-odd-limit), [[werckismic chords]] (11-odd-limit) and [[swetismic chords]] (11-odd-limit).
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	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.		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).

Xenllium at 12:06, 26 November 2023

2023-11-26T12:06:44Z

← Older revision		Revision as of 12:06, 26 November 2023
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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), 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).		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 ~~pair~~ 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>''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), and [[swetismic 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 ~~pair~~ of pentads, for a total of 66 distinct chord structures.		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.

	~~A notable example~~ of this pattern is [[ibnsinmic chords]] (21-odd-limit).		Notable examples of this pattern are [[neosatanismic chords]] (19-odd-limit) and [[ibnsinmic chords]] (21-odd-limit).

Xenllium: Update the article

2023-11-26T02:45:42Z

Update the article

Show changes

Xenllium at 01:17, 3 November 2023

2023-11-03T01:17:10Z

← Older revision		Revision as of 01:17, 3 November 2023
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	The palindromic tetrads are		The palindromic tetrads are
	* 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> with steps ''n''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>1</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>;		* 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> 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>-''d''<sub>2</sub>/''d''<sub>1</sub>;
	* 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> with steps ''n''<sub>2</sub>/''d''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>1</sub>/''n''<sub>2</sub>.		* 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> 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>/''n''<sub>2</sub>.

	The inversely related pairs of tetrads are		The inversely related pairs of tetrads are
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	* 1-''n''<sub>2</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''d''<sub>2</sub> with steps ''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>/''n''<sub>2</sub>;		* 1-''n''<sub>2</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''d''<sub>2</sub> with steps ''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>/''n''<sub>2</sub>;
	* 1-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''d''<sub>2</sub>-''d''<sub>1</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>1</sub>/''n''<sub>2</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>, and its inverse		* 1-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''d''<sub>2</sub>-''d''<sub>1</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>1</sub>/''n''<sub>2</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>, and its inverse
	* 1-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>1</sub> with steps ''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>2</sub>.		* 1-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>2</sub>/''d''<sub>2</sub>-''n''<sub>1</sub>/''d''<sub>1</sub> with steps ''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>2</sub>.

	The inversely related pair of pentads is		The inversely related pair of pentads is

FloraC: Turns out ptolemismic isn't of pattern 1 since the 3's can be stacked to 9

2023-09-21T08:14:02Z

Turns out ptolemismic isn't of pattern 1 since the 3's can be stacked to 9

← Older revision		Revision as of 08:14, 21 September 2023
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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>-''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>.		* 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>.

	~~=== 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 ==

FloraC: Examples

2023-08-16T05:08:24Z

Examples

← Older revision		Revision as of 05:08, 16 August 2023
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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 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).		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 [[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 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.		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]].		Notable examples of this pattern are [[keenanismic chords]] (11-odd-limit), [[werckismic chords]] (11-odd-limit), and [[swetismic chords]] (11-odd-limit).

FloraC: +pattern 2 (wip)

2023-07-27T05:27:42Z

+pattern 2 (wip)

← Older revision		Revision as of 05:27, 27 July 2023
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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 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>.		* 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>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>.		* 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 ===		=== 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>-''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>.		* 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 ===
	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.		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]].

FloraC: +defective pattern 1

2023-07-27T05:07:42Z

+defective pattern 1

← Older revision		Revision as of 05:07, 27 July 2023
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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 ~~pair~~ 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 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.