Island chords - Revision history

ArrowHead294 at 13:59, 14 April 2025

2025-04-14T13:59:30Z

← Older revision		Revision as of 13:59, 14 April 2025
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	== See also ==		== See also ==
	* [[Arto and ~~Tendo Theory~~]]		* [[Arto and tendo theory]]
	* [[The Archipelago]]		* [[The Archipelago]]

FloraC: Cleanup

2025-03-20T14:19:23Z

Cleanup

Show changes

Xenllium at 11:20, 11 November 2023

2023-11-11T11:20:43Z

← Older revision		Revision as of 11:20, 11 November 2023
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	For triads, there are one palindromic chord and four pairs of chords in inverse relationship.		For triads, there are one palindromic chord and four pairs of chords in inverse relationship.

	The palindromic triad consists of two [[semifourth]]s and one [[perfect fifth]], ~~equating~~ two ~~[[15/13]]s and one [[4/3]]~~:		The palindromic triad consists of two [[semifourth]]s and one [[perfect fifth]], splitting a fourth in two:
	* 1-15/13-4/3 with steps of 15/13-15/13-3/2.		* 1-15/13-4/3 with steps of 15/13-15/13-3/2.

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	For tetrads, there are seven palindromic chords and fifteen pairs of chords in inverse relationship.		For tetrads, there are seven palindromic chords and fifteen pairs of chords in inverse relationship.

	One of the palindromic tetrads consists of three semifourths and one [[semisixth]],		One of the palindromic tetrads consists of three semifourths and one [[semisixth]],
	* 1-13/10-3/2-26/15 with steps of 13/10-15/13-15/13-15/13.		* 1-13/10-3/2-26/15 with steps of 13/10-15/13-15/13-15/13.

	Aside from above, the following palindromic tetrad also contains a [[List of root-3rd-P5 triads in JI\|barbados triad]] (otonal 1-13/10-3/2 chord) and its inversion (utonal 1-15/13-3/2 chord),		Aside from above, the following palindromic tetrad also contains a [[List of root-3rd-P5 triads in JI\|barbados triad]] (otonal 1-13/10-3/2 chord) and its inversion (utonal 1-15/13-3/2 chord),
	* 1-15/13-13/10-3/2 with steps of 15/13-9/8-15/13-4/3.		* 1-15/13-13/10-3/2 with steps of 15/13-9/8-15/13-4/3.

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	* 1-13/12-15/13-3/2 with steps of 13/12-16/15-13/10-4/3;		* 1-13/12-15/13-3/2 with steps of 13/12-16/15-13/10-4/3;
	* 1-15/13-4/3-3/2 with steps of 15/13-15/13-9/8-4/3, and its inverse		* 1-15/13-4/3-3/2 with steps of 15/13-15/13-9/8-4/3, and its inverse
	* 1-15/13-4/3~~-16~~/9 with steps of 15/13-15/13-4/3~~-9/8~~;		* 1-9/8-13/10-3/2 with steps of 9/8-15/13-15/13-4/3;
	* 1-5/4-4/3-13/9 with steps of 5/4-16/15-13/~~12-18/13~~, and its inverse		* 1-18/13-3/2-8/5 with steps of 18/13-13/12-16/15-5/4, and its inverse
	* 1-13/12-15/13-13/9 with steps of 13/12-16/15-5/4-18/13;		* 1-13/12-3/2-15/8 with steps of 13/12-18/13-5/4-16/15;
	* 1-15/13-13/10-13/9 with steps of 15/13-9/8-10/9-18/13, and its inverse		* 1-15/13-13/10-13/9 with steps of 15/13-9/8-10/9-18/13, and its inverse
	* 1-10/9-5/4-13/9 with steps of 10/9-9/8-15/13-18/13;		* 1-10/9-5/4-13/9 with steps of 10/9-9/8-15/13-18/13;
	* 1-15/13-4/3-13/9 with steps of 15/13-15/13-~~13/12-18~~/13, and its inverse		* 1-18/13-3/2-26/15 with steps of 18/13-13/12-15/13-15/13, and its inverse
	* 1-13/12-5/4-13/9 with steps of 13/12-15/13-15/13-18/13;		* 1-13/12-3/2-26/15 with steps of 13/12-18/13-15/13-15/13;
	* 1-6/5-13/10-18/13 with steps of 6/5-13/12-16/15-13/9, and its inverse		* 1-6/5-13/10-18/13 with steps of 6/5-13/12-16/15-13/9, and its inverse
	* 1-16/15-15/13-18/13 with steps of 16/15-13/12-6/5-13/9;		* 1-16/15-15/13-18/13 with steps of 16/15-13/12-6/5-13/9;
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	* 1-9/8-5/4-13/8-26/15 with steps of 9/8-10/9-13/10-16/15-15/13, and its inverse		* 1-9/8-5/4-13/8-26/15 with steps of 9/8-10/9-13/10-16/15-15/13, and its inverse
	* 1-15/13-16/13-8/5-16/9 with steps of 15/13-16/15-13/10-10/9-9/8;		* 1-15/13-16/13-8/5-16/9 with steps of 15/13-16/15-13/10-10/9-9/8;
	* 1-15/13-5/4-4/3-20/13 with steps of 15/13-13/12-16/15-15/13~~-13/10~~, and its inverse		* 1-13/10-3/2-13/8-26/15 with steps of 13/10-15/13-13/12-16/15-15/13, and its inverse
	* 1-15/13-16/13-4/3-20/13 with steps of 15/13-16/15-13/12-15/13~~-13/10~~;		* 1-13/10-3/2-8/5-26/15 with steps of 13/10-15/13-16/15-13/12-15/13;
	* 1-15/13-4/3-13/9-20/13 with steps of 15/13-15/13-13/12-16/15~~-13/10~~, and its inverse		* 1-13/10-3/2-26/15-15/8 with steps of 13/10-15/13-15/13-13/12-16/15, and its inverse
	* 1-16/15-15/13-4/3-20/13 with steps of 16/15-13/12-15/13-15/13~~-13/10~~;		* 1-13/10-18/13-3/2-26/15 with steps of 13/10-16/15-13/12-15/13-15/13;
	* 1-15/13-5/4-13/9-20/13 with steps of 15/13-13/12-15/13-16/15~~-13/10~~, and its inverse		* 1-13/10-3/2-13/8-15/8 with steps of 13/10-15/13-13/12-15/13-16/15, and its inverse
	* 1-16/15-16/13-4/3-20/13 with steps of ~~16/15-~~15/13-13/12-15/13-13/10;		* 1-15/13-3/2-8/5-24/13 with steps of 15/13-13/10-16/15-15/13-13/12;
	* 1-6/5-13/10-18/13-3/2 with steps of 6/5-13/12-16/15-13/12-4/3, and its inverse		* 1-6/5-13/10-18/13-3/2 with steps of 6/5-13/12-16/15-13/12-4/3, and its inverse
	* 1-13/12-15/13-5/4-3/2 with steps of 13/12-16/15-13/12-6/5-4/3;		* 1-13/12-15/13-5/4-3/2 with steps of 13/12-16/15-13/12-6/5-4/3;

Xenllium: Update the article

2023-11-11T10:53:40Z

Update the article

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FloraC: Recategorize

2023-05-23T11:57:55Z

Recategorize

← Older revision		Revision as of 11:57, 23 May 2023
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	[[Category:15-odd-limit]]		[[Category:15-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Island~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:Island]]		[[Category:Island]]

FloraC: FloraC moved page Island tetrad to Island chords: It has triads as well as tetrads

2021-12-30T17:20:17Z

FloraC moved page Island tetrad to Island chords: It has triads as well as tetrads

← Older revision	Revision as of 17:20, 30 December 2021
(No difference)

FloraC: Expansion

2021-12-30T17:18:33Z

Expansion

@@ Line 1: / Line 1: @@
-The '''island tetrad''' is an [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] which under [[octave reduction]] consists of three [[15/13]] intervals followed by a [[13/10]], which closes on the octave since the island comma, [[676/675]], is [[tempering out|tempered out]]; in other words a 15/13-15/13-15/13-13/10 chord. It can also be viewed as an island tempered version of 1-15/13-[[4/3]]-[[20/13]]. Contained within it are a [[barbados triad]], the 1-13/10-[[3/2]] chord, and an [[island triad]], the 1-15/13-4/3 chord, which in another position is the 1-3/2-[[26/15]] chord. Another island chord of interest is a 26/15 over a major triad, 1-5/4-3/2-26/15, 5/4-6/5-15/13-15/13 in terms of intervals.
+An '''island chord''' is an [[15-odd-limit]] [[essentially tempered dyadic chord]] which is tempered by [[676/675]] (island comma).
 == See also ==
 * [[Arto and Tendo Theory]]
-[[Category:15-limit]]
+[[Category:15-odd-limit]]
-[[Category:Dyadic]]
+[[Category:Essentially tempered chords]]
 [[Category:Island]]
 [[Category:Tetrad]]

FloraC: Remove repeated link

2020-11-18T03:21:49Z

Remove repeated link

← Older revision		Revision as of 03:21, 18 November 2020
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	The '''island tetrad''' is an [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] which under [[octave reduction]] consists of three [[15/13]] intervals followed by a [[13/10]], which closes on the octave since the [[island comma]], [[676/675]], is [[tempering out\|tempered out]]; in other words a 15/13-15/13-15/13-13/10 chord. It can also be viewed as an island tempered version of 1-15/13-[[4/3]]-[[20/13]]. Contained within it are a [[barbados triad]], the 1-13/10-[[3/2]] chord, and an [[island triad]], the 1-15/13-4/3 chord, which in another position is the 1-3/2-[[26/15]] chord. Another island chord of interest is a 26/15 over a major triad, 1-5/4-3/2-26/15, 5/4-6/5-15/13-15/13 in terms of intervals.		The '''island tetrad''' is an [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] which under [[octave reduction]] consists of three [[15/13]] intervals followed by a [[13/10]], which closes on the octave since the island comma, [[676/675]], is [[tempering out\|tempered out]]; in other words a 15/13-15/13-15/13-13/10 chord. It can also be viewed as an island tempered version of 1-15/13-[[4/3]]-[[20/13]]. Contained within it are a [[barbados triad]], the 1-13/10-[[3/2]] chord, and an [[island triad]], the 1-15/13-4/3 chord, which in another position is the 1-3/2-[[26/15]] chord. Another island chord of interest is a 26/15 over a major triad, 1-5/4-3/2-26/15, 5/4-6/5-15/13-15/13 in terms of intervals.

	== See also ==		== See also ==

Xenwolf: -cat

2020-06-13T16:48:36Z

-cat

← Older revision		Revision as of 16:48, 13 June 2020
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	[[Category:15-limit]]		[[Category:15-limit]]
	~~[[Category:Chords]]~~
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:Island]]		[[Category:Island]]
	[[Category:Tetrad]]		[[Category:Tetrad]]

Xenwolf: +link

2020-06-12T21:27:34Z

+link

← Older revision		Revision as of 21:27, 12 June 2020
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	The '''island tetrad''' is an [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] which under [[octave reduction]] consists of three [[15/13]] intervals followed by a [[13/10]], which closes on the octave since the [[island comma]], [[676/675]], is [[tempering out\|tempered out]]; in other words a 15/13-15/13-15/13-13/10 chord. It can also be viewed as an island tempered version of 1-15/13-[[4/3]]-[[20/13]]. Contained within it are a [[barbados triad]], the 1-13/10-[[3/2]] chord, and an [[island triad]], the 1-15/13-4/3 chord, which in another position is the 1-3/2-[[26/15]] chord. Another island chord of interest is a 26/15 over a major triad, 1-5/4-3/2-26/15, 5/4-6/5-15/13-15/13 in terms of intervals.		The '''island tetrad''' is an [[Dyadic chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] which under [[octave reduction]] consists of three [[15/13]] intervals followed by a [[13/10]], which closes on the octave since the [[island comma]], [[676/675]], is [[tempering out\|tempered out]]; in other words a 15/13-15/13-15/13-13/10 chord. It can also be viewed as an island tempered version of 1-15/13-[[4/3]]-[[20/13]]. Contained within it are a [[barbados triad]], the 1-13/10-[[3/2]] chord, and an [[island triad]], the 1-15/13-4/3 chord, which in another position is the 1-3/2-[[26/15]] chord. Another island chord of interest is a 26/15 over a major triad, 1-5/4-3/2-26/15, 5/4-6/5-15/13-15/13 in terms of intervals.

			== See also ==

			* [[Arto and Tendo Theory]]

	[[Category:15-limit]]		[[Category:15-limit]]
	[[Category:Chords]]		[[Category:Chords]]