Keenanismic chords - Revision history

FloraC: Improve readability; recategorize

2024-10-11T13:32:23Z

Improve readability; recategorize

FloraC: +pattern of chords

2023-08-16T03:37:59Z

+pattern of chords

← Older revision		Revision as of 03:37, 16 August 2023
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	A '''keenanismic chord''' is an ~~[[11-odd-limit]]~~ [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]]. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:		A '''keenanismic chord''' is an [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]].

			Keenanismic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.

			There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:

	* 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse		* 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse
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	* 1-6/5-11/8-3/2-12/7 with steps 6/5-8/7-12/11-8/7-7/6, and its inverse		* 1-6/5-11/8-3/2-12/7 with steps 6/5-8/7-12/11-8/7-7/6, and its inverse
	* 1-12/11-5/4-3/2-7/4 with steps 12/11-8/7-6/5-7/6-8/7.		* 1-12/11-5/4-3/2-7/4 with steps 12/11-8/7-6/5-7/6-8/7.

	~~The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.~~

	If we are willing to go as high as the [[15-odd-limit]], there are many more keenanismic chords, all of which have a step of size [[16/15]]. There are six additional keenanismic triads in the 15-odd-limit, 32 additional keenanismic tetrads and 44 additional pentads.		If we are willing to go as high as the [[15-odd-limit]], there are many more keenanismic chords, all of which have a step of size [[16/15]]. There are six additional keenanismic triads in the 15-odd-limit, 32 additional keenanismic tetrads and 44 additional pentads.

FloraC: Prefer voicing with the perfect fifth and sometimes other harmonics

2023-08-16T03:33:48Z

Prefer voicing with the perfect fifth and sometimes other harmonics

← Older revision		Revision as of 03:33, 16 August 2023
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	* 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse		* 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse
	* 1-7/6-8/5 with steps 7/6-11/8~~-5/4~~;		* 1-5/4-16/11 with steps 5/4-7/6-11/8;
	* 1-6/5-7/4 with steps 6/5-16/11~~-8/7~~, and its inverse		* 1-8/7-11/8 with steps 8/7-6/5-16/11, and its inverse
	* 1-6/5-11/8 with steps 6/5-8/7-16/11;		* 1-6/5-11/8 with steps 6/5-8/7-16/11;
	* 1-8/5-7/4 with steps 8/5-12/11-8/7, and its inverse		* 1-8/5-7/4 with steps 8/5-12/11-8/7, and its inverse
	* 1-8/5-11/6 with steps 8/5-8/7~~-12/11~~.		* 1-12/11-7/4 with steps 12/11-8/5-8/7.

	Keenanismic tetrads are especially interesting; there are fifteen in total. These include three palindromic tetrads:		Keenanismic tetrads are especially interesting; there are fifteen in total. These include three palindromic tetrads:
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	* 1-6/5-11/8-3/2 with steps 6/5-8/7-12/11-4/3, and its inverse		* 1-6/5-11/8-3/2 with steps 6/5-8/7-12/11-4/3, and its inverse
	* 1-6/5-8/5-7/4 with steps 6/5-4/3~~-12/11-8/7~~.		* 1-12/11-5/4-3/2 with steps 12/11-8/7-6/5-4/3.

	Finally, there is the pair		Finally, there is the pair
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	* 1-5/4-11/8-3/2-12/7 with steps 5/4-11/10-12/11-8/7-7/6, and its inverse		* 1-5/4-11/8-3/2-12/7 with steps 5/4-11/10-12/11-8/7-7/6, and its inverse
	* 1-8/7-5/4-11/8-12/7 with steps ~~8/7-~~12/11-11/10-5/4-7/6;		* 1-12/11-6/5-3/2-7/4 with steps 12/11-11/10-5/4-7/6-8/7;

	~~and the pair of pairs~~

	* 1-6/5-11/8-3/2-7/4 with steps 6/5-8/7-12/11-7/6-8/7, and its inverse		* 1-6/5-11/8-3/2-7/4 with steps 6/5-8/7-12/11-7/6-8/7, and its inverse
	* 1-12/11-5/4-3/2-12/7 with steps 12/11-8/7-6/5-8/7-7/6;		* 1-12/11-5/4-3/2-12/7 with steps 12/11-8/7-6/5-8/7-7/6;
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	The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.		The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.

	If we are willing to go as high as the 15-odd limit, there are many more keenanismic chords, all of which have a step of size 16/15. There are six additional keenanismic triads in the 15 limit, 32 additional keenanismic tetrads and 44 additional pentads.		If we are willing to go as high as the [[15-odd-limit]], there are many more keenanismic chords, all of which have a step of size [[16/15]]. There are six additional keenanismic triads in the 15-odd-limit, 32 additional keenanismic tetrads and 44 additional pentads.

	Equal temperaments with keenanismic tetrads include {{EDOs\| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}.		Equal temperaments with keenanismic tetrads include {{EDOs\| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}.

FloraC: Readability; +categories

2023-08-08T16:49:56Z

Readability; +categories

← Older revision		Revision as of 16:49, 8 August 2023
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	A '''keenanismic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]]. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:		A '''keenanismic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]]. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:

	* 1-5/4-12/7 with steps 5/4-11/8-7/6 and 1-7/6-8/5 with steps 7/6-11/8-5/4;		* 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse
	* 1-6/5-7/4 with steps 6/5-16/11-8/7 and 1-6/5-11/8 with steps 6/5-8/7-16/11;		* 1-7/6-8/5 with steps 7/6-11/8-5/4;
	* 1-8/5-7/4 with steps 8/5-12/11-8/7 and 1-8/5-11/6 with steps 8/5-8/7-12/11.		* 1-6/5-7/4 with steps 6/5-16/11-8/7, and its inverse
			* 1-6/5-11/8 with steps 6/5-8/7-16/11;
			* 1-8/5-7/4 with steps 8/5-12/11-8/7, and its inverse
			* 1-8/5-11/6 with steps 8/5-8/7-12/11.

	Keenanismic tetrads are especially interesting; there are fifteen in total. These include three palindromic tetrads:		Keenanismic tetrads are especially interesting; there are fifteen in total. These include three palindromic tetrads:
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	Then there are four remarkable tetrads in two inversely related pairs which are the remaining (circular) permutations of the intervals 5/4, 6/5, 7/6, 8/7 making up the otonal and utonal tetrad after those two chords have been removed. These are		Then there are four remarkable tetrads in two inversely related pairs which are the remaining (circular) permutations of the intervals 5/4, 6/5, 7/6, 8/7 making up the otonal and utonal tetrad after those two chords have been removed. These are

	* 1-5/4-3/2-12/7 with steps 5/4-6/5-8/7-7/6 and 1-6/5-3/2-7/4 with steps 6/5-5/4-7/6-8/7;		* 1-5/4-3/2-12/7 with steps 5/4-6/5-8/7-7/6, and its inverse
	* 1-5/4-10/7-12/7 with steps 5/4-8/7-6/5-7/6 and 1-5/4-16/11-7/4 with steps 5/4-7/6-6/5-8/7.		* 1-6/5-3/2-7/4 with steps 6/5-5/4-7/6-8/7;
			* 1-5/4-10/7-12/7 with steps 5/4-8/7-6/5-7/6, and its inverse
			* 1-5/4-16/11-7/4 with steps 5/4-7/6-6/5-8/7.

	Another set of four tetrads coming in two inverse pairs are		Another set of four tetrads coming in two inverse pairs are

	* 1-11/8-3/2-12/7 with steps 11/8-12/11-8/7-7/6 and 1-12/11-3/2-7/4 with steps 12/11-11/8-7/6-8/7;		* 1-11/8-3/2-12/7 with steps 11/8-12/11-8/7-7/6, and its inverse
	* 1-7/6-8/5-11/6 with steps 7/6-11/8-8/7-12/11 and 1-11/8-8/5-7/4 with steps 11/8-7/6-12/11-8/7.		* 1-12/11-3/2-7/4 with steps 12/11-11/8-7/6-8/7;
			* 1-7/6-8/5-11/6 with steps 7/6-11/8-8/7-12/11, and its inverse
			* 1-11/8-8/5-7/4 with steps 11/8-7/6-12/11-8/7.

	Another pair of inversely related tetrads are		Another pair of inversely related tetrads are

	* 1-6/5-11/8-3/2 with steps 6/5-8/7-12/11-4/3 and 1-6/5-8/5-7/4 with steps 6/5-4/3-12/11-8/7.		* 1-6/5-11/8-3/2 with steps 6/5-8/7-12/11-4/3, and its inverse
			* 1-6/5-8/5-7/4 with steps 6/5-4/3-12/11-8/7.

	Finally, there is the pair		Finally, there is the pair

	* 1-8/7-5/4-11/8 with steps 8/7-12/11-11/10-16/11 and 1-16/11-8/5-7/4 with steps 16/11-11/10-12/11-8/7.		* 1-8/7-5/4-11/8 with steps 8/7-12/11-11/10-16/11, and its inverse
			* 1-16/11-8/5-7/4 with steps 16/11-11/10-12/11-8/7.

	Five of these tetrads, the four which permute the steps of the otonal tetrad and one of the palindromic tetrads, have all step sizes larger than 9/8, and it is these five which are featured in the [[Tablets #The keenanismic tablet\|keenanismic tablet]] section of the article on tablets.		Five of these tetrads, the four which permute the steps of the otonal tetrad and one of the palindromic tetrads, have all step sizes larger than 9/8, and it is these five which are featured in the [[Tablets #The keenanismic tablet\|keenanismic tablet]] section of the article on tablets.
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	Finally, there are six keenanismic pentads coming in three inverse pairs. These are		Finally, there are six keenanismic pentads coming in three inverse pairs. These are

	* 1-5/4-11/8-3/2-12/7 with steps 5/4-11/10-12/11-8/7-7/6 and 1-8/7-5/4-11/8-12/7 with steps 8/7-12/11-11/10-5/4-7/6;		* 1-5/4-11/8-3/2-12/7 with steps 5/4-11/10-12/11-8/7-7/6, and its inverse
			* 1-8/7-5/4-11/8-12/7 with steps 8/7-12/11-11/10-5/4-7/6;

	and the pair of pairs		and the pair of pairs

	* 1-6/5-11/8-3/2-7/4 with steps 6/5-8/7-12/11-7/6-8/7 and 1-12/11-5/4-3/2-12/7 with steps 12/11-8/7-6/5-8/7-7/6;		* 1-6/5-11/8-3/2-7/4 with steps 6/5-8/7-12/11-7/6-8/7, and its inverse
	* 1-6/5-11/8-3/2-12/7 with steps 6/5-8/7-12/11-8/7-7/6 and 1-12/11-5/4-3/2-7/4 with steps 12/11-8/7-6/5-7/6-8/7.		* 1-12/11-5/4-3/2-12/7 with steps 12/11-8/7-6/5-8/7-7/6;
			* 1-6/5-11/8-3/2-12/7 with steps 6/5-8/7-12/11-8/7-7/6, and its inverse
			* 1-12/11-5/4-3/2-7/4 with steps 12/11-8/7-6/5-7/6-8/7.

	The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.		The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
			[[Category:Essentially tempered chords]]
			[[Category:Triads]]
			[[Category:Tetrads]]
			[[Category:Pentads]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]
	~~[[Category:Essentially tempered chords]]~~

Fredg999 category edits: Removing from Category:Chords using Cat-a-lot

2023-04-28T03:51:55Z

Removing from Category:Chords using Cat-a-lot

← Older revision		Revision as of 03:51, 28 April 2023
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]
	~~[[Category:Chords]]~~
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]

Xenwolf: recat

2021-05-20T08:09:33Z

recat

← Older revision		Revision as of 08:09, 20 May 2021
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	Equal temperaments with keenanismic tetrads include {{EDOs\| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}.		Equal temperaments with keenanismic tetrads include {{EDOs\| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}.

	[[Category:11-limit]]		[[Category:11-odd-limit]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]
	[[Category:Chords]]		[[Category:Chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]

Xenwolf: +cat

2021-05-20T07:11:41Z

+cat

← Older revision		Revision as of 07:11, 20 May 2021
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	A '''keenanismic chord''' is an [[11-odd-limit]] [[~~Dyadic_chord\|~~essentially tempered chord]] which is tempered by the keenanisma, [[385/384]]. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:		A '''keenanismic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]]. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:

	* 1-5/4-12/7 with steps 5/4-11/8-7/6 and 1-7/6-8/5 with steps 7/6-11/8-5/4;		* 1-5/4-12/7 with steps 5/4-11/8-7/6 and 1-7/6-8/5 with steps 7/6-11/8-5/4;
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	[[Category:Keenanismic]]		[[Category:Keenanismic]]
	[[Category:Chords]]		[[Category:Chords]]
			[[Category:Essentially tempered chords]]

Inthar at 07:33, 10 April 2021

2021-04-10T07:33:15Z

← Older revision		Revision as of 07:33, 10 April 2021
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	The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.		The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.

	If we are willing to go as high as the 15 limit, there are many more keenanismic chords, all of which have a step of size 16/15. There are six additional keenanismic triads in the 15 limit, 32 additional keenanismic tetrads and 44 additional pentads.		If we are willing to go as high as the 15-odd limit, there are many more keenanismic chords, all of which have a step of size 16/15. There are six additional keenanismic triads in the 15 limit, 32 additional keenanismic tetrads and 44 additional pentads.

	Equal temperaments with keenanismic tetrads include {{EDOs\| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}.		Equal temperaments with keenanismic tetrads include {{EDOs\| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}.

FloraC: Fix category

2021-01-02T04:37:59Z

Fix category

← Older revision		Revision as of 04:37, 2 January 2021
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	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:Keenanismic]]		[[Category:Keenanismic]]
	[[Category:~~Chord~~]]		[[Category:Chords]]

FloraC: Cleanup for readability

2021-01-02T04:34:42Z

Cleanup for readability

@@ Line 1: / Line 1: @@
-A ''keenanismic chord'' is an 11-odd-limit [[Dyadic_chord|essentially tempered chord]] which is tempered by the keenanisma, 385/384. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship: 1-5/4-12/7 with steps 5/4-11/8-7/6 and 1-7/6-8/5 with steps 7/6-11/8-5/4; 1-6/5-7/4 with steps 6/5-16/11-8/7 and 1-6/5-11/8 with steps 6/5-8/7-16/11; and 1-8/5-7/4 with steps 8/5-12/11-8/7 and 1-8/5-11/6 with steps 8/5-8/7-12/11.
+A '''keenanismic chord''' is an [[11-odd-limit]] [[Dyadic_chord|essentially tempered chord]] which is tempered by the keenanisma, [[385/384]]. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:
-Keenanismic tetrads are especially interesting; there are fifteen in total. These include three palindromic tetrads: 1-5/4-11/8-12/7 with steps 5/4-11/10-5/4-7/6; 1-6/5-11/8-7/4 with steps 6/5-8/7-14/11-8/7; and 1-7/5-8/5-7/4 with steps 7/5-8/7-12/11-8/7. Then there are four remarkable tetrads in two inversely related pairs which are the remaining (circular) permutations of the intervals 5/4, 6/5, 7/6, 8/7 making up the otonal and utonal tetrad after those two chords have been removed. These are 1-5/4-3/2-12/7 with steps 5/4-6/5-8/7-7/6 and 1-6/5-3/2-7/4 with steps 6/5-5/4-7/6-8/7; and 1-5/4-10/7-12/7 with steps 5/4-8/7-6/5-7/6 and 1-5/4-16/11-7/4 with steps 5/4-7/6-6/5-8/7. Another set of four tetrads coming in two inverse pairs are 1-11/8-3/2-12/7 with steps 11/8-12/11-8/7-7/6 and 1-12/11-3/2-7/4 with steps 12/11-11/8-7/6-8/7; and 1-7/6-8/5-11/6 with steps 7/6-11/8-8/7-12/11 and 1-11/8-8/5-7/4 with steps 11/8-7/6-12/11-8/7. Another pair of inversely related tetrads are 1-6/5-11/8-3/2 with steps 6/5-8/7-12/11-4/3 and 1-6/5-8/5-7/4 with steps 6/5-4/3-12/11-8/7. Finally, there is the pair 1-8/7-5/4-11/8 with steps 8/7-12/11-11/10-16/11 and 1-16/11-8/5-7/4 with steps 16/11-11/10-12/11-8/7. Five of these tetrads, the four which permute the steps of the otonal tetrad and one of the palindromic tetrads, have all step sizes larger than 9/8, and it is these five which are featured in the [[Tablets#x4et tablets-The keenanismic tablet|keenanismic tablet]] section of the article on tablets.
+* 1-5/4-12/7 with steps 5/4-11/8-7/6 and 1-7/6-8/5 with steps 7/6-11/8-5/4;
-Finally, there are six keenanismic pentads coming in three inverse pairs. These are 1-5/4-11/8-3/2-12/7 with steps 5/4-11/10-12/11-8/7-7/6 and 1-8/7-5/4-11/8-12/7 with steps 8/7-12/11-11/10-5/4-7/6; and the pair of pairs 1-6/5-11/8-3/2-7/4 with steps 6/5-8/7-12/11-7/6-8/7 and 1-12/11-5/4-3/2-12/7 with steps 12/11-8/7-6/5-8/7-7/6 plus 1-6/5-11/8-3/2-12/7 with steps 6/5-8/7-12/11-8/7-7/6 and 1-12/11-5/4-3/2-7/4 with steps 12/11-8/7-6/5-7/6-8/7.
+Keenanismic tetrads are especially interesting; there are fifteen in total. These include three palindromic tetrads:
 The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.
@@ Line 9: / Line 44: @@
 If we are willing to go as high as the 15 limit, there are many more keenanismic chords, all of which have a step of size 16/15. There are six additional keenanismic triads in the 15 limit, 32 additional keenanismic tetrads and 44 additional pentads.
-Equal temperaments with keenanismic tetrads include 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de.
+Equal temperaments with keenanismic tetrads include {{EDOs| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}.
 [[Category:11-limit]]
-[[Category:keenanismic]]
+[[Category:Keenanismic]]
-[[Category:tetrad]]
+[[Category:Chord]]