Swetismic chords - Revision history

FloraC: Improve readability; recategorize

2024-10-11T13:40:05Z

Improve readability; recategorize

FloraC: Name two of the 15-odd-limit tetrads due to their significance in functional harmony

2024-03-29T11:15:55Z

Name two of the 15-odd-limit tetrads due to their significance in functional harmony

← Older revision		Revision as of 11:15, 29 March 2024
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	* 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.		* 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.

	If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4~~, 1~~-7/6-~~3/2-12/~~7~~, 1-11~~/9-10/7-~~5/3 and~~ 1-7/6-15/11-5/3 with steps ~~9/7-~~7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.		If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads, including something important for functional harmony. The ''swetismic dominant seventh chord'' is a tempering of
			* 1-9/7-3/2-7/4 with steps 9/7-7/6-7/6-8/7.

			Its inversion might be called the ''swetismic half-diminished chord'', a tempering of
			* 1-7/6-3/2-12/7 with steps 7/6-9/7-8/7-7/6.

			We also have
			* 1-11/9-10/7-5/3 with steps 11/9-7/6-7/6-6/5; and its inverse
			* 1-7/6-15/11-5/3 with steps 7/6-7/6-11/9-6/5.

	[[Equal temperament]]s with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de }}.		[[Equal temperament]]s with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de }}.

FloraC: +pattern of chords; cleanup

2023-08-16T03:41:57Z

+pattern of chords; cleanup

FloraC: Readability

2023-08-08T16:55:16Z

Readability

← Older revision		Revision as of 16:55, 8 August 2023
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	A '''swetismic chord''' is a [[Swetismic temperaments\|swetismic]] ([[540/539]]) [[11-odd-limit]], [[essentially tempered chord]].		A '''swetismic chord''' is a [[Swetismic temperaments\|swetismic]] ([[540/539]]) [[11-odd-limit]], [[essentially tempered chord]].

	There are six swetismic [[~~Triad\|triads~~]], consisting of three pairs of chords in inverse relationship:		There are six swetismic [[triad]]s, consisting of three pairs of chords in inverse relationship:
			* 1-7/5-12/7 with [[step]]s 7/5-11/9-7/6, and its inverse
			* 1-7/6-10/7 with steps 7/6-11/9-7/5;
			* 1-7/6-9/7 with steps 7/6-11/10-14/9, and its inverse
			* 1-14/9-12/7 with steps 14/9-11/10-7/6;
			* 1-9/7-7/5 with steps 9/7-12/11-10/7, and its inverse
			* 1-10/7-14/9 with steps 10/7-12/11-9/7.

	* 1-7/5-12/7 with [[Step\|steps]] 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;		There are fifteen swetismic [[tetrad]]s, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:
	* 1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;
	* and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.

	There are fifteen swetismic [[~~Tetrad\|tetrads~~]], consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:

	* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;		* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;
	* 1-6/5-7/5-12/7 with steps 6/5-7/6-11/9-7/6;		* 1-6/5-7/5-12/7 with steps 6/5-7/6-11/9-7/6;
	* ~~and~~ 1-9/7-7/5-9/5 with steps 9/7-12/11-9/7-10/9.		* 1-9/7-7/5-9/5 with steps 9/7-12/11-9/7-10/9.

	The six pairs are:		The six pairs are:

	* 1-9/7-3/2-11/6 with steps 9/7-7/6-11/9-12/11 and 1-7/6-3/2-18/11 with steps 7/6-9/7-12/11-11/9;		* 1-9/7-3/2-11/6 with steps 9/7-7/6-11/9-12/11, and its inverse
	* 1-7/6-9/7-10/7 with steps 7/6-11/10-10/9-7/5 and 1-7/5-14/9-12/7 with steps 7/5-10/9-11/10-7/6;		* 1-7/6-3/2-18/11 with steps 7/6-9/7-12/11-11/9;
	* 1-7/6-9/7-18/11 with steps 7/6-11/10-14/11-11/9 and 1-14/11-7/5-18/11 with steps 14/11-11/10-7/6-11/9;		* 1-7/6-9/7-10/7 with steps 7/6-11/10-10/9-7/5, and its inverse
	* 1-7/6-10/7-11/6 with steps 7/6-11/9-9/7-12/11 and 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;		* 1-7/5-14/9-12/7 with steps 7/5-10/9-11/10-7/6;
	* 1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11 and 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11;		* 1-7/6-9/7-18/11 with steps 7/6-11/10-14/11-11/9, and its inverse
	* and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.		* 1-14/11-7/5-18/11 with steps 14/11-11/10-7/6-11/9;
			* 1-7/6-10/7-11/6 with steps 7/6-11/9-9/7-12/11, and its inverse
			* 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;
			* 1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11, and its inverse
			* 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11;
			* and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6, and its inverse
			* 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.

	Finally, there are six swetismic [[~~Pentad\|pentads~~]] coming in three pairs:		Finally, there are six swetismic [[pentad]]s coming in three pairs:

	* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;		* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11, and its inverse
	* 1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11 and 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10;		* 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;
	* and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11 and 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.		* 1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11, and its inverse
			* 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10;
			* and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11, and its inverse
			* 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.

	The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.		The 11-odd-limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.

	If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.		If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.

			[[Equal temperament]]s with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de }}.

	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
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	[[Category:Pentads]]		[[Category:Pentads]]
	[[Category:Swetismic]]		[[Category:Swetismic]]

	[[EDO\|Equal temperaments]] with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.

FloraC: Recategorize

2023-05-23T11:47:22Z

Recategorize

← Older revision		Revision as of 11:47, 23 May 2023
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:~~Pentad~~]]		[[Category:Pentads]]
	[[Category:Swetismic]]		[[Category:Swetismic]]

	[[EDO\|Equal temperaments]] with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.		[[EDO\|Equal temperaments]] with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.

BudjarnLambeth: Added links (as requested by the to:do notice)

2023-04-20T08:02:55Z

Added links (as requested by the to:do notice)

← Older revision		Revision as of 08:02, 20 April 2023
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	A '''swetismic chord''' is a swetismic ([[540/539]]) 11-odd-limit [[essentially tempered chord]].		A '''swetismic chord''' is a [[Swetismic temperaments\|swetismic]] ([[540/539]]) [[11-odd-limit]], [[essentially tempered chord]].

	There are six swetismic triads, consisting of three pairs of chords in inverse relationship:		There are six swetismic [[Triad\|triads]], consisting of three pairs of chords in inverse relationship:

	* 1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;		* 1-7/5-12/7 with [[Step\|steps]] 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;
	* 1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;		* 1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;
	* and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.		* and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.

	There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:		There are fifteen swetismic [[Tetrad\|tetrads]], consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:

	* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;		* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;
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	* and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.		* and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.

	Finally, there are six swetismic pentads coming in three pairs:		Finally, there are six swetismic [[Pentad\|pentads]] coming in three pairs:

	* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;		* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;
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	The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.		The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.

	If we are willing to consider the 15-odd-limit, there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.		If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.

	~~Equal temperaments with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}~~.

	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
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	[[Category:Swetismic]]		[[Category:Swetismic]]

	{{~~Todo~~\| ~~add links~~ }}		[[EDO\|Equal temperaments]] with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.

FloraC: Categories

2022-02-08T18:07:48Z

Xenwolf: recat

2021-05-20T08:10:16Z

recat

← Older revision		Revision as of 08:10, 20 May 2021
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	Equal temperaments with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.		Equal temperaments with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.

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

Xenwolf: +cat

2021-05-20T07:18:22Z

+cat

← Older revision		Revision as of 07:18, 20 May 2021
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	A '''swetismic chord''' is a swetismic (540/539) 11-odd-limit [[~~Dyadic chord\|~~essentially tempered chord]].		A '''swetismic chord''' is a swetismic (540/539) 11-odd-limit [[essentially tempered chord]].

	There are six swetismic triads, consisting of three pairs of chords in inverse relationship:		There are six swetismic triads, consisting of three pairs of chords in inverse relationship:
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	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:Chords]]		[[Category:Chords]]
			[[Category:Essentially tempered chords]]
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:Swetismic]]		[[Category:Swetismic]]
	~~[[Category:~~Todo:add links]]
			{{Todo\|add links}}

FloraC: Cleanup and rename category

2020-09-17T04:04:17Z

Cleanup and rename category

← Older revision		Revision as of 04:04, 17 September 2020
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	A ''swetismic chord'' is a swetismic (540/539) 11-odd-limit [[Dyadic chord\|essentially tempered chord]].		A '''swetismic chord''' is a swetismic (540/539) 11-odd-limit [[Dyadic chord\|essentially tempered chord]].

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

	~~<ul><li>~~1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;~~</li><li>~~1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;~~</li><li>~~and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.~~</li></ul>~~		* 1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;
			* 1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;
			* and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.

	There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:		There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:

	~~<ul><li>~~1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;~~</li><li>~~1-6/5-7/5-12/7 with steps 6/5-7/6-11/9-7/6;~~</li><li>~~and 1-9/7-7/5-9/5 with steps 9/7-12/11-9/7-10/9.~~</li></ul>The six pairs are:~~		* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;
			* 1-6/5-7/5-12/7 with steps 6/5-7/6-11/9-7/6;
			* and 1-9/7-7/5-9/5 with steps 9/7-12/11-9/7-10/9.

	~~<ul><li>~~1-9/7-3/2-11/6 with steps 9/7-7/6-11/9-12/11 and 1-7/6-3/2-18/11 with steps 7/6-9/7-12/11-11/9;~~</li><li>~~1-7/6-9/7-10/7 with steps 7/6-11/10-10/9-7/5 and 1-7/5-14/9-12/7 with steps 7/5-10/9-11/10-7/6;~~</li><li>~~1-7/6-9/7-18/11 with steps 7/6-11/10-14/11-11/9 and 1-14/11-7/5-18/11 with steps 14/11-11/10-7/6-11/9;~~</li><li>~~1-7/6-10/7-11/6 with steps 7/6-11/9-9/7-12/11 and 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;~~</li><li>~~1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11 and 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11;~~</li><li>~~and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.~~</li></ul>~~		The six pairs are:

			* 1-9/7-3/2-11/6 with steps 9/7-7/6-11/9-12/11 and 1-7/6-3/2-18/11 with steps 7/6-9/7-12/11-11/9;
			* 1-7/6-9/7-10/7 with steps 7/6-11/10-10/9-7/5 and 1-7/5-14/9-12/7 with steps 7/5-10/9-11/10-7/6;
			* 1-7/6-9/7-18/11 with steps 7/6-11/10-14/11-11/9 and 1-14/11-7/5-18/11 with steps 14/11-11/10-7/6-11/9;
			* 1-7/6-10/7-11/6 with steps 7/6-11/9-9/7-12/11 and 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;
			* 1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11 and 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11;
			* and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.

	Finally, there are six swetismic pentads coming in three pairs:		Finally, there are six swetismic pentads coming in three pairs:

	~~<ul><li>~~1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;~~</li><li>~~1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11 and 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10;~~</li><li>~~and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11 and 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.~~</li></ul>~~		* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;
			* 1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11 and 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10;
			* and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11 and 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.

	The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.		The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.
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	If we are willing to consider the 15-limit, there are also 15-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.		If we are willing to consider the 15-limit, there are also 15-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.

	Equal temperaments with swetismic chords include 19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de.		Equal temperaments with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.

	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:Chords]]		[[Category:Chords]]
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:~~Swetisma~~]]		[[Category:Swetismic]]
	[[Category:Todo:add links]]		[[Category:Todo:add links]]

← Older revision		Revision as of 03:41, 16 August 2023
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	A '''swetismic chord''' is a [[~~Swetismic temperaments\|swetismic~~]] ([[540/539~~]]) [[11-odd-limit]], [[essentially tempered chord~~]].		A '''swetismic chord''' is an [[essentially tempered chord]] tempered by the swetisma, [[540/539]].

	~~There~~ are ~~six swetismic~~ [[triad]]s, consisting of three pairs of chords in inverse relationship:		Swetismic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 [[triad]]s, 15 [[tetrad]]s and 6 [[pentad]]s, for a total of 27 distinct chord structures.

			There are six swetismic triads, consisting of three pairs of chords in inverse relationship:
	* 1-7/5-12/7 with [[step]]s 7/5-11/9-7/6, and its inverse		* 1-7/5-12/7 with [[step]]s 7/5-11/9-7/6, and its inverse
	* 1-7/6-10/7 with steps 7/6-11/9-7/5;		* 1-7/6-10/7 with steps 7/6-11/9-7/5;
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	* 1-10/7-14/9 with steps 10/7-12/11-9/7.		* 1-10/7-14/9 with steps 10/7-12/11-9/7.

	There are fifteen swetismic ~~[[tetrad]]s~~, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:		There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:

	* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;		* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;
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	* 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;		* 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;
	* 1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11, and its inverse		* 1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11, and its inverse
	* 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11;		* 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11; and
	* ~~and~~ 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6, and its inverse		* 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6, and its inverse
	* 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.		* 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.

	Finally, there are six swetismic ~~[[pentad]]s~~ coming in three pairs:		Finally, there are six swetismic pentads coming in three pairs:

	* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11, and its inverse		* 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11, and its inverse
	* 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;		* 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;
	* 1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11, and its inverse		* 1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11, and its inverse
	* 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10;		* 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10; and
	* ~~and~~ 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11, and its inverse		* 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11, and its inverse
	* 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.		* 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.

	~~The 11-odd-limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.~~

	If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.		If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.

← Older revision		Revision as of 18:07, 8 February 2022
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	A '''swetismic chord''' is a swetismic (540/539) 11-odd-limit [[essentially tempered chord]].		A '''swetismic chord''' is a swetismic ([[540/539]]) 11-odd-limit [[essentially tempered chord]].

	There are six swetismic triads, consisting of three pairs of chords in inverse relationship:		There are six swetismic triads, consisting of three pairs of chords in inverse relationship:
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	The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.		The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.

	If we are willing to consider the 15-limit, there are also 15-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.		If we are willing to consider the 15-odd-limit, there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.

	Equal temperaments with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.		Equal temperaments with swetismic chords include {{EDOs\|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de}}.

	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	~~[[Category:Chords]]~~
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Dyadic~~]]		[[Category:Triad]]
			[[Category:Tetrad]]
			[[Category:Pentad]]
	[[Category:Swetismic]]		[[Category:Swetismic]]

	{{Todo\|add links}}		{{Todo\| add links }}