Charismic chords - Revision history

FloraC: Oops

2025-10-10T07:30:18Z

Oops

← Older revision		Revision as of 07:30, 10 October 2025
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	Equal temperaments with charismic chords include {{Optimal ET sequence\| 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111 }}.		Equal temperaments with charismic chords include {{Optimal ET sequence\| 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111 }}.

	[[Category:~~17–odd–limit~~ chords]]		[[Category:17-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

FloraC: Cleanup

2025-10-10T07:30:04Z

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Godtone: Godtone moved page Diasemismic chords to Charismic chords: see https://en.xen.wiki/w/Talk:256/255 and https://en.xen.wiki/w/Temperament_naming#Contemporary_rules

2024-01-15T19:25:25Z

Godtone moved page Diasemismic chords to Charismic chords: see https://en.xen.wiki/w/Talk:256/255 and https://en.xen.wiki/w/Temperament_naming#Contemporary_rules

← Older revision	Revision as of 19:25, 15 January 2024
(No difference)

Godtone at 19:17, 15 January 2024

2024-01-15T19:17:53Z

← Older revision		Revision as of 19:17, 15 January 2024
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	'''~~Charsmic~~ chords''' (or '''diasemismic chords''') are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the ~~charsma (or diasemisma)~~, [[256/255]].		'''Charismic chords''' (formerly '''diasemismic chords''') are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the [[charisma]], [[256/255]].

	There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.		There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.

	The two ~~charsmic~~ triads are in inverse relationship:		The two charismic triads are in inverse relationship:
	* 1-5/4-24/17 with steps of 5/4-9/8-17/12;		* 1-5/4-24/17 with steps of 5/4-9/8-17/12;
	* 1-9/8-24/17 with steps of 9/8-5/4-17/12.		* 1-9/8-24/17 with steps of 9/8-5/4-17/12.
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	* 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.		* 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.

	Equal temperaments with ~~charsmic~~ chords include {{Optimal ET sequence\|9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.		Equal temperaments with charismic chords include {{Optimal ET sequence\|9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.

	[[Category:17-odd-limit]]		[[Category:17-odd-limit]]
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	[[Category:Pentads]]		[[Category:Pentads]]
	[[Category:Hexads]]		[[Category:Hexads]]
	[[Category:~~Charsmic~~]]		[[Category:Charismic]]

Xenllium at 23:50, 6 January 2024

2024-01-06T23:50:19Z

← Older revision		Revision as of 23:50, 6 January 2024
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	'''~~Diasemismic~~ chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the diasemisma, [[256/255]].		'''Charsmic chords''' (or '''diasemismic chords''') are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the charsma (or diasemisma), [[256/255]].

	There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.		There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.

	The two ~~diasemismic~~ triads are in inverse relationship:		The two charsmic triads are in inverse relationship:
	* 1-5/4-24/17 with steps of 5/4-9/8-17/12;		* 1-5/4-24/17 with steps of 5/4-9/8-17/12;
	* 1-9/8-24/17 with steps of 9/8-5/4-17/12.		* 1-9/8-24/17 with steps of 9/8-5/4-17/12.
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	* 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.		* 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.

	Equal temperaments with ~~diasemismic~~ chords include {{Optimal ET sequence\|9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.		Equal temperaments with charsmic chords include {{Optimal ET sequence\|9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.

	[[Category:17-odd-limit]]		[[Category:17-odd-limit]]
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	[[Category:Pentads]]		[[Category:Pentads]]
	[[Category:Hexads]]		[[Category:Hexads]]
	[[Category:~~Diasemismic~~]]		[[Category:Charsmic]]

Xenllium at 05:23, 25 November 2023

2023-11-25T05:23:57Z

← Older revision		Revision as of 05:23, 25 November 2023
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	There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.		There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.

	The two diasemismic triads are in inverse relationship:		The two diasemismic triads are in inverse relationship:
	* 1-5/4-24/17 with steps of 5/4-9/8-17/12;		* 1-5/4-24/17 with steps of 5/4-9/8-17/12;
	* 1-9/8-24/17 with steps of 9/8-5/4-17/12.		* 1-9/8-24/17 with steps of 9/8-5/4-17/12.
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	* 1-16/15-9/8-6/5 with steps of 16/15-18/17-16/15-5/3.		* 1-16/15-9/8-6/5 with steps of 16/15-18/17-16/15-5/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-5/4-24/17-15/8 with steps of 5/4-9/8-4/3-16/15 and its inverse 1-4/3-3/2-15/8 with steps of 4/3-9/8-5/4-16/15;		* 1-5/4-24/17-15/8 with steps of 5/4-9/8-4/3-16/15, and its inverse
	* 1-5/4-24/17-3/2 with steps of 5/4-9/8-16/15-4/3 and its inverse 1-16/15-6/5-3/2 with steps of 16/15-9/8-5/4-4/3;		* 1-4/3-3/2-15/8 with steps of 4/3-9/8-5/4-16/15;
	* 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12 and its inverse 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12;		* 1-5/4-24/17-3/2 with steps of 5/4-9/8-16/15-4/3, and its inverse
	* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.		* 1-16/15-6/5-3/2 with steps of 16/15-9/8-5/4-4/3;
			* 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12, and its inverse
			* 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12;
			* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12, and its inverse
			* 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.

	For pentads, there are one palindromic chord and eight pairs of chords in inverse relationship. The palindromic chord is		For pentads, there are one palindromic chord and eight pairs of chords in inverse relationship. The palindromic chord is
	* 1-5/4-24/17-30/17-15/8 with steps of 5/4-9/8-5/4-16/15-16/15.		* 1-5/4-24/17-30/17-15/8 with steps of 5/4-9/8-5/4-16/15-16/15.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-9/8-5/4-24/17-3/2 with steps of 9/8-10/9-9/8-16/15-4/3 and its inverse 1-9/8-5/4-24/17-15/8 with steps of 9/8-10/9-9/8-4/3-16/15;		* 1-9/8-5/4-24/17-3/2 with steps of 9/8-10/9-9/8-16/15-4/3, and its inverse
	* 1-5/4-24/17-3/2-15/8 with steps of 5/4-9/8-16/15-5/4-16/15 and its inverse 1-5/4-4/3-5/3-16/9 with steps of 5/4-16/15-5/4-16/15-9/8;		* 1-9/8-5/4-24/17-15/8 with steps of 9/8-10/9-9/8-4/3-16/15;
	* 1-5/4-4/3-24/17-15/8 with steps of 5/4-16/15-18/17-4/3-16/15 and its inverse 1-5/4-4/3-16/9-15/8 with steps of 5/4-16/15-4/3-18/17-16/15;		* 1-5/4-24/17-3/2-15/8 with steps of 5/4-9/8-16/15-5/4-16/15, and its inverse
	* 1-5/4-4/3-24/17-3/2 with steps of 5/4-16/15-18/17-16/15-4/3 and its inverse 1-16/15-9/8-6/5-3/2 with steps of 16/15-18/17-16/15-5/4-4/3;		* 1-5/4-4/3-5/3-16/9 with steps of 5/4-16/15-5/4-16/15-9/8;
	* 1-20/17-5/4-4/3-15/8 with steps of 20/17-16/15-16/15-24/17-16/15 and its inverse 1-20/17-5/4-30/17-15/8 with steps of 20/17-16/15-24/17-16/15-16/15;		* 1-5/4-4/3-24/17-15/8 with steps of 5/4-16/15-18/17-4/3-16/15, and its inverse
	* 1-16/15-5/4-4/3-3/2 with steps of 16/15-20/17-16/15-9/8-4/3 and its inverse 1-9/8-6/5-24/17-3/2 with steps of 9/8-16/15-20/17-16/15-4/3;		* 1-5/4-4/3-16/9-15/8 with steps of 5/4-16/15-4/3-18/17-16/15;
	* 1-20/17-5/4-4/3-24/17 with steps of 20/17-16/15-16/15-18/17-17/12 and its inverse 1-18/17-9/8-6/5-24/17 with steps of 18/17-16/15-16/15-20/17-17/12;		* 1-5/4-4/3-24/17-3/2 with steps of 5/4-16/15-18/17-16/15-4/3, and its inverse
	* 1-5/4-24/17-3/2-30/17 with steps of 5/4-9/8-16/15-20/17-17/15 and its inverse 1-16/15-6/5-3/2-17/10 with steps of 16/15-9/8-5/4-17/15-20/17.		* 1-16/15-9/8-6/5-3/2 with steps of 16/15-18/17-16/15-5/4-4/3;
			* 1-20/17-5/4-4/3-15/8 with steps of 20/17-16/15-16/15-24/17-16/15, and its inverse
			* 1-20/17-5/4-30/17-15/8 with steps of 20/17-16/15-24/17-16/15-16/15;
			* 1-16/15-5/4-4/3-3/2 with steps of 16/15-20/17-16/15-9/8-4/3, and its inverse
			* 1-9/8-6/5-24/17-3/2 with steps of 9/8-16/15-20/17-16/15-4/3;
			* 1-20/17-5/4-4/3-24/17 with steps of 20/17-16/15-16/15-18/17-17/12, and its inverse
			* 1-18/17-9/8-6/5-24/17 with steps of 18/17-16/15-16/15-20/17-17/12;
			* 1-5/4-24/17-3/2-30/17 with steps of 5/4-9/8-16/15-20/17-17/15, and its inverse
			* 1-16/15-6/5-3/2-17/10 with steps of 16/15-9/8-5/4-17/15-20/17.

	For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are		For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
	* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15;		* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15;
	* 1-5/4-4/3-24/17-3/2-15/8 with steps of 5/4-16/15-18/17-16/15-5/4-16/15.		* 1-5/4-4/3-24/17-3/2-15/8 with steps of 5/4-16/15-18/17-16/15-5/4-16/15.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-16/15-5/4-4/3-17/12-3/2 with steps of 16/15-20/17-16/15-16/15-18/17-4/3 and its inverse 1-18/17-9/8-6/5-24/17-3/2 with steps of 18/17-16/15-16/15-20/17-16/15-4/3;		* 1-16/15-5/4-4/3-17/12-3/2 with steps of 16/15-20/17-16/15-16/15-18/17-4/3, and its inverse
	* 1-5/4-24/17-3/2-30/17-15/8 with steps of 5/4-9/8-16/15-20/17-16/15-16/15 and its inverse 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.		* 1-18/17-9/8-6/5-24/17-3/2 with steps of 18/17-16/15-16/15-20/17-16/15-4/3;
			* 1-5/4-24/17-3/2-30/17-15/8 with steps of 5/4-9/8-16/15-20/17-16/15-16/15, and its inverse
			* 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.

	Equal temperaments with diasemismic chords include {{Optimal ET sequence\|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.		Equal temperaments with diasemismic chords include {{Optimal ET sequence\|9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.

	[[Category:17-odd-limit]]		[[Category:17-odd-limit]]

Xenllium at 07:33, 14 August 2023

2023-08-14T07:33:52Z

← Older revision		Revision as of 07:33, 14 August 2023
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	'''Diasemismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the diasemisma, [[256/255]].		'''Diasemismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the diasemisma, [[256/255]].

	~~The [[diasemismic]] temperament contains many possibilities for essentially tempered dyadic chords including two~~ triads and ~~twelve tetrads in the~~ [[17-odd-limit]] ~~of the 2.3.5.17 subgroup~~.		There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.

	The two diasemismic triads are in inverse relationship:		The two diasemismic triads are in inverse relationship:
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	* 1-9/8-24/17 with steps of 9/8-5/4-17/12.		* 1-9/8-24/17 with steps of 9/8-5/4-17/12.

	For tetrads, there are ~~four~~ palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are five palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
	* 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;		* 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;
	* 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;		* 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;
	* 1-16/15-4/3-17/12 with steps of 16/15-5/4-16/15-24/17;		* 1-16/15-4/3-17/12 with steps of 16/15-5/4-16/15-24/17;
			* 1-16/15-5/4-4/3 with steps of 16/15-20/17-16/15-3/2;
	* 1-16/15-9/8-6/5 with steps of 16/15-18/17-16/15-5/3.		* 1-16/15-9/8-6/5 with steps of 16/15-18/17-16/15-5/3.

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	* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.		* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.

	~~Remarkable~~ hexads ~~include following~~ two palindromic chords:		For pentads, there are one palindromic chord and eight pairs of chords in inverse relationship. The palindromic chord is
			* 1-5/4-24/17-30/17-15/8 with steps of 5/4-9/8-5/4-16/15-16/15.

			The inversely related pairs of chords are
			* 1-9/8-5/4-24/17-3/2 with steps of 9/8-10/9-9/8-16/15-4/3 and its inverse 1-9/8-5/4-24/17-15/8 with steps of 9/8-10/9-9/8-4/3-16/15;
			* 1-5/4-24/17-3/2-15/8 with steps of 5/4-9/8-16/15-5/4-16/15 and its inverse 1-5/4-4/3-5/3-16/9 with steps of 5/4-16/15-5/4-16/15-9/8;
			* 1-5/4-4/3-24/17-15/8 with steps of 5/4-16/15-18/17-4/3-16/15 and its inverse 1-5/4-4/3-16/9-15/8 with steps of 5/4-16/15-4/3-18/17-16/15;
			* 1-5/4-4/3-24/17-3/2 with steps of 5/4-16/15-18/17-16/15-4/3 and its inverse 1-16/15-9/8-6/5-3/2 with steps of 16/15-18/17-16/15-5/4-4/3;
			* 1-20/17-5/4-4/3-15/8 with steps of 20/17-16/15-16/15-24/17-16/15 and its inverse 1-20/17-5/4-30/17-15/8 with steps of 20/17-16/15-24/17-16/15-16/15;
			* 1-16/15-5/4-4/3-3/2 with steps of 16/15-20/17-16/15-9/8-4/3 and its inverse 1-9/8-6/5-24/17-3/2 with steps of 9/8-16/15-20/17-16/15-4/3;
			* 1-20/17-5/4-4/3-24/17 with steps of 20/17-16/15-16/15-18/17-17/12 and its inverse 1-18/17-9/8-6/5-24/17 with steps of 18/17-16/15-16/15-20/17-17/12;
			* 1-5/4-24/17-3/2-30/17 with steps of 5/4-9/8-16/15-20/17-17/15 and its inverse 1-16/15-6/5-3/2-17/10 with steps of 16/15-9/8-5/4-17/15-20/17.

			For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
	* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15;		* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15;
	* 1-5/4-4/3-24/17-3/2-15/8 with steps of 5/4-16/15-18/17-16/15-5/4-16/15.		* 1-5/4-4/3-24/17-3/2-15/8 with steps of 5/4-16/15-18/17-16/15-5/4-16/15.

			The inversely related pairs of chords are
			* 1-16/15-5/4-4/3-17/12-3/2 with steps of 16/15-20/17-16/15-16/15-18/17-4/3 and its inverse 1-18/17-9/8-6/5-24/17-3/2 with steps of 18/17-16/15-16/15-20/17-16/15-4/3;
			* 1-5/4-24/17-3/2-30/17-15/8 with steps of 5/4-9/8-16/15-20/17-16/15-16/15 and its inverse 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.

	Equal temperaments with diasemismic chords include {{Optimal ET sequence\|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.		Equal temperaments with diasemismic chords include {{Optimal ET sequence\|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.
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	[[Category:Triads]]		[[Category:Triads]]
	[[Category:Tetrads]]		[[Category:Tetrads]]
			[[Category:Pentads]]
	[[Category:Hexads]]		[[Category:Hexads]]
	[[Category:Diasemismic]]		[[Category:Diasemismic]]

Xenllium at 14:03, 28 July 2023

2023-07-28T14:03:17Z

← Older revision		Revision as of 14:03, 28 July 2023
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	* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.		* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.

	Remarkable hexads include a palindromic ~~chord~~:		Remarkable hexads include following two palindromic chords:
	* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15.		* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15;
			* 1-5/4-4/3-24/17-3/2-15/8 with steps of 5/4-16/15-18/17-16/15-5/4-16/15.

	Equal temperaments with diasemismic chords include {{Optimal ET sequence\|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.		Equal temperaments with diasemismic chords include {{Optimal ET sequence\|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.

Xenllium at 01:54, 22 July 2023

2023-07-22T01:54:06Z

← Older revision		Revision as of 01:54, 22 July 2023
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	'''Diasemismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the diasemisma, [[256/255]].		'''Diasemismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the diasemisma, [[256/255]].

	The [[diasemismic]] temperament contains many possibilities for essentially tempered dyadic chords including two triads and ~~eleven~~ tetrads in the [[17-odd-limit]] of the 2.3.5.17 subgroup.		The [[diasemismic]] temperament contains many possibilities for essentially tempered dyadic chords including two triads and twelve tetrads in the [[17-odd-limit]] of the 2.3.5.17 subgroup.

	The two diasemismic triads are in inverse relationship:		The two diasemismic triads are in inverse relationship:
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	* 1-9/8-24/17 with steps of 9/8-5/4-17/12.		* 1-9/8-24/17 with steps of 9/8-5/4-17/12.

	For tetrads, there are ~~three~~ palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are four palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
	* 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;		* 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;
	* 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;		* 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;
	* 1-16/15-4/3-17/12 with steps of 16/15-5/4-16/15-24/17;		* 1-16/15-4/3-17/12 with steps of 16/15-5/4-16/15-24/17;
			* 1-16/15-9/8-6/5 with steps of 16/15-18/17-16/15-5/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are

Xenllium at 01:45, 22 July 2023

2023-07-22T01:45:21Z

← Older revision		Revision as of 01:45, 22 July 2023
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	* 1-9/8-24/17 with steps of 9/8-5/4-17/12.		* 1-9/8-24/17 with steps of 9/8-5/4-17/12.

	For tetrads, there are three palindromic ~~chors~~ and four pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
	* 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;		* 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;
	* 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;		* 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;
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	* 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12 and its inverse 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12;		* 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12 and its inverse 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12;
	* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.		* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.

			Remarkable hexads include a palindromic chord:
			* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15.

	Equal temperaments with diasemismic chords include {{Optimal ET sequence\|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.		Equal temperaments with diasemismic chords include {{Optimal ET sequence\|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.
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	[[Category:Triads]]		[[Category:Triads]]
	[[Category:Tetrads]]		[[Category:Tetrads]]
			[[Category:Hexads]]
	[[Category:Diasemismic]]		[[Category:Diasemismic]]