Buzurgismic chords - Revision history

FloraC: Cleanup

2025-03-19T13:42:41Z

Cleanup

← Older revision		Revision as of 13:42, 19 March 2025
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	'''Buzurgismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].		'''Buzurgismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].

	The [[buzurgismic]] temperament is very comparable to the [[~~Biyatismic temperaments\|~~biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]].		The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]].

	The two buzurgismic triads are in inverse relationship:		The two buzurgismic triads are in inverse relationship:
	* ~~1-7~~/~~6-13~~/8 with steps 7/6-18/13-16/13;		* 1–7/6–13/8 with steps 7/6, 18/13, 16/13;
	* ~~1-18~~/~~13-13~~/8 with steps 18/13-7/6-16/13.		* 1–18/13–13/8 with steps 18/13, 7/6, 16/13.

	For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are
	* ~~1-9~~/~~8-18~~/~~13-13~~/8 with steps 9/8-16/13-7/6-16/13;		* 1–9/8–18/13–13/8 with steps 9/8, 16/13, 7/6, 16/13;
	* ~~1-3~~/~~2-13~~/~~8-13~~/7 with steps 3/2-13/12-8/7-13/12;		* 1–3/2–13/8–13/7 with steps 3/2, 13/12, 8/7, 13/12;
	* ~~1-13~~/~~12-18~~/~~13-3~~/2 with steps 13/12-9/7-13/12-4/3.		* 1–13/12–18/13–3/2 with steps 13/12, 9/7, 13/12, 4/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* ~~1-18~~/~~13-3~~/~~2-13~~/8 with steps 18/13-13/12-13/12-16/13, and its inverse		* 1–18/13–3/2–13/8 with steps 18/13, 13/12, 13/12, 16/13, and its inverse
	* ~~1-13~~/~~12-3~~/~~2-13~~/7 with steps 13/12-18/13-16/13-13/12;		* 1–13/12–3/2–13/7 with steps 13/12, 18/13, 16/13, 13/12;
	* ~~1-13~~/~~12-3~~/~~2-7~~/4 with steps 13/12-18/13-7/6-8/7, and its inverse		* 1–13/12–3/2–7/4 with steps 13/12, 18/13, 7/6, 8/7, and its inverse
	* ~~1-18~~/~~13-3~~/~~2-12~~/7 with steps 18/13-13/12-8/7-7/6;		* 1–18/13–3/2–12/7 with steps 18/13, 13/12, 8/7, 7/6;
	* ~~1-7~~/~~6-3~~/~~2-13~~/8 with steps 7/6-9/7-13/12-16/13, and its inverse		* 1–7/6–3/2–13/8 with steps 7/6, 9/7, 13/12, 16/13, and its inverse
	* ~~1-9~~/~~7-3~~/~~2-13~~/7 with steps 9/7-7/6-16/13-13/12.		* 1–9/7–3/2–13/7 with steps 9/7, 7/6, 16/13, 13/12.

	For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is		For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
	* ~~1-9~~/~~8-18~~/~~13-3~~/~~2-13~~/8 with steps 9/8-16/13-13/12-13/12-16/13.		* 1–9/8–18/13–3/2–13/8 with steps 9/8, 16/13, 13/12, 13/12, 16/13.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* ~~1-13~~/~~12-7~~/~~6-3~~/~~2-13~~/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse		* 1–13/12–7/6–3/2–13/8 with steps 13/12, 13/12, 9/7, 13/12, 16/13, and its inverse
	* ~~1-9~~/~~7-18~~/~~13-3~~/~~2-13~~/7 with steps 9/7-13/12-13/12-16/13-13/12;		* 1–9/7–18/13–3/2–13/7 with steps 9/7, 13/12, 13/12, 16/13, 13/12;
	* ~~1-13~~/~~12-7~~/~~6-3~~/~~2-7~~/4 with steps 13/12-13/12-9/7-7/6-8/7, and its inverse		* 1–13/12–7/6–3/2–7/4 with steps 13/12, 13/12, 9/7, 7/6, 8/7, and its inverse
	* ~~1-9~~/~~7-18~~/~~13-3~~/~~2-12~~/7 with steps 9/7-13/12-13/12-8/7-7/6;		* 1–9/7–18/13–3/2–12/7 with steps 9/7, 13/12, 13/12, 8/7, 7/6;
	* ~~1-13~~/~~12-3~~/~~2-13~~/~~8-7~~/4 with steps 13/12-18/13-13/12-13/12-8/7, and its inverse		* 1–13/12–3/2–13/8–7/4 with steps 13/12, 18/13, 13/12, 13/12, 8/7, and its inverse
	* ~~1-18~~/~~13-3~~/~~2-12~~/~~7-13~~/7 with steps 18/13-13/12-8/7-13/12-13/12;		* 1–18/13–3/2–12/7–13/7 with steps 18/13, 13/12, 8/7, 13/12, 13/12;

	Finally, there is a palindromic hexad,		Finally, there is a palindromic hexad,
	* ~~1-13~~/~~12-7~~/~~6-3~~/~~2-13~~/~~8-7~~/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7.		* 1–13/12–7/6–3/2–13/8–7/4 with steps 13/12, 13/12, 9/7, 13/12, 13/12, 8/7.

	Equal temperaments with buzurgismic chords include {{Optimal ET sequence\|7, 9, 10, 17, 19, 26, 27, 36, 46, 53, 63 and 72}}.		Equal temperaments with buzurgismic chords include {{Optimal ET sequence\|7, 9, 10, 17, 19, 26, 27, 36, 46, 53, 63 and 72}}.

	[[Category:13-odd-limit]]		[[Category:13-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

Xenllium at 13:48, 1 November 2023

2023-11-01T13:48:53Z

FloraC: Expand

2023-09-09T12:44:04Z

Expand

← Older revision		Revision as of 12:44, 9 September 2023
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	'''Buzurgismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].		'''Buzurgismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].

	The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has 2 triads and ~~6 tetrads~~ in ~~the [[13-odd-limit]] of~~ the 2.3.7.13 subgroup~~, but these all become essentially just in the~~ [[21-odd-limit]].		The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]].

	The two buzurgismic triads are in inverse relationship:		The two buzurgismic triads are in inverse relationship:
	* 1-16/13~~-12~~/7 with steps ~~of 16~~/13-18/13-7/6;		* 1-7/6-13/8 with steps 7/6-18/13-16/13;
	* 1-7/6-13/8 with steps of 7/6~~-18/13~~-16/13.		* 1-18/13-13/8 with steps 18/13-7/6-16/13.

	For tetrads, there are ~~two~~ palindromic chords and ~~two~~ pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are
	* 1-16/13-18/13-12/7 with steps ~~of 16/13-~~9/8-16/13-7/6;		* 1-9/8-18/13-13/8 with steps 9/8-16/13-7/6-16/13;
	* 1-3/2-13/8-13/7 with steps of 3/2-13/12-8/7-13/12.		* 1-3/2-13/8-13/7 with steps 3/2-13/12-8/7-13/12;
			* 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-18/13-3/2-13/8 with steps of 18/13-13/12-13/12-16/13 and 1-13/12-3/2-13/7 with steps of 13/12-18/13-16/13-13/12;		* 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse
	* 1-7/6-3/2-13/8 with steps of 7/6-9/7-13/12-16/13 and 1-9/7-3/2-13/7 with steps of 9/7-7/6-16/13-13/12.		* 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12;
			* 1-13/12-3/2-7/4 with steps 13/12-18/13-7/6-8/7, and its inverse
			* 1-18/13-3/2-12/7 with steps 18/13-13/12-8/7-7/6;
			* 1-7/6-3/2-13/8 with steps 7/6-9/7-13/12-16/13, and its inverse
			* 1-9/7-3/2-13/7 with steps 9/7-7/6-16/13-13/12.

			For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
			* 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13.

			The inversely related pairs of chords are
			* 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse
			* 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12;
			* 1-13/12-7/6-3/2-7/4 with steps 13/12-13/12-9/7-7/6-8/7, and its inverse
			* 1-9/7-18/13-3/2-12/7 with steps 9/7-13/12-13/12-8/7-7/6;
			* 1-13/12-3/2-13/8-7/4 with steps 13/12-18/13-13/12-13/12-8/7, and its inverse
			* 1-18/13-3/2-12/7-13/7 with steps 18/13-13/12-8/7-13/12-13/12;

			Finally, there is a palindromic hexad,
			* 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7.

	[[Category:13-odd-limit]]		[[Category:13-odd-limit]]
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	[[Category:Triads]]		[[Category:Triads]]
	[[Category:Tetrads]]		[[Category:Tetrads]]
			[[Category:Pentads]]
			[[Category:Hexads]]
	[[Category:Buzurgismic]]		[[Category:Buzurgismic]]

FloraC: Recategorize

2023-05-23T11:35:39Z

Recategorize

← Older revision		Revision as of 11:35, 23 May 2023
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	[[Category:13-odd-limit]]		[[Category:13-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:Buzurgismic]]		[[Category:Buzurgismic]]

FloraC: +categories

2023-04-28T15:15:11Z

+categories

← Older revision		Revision as of 15:15, 28 April 2023
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	* 1-7/6-3/2-13/8 with steps of 7/6-9/7-13/12-16/13 and 1-9/7-3/2-13/7 with steps of 9/7-7/6-16/13-13/12.		* 1-7/6-3/2-13/8 with steps of 7/6-9/7-13/12-16/13 and 1-9/7-3/2-13/7 with steps of 9/7-7/6-16/13-13/12.

			[[Category:13-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triad]]		[[Category:Triad]]
	[[Category:Tetrad]]		[[Category:Tetrad]]
	[[Category:Buzurgismic]]		[[Category:Buzurgismic]]

FloraC at 07:30, 23 February 2023

2023-02-23T07:30:59Z

← Older revision		Revision as of 07:30, 23 February 2023
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	'''Buzurgismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].		'''Buzurgismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].

	The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has 2 triads and 6 tetrads in the [[13-odd-limit]] of the 2.3.7.13 subgroup, but all ~~of these~~ become essentially just in the [[21-odd-limit]].		The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has 2 triads and 6 tetrads in the [[13-odd-limit]] of the 2.3.7.13 subgroup, but these all become essentially just in the [[21-odd-limit]].

	The two buzurgismic triads are in inverse relationship:		The two buzurgismic triads are in inverse relationship:
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	* 1-7/6-13/8 with steps of 7/6-18/13-16/13.		* 1-7/6-13/8 with steps of 7/6-18/13-16/13.

	For tetrads, there are two palindromic chords and ~~three~~ pairs of chords in inverse relationship. The palindromic chords are		For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
	* 1-16/13-18/13-12/7 with steps of 16/13-9/8-16/13-7/6;		* 1-16/13-18/13-12/7 with steps of 16/13-9/8-16/13-7/6;
	* 1-3/2-13/8-13/7 with steps of 3/2-13/12-8/7-13/12.		* 1-3/2-13/8-13/7 with steps of 3/2-13/12-8/7-13/12.
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	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	~~[[Category:Dyadic]]~~
	[[Category:Triad]]		[[Category:Triad]]
	[[Category:Tetrad]]		[[Category:Tetrad]]
	[[Category:Buzurgismic]]		[[Category:Buzurgismic]]

FloraC: Created page with "'''Buzurgismic chords''' are essentially tempered dyadic chords tempered by the buzurgisma, 169/168. The buzurgismic temperament is very comparable t..."

2023-01-11T14:45:47Z

Created page with "'''Buzurgismic chords''' are essentially tempered dyadic chords tempered by the buzurgisma, 169/168. The buzurgismic temperament is very comparable t..."

New page

'''Buzurgismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].

The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has 2 triads and 6 tetrads in the [[13-odd-limit]] of the 2.3.7.13 subgroup, but all of these become essentially just in the [[21-odd-limit]].

The two buzurgismic triads are in inverse relationship:
* 1-16/13-12/7 with steps of 16/13-18/13-7/6;
* 1-7/6-13/8 with steps of 7/6-18/13-16/13.

For tetrads, there are two palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are
* 1-16/13-18/13-12/7 with steps of 16/13-9/8-16/13-7/6;
* 1-3/2-13/8-13/7 with steps of 3/2-13/12-8/7-13/12.

The inversely related pairs of chords are
* 1-18/13-3/2-13/8 with steps of 18/13-13/12-13/12-16/13 and 1-13/12-3/2-13/7 with steps of 13/12-18/13-16/13-13/12;
* 1-7/6-3/2-13/8 with steps of 7/6-9/7-13/12-16/13 and 1-9/7-3/2-13/7 with steps of 9/7-7/6-16/13-13/12.

[[Category:Essentially tempered chords]]
[[Category:Dyadic]]
[[Category:Triad]]
[[Category:Tetrad]]
[[Category:Buzurgismic]]

← Older revision		Revision as of 13:48, 1 November 2023
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	'''Buzurgismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].		'''Buzurgismic chords''' are [[Dyadic chord\|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].

	The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]].		The [[buzurgismic]] temperament is very comparable to the [[Biyatismic temperaments\|biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]].

	The two buzurgismic triads are in inverse relationship:		The two buzurgismic triads are in inverse relationship:
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	* 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3.		* 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse		* 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse
	* 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12;		* 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12;
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	* 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13.		* 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13.

	The inversely related pairs of chords are		The inversely related pairs of chords are
	* 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse		* 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse
	* 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12;		* 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12;
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	Finally, there is a palindromic hexad,		Finally, there is a palindromic hexad,
	* 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7.		* 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7.

			Equal temperaments with buzurgismic chords include {{Optimal ET sequence\|7, 9, 10, 17, 19, 26, 27, 36, 46, 53, 63 and 72}}.

	[[Category:13-odd-limit]]		[[Category:13-odd-limit]]