Sextantonismic chords - Revision history

FloraC: Cleanup

2025-12-06T09:19:44Z

Cleanup

← Older revision		Revision as of 09:19, 6 December 2025
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	'''Sextantonismic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the sextantonisma, [[2601/2600]].		'''Sextantonismic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the sextantonisma, [[2601/2600]].

	Sextantonismic chords are of [[~~Dyadic~~ chord/Pattern of essentially tempered chords\|pattern 1b]] in the 2.3.5.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.		Sextantonismic chords are of [[dyadic chord/Pattern of essentially tempered chords\|pattern 1b]] in the 2.3.5.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

	The three sextantonismic triads include a palindrome since it identifies [[18/13]] by a stack of two [[20/17]]s:		The three sextantonismic triads include a palindrome since it identifies [[18/13]] by a stack of two [[20/17]]'s:
	* ~~1-20~~/~~17-18~~/13 with steps of 20/17-20/17-13/9.		* 1–20/17–18/13 with steps of 20/17, 20/17, 13/9.

	And an inversely related pair:		And an inversely related pair:
	* ~~1-20~~/~~17-17~~/13 with steps of 20/17-10/9-26/17, and its inverse		* 1–20/17–17/13 with steps of 20/17, 10/9, 26/17, and its inverse
	* ~~1-10~~/~~9-17~~/13 with steps of 10/9-20/17-26/17.		* 1–10/9–17/13 with steps of 10/9, 20/17, 26/17.

	They can be extended to the following palindromic tetrads:		They can be extended to the following palindromic tetrads:
	* ~~1-10~~/~~9-20~~/~~17-17~~/13 with steps of 10/9-18/17-10/9-26/17;		* 1–10/9–20/17–17/13 with steps of 10/9, 18/17, 10/9, 26/17;
	* ~~1-20~~/~~17-17~~/~~13-20~~/13 with steps of 20/17-10/9-20/17-13/10.		* 1–20/17–17/13–20/13 with steps of 20/17, 10/9, 20/17, 13/10.

	And inversely related tetrads:		And inversely related tetrads:
	* ~~1-20~~/~~17-17~~/~~13-18~~/13 with steps of 20/17-10/9-18/17-13/9, and its inverse		* 1–20/17–17/13–18/13 with steps of 20/17, 10/9, 18/17, 13/9, and its inverse
	* ~~1-18~~/~~17-20~~/~~17-18~~/13 with steps of 18/17-10/9-20/17-13/9;		* 1–18/17–20/17–18/13 with steps of 18/17, 10/9, 20/17, 13/9;
	* ~~1-20~~/~~17-18~~/~~13-20~~/13 with steps of 20/17-20/17-10/9-13/10, and its inverse		* 1–20/17–18/13–20/13 with steps of 20/17, 20/17, 10/9, 13/10, and its inverse
	* ~~1-20~~/~~17-18~~/~~13-9~~/5 with steps of 20/17-20/17-13/10-10/9.		* 1–20/17–18/13–9/5 with steps of 20/17, 20/17, 13/10, 10/9.

	Then there is an inversely related pair of pentads:		Then there is an inversely related pair of pentads:
	* ~~1-10~~/~~9-20~~/~~17-17~~/~~13-20~~/13 with steps of 10/9-18/17-10/9-20/17-13/10, and its inverse		* 1–10/9–20/17–17/13–20/13 with steps of 10/9, 18/17, 10/9, 20/17, 13/10, and its inverse
	* ~~1-10~~/~~9-20~~/~~17-17~~/~~13-17~~/10 with steps of 10/9-18/17-10/9-13/10-20/17.		* 1–10/9–20/17–17/13–17/10 with steps of 10/9, 18/17, 10/9, 13/10, 20/17.

	Equal temperaments with sextantonismic chords include {{Optimal ET sequence\| 34, 46, 60, 72, 77, 106, 111, 137, 140, 171, 183, 217, 243, 277, 354, 388, 460, 494 and 848 }}.		Equal temperaments with sextantonismic chords include {{Optimal ET sequence\| 34, 46, 60, 72, 77, 106, 111, 137, 140, 171, 183, 217, 243, 277, 354, 388, 460, 494 and 848 }}.

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

Xenllium at 04:38, 26 November 2023

2023-11-26T04:38:37Z

← Older revision		Revision as of 04:38, 26 November 2023
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	'''Sextantonismic chords''' are [[essentially tempered ~~dyadic chord~~]]s tempered by the sextantonisma, [[2601/2600]].		'''Sextantonismic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the sextantonisma, [[2601/2600]].

	Sextantonismic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 1b]] in the 2.3.5.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.		Sextantonismic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 1b]] in the 2.3.5.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

	The three sextantonismic triads include a palindrome since it identifies [[18/13]] by a stack of two [[20/17]]'s:		The three sextantonismic triads include a palindrome since it identifies [[18/13]] by a stack of two [[20/17]]s:
	* 1-20/17-18/13 with steps 20/17-20/17-13/9.		* 1-20/17-18/13 with steps of 20/17-20/17-13/9.

	And an inversely related pair:		And an inversely related pair:
	* 1-20/17-17/13 with steps 20/17-10/9-26/17, and its inverse		* 1-20/17-17/13 with steps of 20/17-10/9-26/17, and its inverse
	* 1-10/9-17/13 with steps 10/9-20/17-26/17.		* 1-10/9-17/13 with steps of 10/9-20/17-26/17.

	They can be extended to the following palindromic tetrads:		They can be extended to the following palindromic tetrads:
	* 1-10/9-20/17-17/13 with steps 10/9-18/17-10/9-26/17;		* 1-10/9-20/17-17/13 with steps of 10/9-18/17-10/9-26/17;
	* 1-20/17-17/13-20/13 with steps 20/17-10/9-20/17-13/10.		* 1-20/17-17/13-20/13 with steps of 20/17-10/9-20/17-13/10.

	And inversely related tetrads:		And inversely related tetrads:
	* 1-20/17-17/13-18/13 with steps 20/17-10/9-18/17-13/9, and its inverse		* 1-20/17-17/13-18/13 with steps of 20/17-10/9-18/17-13/9, and its inverse
	* 1-18/17-20/17-18/13 with steps 18/17-10/9-20/17-13/9;		* 1-18/17-20/17-18/13 with steps of 18/17-10/9-20/17-13/9;
	* 1-20/17-18/13-20/13 with steps 20/17-20/17-10/9-13/10, and its inverse		* 1-20/17-18/13-20/13 with steps of 20/17-20/17-10/9-13/10, and its inverse
	* 1-20/17-18/13-9/5 with steps 20/17-20/17-13/10-10/9.		* 1-20/17-18/13-9/5 with steps of 20/17-20/17-13/10-10/9.

	Then there is an inversely related pair of pentads:		Then there is an inversely related pair of pentads:
	* 1-10/9-20/17-17/13-20/13 with steps 10/9-18/17-10/9-20/17-13/10, and its inverse		* 1-10/9-20/17-17/13-20/13 with steps of 10/9-18/17-10/9-20/17-13/10, and its inverse
	* 1-10/9-20/17-17/13-17/10 with steps 10/9-18/17-10/9-13/10-20/17.		* 1-10/9-20/17-17/13-17/10 with steps of 10/9-18/17-10/9-13/10-20/17.

			Equal temperaments with sextantonismic chords include {{Optimal ET sequence\| 34, 46, 60, 72, 77, 106, 111, 137, 140, 171, 183, 217, 243, 277, 354, 388, 460, 494 and 848 }}.

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

FloraC: +pattern of chords

2023-07-27T05:09:24Z

+pattern of chords

← Older revision		Revision as of 05:09, 27 July 2023
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	'''Sextantonismic chords''' are [[essentially tempered dyadic chord]]s tempered by the sextantonisma, [[2601/2600]].		'''Sextantonismic chords''' are [[essentially tempered dyadic chord]]s tempered by the sextantonisma, [[2601/2600]].

	~~There~~ are ~~three sextantonismic triads~~ in the 2.3.5.13.17 subgroup 17-odd-limit, ~~including~~ a ~~palindromic one~~ since it identifies [[18/13]] by a stack of two [[20/17]]'s:		Sextantonismic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 1b]] in the 2.3.5.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

			The three sextantonismic triads include a palindrome since it identifies [[18/13]] by a stack of two [[20/17]]'s:
	* 1-20/17-18/13 with steps 20/17-20/17-13/9.		* 1-20/17-18/13 with steps 20/17-20/17-13/9.

Line 18:		Line 20:
	* 1-20/17-18/13-9/5 with steps 20/17-20/17-13/10-10/9.		* 1-20/17-18/13-9/5 with steps 20/17-20/17-13/10-10/9.

	Then there ~~are two~~ inversely related pentads:		Then there is an inversely related pair of pentads:
	* 1-10/9-20/17-17/13-20/13 with steps 10/9-18/17-10/9-20/17-13/10, and its inverse		* 1-10/9-20/17-17/13-20/13 with steps 10/9-18/17-10/9-20/17-13/10, and its inverse
	* 1-10/9-20/17-17/13-17/10 with steps 10/9-18/17-10/9-13/10-20/17.		* 1-10/9-20/17-17/13-17/10 with steps 10/9-18/17-10/9-13/10-20/17.

FloraC: Recategorize

2023-05-23T11:49:08Z

Recategorize

← Older revision		Revision as of 11:49, 23 May 2023
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	[[Category:17-odd-limit]]		[[Category:17-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
			[[Category:Triads]]
			[[Category:Tetrads]]
			[[Category:Pentads]]
	[[Category:Sextantonismic]]		[[Category:Sextantonismic]]

FloraC: Created page with "'''Sextantonismic chords''' are essentially tempered dyadic chords tempered by the sextantonisma, 2601/2600. There are three sextantonismic triads in the 2.3.5.13.17..."

2023-02-23T13:24:55Z

Created page with "'''Sextantonismic chords''' are essentially tempered dyadic chords tempered by the sextantonisma, 2601/2600. There are three sextantonismic triads in the 2.3.5.13.17..."

New page

'''Sextantonismic chords''' are [[essentially tempered dyadic chord]]s tempered by the sextantonisma, [[2601/2600]].

There are three sextantonismic triads in the 2.3.5.13.17 subgroup 17-odd-limit, including a palindromic one since it identifies [[18/13]] by a stack of two [[20/17]]'s:
* 1-20/17-18/13 with steps 20/17-20/17-13/9.

And an inversely related pair:
* 1-20/17-17/13 with steps 20/17-10/9-26/17, and its inverse
* 1-10/9-17/13 with steps 10/9-20/17-26/17.

They can be extended to the following palindromic tetrads:
* 1-10/9-20/17-17/13 with steps 10/9-18/17-10/9-26/17;
* 1-20/17-17/13-20/13 with steps 20/17-10/9-20/17-13/10.

And inversely related tetrads:
* 1-20/17-17/13-18/13 with steps 20/17-10/9-18/17-13/9, and its inverse
* 1-18/17-20/17-18/13 with steps 18/17-10/9-20/17-13/9;
* 1-20/17-18/13-20/13 with steps 20/17-20/17-10/9-13/10, and its inverse
* 1-20/17-18/13-9/5 with steps 20/17-20/17-13/10-10/9.

Then there are two inversely related pentads:
* 1-10/9-20/17-17/13-20/13 with steps 10/9-18/17-10/9-20/17-13/10, and its inverse
* 1-10/9-20/17-17/13-17/10 with steps 10/9-18/17-10/9-13/10-20/17.

[[Category:17-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Sextantonismic]]