Valinorsmic chords - Revision history

FloraC: Improve readability; recategorize

2024-10-10T09:20:00Z

Improve readability; recategorize

← Older revision		Revision as of 09:20, 10 October 2024
Line 4:		Line 4:

	There are three valinorsmic triads: the valinorsmic version of the augmented triad,		There are three valinorsmic triads: the valinorsmic version of the augmented triad,
	* ~~1-5~~/~~4-8~~/5 with steps 5/4-14/11-5/4,		* 1–5/4–8/5 with steps 5/4, 14/11, 5/4,

	and an inversely related pair,		and an inversely related pair,
	* ~~1-8~~/~~5-7~~/4 with steps 8/5-11/10-8/7, and its inverse		* 1–8/5–7/4 with steps 8/5, 11/10, 8/7, and its inverse
	* ~~1-8~~/~~7-5~~/4 with steps 8/7-11/10-8/5.		* 1–8/7–5/4 with steps 8/7, 11/10, 8/5.

	Valinorsmic tetrads are six in number, consisting of two palindromic chords and ~~a pair of~~ pairs of inversely related chords. The palindromes are		Valinorsmic tetrads are six in number, consisting of two palindromic chords and two pairs of inversely related chords. The palindromes are
	* ~~1-11~~/~~10-5~~/~~4-7~~/4 with steps 11/10-8/7-7/5-8/7, and its inverse		* 1–11/10–5/4–7/4 with steps 11/10, 8/7, 7/5, 8/7, and its inverse
	* ~~1-11~~/~~10-5~~/~~4-11~~/8 with steps 11/10-8/7-11/10-16/11.		* 1–11/10–5/4–11/8 with steps 11/10, 8/7, 11/10, 16/11.

	The rest are		The rest are
	* ~~1-5~~/~~4-8~~/~~5-7~~/4 with steps 5/4-14/11-11/10-8/7, and its inverse		* 1–5/4–8/5–7/4 with steps 5/4, 14/11, 11/10, 8/7, and its inverse
	* ~~1-5~~/~~4-10~~/~~7-11~~/7 with steps 5/4-8/7-11/10-14/11;		* 1–5/4–10/7–11/7 with steps 5/4, 8/7, 11/10, 14/11;
	* ~~1-5~~/~~4-11~~/~~8-11~~/7 with steps 5/4-11/10-8/7-14/11, and its inverse		* 1–5/4–11/8–11/7 with steps 5/4, 11/10, 8/7, 14/11, and its inverse
	~~1-11~~/~~10-11~~/~~8-7~~/4 with steps 11/10-5/4-14/11-8/7.		* 1–11/10–11/8–7/4 with steps 11/10, 5/4, 14/11, 8/7.

	Finally, there are the two inversely related pentads,		Finally, there are the two inversely related pentads,
	* ~~1-11~~/~~10-5~~/~~4-8~~/~~5-7~~/4 with steps 11/10-8/7-14/11-11/10-8/7, and its inverse		* 1–11/10–5/4–8/5–7/4 with steps 11/10, 8/7, 14/11, 11/10, 8/7, and its inverse
	* ~~1-11~~/~~10-5~~/~~4-11~~/~~8-7~~/4 with steps 11/10-8/7-11/10-14/11-8/7.		* 1–11/10–5/4–11/8–7/4 with steps 11/10, 8/7, 11/10, 14/11, 8/7.

	If we are willing to go to the [[15-odd-limit]], we get four alternative, valinorsmic, temperings of the four [[keenanismic chords\|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to ~~1-11~~/~~9-22~~/~~15-5~~/3 chords.		If we are willing to go to the [[15-odd-limit]], we get four alternative, valinorsmic, temperings of the four [[keenanismic chords\|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9, 6/5, 8/7, 6/5, leading to 1–11/9–22/15–5/3 chords.

	Equal ~~temperaments~~ with valinorsmic chords include {{EDOs\| 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 }} with 111edo giving the [[optimal patent val]].		[[Equal temperament]]s with valinorsmic chords include {{EDOs\| 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 }} with 111edo giving the [[optimal patent val]].

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

FloraC: +pattern of chords

2023-08-08T12:44:48Z

+pattern of chords

← Older revision		Revision as of 12:44, 8 August 2023
Line 1:		Line 1:
	A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[essentially tempered chord]] in the 2.5.7.11 subgroup ~~in the~~ [[11-odd-limit]]. There are three valinorsmic triads: the valinorsmic version of the augmented triad,		A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[essentially tempered chord]].

			Valinorsmic chords are of [[Dyadic chord/Pattern of essentially tempered chords\|pattern 1a]] in the 2.5.7.11 [[subgroup]] [[11-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

			There are three valinorsmic triads: the valinorsmic version of the augmented triad,
	* 1-5/4-8/5 with steps 5/4-14/11-5/4,		* 1-5/4-8/5 with steps 5/4-14/11-5/4,

	and an inversely related pair,		and an inversely related pair,
	* 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5.		* 1-8/5-7/4 with steps 8/5-11/10-8/7, and its inverse
			* 1-8/7-5/4 with steps 8/7-11/10-8/5.

	Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are		Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are
	* 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and		* 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7, and its inverse
	* 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11.		* 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11.

	The rest are		The rest are
	* 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11~~, plus~~		* 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7, and its inverse
	* 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7.		* 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11;
			* 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11, and its inverse
			1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7.

	Finally, there are the two inversely related pentads,		Finally, there are the two inversely related pentads,
	* 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.		* 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7, and its inverse
			* 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.
	~~The count is triads: 3, tetrads: 6, pentads: 2; 11 in total~~.

	If we are willing to go to the [[15-odd-limit]], we get four alternative, valinorsmic, temperings of the four [[keenanismic chords\|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.		If we are willing to go to the [[15-odd-limit]], we get four alternative, valinorsmic, temperings of the four [[keenanismic chords\|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.

	Equal temperaments with valinorsmic chords include {{EDOs\| 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 }} with 111edo giving the optimal patent val.		Equal temperaments with valinorsmic chords include {{EDOs\| 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 }} with 111edo giving the [[optimal patent val]].

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

FloraC: Recategorize

2023-05-23T11:47:36Z

Recategorize

← Older revision		Revision as of 11:47, 23 May 2023
Line 24:		Line 24:
	[[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:Valinorsmic]]		[[Category:Valinorsmic]]

FloraC: Oops, there should be a newline

2022-02-05T03:50:13Z

Oops, there should be a newline

← Older revision		Revision as of 03:50, 5 February 2022
Line 6:		Line 6:

	Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are		Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are
	* 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11.		* 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and
			* 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11.

	The rest are		The rest are

FloraC: Categories

2022-02-05T03:02:42Z

FloraC: Improve readability

2022-02-05T03:02:22Z

Improve readability

← Older revision		Revision as of 03:02, 5 February 2022
Line 1:		Line 1:
	A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[~~Dyadic_chord\|~~essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.		A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[essentially tempered chord]] in the 2.5.7.11 subgroup in the [[11-odd-limit]]. There are three valinorsmic triads: the valinorsmic version of the augmented triad,
			* 1-5/4-8/5 with steps 5/4-14/11-5/4,

			and an inversely related pair,
			* 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5.

			Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are
			* 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11.

			The rest are
			* 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus
			* 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7.

			Finally, there are the two inversely related pentads,
			* 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.

	The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.		The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.

	If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four [[~~keenanismic_chords~~\|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.		If we are willing to go to the [[15-odd-limit]], we get four alternative, valinorsmic, temperings of the four [[keenanismic chords\|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.

	Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111~~, 268cd, 326cd and 437cd~~.		Equal temperaments with valinorsmic chords include {{EDOs\| 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 }} with 111edo giving the optimal patent val.

	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	~~[[Category:Chords]]~~
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
			[[Category:Triads]]
			[[Category:Tetrads]]
			[[Category:Pentads]]
	[[Category:Valinorsmic]]		[[Category:Valinorsmic]]

Xenwolf: +cat

2021-05-20T08:08:59Z

+cat

← Older revision		Revision as of 08:08, 20 May 2021
Line 7:		Line 7:
	Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.		Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.

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

Xenwolf: +cats

2021-05-20T07:03:06Z

+cats

← Older revision		Revision as of 07:03, 20 May 2021
Line 7:		Line 7:
	Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.		Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.

			[[Category:Chords]]
			[[Category:Essentially tempered chords]]
	[[Category:Valinorsmic]]		[[Category:Valinorsmic]]

Xenwolf: +cat, +link

2020-10-25T22:03:45Z

+cat, +link

← Older revision		Revision as of 22:03, 25 October 2020
Line 1:		Line 1:
	A ''valinorsmic chord'' is a valinorsma (176/175) tempered [[Dyadic_chord\|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.		A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[Dyadic_chord\|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.

	The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.		The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.
Line 6:		Line 6:

	Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.		Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.

			[[Category:Valinorsmic]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
Line 1:		Line 1:
	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		A ''valinorsmic chord'' is a valinorsma (176/175) tempered [[Dyadic_chord\|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:JosephRuhf\|JosephRuhf]] and made on <tt>2012-10-04 20:21:18 UTC</tt>.<br>~~
	~~: The original revision id was <tt>370396606</tt>.<br>~~
	~~: The revision comment was: <tt></tt><br>~~
	~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~
	~~<h4>Original Wikitext content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A //valinorsmic chord// is a valinorsma (176/175) tempered [[~~Dyadic chord~~\|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.

	The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.		The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.

	If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four [[~~keenanismic chords~~\|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.		If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four [[keenanismic_chords\|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.

	Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.~~</pre></div>~~		Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.
	~~<h4>Original HTML content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>valinorsmic chords</title></head><body>A <em>valinorsmic chord</em> is a valinorsma (176/175) tempered <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chord</a> in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.<br />
	~~<br />~~
	~~The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.<br />~~
	~~<br />~~
	If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four <a class="wiki_link" href="/keenanismic%20chords">keenanismic tetrads</a> which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.<br />
	~~<br />~~
	~~Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.</body></html></pre></div>~~

← Older revision		Revision as of 03:02, 5 February 2022
Line 23:		Line 23:
	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Triads~~]]		[[Category:Triad]]
	[[Category:~~Tetrads~~]]		[[Category:Tetrad]]
	[[Category:~~Pentads~~]]		[[Category:Pentad]]
	[[Category:Valinorsmic]]		[[Category:Valinorsmic]]