Marveltwin chords - Revision history

FloraC: Correction by improving wording

2025-03-19T14:05:16Z

Correction by improving wording

← Older revision		Revision as of 14:05, 19 March 2025
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	There are 6 triads, 18 tetrads, 14 pentads and 3 hexads as 2.3.5.13 subgroup [[13-odd-limit]] essentially tempered chords.		There are 6 triads, 18 tetrads, 14 pentads and 3 hexads as 2.3.5.13 subgroup [[13-odd-limit]] essentially tempered chords.

	One marveltwin triad ~~consists of~~ a stack of two [[6/5]] minor thirds ~~followed by [[18/13]]~~, that is,		One marveltwin triad is a palindrome since it identifies [[13/9]] by a stack of two [[6/5]] minor thirds, that is,
	* 1–6/~~5–[[13~~/9]] with steps of 6/5, 6/5, 18/13.		* 1–6/5–13/9 with steps of 6/5, 6/5, [[18/13]].

	It makes for an instructive comparison with the septimal diminished triad, 1–6/5–[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.		It makes for an instructive comparison with the septimal diminished triad, 1–6/5–[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.

	Another triad consists of a stack of two [[10/9]] whole tones ~~followed by a [[16/13]]~~, that is,		Another palindromic triad consists of [[16/13]] found as a stack of two [[10/9]] whole tones, that is,
	* 1–10/9–16/13 with steps of 10/9, 10/9, [[13/8]],		* 1–10/9–16/13 with steps of 10/9, 10/9, [[13/8]].

	~~as well as~~ those built by		We also have those built by
	* 1–[[5/4]]–18/13 with steps of 5/4, 10/9, 13/9, and its inverse		* 1–[[5/4]]–18/13 with steps of 5/4, 10/9, 13/9, and its inverse
	* 1–10/9–18/13 with steps of 10/9, 5/4, 13/9;		* 1–10/9–18/13 with steps of 10/9, 5/4, 13/9;

FloraC: Cleanup

2025-03-19T14:00:48Z

Cleanup

Show changes

Xenllium at 14:51, 25 November 2023

2023-11-25T14:51:52Z

← Older revision		Revision as of 14:51, 25 November 2023
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	* 1-9/8-5/4-3/2-13/8-9/5 with steps of 9/8-10/9-6/5-13/12-10/9-10/9.		* 1-9/8-5/4-3/2-13/8-9/5 with steps of 9/8-10/9-6/5-13/12-10/9-10/9.

	Equal temperaments with marveltwin ~~triads~~ include {{Optimal ET sequence\| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}, with 333edo giving the [[optimal patent val]].		Equal temperaments with marveltwin chords include {{Optimal ET sequence\| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}, with 333edo giving the [[optimal patent val]].

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

Xenllium: Update the article

2023-11-04T04:41:40Z

Update the article

← Older revision		Revision as of 04:41, 4 November 2023
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	A '''~~marveltwin chord~~''' ~~is a [[13-odd-limit]]~~ [[essentially tempered ~~dyadic chord~~]] tempered by the marveltwin comma, [[325/324]].		'''Marveltwin chords''' are [[Dyadic chord\|essentially tempered chords]] tempered by the marveltwin comma, [[325/324]].

			There are 6 triads, 18 tetrads, 14 pentads and 3 hexads as 2.3.5.13 subgroup [[13-odd-limit]] essentially tempered chords.

	One marveltwin triad consists of a stack of two [[6/5]] minor thirds followed by an [[18/13]], that is,		One marveltwin triad consists of a stack of two [[6/5]] minor thirds followed by an [[18/13]], that is,
	* 1-6/5-[[13/9]] with steps 6/5-6/5-18/13,		* 1-6/5-[[13/9]] with steps of 6/5-6/5-18/13.

	It makes for an instructive comparison with the septimal diminished triad, 1-6/5-[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.		It makes for an instructive comparison with the septimal diminished triad, 1-6/5-[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.

	Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,		Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,
	* 1-10/9-16/13 with steps 10/9-10/9-[[13/8]],		* 1-10/9-16/13 with steps of 10/9-10/9-[[13/8]],

			as well as those built by
			* 1-[[5/4]]-18/13 with steps of 5/4-10/9-13/9, and its inverse
			* 1-10/9-18/13 with steps of 10/9-5/4-13/9;
			* 1-[[5/3]]-[[24/13]] with steps of 5/3-10/9-[[13/12]], and its inverse
			* 1-10/9-24/13 with steps of 10/9-5/3-13/12.

			For tetrads, there are four palindromic chords and seven pairs of chords in inverse relationship. The palindromic chords are
			* 1-10/9-18/13-20/13 with steps of 10/9-5/4-10/9-13/10;
			* 1-10/9-5/4-18/13 with steps of 10/9-9/8-10/9-13/9;
			* 1-10/9-6/5-4/3 with steps of 10/9-13/12-10/9-3/2;
			* 1-13/12-6/5-13/10 with steps of 13/12-10/9-13/12-20/13.

	~~as well as those built by~~		The inversely related pairs of chords are
	* 1-[[5/4]]-18/13 with steps 5/4-10/9-13/9, and its inverse		* 1-18/13-3/2-5/3 with steps of 18/13-13/12-10/9-6/5, and its inverse
	* 1-10/9-18/13 with steps 10/9-5/4-13/9.		* 1-13/12-3/2-9/5 with steps of 13/12-18/13-6/5-10/9;
	* 1-[[5/~~3]]~~-~~[[24~~/13]], with steps 5/3-10/9-[[13/~~12]]~~, and its inverse		* 1-5/4-3/2-9/5 with steps of 5/4-6/5-6/5-10/9, and its inverse
	* 1-10/9-24/13 with steps 10/9-5/3-13/12.		* 1-6/5-3/2-5/3 with steps of 6/5-5/4-10/9-6/5;
			* 1-5/4-18/13-3/2 with steps of 5/4-10/9-13/12-4/3, and its inverse
			* 1-13/12-6/5-3/2 with steps of 13/12-10/9-5/4-4/3;
			* 1-10/9-16/13-4/3 with steps of 10/9-10/9-13/12-3/2, and its inverse
			* 1-13/12-6/5-4/3 with steps of 13/12-10/9-10/9-3/2;
			* 1-5/4-18/13-20/13 with steps of 5/4-10/9-10/9-13/10, and its inverse
			* 1-10/9-16/13-20/13 with steps of 10/9-10/9-5/4-13/10;
			* 1-6/5-13/10-13/9 with steps of 6/5-13/12-10/9-18/13, and its inverse
			* 1-10/9-6/5-13/9 with steps of 10/9-13/12-6/5-18/13;
			* 1-9/8-5/4-18/13 with steps of 9/8-10/9-10/9-13/9, and its inverse
			* 1-10/9-16/13-18/13 with steps of 10/9-10/9-9/8-13/9.

	~~Each~~ of ~~these has multiple ways to extend to tetrads, such as using the [[3/2\|perfect fifth]] as an anchor:~~		For pentads, there are two palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
	* 1-5/4-18/13-~~[[3~~/~~2]]~~ with steps 5/4-10/9-13/~~12-[[4/3]], and its inverse~~		* 1-9/8-5/4-3/2-9/5 with steps of 9/8-10/9-6/5-6/5-10/9;
	* 1-13/12-6/5~~-3/2 with steps 13/12~~-10/9~~-5/4-4/3.~~		* 1-13/12-3/2-13/8-9/5 with steps of 13/12-18/13-13/12-10/9-10/9.
	* 1~~-3/2-5/3-24/13 with steps 3/2-10/9-10/9~~-13/12~~, and its inverse~~
	* 1-3/2-13/8-9/5 with steps 3/2-13/12-10/9-10/9.

	~~A palindrome exists as~~		The inversely related pairs of chords are
	* 1-3/2-5/3-9/5 with steps 3/2-10/9-13/12-10/9.		* 1-18/13-3/2-5/3-9/5 with steps of 18/13-13/12-10/9-13/12-10/9, and its inverse
			* 1-13/12-3/2-5/3-9/5 with steps of 13/12-18/13-10/9-13/12-10/9;
			* 1-5/4-3/2-5/3-9/5 with steps of 5/4-6/5-10/9-13/12-10/9, and its inverse
			* 1-6/5-3/2-5/3-9/5 with steps of 6/5-5/4-10/9-13/12-10/9;
			* 1-5/4-3/2-13/8-9/5 with steps of 5/4-6/5-13/12-10/9-10/9, and its inverse
			* 1-6/5-3/2-5/3-24/13 with steps of 6/5-5/4-10/9-10/9-13/12;
			* 1-5/4-18/13-3/2-9/5 with steps of 5/4-10/9-13/12-6/5-10/9, and its inverse
			* 1-13/12-6/5-3/2-5/3 with steps of 13/12-10/9-5/4-10/9-6/5;
			* 1-9/8-5/4-18/13-3/2 with steps of 9/8-10/9-10/9-13/12-4/3, and its inverse
			* 1-13/12-6/5-4/3-3/2 with steps of 13/12-10/9-10/9-9/8-4/3;
			* 1-9/8-5/4-13/8-9/5 with steps of 9/8-10/9-13/10-10/9-10/9, and its inverse
			* 1-9/8-5/4-18/13-9/5 with steps of 9/8-10/9-10/9-13/10-10/9.

	~~In the 15-odd-limit we may have~~		For hexads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is
	* 1-6/5-13/9~~-[[26~~/~~15]]~~ with steps 6/5-6/5-6/5-~~[[15~~/13]].		* 1-5/4-18/13-3/2-5/3-9/5 with steps of 5/4-10/9-13/12-10/9-13/12-10/9.

	The ~~marveltwin tonestack~~ is ~~a hexad where each interval belongs to the 13-odd-limit consonance set:~~		The inversely related pair of chords is
	* 1-9/8-5/4-3/2-13/8-9/5, with steps 9/8-10/9-6/5-13/12-10/9-10/9, its inverse ~~being~~		* 1-6/5-4/3-3/2-5/3-24/13 with steps of 6/5-10/9-9/8-10/9-10/9-13/12, and its inverse
	* 1-6/5-4/3-3/2-8/5~~-24/13,~~ with steps 6/5-10/9-9/8-10/9-10/9~~-13/12~~.		* 1-9/8-5/4-3/2-13/8-9/5 with steps of 9/8-10/9-6/5-13/12-10/9-10/9.

	Equal temperaments with marveltwin triads include {{~~EDOs~~\| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}, with 333edo giving the [[optimal patent val]].		Equal temperaments with marveltwin triads include {{Optimal ET sequence\| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}, with 333edo giving the [[optimal patent val]].

	[[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:Hexads]]
	[[Category:Marveltwin]]		[[Category:Marveltwin]]

FloraC: Recategorize

2023-05-23T11:41:39Z

Recategorize

← Older revision		Revision as of 11:41, 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:~~Hexad~~]]		[[Category:Hexads]]
	[[Category:Marveltwin]]		[[Category:Marveltwin]]

FloraC: Expansion

2023-04-29T05:55:57Z

Expansion

← Older revision		Revision as of 05:55, 29 April 2023
Line 2:		Line 2:

	One marveltwin triad consists of a stack of two [[6/5]] minor thirds followed by an [[18/13]], that is,		One marveltwin triad consists of a stack of two [[6/5]] minor thirds followed by an [[18/13]], that is,
	* 1-6/5-[[13/9]], with steps 6/5-6/5-18/13,		* 1-6/5-[[13/9]] with steps 6/5-6/5-18/13,

	It makes for an instructive comparison with the septimal diminished triad, 1-6/5-[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.		It makes for an instructive comparison with the septimal diminished triad, 1-6/5-[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.

	Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,		Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,
	* 1-10/9-16/13, with steps 10/9-10/9-[[13/8]],		* 1-10/9-16/13 with steps 10/9-10/9-[[13/8]],

	as well as ~~one~~ built by		as well as those built by
	* 1-[[5/4]]-18/13, with steps 5/4-10/9-13/9, and its inverse		* 1-[[5/4]]-18/13 with steps 5/4-10/9-13/9, and its inverse
	* 1-10/9-18/13, with steps 10/9-5/4-13/9.		* 1-10/9-18/13 with steps 10/9-5/4-13/9.
			* 1-[[5/3]]-[[24/13]], with steps 5/3-10/9-[[13/12]], and its inverse
			* 1-10/9-24/13 with steps 10/9-5/3-13/12.

	Each of these has multiple ways to extend to tetrads~~. For example~~,		Each of these has multiple ways to extend to tetrads, such as using the [[3/2\|perfect fifth]] as an anchor:
	* 1-[[3/2]]-[[5/3]]-[[24/13]] with steps 3/2-10/9-10/9-[[13/12]], and its inverse		* 1-5/4-18/13-[[3/2]] with steps 5/4-10/9-13/12-[[4/3]], and its inverse
			* 1-13/12-6/5-3/2 with steps 13/12-10/9-5/4-4/3.
			* 1-3/2-5/3-24/13 with steps 3/2-10/9-10/9-13/12, and its inverse
	* 1-3/2-13/8-9/5 with steps 3/2-13/12-10/9-10/9.		* 1-3/2-13/8-9/5 with steps 3/2-13/12-10/9-10/9.

FloraC: Expansion

2023-04-29T05:42:52Z

Expansion

← Older revision		Revision as of 05:42, 29 April 2023
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	A '''marveltwin chord''' is a [[13-odd-limit]] [[essentially tempered dyadic chord]] tempered by [[325/324]]~~, the marveltwin comma~~.		A '''marveltwin chord''' is a [[13-odd-limit]] [[essentially tempered dyadic chord]] tempered by the marveltwin comma, [[325/324]].

	One marveltwin triad consists of a stack of two [[6/5]] minor thirds followed by an [[18/13]], that is,		One marveltwin triad consists of a stack of two [[6/5]] minor thirds followed by an [[18/13]], that is,
	* 1-6/5-[[13/9]], with steps 6/5-6/5-18/13,		* 1-6/5-[[13/9]], with steps 6/5-6/5-18/13,

	~~in a temperament tempering out the marveltwin comma.~~		It makes for an instructive comparison with the septimal diminished triad, 1-6/5-[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.

	It makes for an instructive comparison with the septimal diminished triad, 1-6/5-[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad~~. It can be extended to the marveltwin tetrad,~~

	* 1-6/5-13/9-[[26/15]] with steps 6/5-6/5-6/5-[[15/13]],

	~~which is a [[15-odd-limit]] essentially tempered dyadic chord~~.

	Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,		Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,
Line 16:		Line 10:

	as well as one built by		as well as one built by
	* 1-10/9-18/13, with steps 10/9-5/4-13/9		* 1-[[5/4]]-18/13, with steps 5/4-10/9-13/9, and its inverse
			* 1-10/9-18/13, with steps 10/9-5/4-13/9.

			Each of these has multiple ways to extend to tetrads. For example,
			* 1-[[3/2]]-[[5/3]]-[[24/13]] with steps 3/2-10/9-10/9-[[13/12]], and its inverse
			* 1-3/2-13/8-9/5 with steps 3/2-13/12-10/9-10/9.

			A palindrome exists as
			* 1-3/2-5/3-9/5 with steps 3/2-10/9-13/12-10/9.

	~~and its inversion. Each of these has multiple ways to extend to tetrads~~.		In the 15-odd-limit we may have
			* 1-6/5-13/9-[[26/15]] with steps 6/5-6/5-6/5-[[15/13]].

	The marveltwin tonestack is a hexad where each interval belongs to the 13-odd-limit consonance set:		The marveltwin tonestack is a hexad where each interval belongs to the 13-odd-limit consonance set:
	* 1-[[9/8]]-[[5/4]]-[[3/2]]-[[13/8]]-[[9/5]], with steps 9/8-10/9-6/5-13/12-10/9-10/9,		* 1-9/8-5/4-3/2-13/8-9/5, with steps 9/8-10/9-6/5-13/12-10/9-10/9, its inverse being
			* 1-6/5-4/3-3/2-8/5-24/13, with steps 6/5-10/9-9/8-10/9-10/9-13/12.

	Equal temperaments with marveltwin triads include {{EDOs\| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}.		Equal temperaments with marveltwin triads include {{EDOs\| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}, with 333edo giving the [[optimal patent val]].

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

FloraC: Expansion

2021-12-30T20:12:20Z

Expansion

← Older revision		Revision as of 20:12, 30 December 2021
Line 13:		Line 13:

	Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,		Another triad consists of a stack of two [[10/9]] whole tones followed by a [[16/13]], that is,
	* 1-10/9-16/13, with steps 10/9-10/9-[[13/8]].		* 1-10/9-16/13, with steps 10/9-10/9-[[13/8]],

			as well as one built by
			* 1-10/9-18/13, with steps 10/9-5/4-13/9

			and its inversion. Each of these has multiple ways to extend to tetrads.

	The marveltwin tonestack is a hexad where each interval belongs to the 13-odd-limit consonance set:		The marveltwin tonestack is a hexad where each interval belongs to the 13-odd-limit consonance set:

FloraC: FloraC moved page Marveltwin triad to Marveltwin chords: It has triads as well as tetrads

2021-12-30T19:59:16Z

FloraC moved page Marveltwin triad to Marveltwin chords: It has triads as well as tetrads

← Older revision	Revision as of 19:59, 30 December 2021
(No difference)

FloraC: Expansion

2021-12-30T19:56:26Z

Expansion

@@ Line 1: / Line 1: @@
-The marveltwin triad is a 13-limit [[Dyadic_chord|essentially tempered dyadic chord]] which consists of two stacked minor thirds followed by an [[18/13]], that is, a [[6/5]]-[[6/5]]-18/13 chord, tempered in [[marveltwin]]. In other words, an 1-6/5-[[13/9]] chord tempered in a temperament tempering out [[325/324]], the marveltwin comma. It makes for an instructive comparison with the septimal diminished triad, 1-6/5-[[10/7]] in starling, and might also be called a tridecimal diminished triad. It can be extended to the marveltwin tetrad, 1-6/5-13/9-[[26/15]] in marveltwin, which is a 15-limit essentially tempered dyadic chord with steps 6/5-6/5-6/5-[[15/13]]. Another marveltwin chord of interest is the marveltwin tonestack: 1-[[9/8]]-[[5/4]]-[[3/2]]-[[13/8]]-[[9/5]] tempered in marveltwin. Equal temperaments with marveltwin triads include {{EDOs|19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333}}.
+A '''marveltwin chord''' is a [[13-odd-limit]] [[essentially tempered dyadic chord]] tempered by [[325/324]], the marveltwin comma.
-[[Category:13-limit]]
+One marveltwin triad consists of a stack of two [[6/5]] minor thirds followed by an [[18/13]], that is,
 [[Category:Marveltwin]]