Rastmic chords - Revision history

FloraC: Adjust the rotation of certain chords to better contrast their inverses

2024-10-10T10:44:40Z

Adjust the rotation of certain chords to better contrast their inverses

← Older revision		Revision as of 10:44, 10 October 2024
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	* 1–12/11–11/9–3/2 with steps of 12/11, 9/8, 11/9, 4/3;		* 1–12/11–11/9–3/2 with steps of 12/11, 9/8, 11/9, 4/3;
	* 1–9/8–11/9–3/2 with steps of 9/8, 12/11, 11/9, 4/3, and its inverse		* 1–9/8–11/9–3/2 with steps of 9/8, 12/11, 11/9, 4/3, and its inverse
	* ~~1–9~~/~~8–3~~/~~2–11~~/6 with steps of 9/8, 4/3~~, 11/9, 12/11~~.		* 1–11/9–4/3–3/2 with steps of 11/9, 12/11, 9/8, 4/3.

	There are five rastmic pentads: the palindromic pentad,		There are five rastmic pentads: the palindromic pentad,
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	and two inversely related pairs of pentads,		and two inversely related pairs of pentads,
	* 1–9/8–11/8–3/2–11/6 with steps of 9/8, 11/9, 12/11, 11/9, 12/11, and its inverse		* 1–9/8–11/8–3/2–11/6 with steps of 9/8, 11/9, 12/11, 11/9, 12/11, and its inverse
	* ~~1–11~~/~~9–11~~/~~8–3~~/~~2–11~~/6 with steps of 11/9, 9/8, 12/11, 11/9~~, 12/11~~;		* 1–12/11–4/3–3/2–18/11 with steps of 12/11, 11/9, 9/8, 12/11, 11/9;
	* 1–9/8–11/9–11/8–3/2 with steps of 9/8, 12/11, 9/8, 12/11, 4/3, and its inverse		* 1–9/8–11/9–11/8–3/2 with steps of 9/8, 12/11, 9/8, 12/11, 4/3, and its inverse
	* ~~1–9~~/~~8–3~~/~~2–18~~/~~11–11~~/6 with steps of 9/8~~, 4/3~~, 12/11, 9/8, 12/11.		* 1–12/11–11/9–4/3–3/2 with steps of 12/11, 9/8, 12/11, 9/8, 4/3.

	There is also a unique rastmic hexad:		There is also a unique rastmic hexad:
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	\| 9/8, 12/11, 11/9, 4/3		\| 9/8, 12/11, 11/9, 4/3
	\|-		\|-
	\| ~~1–9~~/~~8–3~~/~~2–11~~/6		\| 1–11/9–4/3–3/2
	\| 9/8, 4/3~~, 11/9, 12/11~~		\| 11/9, 12/11, 9/8, 4/3
	\|-		\|-
	\| 1–9/8–11/9–3/2–11/6		\| 1–9/8–11/9–3/2–11/6
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	\| 9/8, 11/9, 12/11, 11/9, 12/11		\| 9/8, 11/9, 12/11, 11/9, 12/11
	\|-		\|-
	\| ~~1–11~~/~~9–11~~/~~8–3~~/~~2–11~~/6		\| 1–12/11–4/3–3/2–18/11
	\| 11/9, 9/8, 12/11, 11/9~~, 12/11~~		\| 12/11, 11/9, 9/8, 12/11, 11/9
	\|-		\|-
	\| 1–9/8–11/9–11/8–3/2		\| 1–9/8–11/9–11/8–3/2
	\| 9/8, 12/11, 9/8, 12/11, 4/3		\| 9/8, 12/11, 9/8, 12/11, 4/3
	\|-		\|-
	\| ~~1–9~~/~~8–3~~/~~2–18~~/~~11–11~~/6		\| 1–12/11–11/9–4/3–3/2
	\| 9/8~~, 4/3~~, 12/11, 9/8, 12/11		\| 12/11, 9/8, 12/11, 9/8, 4/3
	\|-		\|-
	\| 1–9/8–11/9–11/8–3/2–11/6		\| 1–9/8–11/9–11/8–3/2–11/6

FloraC: Improve readability; recategorize; update to contemporary terminology ("neutral" -> neutralized)

2024-10-10T09:34:11Z

Improve readability; recategorize; update to contemporary terminology ("neutral" -> neutralized)

Show changes

Xenllium: Update the article

2023-12-02T02:10:23Z

Update the article

← Older revision		Revision as of 02:10, 2 December 2023
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	A '''~~rastmic chord~~''' ~~is an~~ [[essentially tempered ~~dyadic chord~~]] tempered by the rastma, [[243/242]], in the 2.3.11 [[subgroup]] in the [[11-odd-limit]].		'''Rastmic chords''' are [[dyadic chord\|essentially tempered chords]] tempered by the rastma, [[243/242]], in the 2.3.11 [[subgroup]] in the [[11-odd-limit]].

	The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:		The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:

	* There are three ''rastmic triads'': ~~the classic neutral triad 1-11/9-3/2 with steps 11/9-11/9-4/3, and an inversely related pair of triads, 1-9/8-11/6 with steps 9/8-18/11-12/11 and 1-9/8-11/9 with steps 9/8-12/11-18/11.~~		There are three ''rastmic triads'':

	* ''Rastmic tetrads'' are seven in number: the ~~palindromic~~ classic [[neutral tetrad]] 1-11/9-3/2-11/6 with steps 11/9-11/9-11/9-12/11; the palindromic 1-3/2-18/11-11/6 with steps 3/2-12/11-9/8-12/11; the palindromic 1-9/8-11/9-11/8 with steps 9/8-12/11-9/8-16/11; the inverse pair 1-11/9-11/8-3/2 with steps 11/9-9/8-12/11-4/3 and 1-12/11-11/9-3/2 with steps 12/11-9/8-11/9-4/3; and the inverse pair 1~~-9/8~~-11/9-3/2 with steps ~~9/8-12/~~11~~-11/9-4~~/~~3 and 1-~~9~~/8-3/2~~-11/~~6 with steps~~ 9/8-4/3~~-11/9-12/11.~~		the classic neutral triad,
			* 1-11/9-3/2 with steps of 11/9-11/9-4/3,

	* ~~There are five ''rastmic pentads'': the palindromic pentad~~ 1-9/8~~-11/9-3/2~~-11/6 with steps 9/8-~~12/11-11/9-11/9-12/11; the pair 1-9/8-11/8-3/2-11/6 with steps 9/8-11/9-12/11-11/9-12/11 and 1-11/9-11/8-3~~/2-11~~/6 with steps 11/9-9/8~~-12/11~~-11/9-12/11;~~ and ~~the pair~~ 1-9/8-11/9~~-11/8-3/2~~ with steps 9/8-12/11~~-9/8-12/11-4/3 and 1-9/8-3/2~~-18~~/11-11/6 with steps 9/8-4/3-12/11-9/8-12~~/11.		and an inversely related pair of triads,
			* 1-9/8-11/6 with steps of 9/8-18/11-12/11 and 1-9/8-11/9 with steps of 9/8-12/11-18/11.

	* There is also a ''~~rastmic hexad~~'': 1-9/8-11/9-11/8-3/2-11/6, with steps 9/8-12/11-9/8-12/11-11/9-12/11. This can be extended to the neutral diatonic scale, LsLsLss, which is [[Chromatic_pairs#Neutral\|Neutral[7]]]. In neutral, with the neutral third (~11/9) as generator, the rastmic hexad is a chain of five neutral thirds rather than the six which give [[neutral7]], which therefore has two rastmic hexads and of course many more smaller rastmic chords.		''Rastmic tetrads'' are seven in number:

	~~Equal divisions~~ of the ~~octave~~ with rastmic chords include 10, 17, 24, 31, 41, 58, 72, 130, 202, 736be, 938be, 1075be, 1116be, 1277be, 1318be.		three palindromic tetrads,
			* 1-11/9-3/2-11/6 with steps of 11/9-11/9-11/9-12/11 (→[[neutral tetrad]]);
			* 1-3/2-18/11-11/6 with steps of 3/2-12/11-9/8-12/11;
			* 1-9/8-11/9-11/8 with steps of 9/8-12/11-9/8-16/11;

			and two inversely related pairs of tetrads,
			* 1-11/9-11/8-3/2 with steps of 11/9-9/8-12/11-4/3 and 1-12/11-11/9-3/2 with steps of 12/11-9/8-11/9-4/3;
			* 1-9/8-11/9-3/2 with steps of 9/8-12/11-11/9-4/3 and 1-9/8-3/2-11/6 with steps of 9/8-4/3-11/9-12/11.

			There are five ''rastmic pentads'':

			the palindromic pentad,
			* 1-9/8-11/9-3/2-11/6 with steps of 9/8-12/11-11/9-11/9-12/11;

			and two inversely related pairs of pentads,
			* 1-9/8-11/8-3/2-11/6 with steps of 9/8-11/9-12/11-11/9-12/11 and 1-11/9-11/8-3/2-11/6 with steps of 11/9-9/8-12/11-11/9-12/11;
			* 1-9/8-11/9-11/8-3/2 with steps of 9/8-12/11-9/8-12/11-4/3 and 1-9/8-3/2-18/11-11/6 with steps of 9/8-4/3-12/11-9/8-12/11.

			There is also a ''rastmic hexad'':
			* 1-9/8-11/9-11/8-3/2-11/6 with steps of 9/8-12/11-9/8-12/11-11/9-12/11.

			Equal temperaments with rastmic chords include {{Optimal ET sequence\|10, 17, 24, 31, 41, 58, 72, 130, 202, 736be, 938be, 1075be, 1116be, 1277be and 1318be}}.

	{\| class="wikitable"		{\| class="wikitable"
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	\| 9/8 - 12/11 - 9/8 - 12/11 - 11/9 - 12/11		\| 9/8 - 12/11 - 9/8 - 12/11 - 11/9 - 12/11
	\|}		\|}

			== Rastgross heptad ==
			Rastmic chords can be extended to the neutral diatonic scale, LsLsLss, which is [[Chromatic_pairs#Neutral\|Neutral[7]]]. In neutral, with the neutral third (~11/9) as generator, the rastmic hexad is a chain of five neutral thirds rather than the six which give [[neutral7]], which therefore has two rastmic hexads and of course many more smaller rastmic chords.

			In the 2.3.11.13 subgroup, this scale is interpreted as an essentially tempered heptad, the '''rastgross heptad''', tempered by [[144/143]] (grossma) and 243/242. This heptad is 1-9/8-11/9-11/8-3/2-22/13-11/6 with steps of 9/8-12/11-9/8-12/11-9/8-12/11-12/11 (→[[rastgross1]]).

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

FloraC: Recategorize

2023-05-23T11:45:01Z

Recategorize

← Older revision		Revision as of 11:45, 23 May 2023
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	[[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:~~Hexad~~]]		[[Category:Hexads]]
	[[Category:Rastmic]]		[[Category:Rastmic]]

FloraC: Recategorize; +links

2023-04-28T07:20:40Z

Recategorize; +links

← Older revision		Revision as of 07:20, 28 April 2023
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	A '''rastmic chord''' is an [[essentially tempered dyadic chord]] tempered by the rastma, [[243/242]], in the 2.3.11 subgroup in the 11 odd limit.		A '''rastmic chord''' is an [[essentially tempered dyadic chord]] tempered by the rastma, [[243/242]], in the 2.3.11 [[subgroup]] in the [[11-odd-limit]].

	The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:		The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Dyadic~~]]		[[Category:Triad]]
			[[Category:Tetrad]]
			[[Category:Pentad]]
			[[Category:Hexad]]
	[[Category:Rastmic]]		[[Category:Rastmic]]

Fredg999 category edits: Removing from Category:Chords using Cat-a-lot

2023-04-28T03:51:55Z

Removing from Category:Chords using Cat-a-lot

← Older revision		Revision as of 03:51, 28 April 2023
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	~~[[Category:Chords]]~~
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:Rastmic]]		[[Category:Rastmic]]

Xenwolf: recat

2021-05-20T08:09:16Z

recat

← Older revision		Revision as of 08:09, 20 May 2021
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	\|}		\|}

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

Xenwolf: +cat

2021-05-20T07:11:24Z

+cat

← Older revision		Revision as of 07:11, 20 May 2021
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	A '''rastmic chord''' is an [[~~Dyadic_chord #Essentially tempered dyadic chords\|~~essentially tempered dyadic chord]] tempered by the rastma, [[243/242]], in the 2.3.11 subgroup in the 11 odd limit.		A '''rastmic chord''' is an [[essentially tempered dyadic chord]] tempered by the rastma, [[243/242]], in the 2.3.11 subgroup in the 11 odd limit.

	The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:		The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:
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	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:Chords]]		[[Category:Chords]]
			[[Category:Essentially tempered chords]]
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:Rastmic]]		[[Category:Rastmic]]

FloraC: +categories

2020-09-20T06:48:14Z

+categories

← Older revision		Revision as of 06:48, 20 September 2020
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	A ''rastmic chord'' is an [[Dyadic_chord#Essentially tempered dyadic chords\|essentially tempered dyadic chord]] tempered by the rastma, 243/242, in the 2.3.11 subgroup in the 11 odd limit.		A '''rastmic chord''' is an [[Dyadic_chord #Essentially tempered dyadic chords\|essentially tempered dyadic chord]] tempered by the rastma, [[243/242]], in the 2.3.11 subgroup in the 11 odd limit.

	The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:		The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:
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	\| 9/8 - 12/11 - 9/8 - 12/11 - 11/9 - 12/11		\| 9/8 - 12/11 - 9/8 - 12/11 - 11/9 - 12/11
	\|}		\|}

			[[Category:11-limit]]
			[[Category:Chords]]
			[[Category:Dyadic]]
			[[Category:Rastmic]]

Spt3125: added table, formatting

2018-12-06T04:17:21Z

added table, formatting

@@ Line 1: / Line 1: @@
-A ''rastmic chord'' is an [[Dyadic_chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] tempered by the rastma, 243/242, in the 2.3.11 subgroup in the 11 odd limit. There are three rastmic triads: the classic neutral triad 1-11/9-3/2 with steps 11/9-11/9-4/3, and an inversely related pair of triads, 1-9/8-11/6 with steps 9/8-18/11-12/11 and 1-9/8-11/9 with steps 9/8-12/11-18/11. Rastmic tetrads are seven in number: the palindromic classic [[neutral_tetrad|neutral tetrad]] 1-11/9-3/2-11/6 with steps 11/9-11/9-11/9-12/11; the palindromic 1-3/2-18/11-11/6 with steps 3/2-12/11-9/8-12/11; the palindromic 1-9/8-11/9-11/8 with steps 9/8-12/11-9/8-16/11; the inverse pair 1-11/9-11/8-3/2 with steps 11/9-9/8-12/11-4/3 and 1-12/11-11/9-3/2 with steps 12/11-9/8-11/9-4/3; and the inverse pair 1-9/8-11/9-3/2 with steps 9/8-12/11-11/9-4/3 and 1-9/8-3/2-11/6 with steps 9/8-4/3-11/9-12/11. There are five rastmic pentads, the palindromic pentad 1-9/8-11/9-3/2-11/6 with steps 9/8-12/11-11/9-11/9-12/11; the pair 1-9/8-11/8-3/2-11/6 with steps 9/8-11/9-12/11-11/9-12/11 and 1-11/9-11/8-3/2-11/6 with steps 11/9-9/8-12/11-11/9-12/11; and the pair 1-9/8-11/9-11/8-3/2 with steps 9/8-12/11-9/8-12/11-4/3 and 1-9/8-3/2-18/11-11/6 with steps 9/8-4/3-12/11-9/8-12/11.
+A ''rastmic chord'' is an [[Dyadic_chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] tempered by the rastma, 243/242, in the 2.3.11 subgroup in the 11 odd limit.
-There is also a rastmic hexad: 1-9/8-11/9-11/8-3/2-11/6, with steps 9/8-12/11-9/8-12/11-11/9-12/11. This can be extended to the neutral diatonic scale, LsLsLss, which is [[Chromatic_pairs#Neutral|Neutral[7]]]. In neutral, with the neutral third (~11/9) as generator, the rastmic hexad is a chain of five neutral thirds rather than the six which give [[neutralr7|neutral7]], which therefore has two rastmic hexads and of course many more smaller rastmic chords.
+The count of chords is 3 triads, 7 tetrads, 5 pentads, and 1 hexad, for a total of 16:
-The count of chords is triads: 3, tetrads: 7, pentads: 5, hexads: 1 for a total of 16.
+* There are three ''rastmic triads'': the classic neutral triad 1-11/9-3/2 with steps 11/9-11/9-4/3, and an inversely related pair of triads, 1-9/8-11/6 with steps 9/8-18/11-12/11 and 1-9/8-11/9 with steps 9/8-12/11-18/11.
-Equal divisions with rastmic chords include 10, 17, 24, 31 ,41, 58, 72, 130, 202, 736be, 938be, 1075be, 1116be, 1277be, 1318be.
+* ''Rastmic tetrads'' are seven in number: the palindromic classic [[neutral tetrad]] 1-11/9-3/2-11/6 with steps 11/9-11/9-11/9-12/11; the palindromic 1-3/2-18/11-11/6 with steps 3/2-12/11-9/8-12/11; the palindromic 1-9/8-11/9-11/8 with steps 9/8-12/11-9/8-16/11; the inverse pair 1-11/9-11/8-3/2 with steps 11/9-9/8-12/11-4/3 and 1-12/11-11/9-3/2 with steps 12/11-9/8-11/9-4/3; and the inverse pair 1-9/8-11/9-3/2 with steps 9/8-12/11-11/9-4/3 and 1-9/8-3/2-11/6 with steps 9/8-4/3-11/9-12/11.