7L 3s (4/1-equivalent) - Revision history

ArrowHead294 at 14:22, 5 May 2025

2025-05-05T14:22:01Z

← Older revision		Revision as of 14:22, 5 May 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data~~}}
			=== Intervals ===
			{{MOS intervals}}

			=== Generator chain ===
			{{MOS genchain}}

			=== Modes ===
			{{MOS mode degrees}}

	== Scale tree ==		== Scale tree ==

ArrowHead294 at 17:59, 3 March 2025

2025-03-03T17:59:22Z

Show changes

BudjarnLambeth: Add a line break

2024-12-16T01:42:31Z

Add a line break

← Older revision		Revision as of 01:42, 16 December 2024
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	{{Infobox MOS}}		{{Infobox MOS}}
	'''7L 3s<4/1>''' (sometimes called '''diaquadic''') refers to a non-octave [[MOS scale]] family with a period of a [[4/1]] and which has 7 large and 3 small steps. These scales are in some ways a double octave clone of [[5L 2s\|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685-cent flat fifth and [[5edo]]/10ed4's 720-cent sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720-cent fifth and collapsed is 685-cent fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.		'''7L 3s<4/1>''' (sometimes called '''diaquadic''') refers to a non-octave [[MOS scale]] family with a period of a [[4/1]] and which has 7 large and 3 small steps.

			These scales are in some ways a double octave clone of [[5L 2s\|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685-cent flat fifth and [[5edo]]/10ed4's 720-cent sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720-cent fifth and collapsed is 685-cent fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.

	== Intervals ==		== Intervals ==

CompactStar at 02:12, 8 June 2023

2023-06-08T02:12:34Z

← Older revision		Revision as of 02:12, 8 June 2023
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	\|C		\|C
	\|perfect 0-step		\|perfect 0-step
	\|~~1694~~.16		\|0.00
	\|		\|
	\|0		\|0
	\|C		\|C
	\|perfect 10-step		\|perfect 10-step
	\|~~282~~.36		\|0.00
	\|-		\|-
	\|1		\|1

CompactStar at 02:11, 8 June 2023

2023-06-08T02:11:44Z

← Older revision		Revision as of 02:11, 8 June 2023
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	\|-		\|-
	\|0		\|0
	\|J		\|C
	\|perfect 0-step		\|perfect 0-step
	\|1694.16		\|1694.16
	\|		\|
	\|0		\|0
	\|J		\|C
	\|perfect 10-step		\|perfect 10-step
	\|282.36		\|282.36
	\|-		\|-
	\|1		\|1
	\|M		\|F
	\|perfect 3-step		\|perfect 3-step
	\|705.90		\|705.90
	\|		\|
	\|1		\|1
	\|Q		\|K
	\|perfect 7-step		\|perfect 7-step
	\|1694.16		\|1694.16
	\|-		\|-
	\|2		\|2
	\|Pb		\|Jb
	\|minor 6-step		\|minor 6-step
	\|1411.80		\|1411.80
	\|		\|
	\|2		\|2
	\|N		\|E
	\|major 4-step		\|major 4-step
	\|988.26		\|988.26
	\|-		\|-
	\|3		\|3
	\|Sb		\|Bb
	\|minor 9-step		\|minor 9-step
	\|2117.70		\|2117.70
	\|		\|
	\|3		\|3
	\|K		\|D
	\|major 1-step		\|major 1-step
	\|282.36		\|282.36
	\|-		\|-
	\|4		\|4
	\|Lb		\|Eb
	\|minor 2-step		\|minor 2-step
	\|423.54		\|423.54
	\|		\|
	\|4		\|4
	\|R		\|A
	\|major 8-step		\|major 8-step
	\|1976.52		\|1976.52
	\|-		\|-
	\|5		\|5
	\|Ob		\|Hb
	\|minor 5-step		\|minor 5-step
	\|1129.44		\|1129.44
	\|		\|
	\|5		\|5
	\|O		\|H
	\|major 5-step		\|major 5-step
	\|1270.62		\|1270.62
	\|-		\|-
	\|6		\|6
	\|Rb		\|Ab
	\|minor 8-step		\|minor 8-step
	\|1835.34		\|1835.34
	\|		\|
	\|6		\|6
	\|L		\|E
	\|major 2-step		\|major 2-step
	\|564.72		\|564.72
	\|-		\|-
	\|7		\|7
	\|Kb		\|Db
	\|minor 1-step		\|minor 1-step
	\|141.18		\|141.18
	\|		\|
	\|7		\|7
	\|S		\|B
	\|major 9-step		\|major 9-step
	\|2258.88		\|2258.88
	\|-		\|-
	\|8		\|8
	\|Nb		\|Gb
	\|minor 4-step		\|minor 4-step
	\|847.08		\|847.08
	\|		\|
	\|8		\|8
	\|P		\|J
	\|major 6-step		\|major 6-step
	\|1552.98		\|1552.98

CompactStar at 02:07, 8 June 2023

2023-06-08T02:07:33Z

← Older revision		Revision as of 02:07, 8 June 2023
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	* [[Subgroup]]: 4.5.6		* [[Subgroup]]: 4.5.6
	* [[Comma list]]: [[81/80]]		* [[Comma list]]: [[81/80]]
			* {{Mapping\|legend=1\|1 0 1\|0 4 1}}
	* [[Support]]ing ETs: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]		* [[Support]]ing ETs: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]
	* [[CTE tuning]]: ~[[3/2]] = 697.214		* [[CTE tuning]]: ~[[3/2]] = 697.214
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	* [[Subgroup]]: 4.5.6.7		* [[Subgroup]]: 4.5.6.7
	* [[Comma list]]: [[36/35]], [[64/63]]		* [[Comma list]]: [[36/35]], [[64/63]]
			* {{Mapping\|legend=1\|1 0 1 2\|0 4 1 -2}}
	* [[Support]]ing ETs: 7, 17, 24, 10, 31, 41, 27[+5], 38[+7], 55[+7], 58[+5, +7], 65[+5, +7], 44[+5], 75[+5, +7]		* [[Support]]ing ETs: 7, 17, 24, 10, 31, 41, 27[+5], 38[+7], 55[+7], 58[+5, +7], 65[+5, +7], 44[+5], 75[+5, +7]
	* [[CTE tuning]]: ~[[3/2]] = 699.622		* [[CTE tuning]]: ~[[3/2]] = 699.622
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	* [[Subgroup]]: 4.6.7		* [[Subgroup]]: 4.6.7
	* [[Comma list]]: [[64/63]]		* [[Comma list]]: [[64/63]]
			* {{Mapping\|legend=1\|1 2 0\|0 1 -2}}
	* [[Support]]ing ETs: 10, 17, 7, 27, 37, 44, 13, 24, 47, 11[+7], 23, 57, 16, 41		* [[Support]]ing ETs: 10, 17, 7, 27, 37, 44, 13, 24, 47, 11[+7], 23, 57, 16, 41
	* [[CTE tuning]]: ~[[3/2]] = 709.595		* [[CTE tuning]]: ~[[3/2]] = 709.595

CompactStar at 02:03, 8 June 2023

2023-06-08T02:03:20Z

← Older revision		Revision as of 02:03, 8 June 2023
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	\|-		\|-
	!Dark generators		!Dark generators
	!colspan="2"\|Notation ~~(J = 1/1)~~		!colspan="2"\|Notation
	![[17ed4]] cents		![[17ed4]] cents
	!		!
	!Bright generators		!Bright generators
	!colspan="2"\|Notation ~~(J = 1/1)~~		!colspan="2"\|Notation
	![[17ed4]] cents		![[17ed4]] cents
	\|-		\|-
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	== Scale tree ==		== Scale tree ==
	{{Scale tree		{{Scale tree\|Comments=5/3:Quarchy is around here;3/1:Tetrominant is around here;4/1:Meanquad is around here}}
	\|~~comment_5_3~~=Quarchy is around here
	~~\|comment_2_1=Basic diaquadic~~
	~~\|comment_3_1=~~Tetrominant is around here
	~~\|comment_4_1=~~Meanquad is around here
	}}
	== Temperaments ==		== Temperaments ==
	There are two major rank-2 temperament interpretations of diaquadic, corresponding to double octave clones of [[meantone]] and [[archy]].		There are two major rank-2 temperament interpretations of diaquadic, corresponding to double octave clones of [[meantone]] and [[archy]].

CompactStar at 01:00, 28 May 2023

2023-05-28T01:00:37Z

← Older revision		Revision as of 01:00, 28 May 2023
Line 122:		Line 122:
	{{Scale tree		{{Scale tree
	\|comment_5_3=Quarchy is around here		\|comment_5_3=Quarchy is around here
			\|comment_2_1=Basic diaquadic
	\|comment_3_1=Tetrominant is around here		\|comment_3_1=Tetrominant is around here
	\|comment_4_1=Meanquad is around here		\|comment_4_1=Meanquad is around here

CompactStar at 01:00, 28 May 2023

2023-05-28T01:00:11Z

@@ Line 120: / Line 120: @@
 == Scale tree ==
-{|class="wikitable"
+{{Scale tree
-|-
+|comment_5_3=Quarchy is around here
-!Dark generator
+|comment_3_1=Tetrominant is around here
-!Cents
+|comment_4_1=Meanquad is around here
-!L
+}}
 == Temperaments ==
 There are two major rank-2 temperament interpretations of diaquadic, corresponding to double octave clones of [[meantone]] and [[archy]].

CompactStar at 01:30, 9 May 2023

2023-05-09T01:30:15Z

← Older revision		Revision as of 01:30, 9 May 2023
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	== Modes ==		== Modes ==
			The darker modes contain both major triads and augmented triads on the root, and the brighter modes contain both minor and diminished triads on the root.

	* LLLsLLsLLs 9\|0		* LLLsLLsLLs 9\|0
	* LLsLLLsLLs 8\|1		* LLsLLLsLLs 8\|1