5L 7s (3/1-equivalent) - Revision history

ArrowHead294 at 14:27, 5 May 2025

2025-05-05T14:27:38Z

← Older revision		Revision as of 14:27, 5 May 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data\|modes note~~=~~The modes have step patterns which are the same as the modes of the p-chromatic scale.~~}}
			=== Intervals ===
			{{MOS intervals}}

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

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

	== Notation ==		== Notation ==

ArrowHead294 at 18:26, 3 March 2025

2025-03-03T18:26:46Z

← Older revision		Revision as of 18:26, 3 March 2025
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	It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied no-twos subgroups like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].		It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied no-twos subgroups like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].

	==~~Modes~~==		== Scale properties ==
	The modes have step patterns which are the same as the modes of the p-chromatic scale.		{{TAMNAMS use}}
	~~{{MOS modes}}~~		{{MOS data\|modes note=The modes have step patterns which are the same as the modes of the p-chromatic scale.}}

	~~=== Scale degrees ===~~
	~~{{MOS mode degrees~~}}

	== Notation ==		== Notation ==
	Being a descendant of a macrodiatonic scale, it can notated using the traditional diatonic notation, if all intervals are reinterpreted as their stretched versions (like octaves as tritaves). However, this approach involves 1-based indexing for a non-diatonic MOS which is generally discouraged. Alternatively, a generic MOS notation may be used like [[diamond MOS notation]], which enables 0-based indexing at the cost of obscuring the connection to the standard diatonic scale.		Being a descendant of a macrodiatonic scale, it can notated using the traditional diatonic notation, if all intervals are reinterpreted as their stretched versions (like octaves as tritaves). However, this approach involves 1-based indexing for a non-diatonic MOS which is generally discouraged. Alternatively, a generic MOS notation may be used like [[diamond MOS notation]], which enables 0-based indexing at the cost of obscuring the connection to the standard diatonic scale.

	~~== Intervals ==~~
	~~{{MOS intervals}}~~

	== Scale tree ==		== Scale tree ==
	{{~~Scale tree~~\|~~Comments=~~2/1: Just [[21/11]] generator (1119.~~463c~~); 12/5: [[Mintra]]; 3/1: [[Mintaka]] is around here; 10/3: [[No-twos subgroup temperaments#Nekkar\|Nekkar]]; 4/1: [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]}}		{{MOS tuning spectrum
			\| 2/1 = Just [[21/11]] generator (1119.463{{c}})
			\| 12/5 = [[Mintra]]
			\| 3/1 = [[Mintaka]] is around here
			\| 10/3 = [[No-twos subgroup temperaments#Nekkar\|Nekkar]]
			\| 4/1 = [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]
			}}

BudjarnLambeth: == Intervals == {{MOS intervals}}

2024-12-16T00:43:12Z

== Intervals == {{MOS intervals}}

← Older revision		Revision as of 00:43, 16 December 2024
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	== Notation ==		== Notation ==
	Being a descendant of a macrodiatonic scale, it can notated using the traditional diatonic notation, if all intervals are reinterpreted as their stretched versions (like octaves as tritaves). However, this approach involves 1-based indexing for a non-diatonic MOS which is generally discouraged. Alternatively, a generic MOS notation may be used like [[diamond MOS notation]], which enables 0-based indexing at the cost of obscuring the connection to the standard diatonic scale.		Being a descendant of a macrodiatonic scale, it can notated using the traditional diatonic notation, if all intervals are reinterpreted as their stretched versions (like octaves as tritaves). However, this approach involves 1-based indexing for a non-diatonic MOS which is generally discouraged. Alternatively, a generic MOS notation may be used like [[diamond MOS notation]], which enables 0-based indexing at the cost of obscuring the connection to the standard diatonic scale.

			== Intervals ==
			{{MOS intervals}}

	== Scale tree ==		== Scale tree ==
	{{Scale tree\|Comments=2/1: Just [[21/11]] generator (1119.463c); 12/5: [[Mintra]]; 3/1: [[Mintaka]] is around here; 10/3: [[No-twos subgroup temperaments#Nekkar\|Nekkar]]; 4/1: [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]}}		{{Scale tree\|Comments=2/1: Just [[21/11]] generator (1119.463c); 12/5: [[Mintra]]; 3/1: [[Mintaka]] is around here; 10/3: [[No-twos subgroup temperaments#Nekkar\|Nekkar]]; 4/1: [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]}}

Lériendil: /* Temperament interpretations */

2024-10-11T05:18:59Z

Temperament interpretations

← Older revision		Revision as of 05:18, 11 October 2024
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	=== Temperament interpretations ===		=== Temperament interpretations ===
	It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied [[no-twos ~~subgroup]]s~~ like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].		It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied no-twos subgroups like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].

	==Modes==		==Modes==

Lériendil: /* Theory */

2024-10-11T03:46:51Z

Theory

← Older revision		Revision as of 03:46, 11 October 2024
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	== Theory ==		== Theory ==
	=== As a macrochromatic scale ===		=== As a macrochromatic scale ===
	It is a stretched [[p-chromatic]] scale, and an extension of a [[macrodiatonic]] scale ([[5L 2s (3/1-equivalent)]]) with the period of a [[3/1\|tritave]]. This means it is a [[5L 7s\|chromatic scale]], but has [[2/1\|octave]]s stretched out to the size of a [[3/1\|tritave]]. Other intervals are also stretched in a way that makes ~~the~~ unrecognizable: the diatonic fifth is now the size of a major seventh. Interestingly, [[27edt]], an approximation of [[17edo]], has a tuning of this scale, meaning it contains both an octave-equivalent and tritave-equivalent p-chromatic.		It is a stretched [[p-chromatic]] scale, and an extension of a [[macrodiatonic]] scale ([[5L 2s (3/1-equivalent)]]) with the period of a [[3/1\|tritave]]. This means it is a [[5L 7s\|chromatic scale]], but has [[2/1\|octave]]s stretched out to the size of a [[3/1\|tritave]]. Other intervals are also stretched in a way that makes them unrecognizable: the diatonic fifth is now the size of a major seventh. Interestingly, [[27edt]], an approximation of [[17edo]], has a tuning of this scale, meaning it contains both an octave-equivalent and tritave-equivalent p-chromatic.

	=== Temperament interpretations ===		=== Temperament interpretations ===

Lériendil: /* Modes */

2024-10-11T03:25:50Z

Modes

← Older revision		Revision as of 03:25, 11 October 2024
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	==Modes==		==Modes==
	The modes have step patterns which are the same as the modes of the ~~diatonic~~ scale.		The modes have step patterns which are the same as the modes of the p-chromatic scale.
	{{MOS modes}}		{{MOS modes}}

Lériendil: /* Scale tree */

2024-10-11T00:20:46Z

Scale tree

← Older revision		Revision as of 00:20, 11 October 2024
Line 20:		Line 20:

	== Scale tree ==		== Scale tree ==
	{{Scale tree\|Comments=2/1: Just [[21/11]] generator (1119.463c); 5/2: [[Mintra]]; 3/1: [[Mintaka]] is around here; 10/3: [[No-twos subgroup temperaments#Nekkar\|Nekkar]]; 4/1: [[Minalzidar]]}}		{{Scale tree\|Comments=2/1: Just [[21/11]] generator (1119.463c); 12/5: [[Mintra]]; 3/1: [[Mintaka]] is around here; 10/3: [[No-twos subgroup temperaments#Nekkar\|Nekkar]]; 4/1: [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]}}

Lériendil: /* Scale tree */

2024-10-11T00:20:15Z

Scale tree

← Older revision		Revision as of 00:20, 11 October 2024
Line 20:		Line 20:

	== Scale tree ==		== Scale tree ==
	{{Scale tree\|Comments=2/1: Just [[21/11]] generator (1119.463c); 5/2: [[Mintra]]; 3/1: [[Mintaka]] is around here}}		{{Scale tree\|Comments=2/1: Just [[21/11]] generator (1119.463c); 5/2: [[Mintra]]; 3/1: [[Mintaka]] is around here; 10/3: [[No-twos subgroup temperaments#Nekkar\|Nekkar]]; 4/1: [[Minalzidar]]}}

Lériendil: /* Scale tree */

2024-10-11T00:19:08Z

Scale tree

← Older revision		Revision as of 00:19, 11 October 2024
Line 20:		Line 20:

	== Scale tree ==		== Scale tree ==
	{{Scale tree\|Comments=2/1: Just [[21/11]] generator (1119.463c); 3/1: [[Mintaka]] is around here}}		{{Scale tree\|Comments=2/1: Just [[21/11]] generator (1119.463c); 5/2: [[Mintra]]; 3/1: [[Mintaka]] is around here}}

Lériendil: /* Temperament interpretations */

2024-10-11T00:17:16Z

Temperament interpretations

← Older revision		Revision as of 00:17, 11 October 2024
Line 7:		Line 7:

	=== Temperament interpretations ===		=== Temperament interpretations ===
	It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied [[no-twos subgroup]]s like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. ~~Harder~~ scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].		It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied [[no-twos subgroup]]s like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].

	==Modes==		==Modes==