5L 2s (3/1-equivalent) - Revision history

ArrowHead294 at 23:10, 7 March 2025

2025-03-07T23:10:25Z

← Older revision		Revision as of 23:10, 7 March 2025
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	=== Modes ===		=== Modes ===
	The modes of {{MOS scalesig}} have step patterns which are the same as the modes of the diatonic scale.		The modes of {{MOS scalesig\|5L 2s <3/1>}} have step patterns which are the same as the modes of the diatonic scale.
	{{MOS mode degrees}}		{{MOS mode degrees}}

Ganaram inukshuk: /* As a macrodiatonic scale */

2025-03-07T08:54:27Z

As a macrodiatonic scale

← Older revision		Revision as of 08:54, 7 March 2025
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	== Theory ==		== Theory ==
	=== As a macrodiatonic scale ===		=== As a macrodiatonic scale ===
	{{MOS scalesig}} is a [[macrodiatonic and microdiatonic scales\|macrodiatonic scale]] with the period of a [[3/1\|tritave]]. This means it is a [[5L 2s\|diatonic scale]], but its intervals are all stretched to the point of being unrecognizable—the diatonic fifth is now the size of a major seventh, and octaves are stretched out to tritaves. Interestingly, [[19edt]], an approximation of [[12edo]], has a tuning of this scale, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a triatonic scale.		{{MOS scalesig\|5L 2s <3/1>}} is a [[macrodiatonic and microdiatonic scales\|macrodiatonic scale]] with the period of a [[3/1\|tritave]]. This means it is a [[5L 2s\|diatonic scale]], but its intervals are all stretched to the point of being unrecognizable—the diatonic fifth is now the size of a major seventh, and octaves are stretched out to tritaves. Interestingly, [[19edt]], an approximation of [[12edo]], has a tuning of this scale, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a triatonic scale.

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

ArrowHead294: Replace MOSPAGENAME with MOS scalesig

2025-03-06T19:24:16Z

Replace MOSPAGENAME with MOS scalesig

← Older revision		Revision as of 19:24, 6 March 2025
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	=== Modes ===		=== Modes ===
	The modes of {{~~MOSPAGENAME~~}} have step patterns which are the same as the modes of the diatonic scale.		The modes of {{MOS scalesig}} have step patterns which are the same as the modes of the diatonic scale.
	{{MOS mode degrees}}		{{MOS mode degrees}}

	== Theory ==		== Theory ==
	=== As a macrodiatonic scale ===		=== As a macrodiatonic scale ===
	{{~~MOSPAGENAME~~}} is a [[macrodiatonic and microdiatonic scales\|macrodiatonic scale]] with the period of a [[3/1\|tritave]]. This means it is a [[5L 2s\|diatonic scale]], but its intervals are all stretched to the point of being unrecognizable—the diatonic fifth is now the size of a major seventh, and octaves are stretched out to tritaves. Interestingly, [[19edt]], an approximation of [[12edo]], has a tuning of this scale, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a triatonic scale.		{{MOS scalesig}} is a [[macrodiatonic and microdiatonic scales\|macrodiatonic scale]] with the period of a [[3/1\|tritave]]. This means it is a [[5L 2s\|diatonic scale]], but its intervals are all stretched to the point of being unrecognizable—the diatonic fifth is now the size of a major seventh, and octaves are stretched out to tritaves. Interestingly, [[19edt]], an approximation of [[12edo]], has a tuning of this scale, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a triatonic scale.

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

ArrowHead294 at 18:46, 6 March 2025

2025-03-06T18:46:07Z

← Older revision		Revision as of 18:46, 6 March 2025
Line 14:		Line 14:

	=== Modes ===		=== Modes ===
	The modes of ~~5L 2s~~{{~~angbr\|3/1~~}} have step patterns which are the same as the modes of the diatonic scale.		The modes of {{MOSPAGENAME}} have step patterns which are the same as the modes of the diatonic scale.
	{{MOS mode degrees}}		{{MOS mode degrees}}

	== Theory ==		== Theory ==
	=== As a macrodiatonic scale ===		=== As a macrodiatonic scale ===
	~~5L 2s~~{{~~angbr\|3/1~~}} is a [[macrodiatonic and microdiatonic scales\|macrodiatonic scale]] with the period of a [[3/1\|tritave]]. This means it is a [[5L 2s\|diatonic scale]], but its intervals are all stretched to the point of being unrecognizable—the diatonic fifth is now the size of a major seventh, and octaves are stretched out to tritaves. Interestingly, [[19edt]], an approximation of [[12edo]], has a tuning of this scale, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a triatonic scale.		{{MOSPAGENAME}} is a [[macrodiatonic and microdiatonic scales\|macrodiatonic scale]] with the period of a [[3/1\|tritave]]. This means it is a [[5L 2s\|diatonic scale]], but its intervals are all stretched to the point of being unrecognizable—the diatonic fifth is now the size of a major seventh, and octaves are stretched out to tritaves. Interestingly, [[19edt]], an approximation of [[12edo]], has a tuning of this scale, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a triatonic scale.

	=== Temperament interpretations ===		=== Temperament interpretations ===
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	\| 4/1 = [[Mintaka]] is around here		\| 4/1 = [[Mintaka]] is around here
	\| 5/1 = [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]		\| 5/1 = [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]

	}}		}}

ArrowHead294 at 16:33, 5 March 2025

2025-03-05T16:33:50Z

← Older revision		Revision as of 16:33, 5 March 2025
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	{{MOS intro\|Other Names=triatonic}}		{{MOS intro\|Other Names=triatonic}}
	== Name ==		== Name ==
	The name '''triatonic''' was coined by [[User:CompactStar\|CompactStar]], ~~and is~~ a back-formation from "diatonic" with di- being interpreted as 2 (the [[2/1\|octave]]) and ~~replaced with~~ tri- ~~for~~ 3 (the [[3/1\|tritave]])~~. It~~ is not an official name in [[TAMNAMS]].		The name '''triatonic''' was coined by [[User:CompactStar\|CompactStar]], as a back-formation from "diatonic" with di- being interpreted as 2 (the [[2/1\|octave]]) and tri- being interpreted as 3 (the [[3/1\|tritave]]), though it is not an official name in [[TAMNAMS]].

	== Scale properties ==		== Scale properties ==

ArrowHead294: /* Intervals */ Move up

2025-03-03T21:52:42Z

Intervals: Move up

← Older revision		Revision as of 21:52, 3 March 2025
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	== Notation ==		== Notation ==
	Being 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 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 ==

ArrowHead294 at 21:52, 3 March 2025

2025-03-03T21:52:03Z

← Older revision		Revision as of 21:52, 3 March 2025
Line 14:		Line 14:

	=== Modes ===		=== Modes ===
			The modes of 5L 2s{{angbr\|3/1}} have step patterns which are the same as the modes of the diatonic scale.
	{{MOS mode degrees}}		{{MOS mode degrees}}

ArrowHead294 at 21:51, 3 March 2025

2025-03-03T21:51:53Z

← Older revision		Revision as of 21:51, 3 March 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data\|modes note~~=~~The modes of 5L 2s~~{{~~angbr\|3/1~~}} ~~have step patterns which are the same as the modes of the diatonic scale.~~}}
			=== Intervals ===
			{{MOS intervals}}

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

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

	== Theory ==		== Theory ==

ArrowHead294 at 18:19, 3 March 2025

2025-03-03T18:19:28Z

← Older revision		Revision as of 18:19, 3 March 2025
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	== Scale tree ==		== Scale tree ==
	{{~~Scale tree~~\|~~name~~=triatonic\|~~Comments=~~11/8:[[No-twos subgroup temperaments#Mizar\|Mizar]]; 3/2:Just [[17/9]] generator (1101.~~045¢~~); 2/1:[[CTE tuning]] for the b12 & b5 temperament (1109.~~689¢~~); 3/1: Just [[21/11]] generator (1119.~~463¢~~); 7/2: [[Mintra]]; 4/1: [[Mintaka]] is around here; 5/1: [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]}}		{{MOS tuning spectrum
			\| Name=triatonic
			\| 11/8 = [[No-twos subgroup temperaments#Mizar\|Mizar]]
			\| 3/2 = Just [[17/9]] generator (1101.045{{c}})
			\| 2/1 = [[CTE tuning]] for the {{nowrap\|b12 & b5}} temperament (1109.689{{c}})
			\| 3/1 = Just [[21/11]] generator (1119.463{{c}})
			\| 7/2 = [[Mintra]]
			\| 4/1 = [[Mintaka]] is around here
			\| 5/1 = [[No-twos subgroup temperaments#Minalzidar\|Minalzidar]]

			}}

ArrowHead294: /* Scale properties */

2025-02-25T14:42:48Z

Scale properties

← Older revision		Revision as of 14:42, 25 February 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS data}}		{{MOS data\|modes note=The modes of 5L 2s{{angbr\|3/1}} have step patterns which are the same as the modes of the diatonic scale.}}
	The modes of 5L 2s{{angbr\|3/1}} have step patterns which are the same as the modes of the diatonic scale.

	== Theory ==		== Theory ==