Collection of scales - Revision history

Vector at 03:07, 15 May 2026

2026-05-15T03:07:07Z

← Older revision		Revision as of 03:07, 15 May 2026
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	== Kee'ra ==		== Kee'ra ==
	The '''kee'ra''' scale, or the Chair of Mr. Bob as named by dotuXil, is the prototype of a family of "chair scales", so named for the lattice's resemblance to a chair. Its intervals are [21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1]; {{Interval ruler\|41\|0, 85, 150, 315, 460, 580, 700, 820, 850, 970, 1200}}. Its intervals give it a "minor" sound in the default mode, with some characteristics of Phrygian; it supports the 6/5-3/2-7/4 tetrad on the root, with the interval 35/24 (roughly 16/11) between the third and seventh.		The '''kee'ra''' scale, or the Chair of Mr. Bob as named by dotuXil, is the prototype of a family of "chair scales", so named for the lattice's resemblance to a chair. Its intervals are [21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1]; {{Interval ruler\|41\|0, 85, 150, 315, 460, 580, 700, 820, 850, 970, 1200}} (41edo tuning - the JI scale distinguishes 15/14 and 16/15-sized steps). Its intervals give it a "minor" sound in the default mode, with some characteristics of Phrygian; it supports the 6/5-3/2-7/4 tetrad on the root, with the interval 35/24 (roughly 16/11) between the third and seventh.

	== Roklotian ==		== Roklotian ==
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	=== Just intonation ===		=== Just intonation ===
	In just intonation (and temperaments that do not equate or temper out any of the relevant intervals, such as 46edo), it is a ternary scale: msmLmLmsmLmLmsm, with s = 648/625, m = 25/24, and L = 16/15; {{Interval ruler\|46\|0, 80, 130, 200, 310, 390, 500, 580, 630, 700, 810, 890, 1000, 1070, 1130, 1200}}.		In just intonation (and temperaments that do not equate or temper out any of the relevant intervals, such as 46edo), it is a ternary scale: msmLmLmsmLmLmsm, with s = 648/625, m = 25/24, and L = 16/15; {{Interval ruler\|46\|0, 80, 130, 200, 310, 390, 500, 580, 630, 700, 810, 890, 1000, 1070, 1130, 1200}} (46edo tuning).

	=== Kleismic temperament ===		=== Kleismic temperament ===
	The most common form of the Roklotian scale is the kleismic form, which is supported by edos such as 34edo and divides the 9/8 into three equal parts. It is binary but MV3, with the step signature sssLsLsssLsLsss: {{Interval ruler\|34\|0, 80, 130, 200, 310, 390, 500, 580, 630, 700, 810, 890, 1000, 1070, 1130, 1200}}. It is a MODMOS of 4L 11s, a notable kleismic MOS.		The most common form of the Roklotian scale is the kleismic form, which is supported by edos such as 34edo and divides the 9/8 into three equal parts. It is binary but MV3, with the step signature sssLsLsssLsLsss: {{Interval ruler\|34\|0, 80, 130, 200, 310, 390, 500, 580, 630, 700, 810, 890, 1000, 1070, 1130, 1200}} (34edo tuning). It is a MODMOS of 4L 11s, a notable kleismic MOS.

	=== Porcupine temperament ===		=== Porcupine temperament ===
	Roklotian also reduces to a binary scale in porcupine, which equates the 648/625 and 16/15 steps. This is actually a MOS - it is porcupine[15]: {{Interval ruler\|37\|0, 80, 160, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1040, 1130, 1200}}.		Roklotian also reduces to a binary scale in porcupine, which equates the 648/625 and 16/15 steps. This is actually a MOS - it is porcupine[15]: {{Interval ruler\|37\|0, 80, 160, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1040, 1130, 1200}} (37edo tuning).

	=== Augmented temperament ===		=== Augmented temperament ===
	Augmented temperament equates the 16/15 and 25/24 steps. The result is the scale LsLLLLLsLLLLLsL, which is a MODMOS of augmented[15] - {{Interval ruler\|27\|0, 80, 140, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1060, 1130, 1200}}.		Augmented temperament equates the 16/15 and 25/24 steps. The result is the scale LsLLLLLsLLLLLsL, which is a MODMOS of augmented[15] - {{Interval ruler\|27\|0, 80, 140, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1060, 1130, 1200}} (27edo tuning).

	=== Diminished temperament ===		=== Diminished temperament ===
	Diminished temperament tempers out the 648/625 entirely, resulting in ssLsLssLsLss, a MODMOS of diminished[12] - {{Interval ruler\|40\|0, 90, 180, 300, 390, 510, 600, 690, 810, 900, 1020, 1110, 1200}}.		Diminished temperament tempers out the 648/625 entirely, resulting in ssLsLssLsLss, a MODMOS of diminished[12] - {{Interval ruler\|40\|0, 90, 180, 300, 390, 510, 600, 690, 810, 900, 1020, 1110, 1200}} (40edo tuning).

	=== Dicot temperament ===		=== Dicot temperament ===
	Dicot temperament tempers out 25/24, notably equating 648/625 to 9/8. Since the majority of the scale's steps are 25/24, the scale's cardinality is reduced drastically, and the result is LssLssL, a MODMOS of dicot[7] - {{Interval ruler\|17\|0, 200, 350, 500, 700, 850, 1000, 1200}}.		Dicot temperament tempers out 25/24, notably equating 648/625 to 9/8. Since the majority of the scale's steps are 25/24, the scale's cardinality is reduced drastically, and the result is LssLssL, a MODMOS of dicot[7] - {{Interval ruler\|17\|0, 200, 350, 500, 700, 850, 1000, 1200}} (17edo tuning).

Vector at 23:51, 19 April 2026

2026-04-19T23:51:59Z

← Older revision		Revision as of 23:51, 19 April 2026
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	== Kee'ra ==		== Kee'ra ==
	The '''kee'ra''' scale, or the Chair of Mr. Bob as named by dotuXil, is the prototype of a family of "chair scales", so named for the lattice's resemblance to a chair. Its intervals are [21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1]; {{Interval ruler\|41\|0, 85, 150, 315, 460, 580, 700, 820, 850, 970, 1200}}.		The '''kee'ra''' scale, or the Chair of Mr. Bob as named by dotuXil, is the prototype of a family of "chair scales", so named for the lattice's resemblance to a chair. Its intervals are [21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1]; {{Interval ruler\|41\|0, 85, 150, 315, 460, 580, 700, 820, 850, 970, 1200}}. Its intervals give it a "minor" sound in the default mode, with some characteristics of Phrygian; it supports the 6/5-3/2-7/4 tetrad on the root, with the interval 35/24 (roughly 16/11) between the third and seventh.

	== Roklotian ==		== Roklotian ==

Vector at 03:29, 19 April 2026

2026-04-19T03:29:55Z

← Older revision		Revision as of 03:29, 19 April 2026
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	[[File:Mr bob.png\|thumb\|218x218px\|The lattice for the Chair of Mr. Bob]]		[[File:Mr bob.png\|thumb\|218x218px\|The lattice for the Chair of Mr. Bob]]
	~~{\| class~~=~~"wikitable"~~
	\|+		== Kee'ra ==
	~~!Name~~		The '''kee'ra''' scale, or the Chair of Mr. Bob as named by dotuXil, is the prototype of a family of "chair scales", so named for the lattice's resemblance to a chair. Its intervals are [21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1]; {{Interval ruler\|41\|0, 85, 150, 315, 460, 580, 700, 820, 850, 970, 1200}}.
	~~!Intervals~~
	~~!Comments~~		== Roklotian ==
	~~!Good edos~~		The Roklotian scale is constructed in just intonation or an equal temperament from the DKW signature of the 5-limit; 9/8-16/15-25/24-16/15-9/8-16/15-25/24-16/15-9/8 (which contains the 5-odd-limit, 9/8, and 16/9) - steps of 25/24 are added into each 9/8, bounding a middle interval of 648/625. This has differing behavior depending on the temperament.
	\|-
	~~\|Kee~~'ra, Chair of Mr. Bob		Studying scales like Roklotian is useful because it illustrates how temperaments affect the structure of just intonation.
	\|21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1
	\|~~When it is loaded in Scale Workshop~~, ~~the lattice resembles a chair~~.		=== Just intonation ===
	~~\|31~~		In just intonation (and temperaments that do not equate or temper out any of the relevant intervals, such as 46edo), it is a ternary scale: msmLmLmsmLmLmsm, with s = 648/625, m = 25/24, and L = 16/15; {{Interval ruler\|46\|0, 80, 130, 200, 310, 390, 500, 580, 630, 700, 810, 890, 1000, 1070, 1130, 1200}}.
	\|-
	~~\|Duodene~~		=== Kleismic temperament ===
	\|16/15 9/8 6/~~5 5~~/~~4 4~~/~~3 45~~/~~32 3~~/2 8/~~5 5~~/3 9~~/5 15~~/8 2/1		The most common form of the Roklotian scale is the kleismic form, which is supported by edos such as 34edo and divides the 9/8 into three equal parts. It is binary but MV3, with the step signature sssLsLsssLsLsss: {{Interval ruler\|34\|0, 80, 130, 200, 310, 390, 500, 580, 630, 700, 810, 890, 1000, 1070, 1130, 1200}}. It is a MODMOS of 4L 11s, a notable kleismic MOS.
	\|~~5-limit detempering~~ of ~~12edo formed~~ by ~~all ratios~~ with ~~powers -1~~, 0, 1, ~~and 2~~ of the ~~third harmonic~~ and ~~powers~~ -1, 0, and 1 of ~~the fifth~~.
	\|12, 34, 41, 53		=== Porcupine temperament ===
	\|}		Roklotian also reduces to a binary scale in porcupine, which equates the 648/625 and 16/15 steps. This is actually a MOS - it is porcupine[15]: {{Interval ruler\|37\|0, 80, 160, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1040, 1130, 1200}}.

			=== Augmented temperament ===
			Augmented temperament equates the 16/15 and 25/24 steps. The result is the scale LsLLLLLsLLLLLsL, which is a MODMOS of augmented[15] - {{Interval ruler\|27\|0, 80, 140, 220, 310, 390, 500, 560, 640, 700, 810, 890, 980, 1060, 1130, 1200}}.

			=== Diminished temperament ===
			Diminished temperament tempers out the 648/625 entirely, resulting in ssLsLssLsLss, a MODMOS of diminished[12] - {{Interval ruler\|40\|0, 90, 180, 300, 390, 510, 600, 690, 810, 900, 1020, 1110, 1200}}.

			=== Dicot temperament ===
			Dicot temperament tempers out 25/24, notably equating 648/625 to 9/8. Since the majority of the scale's steps are 25/24, the scale's cardinality is reduced drastically, and the result is LssLssL, a MODMOS of dicot[7] - {{Interval ruler\|17\|0, 200, 350, 500, 700, 850, 1000, 1200}}.

Hkm at 23:17, 8 January 2026

2026-01-08T23:17:16Z

← Older revision		Revision as of 23:17, 8 January 2026
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	\|Duodene		\|Duodene
	\|16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1		\|16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1
	\|~~Obvious~~ 5-limit detempering of 12edo.		\|5-limit detempering of 12edo formed by all ratios with powers -1, 0, 1, and 2 of the third harmonic and powers -1, 0, and 1 of the fifth.
	\|12, 34, 41, 53		\|12, 34, 41, 53
	\|}		\|}

Vector at 01:44, 5 January 2026

2026-01-05T01:44:01Z

← Older revision		Revision as of 01:44, 5 January 2026
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	This page serves as a collection of less notable [[Scale\|scales.]]		This page serves as a collection of less notable [[Scale\|scales]], other than MOSes, which are covered at [[MOS]].

	~~== JI lattices ==~~
	[[File:Mr bob.png\|thumb\|218x218px\|The lattice for the Chair of Mr. Bob]]		[[File:Mr bob.png\|thumb\|218x218px\|The lattice for the Chair of Mr. Bob]]
			{\| class="wikitable"
	~~===~~ Kee'ra (Chair of Mr. Bob~~) ===~~		\|+
	~~This scale consists of the intervals~~ 21/20, 35/32, 6/5, 21/16, 7/5, 3/2, 8/5, 105/64~~, and~~ 7/4 ~~within the octave~~ 2/1. When it is loaded in Scale Workshop, the lattice resembles a chair. ~~The name "Chair of Mr. Bob" was given by [[dotuXil]]. The name "Kee'ra" was given by [[Vector Graphics]] to serve as a single~~-~~word name consistent with the most common scale names.~~		!Name
			!Intervals
	~~===~~ Duodene ~~===~~		!Comments
			!Good edos
	~~== MOSes ==~~		\|-
			\|Kee'ra, Chair of Mr. Bob
	~~=== Mellow chromatic ===~~		\|21/20 35/32 6/5 21/16 7/5 3/2 8/5 105/64 7/4 2/1
	~~The mellow chromatic scale is the [[MOS]] pattern 7L 5s. It is the soft child of the MOS [[diatonic]] scale~~, ~~and is the chromatic scale of [[meantone]]. It lacks a symmetric [[mode]]~~, ~~having an even number of steps per period.~~		\|When it is loaded in Scale Workshop, the lattice resembles a chair.
			\|31
	~~=== Pychromatic ===~~		\|-
	~~The pychromatic scale is the MOS pattern 5L 7s. It is the hard child of the MOS [[diatonic]] scale and is the [[Scale size~~\|~~chromatic]] scale of [[superpyth]] and of [[Pythagorean tuning\|Pythagorean]] tuning. It lacks a symmetric [[mode]], having an even number of steps per period.~~		\|Duodene
			\|16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1
			\|Obvious 5-limit detempering of 12edo.
			\|12, 34, 41, 53
			\|}

Vector at 04:03, 11 December 2025

2025-12-11T04:03:23Z

← Older revision		Revision as of 04:03, 11 December 2025
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	=== Mellow chromatic ===		=== Mellow chromatic ===
	The mellow chromatic scale is the MOS pattern 7L 5s. It is the soft child of the MOS [[diatonic]] scale, and is the chromatic scale of [[meantone]]. It lacks a symmetric [[mode]], having an even number of steps per period.		The mellow chromatic scale is the [[MOS]] pattern 7L 5s. It is the soft child of the MOS [[diatonic]] scale, and is the chromatic scale of [[meantone]]. It lacks a symmetric [[mode]], having an even number of steps per period.

	=== Pychromatic ===		=== Pychromatic ===
	The pychromatic scale is the MOS pattern 5L 7s. It is the hard child of the MOS [[diatonic]] scale and is the [[Scale size\|chromatic]] scale of [[superpyth]] and of [[Pythagorean tuning\|Pythagorean]] tuning. It lacks a symmetric [[mode]], having an even number of steps per period.		The pychromatic scale is the MOS pattern 5L 7s. It is the hard child of the MOS [[diatonic]] scale and is the [[Scale size\|chromatic]] scale of [[superpyth]] and of [[Pythagorean tuning\|Pythagorean]] tuning. It lacks a symmetric [[mode]], having an even number of steps per period.

Vector: Created page with "This page serves as a collection of less notable scales. == JI lattices == The lattice for the Chair of Mr. Bob === Kee'ra (Chair of Mr. Bob) === This scale consists of the intervals 21/20, 35/32, 6/5, 21/16, 7/5, 3/2, 8/5, 105/64, and 7/4 within the octave 2/1. When it is loaded in Scale Workshop, the lattice resembles a chair. The name "Chair of Mr. Bob" was given by dotuXil. The name "Kee'ra" was given by Vector Gr..."

2025-12-11T04:03:11Z

Created page with "This page serves as a collection of less notable scales. == JI lattices == thumb|218x218px|The lattice for the Chair of Mr. Bob === Kee'ra (Chair of Mr. Bob) === This scale consists of the intervals 21/20, 35/32, 6/5, 21/16, 7/5, 3/2, 8/5, 105/64, and 7/4 within the octave 2/1. When it is loaded in Scale Workshop, the lattice resembles a chair. The name "Chair of Mr. Bob" was given by dotuXil. The name "Kee'ra" was given by Vector Gr..."

New page

This page serves as a collection of less notable [[Scale|scales.]]

== JI lattices ==
[[File:Mr bob.png|thumb|218x218px|The lattice for the Chair of Mr. Bob]]

=== Kee'ra (Chair of Mr. Bob) ===
This scale consists of the intervals 21/20, 35/32, 6/5, 21/16, 7/5, 3/2, 8/5, 105/64, and 7/4 within the octave 2/1. When it is loaded in Scale Workshop, the lattice resembles a chair. The name "Chair of Mr. Bob" was given by [[dotuXil]]. The name "Kee'ra" was given by [[Vector Graphics]] to serve as a single-word name consistent with the most common scale names.

=== Duodene ===

== MOSes ==

=== Mellow chromatic ===
The mellow chromatic scale is the MOS pattern 7L 5s. It is the soft child of the MOS [[diatonic]] scale, and is the chromatic scale of [[meantone]]. It lacks a symmetric [[mode]], having an even number of steps per period.

=== Pychromatic ===
The pychromatic scale is the MOS pattern 5L 7s. It is the hard child of the MOS [[diatonic]] scale and is the [[Scale size|chromatic]] scale of [[superpyth]] and of [[Pythagorean tuning|Pythagorean]] tuning. It lacks a symmetric [[mode]], having an even number of steps per period.