MOS - Revision history

Dogwithabome: added hardness audio demos

2026-04-04T16:33:51Z

added hardness audio demos

← Older revision		Revision as of 16:33, 4 April 2026
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	Examples for MOS diatonic:		Examples for MOS diatonic:
	* 12edo diatonic is "2 2 2 1 2 2 1", so it has hardness 2/1.		* 12edo diatonic is "2 2 2 1 2 2 1", so it has hardness 2/1. [[:File:Diatonic basic hardness demo.mp3]]
	* 17edo diatonic is "3 3 3 1 3 3 1", so it has hardness 3/1.		* 17edo diatonic is "3 3 3 1 3 3 1", so it has hardness 3/1. [[:File:Diatonic hard hardness demo.mp3]]
	* 19edo diatonic is "3 3 3 2 3 3 2", so it has hardness 3/2.		* 19edo diatonic is "3 3 3 2 3 3 2", so it has hardness 3/2. [[:File:Diatonic soft hardness demo.mp3]]
	* The equalized tuning is 7edo (1 1 1 1 1 1 1).		* The equalized tuning is 7edo (1 1 1 1 1 1 1). [[:File:Diatonic equalized hardness demo.mp3]]
	* The collapsed tuning is 5edo (1 1 1 0 1 1 0).		* The collapsed tuning is 5edo (1 1 1 0 1 1 0). [[:File:Diatonic collapsed hardness demo.mp3]]

	== Table of MOS scales ==		== Table of MOS scales ==

Inthar: /* Hardness */

2026-03-22T23:06:15Z

Hardness

← Older revision		Revision as of 23:06, 22 March 2026
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	Examples for MOS diatonic:		Examples for MOS diatonic:
	* 12edo diatonic is ~~2221221~~, so it has hardness 2/1.		* 12edo diatonic is "2 2 2 1 2 2 1", so it has hardness 2/1.
	* 17edo diatonic is ~~3331331~~, so it has hardness 3/1.		* 17edo diatonic is "3 3 3 1 3 3 1", so it has hardness 3/1.
	* 19edo diatonic is ~~3332332~~, so it has hardness 3/2.		* 19edo diatonic is "3 3 3 2 3 3 2", so it has hardness 3/2.
	* The equalized tuning is 7edo (~~1111111~~).		* The equalized tuning is 7edo (1 1 1 1 1 1 1).
	* The collapsed tuning is 5edo (~~1110110~~).		* The collapsed tuning is 5edo (1 1 1 0 1 1 0).

	== Table of MOS scales ==		== Table of MOS scales ==

Overthink: /* Table of MOS scales */ link all of them (also expand a few descriptions)

2026-03-21T03:50:34Z

Table of MOS scales: link all of them (also expand a few descriptions)

Show changes

2^67-1 at 10:51, 27 February 2026

2026-02-27T10:51:18Z

← Older revision		Revision as of 10:51, 27 February 2026
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	\|2\7 (342.9c)		\|2\7 (342.9c)
	\|		\|
	\|The 10-note MOS generated by neutral thirds. So named because of the exotemperament Dichotic.		\|The 10-note MOS generated by neutral thirds. So named because of the exotemperament [[Dichotic]].
	\|-		\|-
	!\|taric		!\|taric

Hkm at 20:39, 13 February 2026

2026-02-13T20:39:50Z

← Older revision		Revision as of 20:39, 13 February 2026
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	[[File:MOS.png\|thumb\|401x401px\|The comparison of non-MOS and MOS diatonic scales.]]		[[File:MOS.png\|thumb\|401x401px\|The comparison of non-MOS and MOS diatonic scales.]]
	A '''MOS''' (or '''mos''', or '''moment of symmetry''' scale) is a member of a family of scales which generalize properties of the diatonic and pentatonic scales within 12 equal temperament. Microtonal MOS scales are often seen as some of the easier microtonal scales to work with, because the ~~umber~~ of distinct intervals within the scale is quite low.		A '''MOS''' (or '''mos''', or '''moment of symmetry''' scale) is a member of a family of scales which generalize properties of the diatonic and pentatonic scales within 12 equal temperament. Microtonal MOS scales are often seen as some of the easier microtonal scales to work with, because the number of distinct intervals within the scale is quite low.

	Formally, a MOS is a scale where ~~every step is either small or large (with no in-between)~~, ~~and the same is true with any interval formed by~~ two ~~adjacent steps (a "2-step"), by three consecutive steps (a "3~~-step~~"), etc~~. Any multiple of the period (which is usually an octave or a fraction thereof) has only one size.[https://en.xen.wiki/w/MOS_scale] MOS scales are also known as '''MV2''' (or '''maximum variety 2''') scales.		As in any scale, we can define "n-step interval" to refer to one of many intervals that arise from ascending by n steps of the scale. Formally, a MOS is a scale where, for all n, there are at most two distinct sizes of n-step intervals. Any multiple of the period (which is usually an octave or a fraction thereof) has only one size.[https://en.xen.wiki/w/MOS_scale] MOS scales are also known as '''MV2''' (or '''maximum variety 2''') scales.

	MOS scales are often referred to as MOSes, thus MOS can be used as either an adjective or a noun.		MOS scales are often referred to as MOSes, thus MOS can be used as either an adjective or a noun.

			MOSses can be named according to their number of large and small steps (for example, 5L 2s for the diatonic MOS), because there is exactly one step pattern that fits the MOS criteria with any given number of small and large steps. This form of name does not specify the tuning of the MOS or which scale degree is defined as the tonic.

	== Examples ==		== Examples ==
	The most widely used MOS scale is the ~~MOS form of the~~ [[diatonic]] scale, which has five equal large steps (major seconds) and two equal small steps (minor seconds) within the octave. It can thus be notated 5L 2s~~, and it can be shown that there is a unique scale (counting [[Mode\|rotation]]s as the same scale) that meets the MOS criteria with a given number of large and small steps~~. ~~For example~~, the melodic minor scale (LsLLLLs) has only two step sizes, ~~but~~ it is not MOS since it has three different sizes of fifths: perfect, diminished, and augmented.		The most widely used MOS scale is the 12edo [[diatonic]] scale, which has five equal large steps (major seconds) and two equal small steps (minor seconds) within the octave. It can thus be notated 5L 2s. In contrast, while the melodic minor scale (LsLLLLs) has only two step sizes, it is still not MOS since it has three different sizes of fifths: perfect, diminished, and augmented.

	A MOS exists for any whole number of large and small steps, for example [[Mosh\|3L 4s]] (mosh), which functions as a "neutral" version of the diatonic scale, and [[Onyx\|1L 6s]] (onyx), which has 1 large step and thus a very wide range of tunings.		A MOS exists for any whole number of large and small steps, for example [[Mosh\|3L 4s]] (mosh), which functions as a "neutral" version of the diatonic scale, and [[Onyx\|1L 6s]] (onyx), which has 1 large step and thus a very wide range of tunings.
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	== Periods and generators ==		== Periods and generators ==
	Every MOS scale can be ''generated'' by stacking a certain interval called the [[generator]] ~~and [[octave-reducing]] (or more generally~~, ~~[[Generator\|~~period~~]]-reducing~~).[https://www.anaphoria.com/wilsonintroMOS.html] For example, the diatonic scale is generated by stacking 6 fifths (or equivalently, 6 fourths) and octave-reducing to get a 7 note scale. Another example, [[Pentic\|2L 3s]], is generated by stacking 4 fifths to get 5 notes. However, stacking 5 fifths to get a hexatonic scale such as C D E F G A C does not produce a MOS, because there are more than 2 sizes of ~~each~~ interval ~~class~~.		Every MOS scale can be ''generated'' by stacking a certain interval called the [[generator]] a number of times, then moving each note by multiples of the period (which is usually the octave) to fit within the span of one period.[https://www.anaphoria.com/wilsonintroMOS.html] The latter step is called period reduction. For example, the diatonic scale is generated by stacking 6 fifths (or equivalently, 6 fourths) and octave-reducing to get a 7 note scale. Another example, [[Pentic\|2L 3s]], is generated by stacking 4 fifths to get 5 notes. However, stacking 5 fifths to get a hexatonic scale such as C D E F G A C does not produce a MOS, because there are more than 2 sizes of some interval classes.

	The amount of stacking that produces a MOS scale depends only on the size of the generator relative to the size to the period. For a just fifth and a just octave, the valid scale sizes are 2, 3, 5, 7, 12, 17, 29, 41, 53... However for a quarter-comma [[meantone]] fifth, the valid sizes are 2, 3, 5, 7, 12, 19, 31, 50...		The amount of stacking that produces a MOS scale depends only on the size of the generator relative to the size to the period. For a just fifth and a just octave, the valid scale sizes are 2, 3, 5, 7, 12, 17, 29, 41, 53... However for a quarter-comma [[meantone]] fifth, the valid sizes are 2, 3, 5, 7, 12, 19, 31, 50...
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	== Table of MOS scales ==		== Table of MOS scales ==
			The following table lists common MOS scales grouped by scale size, along with their step patterns and associated [[Temperament\|temperaments]]. All temperaments mentioned in the table be found in the [[List of regular temperaments]]. All names in the first column do not specify anything about tuning or which scale degree is the tonic. Common MOSes are highlighted.
	{\| class="wikitable"		{\| class="wikitable"
	\|+ Table of some 2/1-equivalent MOSes~~. Temperaments are capitalized and can be found in the [[List of regular temperaments]]. Common MOSes are highlighted~~.		\|+ Table of some 2/1-equivalent MOSes.
	\|-		\|-
	!Name		!Name
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	!Equalized (softest) gen.		!Equalized (softest) gen.
	!Collapsed (hardest) gen.		!Collapsed (hardest) gen.
	!Period<br/>(1\1 (1200c) unless otherwise stated)		!Period<br />(1\1 (1200c) unless otherwise stated)
	!Description		!Description
	\|-		\|-
	! colspan="7" \|5-note MOSses		! colspan="7" \|5-note MOSses
	\|-		\|-
	!class="thl"\|pentic		! class="thl" \|pentic
	!class="thl"\|2L3s		! class="thl" \|2L3s
	\|LsLss		\|LsLss
	\|2\5 (480c)		\|2\5 (480c)
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	! colspan="7" \|7-note MOSses		! colspan="7" \|7-note MOSses
	\|-		\|-
	!class="thl"\|onyx		! class="thl" \|onyx
	!class="thl"\|1L6s		! class="thl" \|1L6s
	\|Lssssss		\|Lssssss
	\|1\7 (171.4c)		\|1\7 (171.4c)
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	\|When using a very flat fifth, reverses the interval qualities of diatonic. One temperament interpretation is Mabilic[7].		\|When using a very flat fifth, reverses the interval qualities of diatonic. One temperament interpretation is Mabilic[7].
	\|-		\|-
	!class="thl"\|mosh		! class="thl" \|mosh
	!class="thl"\|3L4s		! class="thl" \|3L4s
	\|LsLsLss		\|LsLsLss
	\|2\7 (342.9c)		\|2\7 (342.9c)
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	\|So named because the generator is a sharp minor third. Inthar finds that it sounds like a brighter, stretched version of the diatonic scale. In fact, it can be seen as a "warped" diatonic scale, because it can be found by replacing one large step of diatonic with a small step. One temperament interpretation is Orgone[7].		\|So named because the generator is a sharp minor third. Inthar finds that it sounds like a brighter, stretched version of the diatonic scale. In fact, it can be seen as a "warped" diatonic scale, because it can be found by replacing one large step of diatonic with a small step. One temperament interpretation is Orgone[7].
	\|-		\|-
	!class="thl"\|(MOS) diatonic		! class="thl" \|(MOS) diatonic
	!class="thl"\|5L2s		! class="thl" \|5L2s
	\|LLLsLLs		\|LLLsLLs
	\|4\7 (685.7c)		\|4\7 (685.7c)
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	\|1\6 (200c)		\|1\6 (200c)
	\|1\2 (600c)		\|1\2 (600c)
	\|Adv\|The 22edo (step ratio L:s = 3:2) tuning is associated with Hedgehog temperament. Lumi Pakkanen has described the sound of this MOS as "dreamy, yet oppressing", especially when tuned to step ratio 3:1.[https://en.xen.wiki/w/6L_2s]		\| Adv \|The 22edo (step ratio L:s = 3:2) tuning is associated with Hedgehog temperament. Lumi Pakkanen has described the sound of this MOS as "dreamy, yet oppressing", especially when tuned to step ratio 3:1.[https://en.xen.wiki/w/6L_2s]
	\|-		\|-
	!class="thl"\|pine		! class="thl" \|pine
	!class="thl"\|7L1s		! class="thl" \|7L1s
	\|LLLLLLLs		\|LLLLLLLs
	\|1\8 (150c)		\|1\8 (150c)
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	\|So named because the generator is a grave minor third. Associated with Orwell temperament. One of the more consonant 9-note MOSses, especially when tuned with a step ratio 4:3 < L:s < 3:2.		\|So named because the generator is a grave minor third. Associated with Orwell temperament. One of the more consonant 9-note MOSses, especially when tuned with a step ratio 4:3 < L:s < 3:2.
	\|-		\|-
	!class="thl"\|semiquartal		! class="thl" \|semiquartal
	!class="thl"\|5L4s		! class="thl" \|5L4s
	\|LLsLsLsLs		\|LLsLsLsLs
	\|2\9 (266.7c)		\|2\9 (266.7c)
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	\|{{Adv\|So named because of Pajara[10] and Injera[10] interpretations. Interpreted as Diaschismic[10] in 34edo and 46edo.}}		\|{{Adv\|So named because of Pajara[10] and Injera[10] interpretations. Interpreted as Diaschismic[10] in 34edo and 46edo.}}
	\|-		\|-
	!class="thl"\|pentawood		! class="thl" \|pentawood
	!class="thl"\|5L5s		! class="thl" \|5L5s
	\|LsLsLsLsLs		\|LsLsLsLsLs
	\|1\10 (120c)		\|1\10 (120c)
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	\|The 11-note MOS associated with Kleismic/Cata and Orgone, both accurate temperaments. Older material may call this scale "kleistonic."		\|The 11-note MOS associated with Kleismic/Cata and Orgone, both accurate temperaments. Older material may call this scale "kleistonic."
	\|-		\|-
	!class="thl"\|p-chromatic		! class="thl" \|p-chromatic
	!class="thl"\|5L7s		! class="thl" \|5L7s
	\|LsLsLssLsLss		\|LsLsLssLsLss
	\|7\12 (700c)		\|7\12 (700c)
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	\|A "straddle-fifth chromatic scale", as it can be constructed by stacking alternating flat and sharp fifths as long as they stack to 1\6, in e.g. 18edo.		\|A "straddle-fifth chromatic scale", as it can be constructed by stacking alternating flat and sharp fifths as long as they stack to 1\6, in e.g. 18edo.
	\|-		\|-
	!class="thl"\|m-chromatic		! class="thl" \|m-chromatic
	!class="thl"\|7L5s		! class="thl" \|7L5s
	\|LLsLsLLsLsLs		\|LLsLsLLsLsLs
	\|7\12 (700c)		\|7\12 (700c)

Hkm: not done fixing this page. i hope to do some more work on it later

2026-02-12T07:01:58Z

not done fixing this page. i hope to do some more work on it later

← Older revision		Revision as of 07:01, 12 February 2026
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	[[File:MOS.png\|thumb\|401x401px\|The comparison of non-MOS and MOS diatonic scales.]]		[[File:MOS.png\|thumb\|401x401px\|The comparison of non-MOS and MOS diatonic scales.]]
	A '''MOS''' (or '''mos''', or '''moment of symmetry''' scale) is a scale where every step is either small or large (with no in-between), and the same is true with any interval formed by two adjacent steps (a "2-step"), by three consecutive steps (a "3-step"), etc. Any multiple of the period (which is usually an octave or a fraction thereof) has only one size.[https://en.xen.wiki/w/MOS_scale] MOS scales are also known as '''MV2''' (or '''maximum variety 2''') scales.		A '''MOS''' (or '''mos''', or '''moment of symmetry''' scale) is a member of a family of scales which generalize properties of the diatonic and pentatonic scales within 12 equal temperament. Microtonal MOS scales are often seen as some of the easier microtonal scales to work with, because the umber of distinct intervals within the scale is quite low.

			Formally, a MOS is a scale where every step is either small or large (with no in-between), and the same is true with any interval formed by two adjacent steps (a "2-step"), by three consecutive steps (a "3-step"), etc. Any multiple of the period (which is usually an octave or a fraction thereof) has only one size.[https://en.xen.wiki/w/MOS_scale] MOS scales are also known as '''MV2''' (or '''maximum variety 2''') scales.

	MOS scales are often referred to as MOSes, thus MOS can be used as either an adjective or a noun.		MOS scales are often referred to as MOSes, thus MOS can be used as either an adjective or a noun.

Vector at 20:44, 8 February 2026

2026-02-08T20:44:44Z

← Older revision		Revision as of 20:44, 8 February 2026
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			[[File:MOS.png\|thumb\|401x401px\|The comparison of non-MOS and MOS diatonic scales.]]
	A '''MOS''' (or '''mos''', or '''moment of symmetry''' scale) is a scale where every step is either small or large (with no in-between), and the same is true with any interval formed by two adjacent steps (a "2-step"), by three consecutive steps (a "3-step"), etc. Any multiple of the period (which is usually an octave or a fraction thereof) has only one size.[https://en.xen.wiki/w/MOS_scale] MOS scales are also known as '''MV2''' (or '''maximum variety 2''') scales.		A '''MOS''' (or '''mos''', or '''moment of symmetry''' scale) is a scale where every step is either small or large (with no in-between), and the same is true with any interval formed by two adjacent steps (a "2-step"), by three consecutive steps (a "3-step"), etc. Any multiple of the period (which is usually an octave or a fraction thereof) has only one size.[https://en.xen.wiki/w/MOS_scale] MOS scales are also known as '''MV2''' (or '''maximum variety 2''') scales.

Hkm: Is there a problem with "adv" in tables??

2026-01-22T22:05:23Z

Is there a problem with "adv" in tables??

← Older revision		Revision as of 22:05, 22 January 2026
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	\|1\6 (200c)		\|1\6 (200c)
	\|1\2 (600c)		\|1\2 (600c)
	\|{{Adv\|The 22edo (step ratio L:s = 3:2) tuning is associated with Hedgehog temperament}}. Lumi Pakkanen has described the sound of this MOS as "dreamy, yet oppressing", especially when tuned to step ratio 3:1.[https://en.xen.wiki/w/6L_2s]		\|Adv\|The 22edo (step ratio L:s = 3:2) tuning is associated with Hedgehog temperament. Lumi Pakkanen has described the sound of this MOS as "dreamy, yet oppressing", especially when tuned to step ratio 3:1.[https://en.xen.wiki/w/6L_2s]
	\|-		\|-
	!class="thl"\|pine		!class="thl"\|pine

Hkm at 22:04, 22 January 2026

2026-01-22T22:04:14Z

← Older revision		Revision as of 22:04, 22 January 2026
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	\|1\6 (200c)		\|1\6 (200c)
	\|1\2 (600c)		\|1\2 (600c)
	\|The 22edo (step ratio L:s = 3:2) tuning is associated with Hedgehog temperament. Lumi Pakkanen has described the sound of this MOS as "dreamy, yet oppressing", especially when tuned to step ratio 3:1.[https://en.xen.wiki/w/6L_2s]		\|{{Adv\|The 22edo (step ratio L:s = 3:2) tuning is associated with Hedgehog temperament}}. Lumi Pakkanen has described the sound of this MOS as "dreamy, yet oppressing", especially when tuned to step ratio 3:1.[https://en.xen.wiki/w/6L_2s]
	\|-		\|-
	!class="thl"\|pine		!class="thl"\|pine

Hkm at 22:03, 22 January 2026

2026-01-22T22:03:29Z

← Older revision		Revision as of 22:03, 22 January 2026
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	\|1\6 (200c)		\|1\6 (200c)
	\|		\|
	\|{{Adv\|Some temperament interpretations: Tetracot[7], Didacus[7].}		\|{{Adv\|Some temperament interpretations: Tetracot[7], Didacus[7].}}
	\|-		\|-
	! colspan="7" \|8-note MOSses		! colspan="7" \|8-note MOSses