User:Ganaram inukshuk/MOS scale - Revision history

Ganaram inukshuk: /* An example with the diatonic scale */

2024-05-24T00:50:07Z

An example with the diatonic scale

← Older revision		Revision as of 00:50, 24 May 2024
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	{{User:Ganaram inukshuk/Template:Rewrite draft\|MOS scale\|compare=https://en.xen.wiki/w/Special:ComparePages?page1=MOS+scale&rev1=&page2=User%3AGanaram+inukshuk%2FMOS+scale&rev2=&action=&diffonly=&unhide=		{{User:Ganaram inukshuk/Template:Rewrite draft\|MOS scale\|compare=https://en.xen.wiki/w/Special:ComparePages?page1=MOS+scale&rev1=&page2=User%3AGanaram+inukshuk%2FMOS+scale&rev2=&action=&diffonly=&unhide=
	\|changes=make lead section up-to-date with how mos/MOS is written; general rewrites aimed at the page being beginner page (so some stuff ''may'' need to be moved)		\|changes=make lead section up-to-date with how mos/MOS is written; general rewrites aimed at the page being beginner page (so some stuff ''may'' need to be moved)
	}}A '''moment-of-symmetry scale''' (~~also~~ called '''moment-of-symmetry''', commonly abbreviated as '''MOS scale''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''' or '''MOSS''', pronounced "moss"; plural '''MOS scales''', '''MOSes''', or '''mosses''') is a type of [[binary]], [[Periods and generators\|periodic scale constructed using a generator]]. The concept of moment-of-symmetry scales were originally invented by [[Erv Wilson]].		}}A '''moment-of-symmetry scale''' (originally called '''moment of symmetry'''; commonly abbreviated as '''MOS scale''' or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''' or '''MOSS''', pronounced "moss"; plural '''moments of symmetry''', '''moment of symmetry scales''', '''MOS scales''', '''MOSes''', or '''mosses''') is a type of [[binary]], [[Periods and generators\|periodic scale constructed using a generator]]. The concept of moment of symmetry scales were originally invented by [[Erv Wilson]].

	== An example with the diatonic scale ==		== An example with the diatonic scale ''(for beginner page)'' ==
			''Use sintel's example here.''

	== ~~Definition~~ ''(for advanced page)'' ==		== An example with the diatonic scale ''(for advanced page)''==
	=== Erv Wilson's original definition ===		=== Erv Wilson's original definition ===
	Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of:		Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of:

Ganaram inukshuk at 03:06, 7 May 2024

2024-05-07T03:06:52Z

← Older revision		Revision as of 03:06, 7 May 2024
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	{{User:Ganaram inukshuk/Template:Rewrite draft\|MOS scale\|compare=https://en.xen.wiki/w/Special:ComparePages?page1=MOS+scale&rev1=&page2=User%3AGanaram+inukshuk%2FMOS+scale&rev2=&action=&diffonly=&unhide=		{{User:Ganaram inukshuk/Template:Rewrite draft\|MOS scale\|compare=https://en.xen.wiki/w/Special:ComparePages?page1=MOS+scale&rev1=&page2=User%3AGanaram+inukshuk%2FMOS+scale&rev2=&action=&diffonly=&unhide=
	\|changes=~~general rewrites; definition; wrangle different ways~~ to ~~say "~~mos"; ~~making mos theory feel more unified as it~~'~~s presented on the wiki~~		\|changes=make lead section up-to-date with how mos/MOS is written; general rewrites aimed at the page being beginner page (so some stuff ''may'' need to be moved)
	}}A '''moment-of-symmetry scale''' (also called '''moment-of-symmetry''', commonly abbreviated as '''MOS scale''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''' or '''MOSS''', pronounced "moss"; plural '''MOS scales''', '''MOSes''', or '''mosses''') is a type of [[binary]], [[Periods and generators\|periodic scale constructed using a generator]]. The concept of moment-of-symmetry scales were originally invented by [[Erv Wilson]].		}}A '''moment-of-symmetry scale''' (also called '''moment-of-symmetry''', commonly abbreviated as '''MOS scale''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''' or '''MOSS''', pronounced "moss"; plural '''MOS scales''', '''MOSes''', or '''mosses''') is a type of [[binary]], [[Periods and generators\|periodic scale constructed using a generator]]. The concept of moment-of-symmetry scales were originally invented by [[Erv Wilson]].

Ganaram inukshuk at 02:51, 7 May 2024

2024-05-07T02:51:36Z

← Older revision		Revision as of 02:51, 7 May 2024
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	}}A '''moment-of-symmetry scale''' (also called '''moment-of-symmetry''', commonly abbreviated as '''MOS scale''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''' or '''MOSS''', pronounced "moss"; plural '''MOS scales''', '''MOSes''', or '''mosses''') is a type of [[binary]], [[Periods and generators\|periodic scale constructed using a generator]]. The concept of moment-of-symmetry scales were originally invented by [[Erv Wilson]].		}}A '''moment-of-symmetry scale''' (also called '''moment-of-symmetry''', commonly abbreviated as '''MOS scale''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''' or '''MOSS''', pronounced "moss"; plural '''MOS scales''', '''MOSes''', or '''mosses''') is a type of [[binary]], [[Periods and generators\|periodic scale constructed using a generator]]. The concept of moment-of-symmetry scales were originally invented by [[Erv Wilson]].

	== ~~Definition~~ ==		== An example with the diatonic scale ==
	~~''Move to advanced page.''~~

			== Definition ''(for advanced page)'' ==
	=== Erv Wilson's original definition ===		=== Erv Wilson's original definition ===
	Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of:		Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of:

Ganaram inukshuk: Setup for adding more suggestions

2024-05-07T00:13:00Z

Setup for adding more suggestions

← Older revision		Revision as of 00:13, 7 May 2024
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	== Definition ==		== Definition ==
			''Move to advanced page.''

	=== Erv Wilson's original definition ===		=== Erv Wilson's original definition ===

Ganaram inukshuk: Added suggestions from discord wiki discussion; wip-in-progress

2024-05-06T20:11:11Z

Added suggestions from discord wiki discussion; wip-in-progress

← Older revision		Revision as of 20:11, 6 May 2024
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	{{User:Ganaram inukshuk/Template:Rewrite draft\|MOS scale\|compare=https://en.xen.wiki/w/Special:ComparePages?page1=MOS+scale&rev1=&page2=User%3AGanaram+inukshuk%2FMOS+scale&rev2=&action=&diffonly=&unhide=		{{User:Ganaram inukshuk/Template:Rewrite draft\|MOS scale\|compare=https://en.xen.wiki/w/Special:ComparePages?page1=MOS+scale&rev1=&page2=User%3AGanaram+inukshuk%2FMOS+scale&rev2=&action=&diffonly=&unhide=
	\|changes=general rewrites; definition; wrangle different ways to say "mos"; making mos theory feel more unified as it's presented on the wiki		\|changes=general rewrites; definition; wrangle different ways to say "mos"; making mos theory feel more unified as it's presented on the wiki
	}}A '''moment-of-symmetry scale''' (also called '''moment-of-symmetry''', commonly abbreviated as '''MOS scale~~''', '''MOSS~~''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''', pronounced "moss"; plural '''MOS scales''', '''MOSes''', or '''mosses''') is a type of [[binary]], [[Periods and generators\|periodic scale constructed using a generator]]. The concept of moment-of-symmetry scales were originally invented by [[Erv Wilson]].		}}A '''moment-of-symmetry scale''' (also called '''moment-of-symmetry''', commonly abbreviated as '''MOS scale''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''' or '''MOSS''', pronounced "moss"; plural '''MOS scales''', '''MOSes''', or '''mosses''') is a type of [[binary]], [[Periods and generators\|periodic scale constructed using a generator]]. The concept of moment-of-symmetry scales were originally invented by [[Erv Wilson]].

	== Definition ==		== Definition ==
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	* A quantity of large and small steps that is coprime, meaning they have no common factors other than 1.		* A quantity of large and small steps that is coprime, meaning they have no common factors other than 1.

			=== An example with the diatonic scale ===
	The prototypical example of a moment-of-symmetry is the common diatonic scale of [[12edo]], which can be produced using a generator of 7 edosteps.		The prototypical example of a moment-of-symmetry is the common diatonic scale of [[12edo]], which can be produced using a generator of 7 edosteps.
	{\| class="wikitable"		{\| class="wikitable"
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	\|0 1 2 ... 11 12		\|0 1 2 ... 11 12
	\|}		\|}
	With the above example, valid MOS scales are produced at 2L 3s (the common pentatonic scale) and 5L 2s (the common diatonic scale). ~~The pattern shown here can continue until~~ every ~~scale degree~~ of ~~12edo is added~~, ~~producing~~ the ~~common chromatic~~ scale.		With the above example, valid MOS scales are produced at 2L 3s (the common pentatonic scale) and 5L 2s (the common diatonic scale).

			A familiar property with the diatonic scale is that every interval – seconds, thirds, etc – has two sizes of major and minor. With the perfect 4th, these sizes are perfect and augmented, and with the perfect 5th, these sizes are perfect and diminsihed. These different sizes are accessed through the scale's different modes: lydian, ionian, mixolydian, dorian, aeolian, phrygian, and locrian. This property holds for all MOS scales, ''regardless of how many large and small steps there are''.

	~~==== Splitting of large steps ====~~
	It should be noted that the intermediate steps (adding generators 7 through 10) suggest that they are also MOS scales, as there are two unique step sizes of 2 and 1, but this is not the case. Looking at 2L 3s and 5L 2s, a pattern can be observed in which the large step of the preceding scale splits into both a large and small step of the next scale. This observation allows for this construction to be simplified further, and disallows the intermediate scales (7 to 10 generators added) from being counted as MOS scales.		It should be noted that the intermediate steps (adding generators 7 through 10) suggest that they are also MOS scales, as there are two unique step sizes of 2 and 1, but this is not the case. Looking at 2L 3s and 5L 2s, a pattern can be observed in which the large step of the preceding scale splits into both a large and small step of the next scale. This observation allows for this construction to be simplified further, and disallows the intermediate scales (7 to 10 generators added) from being counted as MOS scales.
	{\| class="wikitable"		{\| class="wikitable"
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	\|The common chromatic scale.		\|The common chromatic scale.
	\|}		\|}

	~~==== Modes ====~~

	=== Equivalent definitions ===		=== Equivalent definitions ===

Ganaram inukshuk: /* Modes */

2024-05-06T08:38:44Z

Modes

← Older revision		Revision as of 08:38, 6 May 2024
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	==== Splitting of large steps ====		==== Splitting of large steps ====
	It should be noted that the intermediate steps suggest that they are also MOS scales, as there are two unique step sizes of 2 and 1, but this is not the case. Looking at 2L 3s and 5L 2s, a pattern can be observed in which the large step of the preceding scale splits into both a large and small step of the next scale. This observation allows for this construction to be simplified further, and disallows the intermediate scales (7 to 10 generators added) from being counted as MOS scales.		It should be noted that the intermediate steps (adding generators 7 through 10) suggest that they are also MOS scales, as there are two unique step sizes of 2 and 1, but this is not the case. Looking at 2L 3s and 5L 2s, a pattern can be observed in which the large step of the preceding scale splits into both a large and small step of the next scale. This observation allows for this construction to be simplified further, and disallows the intermediate scales (7 to 10 generators added) from being counted as MOS scales.
	{\| class="wikitable"		{\| class="wikitable"
			\|+Constructing a scale in 12edo using a generator of 7 edosteps, simplified
	!Generators added		!Generators added
	!Step visualization		!Step visualization

Ganaram inukshuk: /* Splitting of large steps */

2024-05-06T08:34:12Z

Splitting of large steps

← Older revision		Revision as of 08:34, 6 May 2024
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	==== Splitting of large steps ====		==== Splitting of large steps ====
	It should be noted that the intermediate steps suggest that they are also MOS scales, but this is not the case. Looking at 2L 3s and 5L 2s, a pattern can be observed in which the large step of the preceding scale splits into both a large and small step of the next scale. This observation allows for this construction to be simplified further, and disallows the intermediate scales (7 to 10 generators added) from being counted as MOS scales.		It should be noted that the intermediate steps suggest that they are also MOS scales, as there are two unique step sizes of 2 and 1, but this is not the case. Looking at 2L 3s and 5L 2s, a pattern can be observed in which the large step of the preceding scale splits into both a large and small step of the next scale. This observation allows for this construction to be simplified further, and disallows the intermediate scales (7 to 10 generators added) from being counted as MOS scales.
	{\| class="wikitable"		{\| class="wikitable"
	!Generators added		!Generators added

Ganaram inukshuk: /* Erv Wilson's original definition */

2024-05-06T08:32:12Z

Erv Wilson's original definition

@@ Line 8: / Line 8: @@
 Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of:
-* A generator and an [[equivalence interval]], called the period, which is usually the [[octave]].
+* A generator, an interval that is repeatedly stacked.
-** The generator is commonly denoted using a quantity of steps from an [[EDO|equal division of the octave]], where both the edo and generator are coprime, meaning they do not share any common factors greater than 1.
+* An equivalence interval, commonly called a period, which is usually the octave.
-* Two unique step sizes, called ''large'' and ''small'', commonly denoted using the letters L and s.
+* Two unique step sizes, called ''large'' and ''small'', commonly denoted using the letters L and s, respectively.
-** The quantities of these steps are also coprime.
+* A quantity of large and small steps that is coprime, meaning they have no common factors other than 1.
 The prototypical example of a moment-of-symmetry is the common diatonic scale of [[12edo]], which can be produced using a generator of 7 edosteps.
 {| class="wikitable"
 |+Constructing a scale in 12edo using a generator of 7 edosteps
 !Step visualization
 !Step pattern
@@ Line 22: / Line 23: @@
 !Scale produced
 |-
 |{{Step vis|7 5}}
 |7 5
@@ Line 28: / Line 30: @@
+|
 |-
 |{{Step vis|2 5 5}}
 |2 5 5
@@ Line 34: / Line 37: @@
+|
 |-
 |{{Step vis|2 5 2 3}}
 |2 5 2 3
@@ Line 40: / Line 44: @@
+|
 |-
 |{{Step vis|2 2 3 2 3}}
 |2 2 3 2 3
@@ Line 46: / Line 51: @@
 |The common pentatonic scale, denoted as '''2L 3s'''.
 |-
 |{{Step vis|2 2 3 2 2 1}}
 |2 2 3 2 2 1
@@ Line 52: / Line 58: @@
+|
 |-
 |{{Step vis|2 2 2 1 2 2 1}}
 |2 2 2 1 2 2 1
@@ Line 57: / Line 64: @@
 |The next degree is at 18 edosteps. This is reduced (18 mod 12) to 6.
 |The common diatonic scale, denoted as '''5L 2s'''. This is the lydian mode, equivalent to WWWHWWH.
 |}
 === Equivalent definitions ===
@@ Line 148: / Line 231: @@
 *The Wilson Archives on moment-of-symmetry scales: https://anaphoria.com/wilsonintroMOS.html
-*Erv Wilson's paper ''Moments of Symmetry'': http://anaphoria.com/wilsonintroMOS.html
+*Erv Wilson's paper ''Moments of Symmetry'': https://anaphoria.com/mos.pdf

Ganaram inukshuk: /* Notation and naming */

2024-05-06T06:02:12Z

Notation and naming

← Older revision		Revision as of 06:02, 6 May 2024
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	=== Erv Wilson's original definition ===		=== Erv Wilson's original definition ===
	Erv Wilson's 1975 ~~paper~~ ''Moments of Symmetry'' ~~provides the original definition of a moment-of-symmetry scale~~. A moment-of-symmetry scale consists of:		Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of:

	* A generator and an [[equivalence interval]], called the period, which is usually the [[octave]].		* A generator and an [[equivalence interval]], called the period, which is usually the [[octave]].
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	== Notation and naming==		== Notation and naming==
	{{See also\|MOS naming}}		{{See also\|MOS naming}}
	A moment-of-symmetry scale of ''x'' large steps and ''y'' small steps, where ''x'' and ''y'' are whole numbers, is denoted using the [[scale signature]] ''x''L ''y''s. In cases where one does not wish to distinguish between step sizes, the notation ''x''A ''y''B can be used instead, which can either refer to ''x''L ''y''s or ''y''L ''x''s.		A moment-of-symmetry scale of ''x'' large steps and ''y'' small steps, where ''x'' and ''y'' are whole numbers, is denoted using the [[scale signature]] ''x''L ''y''s. In cases where one does not wish to distinguish between step sizes, the notation ''x''A ''y''B can be used instead, which can either refer to ''x''L ''y''s or ''y''L ''x''s. Other notations may use different symbols for ''x''L ''y''s, such as ''a''L ''b''s, but these notations are identical.

	By default, the [[Equave\|equivalence interval]], or equave, of a MOS scale is assumed to be the [[octave]]. In discussions regarding MOS scales with [[non-octave]] equivalence intervals, the equivalence interval can be enclosed in angle brackets of either < > (less-than and greater-than symbols) or {{Angbr\| }} (Unicode symbols U+27E8 and U+27E9). Whereas "5L 2s", for example, refers to an octave-equivalent pattern of 5 large and 2 small steps, 5L 2s{{Angbr\|3/1}} refers to the same pattern but with 3/1 as the equivalence interval. To avoid conflicts with HTML tags, the use of Unicode symbols is advised over the former.		By default, the [[Equave\|equivalence interval]], or equave, of a MOS scale is assumed to be the [[octave]]. In discussions regarding MOS scales with [[non-octave]] equivalence intervals, the equivalence interval can be enclosed in angle brackets of either < > (less-than and greater-than symbols) or {{Angbr\| }} (Unicode symbols U+27E8 and U+27E9). Whereas "5L 2s", for example, refers to an octave-equivalent pattern of 5 large and 2 small steps, 5L 2s{{Angbr\|3/1}} refers to the same pattern but with 3/1 as the equivalence interval. To avoid conflicts with HTML tags, the use of Unicode symbols is advised over the former.
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	=== Step ratio ===		=== Step ratio ===
	{{Main~~\|Operations on MOSes}}{{See also~~\|Step ratio}}{{See also\|TAMNAMS#Step ratio spectrum}}		{{Main\|Step ratio}}{{See also\|TAMNAMS#Step ratio spectrum}}

	When it comes to musical applications, the ''step ratio'', the ratio between the size of the scale's large and small step, can have a profound effect on how the overall scale sounds. The step ratio is usually denoted as L:s, to disambiguate it from [[Ratios\|frequency ratios]], though the notation s:L is sometimes used to avoid division-by-zero.		When it comes to musical applications, the ''step ratio'', the ratio between the size of the scale's large and small step, can have a profound effect on how the overall scale sounds. The step ratio is usually denoted as L:s, to disambiguate it from [[Ratios\|frequency ratios]], though the notation s:L is sometimes used to avoid division-by-zero.
	===Relationship between MOS scales===		===Relationship between MOS scales===
			{{Main\|Operations on MOSes}}{{See also\|Recursive structure of MOS scales}}{{See also\|MOS scale family tree}}

	=== ~~Recursive~~ properties ===		=== Advanced properties ===

Ganaram inukshuk: /* Step ratio */

2024-05-06T05:48:12Z

Step ratio

← Older revision		Revision as of 05:48, 6 May 2024
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	When it comes to musical applications, the ''step ratio'', the ratio between the size of the scale's large and small step, can have a profound effect on how the overall scale sounds. The step ratio is usually denoted as L:s, to disambiguate it from [[Ratios\|frequency ratios]], though the notation s:L is sometimes used to avoid division-by-zero.		When it comes to musical applications, the ''step ratio'', the ratio between the size of the scale's large and small step, can have a profound effect on how the overall scale sounds. The step ratio is usually denoted as L:s, to disambiguate it from [[Ratios\|frequency ratios]], though the notation s:L is sometimes used to avoid division-by-zero.
	===~~Advanced discussion~~===		===Relationship between MOS scales===

			=== Recursive properties ===