User:Ganaram inukshuk/MOS scale: Difference between revisions

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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=

|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'''~~, '''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''' (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]].

== ~~Definition~~ ==

== An example with the diatonic scale ''(for beginner page)'' ==

''Use sintel's example here.''

== An example with the diatonic scale ''(for advanced page)''==

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

Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of:

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* 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.

{| class="wikitable"

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|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.

{| class="wikitable"

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|The common chromatic scale.

|}

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

=== Equivalent definitions ===

@@ Line 1: / Line 1: @@
 {{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''', '''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''' (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]].
-== Definition ==
+== An example with the diatonic scale ''(for beginner page)'' ==
+''Use sintel's example here.''
+== An example with the diatonic scale ''(for advanced page)''==
 === Erv Wilson's original definition ===
 Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of:
@@ Line 13: / Line 15: @@
 * 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.
 {| class="wikitable"
@@ Line 92: / Line 95: @@
 |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.
 {| class="wikitable"
@@ Line 140: / Line 144: @@
 |The common chromatic scale.
 |}
-==== Modes ====
 === Equivalent definitions ===