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"

}}A '''moment-of-symmetry scale''' (abbreviated as '''MOS scale''', '''MOSS''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''', pronounced "moss"; plural '''MOSes''' or '''mosses''') is a type of [[binary]] [[scale]].

}}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]].

== Definition ==

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

The concept of MOS scales were invented by [[Erv Wilson]] in 1975 in his paper ''Moments of Symmetry''~~, where, given an [[edo]]~~ of ~~''n'' equal divisions, a generator~~ of ~~''g'' edosteps can be stacked repeatedly to divide the octave.~~

The concept of MOS scales were invented by [[Erv Wilson]] in 1975 in his paper ''Moments of Symmetry''. A moment-of-symmetry scale consists of:

~~=== Equivalent definitions ===~~

* A generator and an [[equivalence interval]], called the period, usually the octave.

The ~~definition~~ of ~~a moment-~~of~~-symmetry scale has several equivalences to other concepts:~~

** 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.

* Two unique step sizes, called ''large'' and ''small'', commonly denoted using the letters L and s.

** The quantities of these steps are coprime, meaning they do not share any common factors greater than 1.

*[[~~Maximum variety~~]] 2~~: every interval that spans the same number of steps has two distinct varieties~~.

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.

*Binary and [[distributionally even]]: there are two distinct step sizes ~~that are distributed~~ as ~~evenly~~ as ~~possible~~. This is equivalent to ~~maximum variety 2~~.

{| class="wikitable"

*Binary and [[balanced]]: every interval that spans the same number of steps differs by having one large step being replaced with one small step.

|+Constructing a scale in 12edo using a generator of 7 edosteps

!Step visualization

!Step pattern

!Scale degrees

!Added scale degrees

!Scale produced

|-

|{{Step vis|7 5}}

|7 5

|0 7 12

|The first scale degree is at 7 edosteps from the root.

|

|-

|{{Step vis|2 5 5}}

|2 5 5

|0 2 7 12

|The next degree is at 14 edosteps. This is reduced (14 mod 12) to 2.

|

|-

|{{Step vis|2 5 2 3}}

|2 5 2 3

|0 2 7 9 12

|The next degree is at 9 edosteps, but this results in three step sizes.

|

|-

|{{Step vis|2 2 3 2 3}}

|2 2 3 2 3

|0 2 4 7 9 12

|The next degree is at 16 edosteps. This is reduced (16 mod 12) to 4.

|The common pentatonic scale, denoted as '''2L 3s'''.

|-

|{{Step vis|2 2 3 2 2 1}}

|2 2 3 2 2 1

|0 2 4 7 9 11 12

|The next degree is at 11 edosteps, but this results in three step sizes.

|

|-

|{{Step vis|2 2 2 1 2 2 1}}

|2 2 2 1 2 2 1

|0 2 4 6 7 9 11 12

|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.

|}

=== Single-period and multi-period MOS scales ===

Wilson's original definition primarily focused on the period and equivalence interval being the same.

MOS scales in which the equivalence interval is a multiple of the period (or alternatively, the step pattern repeats multiple times within the equivalence interval), is commonly called a '''multi-MOS''' or '''multi-period MOS'''. This is to distinguish them from what Wilson had defined, called '''strict MOS''' or '''single-period MOS'''.

== Notation ==

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== Properties ==

The definition of a moment-of-symmetry scale has several equivalences to other concepts:

*[[Maximum variety]] 2: every interval that spans the same number of steps has two distinct varieties.

*Binary and [[distributionally even]]: there are two distinct step sizes that are distributed as evenly as possible. This is equivalent to maximum variety 2.

*Binary and [[balanced]]: every interval that spans the same number of steps differs by having one large step being replaced with one small step.

== Applications ==

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*[http://anaphoria.com/horo2.pdf More on Horogram Rhythms]

==Listen==

This is an algorithmically generated recording of every MOS scale that has 14 or fewer notes for a total of 91 scales being showcased here. Each MOS scale played has its simplest step ratio (large step is 2 small step is 1) and therefore is inside the smallest EDO that can support it. Each MOS scale is also in its brightest mode. And rhythmically, each scale is being played with its respective MOS rhythm. Note that changing the mode or step ratio of any of these MOSes may dramatically alter the sound and therefore this recording is not thoroughly representative of each MOS but rather a small taste.[[File:Every-MOS-Scale-With-14-Or-Fewer-Notes.mp3|left|~~800x800px~~]]

This is an algorithmically generated recording of every MOS scale that has 14 or fewer notes for a total of 91 scales being showcased here. Each MOS scale played has its simplest step ratio (large step is 2 small step is 1) and therefore is inside the smallest EDO that can support it. Each MOS scale is also in its brightest mode. And rhythmically, each scale is being played with its respective MOS rhythm. Note that changing the mode or step ratio of any of these MOSes may dramatically alter the sound and therefore this recording is not thoroughly representative of each MOS but rather a small taste.[[File:Every-MOS-Scale-With-14-Or-Fewer-Notes.mp3|left|95x95px]]

==See also==

*[[Diamond-mos notation]], a microtonal notation system focussed on MOS scales

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*[[:Category:MOS scales]], the category including all MOS-related articles on this wiki

*[[Gallery of MOS patterns]]

== External links ==

* 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

@@ 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"
-}}A '''moment-of-symmetry scale''' (abbreviated as '''MOS scale''', '''MOSS''', or '''MOS''', pronounced "em-oh-ess"; also spelled as '''mos''', pronounced "moss"; plural '''MOSes''' or '''mosses''') is a type of [[binary]] [[scale]].
+}}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]].
 == Definition ==
 === Erv Wilson's original definition ===
-The concept of MOS scales were invented by [[Erv Wilson]] in 1975 in his paper ''Moments of Symmetry'', where, given an [[edo]] of ''n'' equal divisions, a generator of ''g'' edosteps can be stacked repeatedly to divide the octave.
+The concept of MOS scales were invented by [[Erv Wilson]] in 1975 in his paper ''Moments of Symmetry''. A moment-of-symmetry scale consists of:
-=== Equivalent definitions ===
+* A generator and an [[equivalence interval]], called the period, usually the octave.
-The definition of a moment-of-symmetry scale has several equivalences to other concepts:
+** 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.
+* Two unique step sizes, called ''large'' and ''small'', commonly denoted using the letters L and s.
+** The quantities of these steps are coprime, meaning they do not share any common factors greater than 1.
-*[[Maximum variety]] 2: every interval that spans the same number of steps has two distinct varieties.
+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.
-*Binary and [[distributionally even]]: there are two distinct step sizes that are distributed as evenly as possible. This is equivalent to maximum variety 2.
+{| class="wikitable"
-*Binary and [[balanced]]: every interval that spans the same number of steps differs by having one large step being replaced with one small step.
+|+Constructing a scale in 12edo using a generator of 7 edosteps
+!Step visualization
+!Step pattern
+!Scale degrees
+!Added scale degrees
+!Scale produced
+|-
+|{{Step vis|7 5}}
+|7 5
+|0 7 12
+|The first scale degree is at 7 edosteps from the root.
+|
+|-
+|{{Step vis|2 5 5}}
+|2 5 5
+|0 2 7 12
+|The next degree is at 14 edosteps. This is reduced (14 mod 12) to 2.
+|
+|-
+|{{Step vis|2 5 2 3}}
+|2 5 2 3
+|0 2 7 9 12
+|The next degree is at 9 edosteps, but this results in three step sizes.
+|
+|-
+|{{Step vis|2 2 3 2 3}}
+|2 2 3 2 3
+|0 2 4 7 9 12
+|The next degree is at 16 edosteps. This is reduced (16 mod 12) to 4.
+|The common pentatonic scale, denoted as '''2L 3s'''.
+|-
+|{{Step vis|2 2 3 2 2 1}}
+|2 2 3 2 2 1
+|0 2 4 7 9 11 12
+|The next degree is at 11 edosteps, but this results in three step sizes.
+|
+|-
+|{{Step vis|2 2 2 1 2 2 1}}
+|2 2 2 1 2 2 1
+|0 2 4 6 7 9 11 12
+|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.
+|}
 === Single-period and multi-period MOS scales ===
+Wilson's original definition primarily focused on the period and equivalence interval being the same.
+MOS scales in which the equivalence interval is a multiple of the period (or alternatively, the step pattern repeats multiple times within the equivalence interval), is commonly called a '''multi-MOS''' or '''multi-period MOS'''. This is to distinguish them from what Wilson had defined, called '''strict MOS''' or '''single-period MOS'''.
 == Notation ==
@@ Line 27: / Line 74: @@
 == Properties ==
+The definition of a moment-of-symmetry scale has several equivalences to other concepts:
+*[[Maximum variety]] 2: every interval that spans the same number of steps has two distinct varieties.
+*Binary and [[distributionally even]]: there are two distinct step sizes that are distributed as evenly as possible. This is equivalent to maximum variety 2.
+*Binary and [[balanced]]: every interval that spans the same number of steps differs by having one large step being replaced with one small step.
 == Applications ==
@@ Line 83: / Line 134: @@
 *[http://anaphoria.com/horo2.pdf More on Horogram Rhythms]
 ==Listen==
-This is an algorithmically generated recording of every MOS scale that has 14 or fewer notes for a total of 91 scales being showcased here. Each MOS scale played has its simplest step ratio (large step is 2 small step is 1) and therefore is inside the smallest EDO that can support it. Each MOS scale is also in its brightest mode. And rhythmically, each scale is being played with its respective MOS rhythm. Note that changing the mode or step ratio of any of these MOSes may dramatically alter the sound and therefore this recording is not thoroughly representative of each MOS but rather a small taste.[[File:Every-MOS-Scale-With-14-Or-Fewer-Notes.mp3|left|800x800px]]
+This is an algorithmically generated recording of every MOS scale that has 14 or fewer notes for a total of 91 scales being showcased here. Each MOS scale played has its simplest step ratio (large step is 2 small step is 1) and therefore is inside the smallest EDO that can support it. Each MOS scale is also in its brightest mode. And rhythmically, each scale is being played with its respective MOS rhythm. Note that changing the mode or step ratio of any of these MOSes may dramatically alter the sound and therefore this recording is not thoroughly representative of each MOS but rather a small taste.[[File:Every-MOS-Scale-With-14-Or-Fewer-Notes.mp3|left|95x95px]]
 ==See also==
 *[[Diamond-mos notation]], a microtonal notation system focussed on MOS scales
@@ Line 89: / Line 142: @@
 *[[:Category:MOS scales]], the category including all MOS-related articles on this wiki
 *[[Gallery of MOS patterns]]<!-- sort order in category: this page shows above A -->
+== External links ==
+* 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