MOS substitution: Difference between revisions

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'''MOS substitution''' is a procedure for obtaining a ternary (3 step sizes) scale from two [[MOS]] patterns. It consists of substituting the step pattern of one MOS pattern (called the filling MOS), scale step for scale step, for all occurrences of a chosen step size of another MOS pattern (called the template MOS). Unlike MV3 scales, a MOS substitution scale may have any combination of step sizes.

~~For example, if the template~~ MOS ~~is '''LXLXX'''~~, ~~and the filling MOS is '''mss''', then the resulting~~ MOS substitution scales are ~~'''LmLss''', '''LsLms''', and '''LsLsm'''. The first scale is~~ denoted "~~{{nowrap|~~subst 2L(~~1m2s 2{{pipe}}0~~)}}"~~, using [[UDP]] notation for the filling~~ MOS~~, and~~ is said to be a "{{nowrap|~~subst 2L~~(~~1m2s~~)}}~~". We always substitute into~~ the brightest mode of the template MOS, ~~where~~ X ~~is treated~~ as the smaller step.

[[Aberrismic theory]] uses MOS substitution. In fact, groundfault reports having come up with a similar concept but not following up on it.

== Convention ==

MOS substitution scales are denoted using the notation "subst ax(bycz)" or just "aX(bYcZ)". Any particular scale of a given MOS substitution type is said to be "a subst ax(bycz)" or "a scale of type ax(bycz)". A specific MOS substitution scale may be denoted {{nowrap|template_MOS_with_slot_letter_X(filling_MOS)}}; to make this notation unique for a particular given MOS-substitution scale, the brightest mode for the template MOS is conventionally used, treating the slot letter X as the smaller step.

{| class="wikitable"

|+ style="font-size: 105%;" | The three ~~{{nowrap|~~subst 2'''L'''(1'''m'''2'''s''')}} scales

|+ style="font-size: 105%;" | The three subst 2'''L'''(1'''m'''2'''s''') scales

|-

! rowspan="2" | [[Simplified UDP]] for filling MOS

Line 17:

Line 19:

| style="text-align: right;" | <code>mss</code>

| colspan="2" style="text-align: right;" | <code>LmLss</code>

| ~~{{nowrap|subst 2L~~(~~1m2s 2{{pipe}}0~~)}}

| LXLXX(mss)

|-

| 1{{pipe}}1

| style="text-align: right;" | <code>sms</code>

| colspan="2" style="text-align: right;" | <code>LsLms</code>

| ~~{{nowrap|subst 2L~~(~~1m2s 1{{pipe}}1~~)}}

| LXLXX(sms)

|-

| 0{{pipe}}2

| style="text-align: right;" | <code>ssm</code>

| colspan="2" style="text-align: right;" | <code>LsLsm</code>

| ~~{{nowrap|subst 2L~~(~~1m2s 0{{pipe}}2~~)}}

| LXLXX(ssm)

|}

~~Under defined conditions, MOS substitution scales have the advantage of having a [[generator sequence]].~~

The same operation can be done even when the scales involved are not MOS scales or necessarily even binary scales, in which context it may be called '''letterwise substitution''' or simply '''substitution'''.

~~[[Aberrismic theory]] uses MOS substitution. In fact, groundfault reports having come up with a similar concept but not following up on it.~~

== Todo ==

@@ Line 1: / Line 1: @@
 '''MOS substitution''' is a procedure for obtaining a ternary (3 step sizes) scale from two [[MOS]] patterns. It consists of substituting the step pattern of one MOS pattern (called the filling MOS), scale step for scale step, for all occurrences of a chosen step size of another MOS pattern (called the template MOS). Unlike MV3 scales, a MOS substitution scale may have any combination of step sizes.
-For example, if the template MOS is '''LXLXX''', and the filling MOS is '''mss''', then the resulting MOS substitution scales are '''LmLss''', '''LsLms''', and '''LsLsm'''. The first scale is denoted "{{nowrap|subst 2L(1m2s 2{{pipe}}0)}}", using [[UDP]] notation for the filling MOS, and is said to be a "{{nowrap|subst 2L(1m2s)}}". We always substitute into the brightest mode of the template MOS, where X is treated as the smaller step.
+[[Aberrismic theory]] uses MOS substitution. In fact, groundfault reports having come up with a similar concept but not following up on it.
+== Convention ==
+MOS substitution scales are denoted using the notation "subst ax(bycz)" or just "aX(bYcZ)". Any particular scale of a given MOS substitution type is said to be "a subst ax(bycz)" or "a scale of type ax(bycz)". A specific MOS substitution scale may be denoted {{nowrap|template_MOS_with_slot_letter_X(filling_MOS)}}; to make this notation unique for a particular given MOS-substitution scale, the brightest mode for the template MOS is conventionally used, treating the slot letter X as the smaller step.
 {| class="wikitable"
-|+ style="font-size: 105%;" | The three {{nowrap|subst 2'''L'''(1'''m'''2'''s''')}} scales
+|+ style="font-size: 105%;" | The three subst 2'''L'''(1'''m'''2'''s''') scales
 |-
 ! rowspan="2" | [[Simplified UDP]] for filling MOS
@@ Line 17: / Line 19: @@
 | style="text-align: right;" | <code>mss</code>
 | colspan="2" style="text-align: right;" | <code>LmLss</code>
-| {{nowrap|subst 2L(1m2s 2{{pipe}}0)}}
+| LXLXX(mss)
 |-
 | 1{{pipe}}1
 | style="text-align: right;" | <code>sms</code>
 | colspan="2" style="text-align: right;" | <code>LsLms</code>
-| {{nowrap|subst 2L(1m2s 1{{pipe}}1)}}
+| LXLXX(sms)
 |-
 | 0{{pipe}}2
 | style="text-align: right;" | <code>ssm</code>
 | colspan="2" style="text-align: right;" | <code>LsLsm</code>
-| {{nowrap|subst 2L(1m2s 0{{pipe}}2)}}
+| LXLXX(ssm)
 |}
-Under defined conditions, MOS substitution scales have the advantage of having a [[generator sequence]].
-The same operation can be done even when the scales involved are not MOS scales or necessarily even binary scales, in which context it may be called '''letterwise substitution''' or simply '''substitution'''.
-[[Aberrismic theory]] uses MOS substitution. In fact, groundfault reports having come up with a similar concept but not following up on it.
 == Todo ==