MOS substitution: Difference between revisions

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'''MOS substitution'''{{idiosyncratic}} 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 "subst 2L(1m2s 2|0)", using [[UDP]] notation for the filling MOS, and is said to be a "subst 2L(1m2s)". We always substitute into the brightest mode of the template MOS, where X is treated as the smaller step.

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.

{| class="wikitable"

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

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

|-

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

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Just as rotating the filling MOS while fixing the mode of the template MOS serves to distinguish different MOS substitution scales, we take the mode of the template MOS (treating the slot letter as the smaller step) and write it in UDP to indicate the mode of a given MOS substitution scale.

For example: Taking the 5|5 mode of the template MOS in ~~subst~~ {{nowrap|5'''L'''(2'''m'''4'''s''' 4{{!}}0(2))}} ('''LmLsLsLmLss''') yields the mode '''sLmLsLsLmLs''', denoted {{nowrap|"subst 5'''L'''(2'''m'''4'''s''' 4{{!}}0(2))}} 5|5".

For example: Taking the 5|5 mode of the template MOS in {{nowrap|subst 5'''L'''(2'''m'''4'''s''' 4{{pipe}}0(2))}} ('''LmLsLsLmLss''') yields the mode '''sLmLsLsLmLs''', denoted {{nowrap|"subst 5'''L'''(2'''m'''4'''s''' 4{{pipe}}0(2)) 5{{pipe}}5}}".

== Examples ==

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To derive groundfault's [[diamech]] scale which has step pattern <math>5\mathbf{L}2\mathbf{m}4\mathbf{s}</math> as <math>\mathsf{MOS\_subst}(5, 2, 4; \mathbf{m}, \mathbf{s}; k)</math>, we exploit <math>(b, c) = 2</math> and substitute <math>2\mathbf{m}4\mathbf{s}</math> into the template MOS <math>5\mathbf{L}6\mathbf{X}</math> (<math>\mathbf{LXLXLXLXLXX}</math>). Since <math>2\mathbf{m}4\mathbf{s}</math> has three distinct modes (<math>\mathbf{ssmssm}, \mathbf{smssms}, \mathbf{mssmss}</math>) and <math>5\mathbf{L}6\mathbf{X}</math> is primitive, we obtain three distinct scales, all of which admit length-3 generator sequences of 2-steps, representing all 3 possible rotations of <math>(\mathbf{L}+\mathbf{m}, \mathbf{L}+\mathbf{s}, \mathbf{L}+\mathbf{s})</math> as displayed in the following table:

{| class="wikitable"

|+ style="font-size: 105%;" | Diamech as subst 5'''L'''(2'''m'''4'''s''')

|+ style="font-size: 105%;" | Diamech as {{nowrap|subst 5'''L'''(2'''m'''4'''s''')}}

|-

! rowspan="2" | <math>k</math>

@@ Line 1: / Line 1: @@
 '''MOS substitution'''{{idiosyncratic}} 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 "subst 2L(1m2s 2|0)", using [[UDP]] notation for the filling MOS, and is said to be a "subst 2L(1m2s)". We always substitute into the brightest mode of the template MOS, where X is treated as the smaller step.
+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.
 {| class="wikitable"
-|+ style="font-size: 105%;" | The three subst 2'''L'''(1'''m'''2'''s''') scales
+|+ style="font-size: 105%;" | The three {{nowrap|subst 2'''L'''(1'''m'''2'''s''')}} scales
 |-
 ! rowspan="2" | [[UDP]] for filling MOS
@@ Line 68: / Line 68: @@
 Just as rotating the filling MOS while fixing the mode of the template MOS serves to distinguish different MOS substitution scales, we take the mode of the template MOS (treating the slot letter as the smaller step) and write it in UDP to indicate the mode of a given MOS substitution scale.
-For example: Taking the 5|5 mode of the template MOS in subst {{nowrap|5'''L'''(2'''m'''4'''s''' 4{{!}}0(2))}} ('''LmLsLsLmLss''') yields the mode '''sLmLsLsLmLs''', denoted {{nowrap|"subst 5'''L'''(2'''m'''4'''s''' 4{{!}}0(2))}} 5|5".
+For example: Taking the 5|5 mode of the template MOS in {{nowrap|subst 5'''L'''(2'''m'''4'''s''' 4{{pipe}}0(2))}} ('''LmLsLsLmLss''') yields the mode '''sLmLsLsLmLs''', denoted {{nowrap|"subst 5'''L'''(2'''m'''4'''s''' 4{{pipe}}0(2)) 5{{pipe}}5}}".
 == Examples ==
@@ Line 76: / Line 76: @@
 To derive groundfault's [[diamech]] scale which has step pattern <math>5\mathbf{L}2\mathbf{m}4\mathbf{s}</math> as <math>\mathsf{MOS\_subst}(5, 2, 4; \mathbf{m}, \mathbf{s}; k)</math>, we exploit <math>(b, c) = 2</math> and substitute <math>2\mathbf{m}4\mathbf{s}</math> into the template MOS <math>5\mathbf{L}6\mathbf{X}</math> (<math>\mathbf{LXLXLXLXLXX}</math>). Since <math>2\mathbf{m}4\mathbf{s}</math> has three distinct modes (<math>\mathbf{ssmssm}, \mathbf{smssms}, \mathbf{mssmss}</math>) and <math>5\mathbf{L}6\mathbf{X}</math> is primitive, we obtain three distinct scales, all of which admit length-3 generator sequences of 2-steps, representing all 3 possible rotations of <math>(\mathbf{L}+\mathbf{m}, \mathbf{L}+\mathbf{s}, \mathbf{L}+\mathbf{s})</math> as displayed in the following table:
 {| class="wikitable"
-|+ style="font-size: 105%;" | Diamech as subst 5'''L'''(2'''m'''4'''s''')
+|+ style="font-size: 105%;" | Diamech as {{nowrap|subst 5'''L'''(2'''m'''4'''s''')}}
 |-
 ! rowspan="2" | <math>k</math>