Operations on MOSes: Difference between revisions

Line 75:

=== Daughter MOS ===

Given a MOS pattern ''x''L ''y''s, its '''daughters''' are obtained by splitting its large steps into two more smaller steps ''s'' and ''c'', where the size of ''c'' is defined as {{nowrap|''c'' {{=}} L − ''s''}}. This process creates a ''superset MOS'', called so since the original scale's degrees can be found in the daughter scale.

Given a MOS pattern ''x''L ''y''s, its '''daughters''' are obtained by splitting its large steps into two more smaller steps ''s'' and ''c'', where the size of ''c'' is defined as {{nowrap|''c'' {{=}} ''L'' − ''s''}}. This process creates a ''superset MOS'', called so since the original scale's degrees can be found in the daughter scale.

{| class="wikitable"

Line 98:

| 7L 5s

| sLsLsLLsLsLL

| If the step ''s'' is larger than ''c'', then ''c'' becomes the new small step and the ''s''{{'}}s become the new large step.

| If the step ''s'' is larger than ''c'', then ''c'' becomes the new small step and the ''s''{{`s}} become the new large step.

|}

The daughters have two forms, depending on whether ''s'' or ''c'' is larger. Note that when working with abstract step values, it makes sense to talk about both daughters, but if the step sizes L and ''s'' are specified, then there will only be one daughter.

The daughters have two forms, depending on whether ''s'' or ''c'' is larger. Note that when working with abstract step values, it makes sense to talk about both daughters, but if the step sizes ''L'' and ''s'' are specified, then there will only be one daughter.

* If ''s'' is larger than ''c'', then ''s'' becomes the new large step and ''c'' becomes the new small step. The daughter scale is {{nowrap|(''x'' + ''y'')L ''x''s}}.

Line 130:

| 4n 3L

| LL'''nn'''L'''nn'''

| Replacing adjacent L's and s's doesn't produce a valid MOS, but the steps can be rearranged to produce one.

| Replacing adjacent ''L''{{'s}} and ''s''{{`s}} doesn't produce a valid MOS, but the steps can be rearranged to produce one.

|-

| 3L 4s

| LsLsLss

| After rearranging, the neutralized scale is 3L 4s since:

| After rearranging, the neutralized scale is 3L 4s since:

* Original large step becomes the new scale's large step.

* Neutral step becomes the small step as it's smaller than the original large step.

Line 156:

Unlike all the other operations, this operation only applies to a MOS tuned to an edo. The resulting MOS varies depending on the specific edo.

Given a MOS pattern ''x''L ''y''s with whole-number step sizes L and s, '''dualization''' is the process in which the values of ''x'' and L are swapped, the values of ''y'' and s are swapped, or both are swapped. This is not to be confused with the sister operation.

Given a MOS pattern ''x''L ''y''s with whole-number step sizes ''L'' and ''s'', '''dualization''' is the process in which the values of ''x'' and ''L'' are swapped, the values of ''y'' and ''s'' are swapped, or both are swapped. This is not to be confused with the sister operation.

Depending on which values are swapped, a different MOS scale is produced; however, the relationship between these scales depends on the sizes of L and s, and since {{nowrap|''x''L + ''y''s}} corresponds to the edo that supports the MOS, these relationships also depends on the edo. Additionally, it's possible for a dual to be itself, if either ''x'' and L are the same or ''y'' and s are the same.

Depending on which values are swapped, a different MOS scale is produced; however, the relationship between these scales depends on the sizes of ''L'' and ''s'', and since {{nowrap|''x''L + ''y''s}} corresponds to the edo that supports the MOS, these relationships also depends on the edo. Additionally, it is possible for a dual to be itself, if either ''x'' and ''L'' are the same or ''y'' and ''s'' are the same.

{| class="wikitable"

Line 175:

| 7L 2s

| LLLLsLLLs

| {{nowrap|L {{=}} 5|s {{=}} 4}} L-dual, as ''x'' and L are swapped

| {{nowrap|L {{=}} 5|s {{=}} 4}} ''L''-dual, as ''x'' and ''L'' are swapped

| {{Step vis|5 5 5 5 4 5 5 5 4}}

|-

| 5L 4s

| LLsLsLsLs

| {{nowrap|L {{=}} 7|s {{=}} 2}} s-dual, as ''y'' and s are swapped

| {{nowrap|L {{=}} 7|s {{=}} 2}} ''s''-dual, as ''y'' and ''s'' are swapped

| {{Step vis|7 7 2 7 2 7 2 7 2}}

|-

| 7L 4s

| LLsLLsLLsLs

| {{nowrap|L {{=}} 5|s {{=}} 2}} Ls-dual, as ''x'' and L are swapped, as are ''y'' with s

| {{nowrap|L {{=}} 5|s {{=}} 2}} ''Ls''-dual, as ''x'' and ''L'' are swapped, as are ''y'' with ''s''

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

|}

[[Category:MOS scale]]

@@ Line 75: / Line 75: @@
 === Daughter MOS ===
-Given a MOS pattern ''x''L&nbsp;''y''s, its '''daughters''' are obtained by splitting its large steps into two more smaller steps ''s'' and ''c'', where the size of ''c'' is defined as {{nowrap|''c'' {{=}} L − ''s''}}. This process creates a ''superset MOS'', called so since the original scale's degrees can be found in the daughter scale.
+Given a MOS pattern ''x''L&nbsp;''y''s, its '''daughters''' are obtained by splitting its large steps into two more smaller steps ''s'' and ''c'', where the size of ''c'' is defined as {{nowrap|''c'' {{=}} ''L'' − ''s''}}. This process creates a ''superset MOS'', called so since the original scale's degrees can be found in the daughter scale.
 {| class="wikitable"
@@ Line 98: / Line 98: @@
 | 7L&nbsp;5s
 | sLsLsLLsLsLL
-| If the step ''s'' is larger than ''c'', then ''c'' becomes the new small step and the ''s''{{'}}s become the new large step.
+| If the step ''s'' is larger than ''c'', then ''c'' becomes the new small step and the ''s''{{`s}} become the new large step.
 |}
-The daughters have two forms, depending on whether ''s'' or ''c'' is larger. Note that when working with abstract step values, it makes sense to talk about both daughters, but if the step sizes L and ''s'' are specified, then there will only be one daughter.
+The daughters have two forms, depending on whether ''s'' or ''c'' is larger. Note that when working with abstract step values, it makes sense to talk about both daughters, but if the step sizes ''L'' and ''s'' are specified, then there will only be one daughter.
 * If ''s'' is larger than ''c'', then ''s'' becomes the new large step and ''c'' becomes the new small step. The daughter scale is {{nowrap|(''x'' + ''y'')L ''x''s}}.
@@ Line 130: / Line 130: @@
 | 4n&nbsp;3L
 | LL'''nn'''L'''nn'''
-| Replacing adjacent L's and s's doesn't produce a valid MOS, but the steps can be rearranged to produce one.
+| Replacing adjacent ''L''{{'s}} and ''s''{{`s}} doesn't produce a valid MOS, but the steps can be rearranged to produce one.
 |-
 | 3L&nbsp;4s
 | LsLsLss
-| After rearranging, the neutralized scale is 3L 4s since:<br />
+| After rearranging, the neutralized scale is 3L&nbsp;4s since:<br />
 * Original large step becomes the new scale's large step.
 * Neutral step becomes the small step as it's smaller than the original large step.
@@ Line 156: / Line 156: @@
 Unlike all the other operations, this operation only applies to a MOS tuned to an edo. The resulting MOS varies depending on the specific edo.
-Given a MOS pattern ''x''L&nbsp;''y''s with whole-number step sizes L and s, '''dualization''' is the process in which the values of ''x'' and L are swapped, the values of ''y'' and s are swapped, or both are swapped. This is not to be confused with the sister operation.
+Given a MOS pattern ''x''L&nbsp;''y''s with whole-number step sizes ''L'' and ''s'', '''dualization''' is the process in which the values of ''x'' and ''L'' are swapped, the values of ''y'' and ''s'' are swapped, or both are swapped. This is not to be confused with the sister operation.
-Depending on which values are swapped, a different MOS scale is produced; however, the relationship between these scales depends on the sizes of L and s, and since {{nowrap|''x''L + ''y''s}} corresponds to the edo that supports the MOS, these relationships also depends on the edo. Additionally, it's possible for a dual to be itself, if either ''x'' and L are the same or ''y'' and s are the same.
+Depending on which values are swapped, a different MOS scale is produced; however, the relationship between these scales depends on the sizes of ''L'' and ''s'', and since {{nowrap|''x''L + ''y''s}} corresponds to the edo that supports the MOS, these relationships also depends on the edo. Additionally, it is possible for a dual to be itself, if either ''x'' and ''L'' are the same or ''y'' and ''s'' are the same.
 {| class="wikitable"
@@ Line 175: / Line 175: @@
 | 7L&nbsp;2s
 | LLLLsLLLs
-| {{nowrap|L {{=}} 5|s {{=}} 4}}<br />L-dual, as ''x'' and L are swapped
+| {{nowrap|L {{=}} 5|s {{=}} 4}}<br />''L''-dual, as ''x'' and ''L'' are swapped
 | {{Step vis|5 5 5 5 4 5 5 5 4}}
 |-
 | 5L&nbsp;4s
 | LLsLsLsLs
-| {{nowrap|L {{=}} 7|s {{=}} 2}}<br />s-dual, as ''y'' and s are swapped
+| {{nowrap|L {{=}} 7|s {{=}} 2}}<br />''s''-dual, as ''y'' and ''s'' are swapped
 | {{Step vis|7 7 2 7 2 7 2 7 2}}
 |-
 | 7L&nbsp;4s
 | LLsLLsLLsLs
-| {{nowrap|L {{=}} 5|s {{=}} 2}}<br />Ls-dual, as ''x'' and L are swapped, as are ''y'' with s
+| {{nowrap|L {{=}} 5|s {{=}} 2}}<br />''Ls''-dual, as ''x'' and ''L'' are swapped, as are ''y'' with ''s''
 | {{Step vis|5 5 2 5 5 2 5 5 2 5 2}}
 |}
 [[Category:MOS scale]]