Operations on MOSes: Difference between revisions
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This page describes common operations that can be performed on [[MOS scale|MOS scales]]. These operations, with a few exceptions, assume an [[abstract step pattern]] – a step pattern for which the step sizes are not specified – but can also apply to a [[concrete step pattern]]. Additionally, although the step patterns described here assume [[Octave equivalence|an equivalence interval of an octave]], these operations apply to any MOS pattern regardless of [[equivalence interval]]. | This page describes common operations that can be performed on [[MOS scale|MOS scales]]. These operations, with a few exceptions, assume an [[abstract step pattern]] – a step pattern for which the step sizes are not specified – but can also apply to a [[concrete step pattern]]. Additionally, although the step patterns described here assume [[Octave equivalence|an equivalence interval of an octave]], these operations apply to any MOS pattern regardless of [[equivalence interval]]. | ||
== Parent MOS == | == Relationship-based operations == | ||
=== Parent MOS === | |||
Given a MOS pattern ''x''L ''y''s, its '''parent''' is obtained by merging pairs of large and small steps together into one single step. The unpaired steps, regardless of their size, become the parent scale's small step. This process creates a subset MOS, called so since its scale degrees are a subset of the original scale's degrees. | Given a MOS pattern ''x''L ''y''s, its '''parent''' is obtained by merging pairs of large and small steps together into one single step. The unpaired steps, regardless of their size, become the parent scale's small step. This process creates a subset MOS, called so since its scale degrees are a subset of the original scale's degrees. | ||
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* The parent of 5L 3s is 3L 2s. | * The parent of 5L 3s is 3L 2s. | ||
== Sister MOS == | === Sister MOS === | ||
Given a MOS pattern ''x''L ''y''s, its '''sister''' is obtained by swapping the quantities of large and small steps, thus creating the step pattern ''y''L ''x''s. It is called such because both ''x''L ''y''s and ''y''L ''x''s have the same parent scale of ''z''L ''w''s, where ''z'' = min(''x'', ''y'') and ''w'' = abs(''x'' - ''y''). | Given a MOS pattern ''x''L ''y''s, its '''sister''' is obtained by swapping the quantities of large and small steps, thus creating the step pattern ''y''L ''x''s. It is called such because both ''x''L ''y''s and ''y''L ''x''s have the same parent scale of ''z''L ''w''s, where ''z'' = min(''x'', ''y'') and ''w'' = abs(''x'' - ''y''). | ||
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* The sister of 4L 4s is itself. | * The sister of 4L 4s is itself. | ||
== Daughter MOS == | === 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 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 c = L - s. This process creates a superset MOS, called so since the original scale's degrees can be found in the daughter scale. | ||
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* The daughters of 5L 3s are 8L 5s and 5L 8s. | * The daughters of 5L 3s are 8L 5s and 5L 8s. | ||
== Neutralization == | == Other operations == | ||
=== Neutralization === | |||
Given a MOS pattern ''x''L ''y''s, '''neutralization''' is the process in which pairs of large and small steps are each replaced with two neutral mossteps, whose size is defined as n = (L+s) / 2, with respect to the original scale. | Given a MOS pattern ''x''L ''y''s, '''neutralization''' is the process in which pairs of large and small steps are each replaced with two neutral mossteps, whose size is defined as n = (L+s) / 2, with respect to the original scale. | ||
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* Neutralizing 4L 4s produces 8 neutral steps with no large or small steps left over, thus produces 8 equal divisions of the octave. | * Neutralizing 4L 4s produces 8 neutral steps with no large or small steps left over, thus produces 8 equal divisions of the octave. | ||
== Dualization == | === Dualization === | ||
Given a MOS pattern ''x''L ''y''s with concrete 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 concrete 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. | ||