Operations on MOSes - Revision history

ArrowHead294 at 02:26, 26 January 2026

2026-01-26T02:26:31Z

← Older revision		Revision as of 02:26, 26 January 2026
Line 75:		Line 75:

	=== 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 {{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"		{\| class="wikitable"
Line 98:		Line 98:
	\| 7L 5s		\| 7L 5s
	\| sLsLsLLsLsLL		\| 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}}.		* 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 3L		\| 4n 3L
	\| LL'''nn'''L'''nn'''		\| 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		\| 3L 4s
	\| LsLsLss		\| LsLsLss
	\| After rearranging, the neutralized scale is 3L 4s since:<br />		\| After rearranging, the neutralized scale is 3L 4s since:<br />
	* Original large step becomes the new scale's large step.		* 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.		* 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.		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"		{\| class="wikitable"
Line 175:		Line 175:
	\| 7L 2s		\| 7L 2s
	\| LLLLsLLLs		\| 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}}		\| {{Step vis\|5 5 5 5 4 5 5 5 4}}
	\|-		\|-
	\| 5L 4s		\| 5L 4s
	\| LLsLsLsLs		\| 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}}		\| {{Step vis\|7 7 2 7 2 7 2 7 2}}
	\|-		\|-
	\| 7L 4s		\| 7L 4s
	\| LLsLLsLLsLs		\| 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}}		\| {{Step vis\|5 5 2 5 5 2 5 5 2 5 2}}
	\|}		\|}

	[[Category:MOS scale]]		[[Category:MOS scale]]

TallKite: /* Dualization */ clarifications

2025-04-18T20:32:34Z

Dualization: clarifications

← Older revision		Revision as of 20:32, 18 April 2025
Line 154:		Line 154:

	=== 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.		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.

	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's possible for a dual to be itself, if either ''x'' and L are the same or ''y'' and s are the same.

ArrowHead294: /* Dualization */

2025-03-14T13:45:20Z

Dualization

← Older revision		Revision as of 13:45, 14 March 2025
Line 156:		Line 156:
	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.

	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's possible for a dual to be itself, if either ''x'' and L are the same or ''y'' and s are the same.

	{\| class="wikitable"		{\| class="wikitable"

ArrowHead294 at 13:44, 14 March 2025

2025-03-14T13:44:43Z

Show changes

ArrowHead294 at 08:56, 27 December 2024

2024-12-27T08:56:08Z

← Older revision		Revision as of 08:56, 27 December 2024
Line 7:		Line 7:
	\| ro = Operații asupra G2S		\| ro = Operații asupra G2S
	}}		}}
	:''This page assumes the reader is familiar with the concept of [[MOS scales]].''		: ''This page assumes the reader is familiar with the concept of [[MOS scales]].''

	This page describes common operations that can be performed on [[MOS scale\|MOS scales]]. These operations, unless otherwise specified, 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, unless otherwise specified, 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]].

ArrowHead294: Formatting

2024-12-27T08:55:48Z

Formatting

Show changes

AraMax at 21:41, 26 December 2024

2024-12-26T21:41:26Z

← Older revision		Revision as of 21:41, 26 December 2024
Line 1:		Line 1:
	~~{{Foreign language\|Romanian}}~~{{interwiki		{{interwiki
	\| en = Operations on MOSes		\| en = Operations on MOSes
	\| de =		\| de =

AraMax at 21:40, 26 December 2024

2024-12-26T21:40:56Z

← Older revision		Revision as of 21:40, 26 December 2024
Line 1:		Line 1:
			{{Foreign language\|Romanian}}{{interwiki
			\| en = Operations on MOSes
			\| de =
			\| es =
			\| ja =
			\| ko =
			\| ro = Operații asupra G2S
			}}
	:''This page assumes the reader is familiar with the concept of [[MOS scales]].''		:''This page assumes the reader is familiar with the concept of [[MOS scales]].''

Ganaram inukshuk: Wording in lead section

2024-05-10T06:27:50Z

Wording in lead section

← Older revision		Revision as of 06:27, 10 May 2024
Line 1:		Line 1:
	:''This page assumes the reader is familiar with the concept of [[MOS scales]].''		:''This page assumes the reader is familiar with the concept of [[MOS scales]].''

	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, unless otherwise specified, 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]].

	== Relationship-based operations ==		== Relationship-based operations ==

Ganaram inukshuk: formatting, some rewording

2024-05-06T20:44:09Z

formatting, some rewording

← Older revision		Revision as of 20:44, 6 May 2024
Line 6:		Line 6:

	=== Parent MOS ===		=== 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.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Example with 5L 2s and its parent of 2L 3s		\|+Example with 5L 2s and its parent of 2L 3s
Line 60:		Line 60:

	=== 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.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Example with 5L 2s and its daughters of 5L 7s and 7L 5s		\|+Example with 5L 2s and its daughters of 5L 7s and 7L 5s
Line 98:		Line 98:

	=== Neutralization ===		=== 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. The resulting scale, after rearranging the steps, is also a MOS scale since it has two step sizes: the neutral steps and either the large step or small step, depending on which step size is left over.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Example with 5L 2s neutralized to 3L 4s		\|+Example with 5L 2s neutralized to 3L 4s