MOS inflection - Revision history

BudjarnLambeth: /* MOS vs MODMOS vs MOS inflection */ correction

2026-04-27T23:24:29Z

MOS vs MODMOS vs MOS inflection: correction

← Older revision		Revision as of 23:24, 27 April 2026
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	If we take a MOS scale, and adjust one or more its notes up or down by some ''other'' consistent interval besides a chroma, we instead obtain an inflected MOS scale. This process is called '''MOS inflection'''.		If we take a MOS scale, and adjust one or more its notes up or down by some ''other'' consistent interval besides a chroma, we instead obtain an inflected MOS scale. This process is called '''MOS inflection'''.

	A scale ~~constructed in this way lacks many useful structural properties of~~ a MODMOS, most importantly [[epimorphism]]. Compared to a MODMOS, it also preserves less of the character of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.		A scale being a MODMOS guarantees a number of useful characteristics, most importantly [[epimorphism]]. A MOS inflection ''might'' sometimes have these properties, but it often doesn't. Compared to a MODMOS, it also typically preserves less of the 'character' of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.

	== Types of MOS inflection ==		== Types of MOS inflection ==

BudjarnLambeth: /* Types of MOS inflection */ Replaced 4 inline idiosyncratics with 1 messagebox

2024-03-02T03:11:56Z

Types of MOS inflection: Replaced 4 inline idiosyncratics with 1 messagebox

← Older revision		Revision as of 03:11, 2 March 2024
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	== Types of MOS inflection ==		== Types of MOS inflection ==
			{{Idiosyncratic terms\|The terms for the different kinds of MOS inflection, proposed by [[Budjarn Lambeth]]}}

	It’s likely that many more types could be conceived of. Feel free to edit this page and add any which you find useful or interesting.		It’s likely that many more types could be conceived of. Feel free to edit this page and add any which you find useful or interesting.
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	=== Robust MOS inflection ===		=== Robust MOS inflection ===

	Robust MOS inflection~~{{idiosyncratic}}~~ is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.		Robust MOS inflection is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.

	This will result in a scale which is a subset of some larger MOS scale with the same generator and period.		This will result in a scale which is a subset of some larger MOS scale with the same generator and period.
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	=== Semirobust MOS inflection ===		=== Semirobust MOS inflection ===

	Semirobust MOS inflection~~{{idiosyncratic}}~~ is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.		Semirobust MOS inflection is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.

	For example, if you take this Negri[8] MOS:		For example, if you take this Negri[8] MOS:
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	=== Frankenstein MOS inflection ===		=== Frankenstein MOS inflection ===

	Frankenstein MOS inflection~~{{idiosyncratic}}~~ is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).		Frankenstein MOS inflection is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).

	For example, if you take this Negri[7] MOS in [[67edo]]:		For example, if you take this Negri[7] MOS in [[67edo]]:
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	=== Aspirational MOS inflection ===		=== Aspirational MOS inflection ===

	Aspirational MOS inflection~~{{idiosyncratic}}~~ is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.		Aspirational MOS inflection is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.

	For example, if you take this Negri[7] MOS in 67edo:		For example, if you take this Negri[7] MOS in 67edo:

Fredg999: Marked MOS inflection types as idiosyncratic for now

2024-01-23T06:39:14Z

Marked MOS inflection types as idiosyncratic for now

FloraC: Link "octave reduction" for "octave-reduce"

2024-01-16T13:21:42Z

Link "octave reduction" for "octave-reduce"

← Older revision		Revision as of 13:21, 16 January 2024
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	* 1200.000		* 1200.000

	Then alter two of its steps by increments of 125.373 [[cents]], and then [[octave reduce]] the result, you get the following robust inflected MOS:		Then alter two of its steps by increments of 125.373 [[cents]], and then [[octave reduction\|octave-reduce]] the result, you get the following robust inflected MOS:

	* 125.373		* 125.373

BudjarnLambeth at 18:48, 14 January 2024

2024-01-14T18:48:43Z

← Older revision		Revision as of 18:48, 14 January 2024
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	Aspirational MOS inflection may be conducted with similar goals to [[well temperament]]: it may be used to blunt the rough edges of an MOS by sanding over one or two of its [[wolf interval]]s.		Aspirational MOS inflection may be conducted with similar goals to [[well temperament]]: it may be used to blunt the rough edges of an MOS by sanding over one or two of its [[wolf interval]]s.

	[[Category:MOS scale~~]][[Category:MODMOS~~]]		[[Category:MOS scale]]

BudjarnLambeth: /* MOS vs MODMOS vs MOS inflection */

2024-01-14T18:44:28Z

MOS vs MODMOS vs MOS inflection

← Older revision		Revision as of 18:44, 14 January 2024
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	If we take a MOS scale, and adjust one or more its notes up or down by some ''other'' consistent interval besides a chroma, we instead obtain an inflected MOS scale. This process is called '''MOS inflection'''.		If we take a MOS scale, and adjust one or more its notes up or down by some ''other'' consistent interval besides a chroma, we instead obtain an inflected MOS scale. This process is called '''MOS inflection'''.

	~~An inflected MOS~~ lacks many useful structural properties of a MODMOS, most importantly [[epimorphism]]. Compared to a MODMOS, it also preserves less of the character of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.		A scale constructed in this way lacks many useful structural properties of a MODMOS, most importantly [[epimorphism]]. Compared to a MODMOS, it also preserves less of the character of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.

	== Types of MOS inflection ==		== Types of MOS inflection ==

BudjarnLambeth: /* Robust MOS inflection */

2024-01-14T18:37:25Z

Robust MOS inflection

← Older revision		Revision as of 18:37, 14 January 2024
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	This will result in a scale which is a subset of some larger MOS scale with the same generator and period.		This will result in a scale which is a subset of some larger MOS scale with the same generator and period.

	Compared to other ~~forms~~ of MOS inflection, a robust ~~inflected~~ MOS more closely preserves the harmonic flavors of the original MOS, though it still doesn’t preserve them as well as a MODMOS would.		Compared to other types of MOS inflection, robust MOS inflection more closely preserves the harmonic flavors of the original MOS, though it still doesn’t preserve them as well as a MODMOS would.

	For example, if you take this [[Negri]][8] MOS:		For example, if you take this [[Negri]][8] MOS:

BudjarnLambeth: /* Robust MOS inflection */

2024-01-14T18:37:05Z

Robust MOS inflection

← Older revision		Revision as of 18:37, 14 January 2024
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	This will result in a scale which is a subset of some larger MOS scale with the same generator and period.		This will result in a scale which is a subset of some larger MOS scale with the same generator and period.

	Compared to other ~~inflected~~ MOS ~~scales~~, a robust inflected MOS more closely preserves the harmonic flavors of the original MOS, though it still doesn’t preserve them as well as a MODMOS would.		Compared to other forms of MOS inflection, a robust inflected MOS more closely preserves the harmonic flavors of the original MOS, though it still doesn’t preserve them as well as a MODMOS would.

	For example, if you take this [[Negri]][8] MOS:		For example, if you take this [[Negri]][8] MOS:

BudjarnLambeth at 18:36, 14 January 2024

2024-01-14T18:36:14Z

← Older revision		Revision as of 18:36, 14 January 2024
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	~~Temporary~~

	== MOS vs MODMOS vs MOS inflection ==		== MOS vs MODMOS vs MOS inflection ==

BudjarnLambeth: Re worded page to be about the process instead of the end result

2024-01-14T18:36:04Z

Re worded page to be about the process instead of the end result

← Older revision		Revision as of 18:36, 14 January 2024
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	== MOS vs MODMOS vs ~~inflected~~ MOS ==		Temporary

			== MOS vs MODMOS vs MOS inflection ==

	A [[MOS scale]] is constructed by iterating a [[generator]] g inside of a [[period]] R. That is, for non-negative integers n, we take n*g and reduce it modulo the period R to the range 0 ≤ i < R. We stop only at points when there are exactly two sizes of [[interval]]s in the scale, the large interval L and the small interval s. If the period R is 1/P [[octave]] for some integer P, we obtain an octave-repeating periodic scale by conjoining P copies of the MOS scale inside R so as to produce a MOS scale for the whole octave.		A [[MOS scale]] is constructed by iterating a [[generator]] g inside of a [[period]] R. That is, for non-negative integers n, we take n*g and reduce it modulo the period R to the range 0 ≤ i < R. We stop only at points when there are exactly two sizes of [[interval]]s in the scale, the large interval L and the small interval s. If the period R is 1/P [[octave]] for some integer P, we obtain an octave-repeating periodic scale by conjoining P copies of the MOS scale inside R so as to produce a MOS scale for the whole octave.
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	If we take a MOS scale, and adjust one or more its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a [[MODMOS]] scale.		If we take a MOS scale, and adjust one or more its notes up or down by a chroma consistently, so that octave periodicity is respected, and do not obtain another MOS, then we obtain a [[MODMOS]] scale.

	If we take a MOS scale, and adjust one or more its notes up or down by some ''other'' consistent interval besides a chroma, we obtain an '''~~inflected~~ MOS ~~scale~~'''.		If we take a MOS scale, and adjust one or more its notes up or down by some ''other'' consistent interval besides a chroma, we instead obtain an inflected MOS scale. This process is called '''MOS inflection'''.

	An inflected MOS lacks many useful structural properties of a MODMOS, most importantly [[epimorphism]]. Compared to a MODMOS, it also preserves less of the character of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.		An inflected MOS lacks many useful structural properties of a MODMOS, most importantly [[epimorphism]]. Compared to a MODMOS, it also preserves less of the character of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.

	== Types of ~~inflected~~ MOS ==		== Types of MOS inflection ==

	It’s likely that many more types could be conceived of. Feel free to edit this page and add any which you find useful or interesting.		It’s likely that many more types could be conceived of. Feel free to edit this page and add any which you find useful or interesting.

	=== Robust ~~inflected~~ MOS ===		=== Robust MOS inflection ===

	~~A robust inflected~~ MOS is ~~an inflected MOS~~ where the interval of adjustment is one of the intervals which was already present within the original MOS scale.		Robust MOS inflection is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.

	This will result in a scale which is a subset of some larger MOS scale with the same generator and period.		This will result in a scale which is a subset of some larger MOS scale with the same generator and period.
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	Which itself is a subset of the larger MOS, Negri[19].		Which itself is a subset of the larger MOS, Negri[19].

	=== Semirobust ~~inflected~~ MOS ===		=== Semirobust MOS inflection ===

	~~A semirobust inflected~~ MOS is ~~an inflected MOS~~ where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.		Semirobust MOS inflection is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.

	For example, if you take this Negri[8] MOS:		For example, if you take this Negri[8] MOS:
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	Like robust scales, semirobust ones also turn out to be subsets of some larger MOS. However, said larger MOS are sometimes large enough that they lose the character of the original tuning: Especially so if the MOS belongs to a low [[complexity]] [[temperament]]. If preserving the harmonic character of the original MOS is desired, then it might be preferable to use only a small number of adjustments.		Like robust scales, semirobust ones also turn out to be subsets of some larger MOS. However, said larger MOS are sometimes large enough that they lose the character of the original tuning: Especially so if the MOS belongs to a low [[complexity]] [[temperament]]. If preserving the harmonic character of the original MOS is desired, then it might be preferable to use only a small number of adjustments.

	=== Frankenstein ~~inflected~~ MOS ===		=== Frankenstein MOS inflection ===

	A Frankenstein ~~inflected~~ MOS is ~~an inflected MOS~~ where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).		Frankenstein MOS inflection is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).

	For example, if you take this Negri[7] MOS in [[67edo]]:		For example, if you take this Negri[7] MOS in [[67edo]]:
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	* 1200.000		* 1200.000

	=== ~~Justly inflected~~ MOS ===		=== Aspirational MOS inflection ===

	~~A justly inflected~~ MOS is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.		Aspirational MOS inflection is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.

	For example, if you take this Negri[7] MOS in 67edo:		For example, if you take this Negri[7] MOS in 67edo:
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	* 1200.000		* 1200.000

	Then alter, say, two of its other steps by increments of the same amount. Then you get the following ~~justly~~ inflected MOS:		Then alter, say, two of its other steps by increments of the same amount. Then you get the following aspirational inflected MOS:

	* 125.373		* 125.373
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	* 1200.000		* 1200.000

	~~A justly inflected~~ MOS may be ~~constructed~~ with similar goals to a [[well temperament]]: it may be ~~designed~~ to blunt the rough edges of an MOS by sanding over one or two of its [[wolf interval]]s.		Aspirational MOS inflection may be conducted with similar goals to [[well temperament]]: it may be used to blunt the rough edges of an MOS by sanding over one or two of its [[wolf interval]]s.

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

← Older revision		Revision as of 06:39, 23 January 2024
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	=== Robust MOS inflection ===		=== Robust MOS inflection ===

	Robust MOS inflection is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.		Robust MOS inflection{{idiosyncratic}} is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.

	This will result in a scale which is a subset of some larger MOS scale with the same generator and period.		This will result in a scale which is a subset of some larger MOS scale with the same generator and period.
Line 49:		Line 49:
	=== Semirobust MOS inflection ===		=== Semirobust MOS inflection ===

	Semirobust MOS inflection is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.		Semirobust MOS inflection{{idiosyncratic}} is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.

	For example, if you take this Negri[8] MOS:		For example, if you take this Negri[8] MOS:
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	=== Frankenstein MOS inflection ===		=== Frankenstein MOS inflection ===

	Frankenstein MOS inflection is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).		Frankenstein MOS inflection{{idiosyncratic}} is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).

	For example, if you take this Negri[7] MOS in [[67edo]]:		For example, if you take this Negri[7] MOS in [[67edo]]:
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	=== Aspirational MOS inflection ===		=== Aspirational MOS inflection ===

	Aspirational MOS inflection is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.		Aspirational MOS inflection{{idiosyncratic}} is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.

	For example, if you take this Negri[7] MOS in 67edo:		For example, if you take this Negri[7] MOS in 67edo: