Neutral second - Revision history

FloraC: - abuse of bold

2026-03-30T13:50:14Z

- abuse of bold

← Older revision		Revision as of 13:50, 30 March 2026
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	=== By prime limit ===		=== By prime limit ===
	The [[3-limit]] does not have a simple neutral second, so we start with the 5-limit:		The [[3-limit]] does not have a simple neutral second, so we start with the 5-limit:
			* The 5-limit acute minor second or large limma is a ratio of [[27/25]], and is about 133{{c}}.
	* The 5-limit ~~'''~~acute minor second~~'''~~ or ~~'''~~large limma~~'''~~ is a ratio of [[27/25]], and is about 133{{c}}.		* The 7-limit septimal neutral second is a ratio of [[35/32]], and is about 155{{c}}.
	* The 7-limit ~~'''~~septimal neutral second~~'''~~ is a ratio of [[35/32]], and is about 155{{c}}.		** There is also a 7-limit swetismic neutral second, which is a ratio of [[49/45]], and is about 147{{c}}.
	** There is also a 7-limit ~~'''~~swetismic neutral second~~'''~~, which is a ratio of [[49/45]], and is about 147{{c}}.		* The 11-limit (undecimal) neutral/submajor seconds are the ratios of [[12/11]] and [[11/10]], which are about 151{{c}} and 165{{c}}, respectively; 11/10 in particular can also be analyzed as a [[major second]]. Despite that, it is also here for completeness.
	* The 11-limit ~~'''~~(undecimal) neutral/submajor seconds~~'''~~ are the ratios of [[12/11]] and [[11/10]], which are about 151{{c}} and 165{{c}}, respectively; 11/10 in particular can also be analyzed as a [[major second]]. Despite that, it is also here for completeness.		* The 13-limit (tridecimal) neutral/supraminor seconds are the ratios of [[14/13]] and [[13/12]], which are about 128{{c}} and 139{{c}}, respectively; 14/13 in particular can also be analyzed as a [[semitone]]. Despite that, it is also here for completeness.
	* The 13-limit ~~'''~~(tridecimal) neutral/supraminor seconds~~'''~~ are the ratios of [[14/13]] and [[13/12]], which are about 128{{c}} and 139{{c}}, respectively; 14/13 in particular can also be analyzed as a [[semitone]]. Despite that, it is also here for completeness.

	== In mos scales ==		== In mos scales ==
	Intervals between 120 and 171{{c}} generate the following [[mos]] scales:		Intervals between 120 and 171{{c}} generate the following [[mos]] scales. These tables start from the last monolarge mos generated by the interval range. Scales with more than 12 notes are not included.

	These tables start from the last monolarge mos generated by the interval range.

	Scales with more than 12 notes are not included.

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

FloraC: Rework intro to hopefully make it make sense

2026-03-30T13:49:26Z

Rework intro to hopefully make it make sense

← Older revision		Revision as of 13:49, 30 March 2026
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	\| Complement = [[Neutral seventh]]		\| Complement = [[Neutral seventh]]
	\| Lower region = [[Semitone (interval region)\|Semitone]]		\| Lower region = [[Semitone (interval region)\|Semitone]]
	\| Higher region = [[~~Major_second_(interval_region)\|~~Major second]]		\| Higher region = [[Major second]]
	}}		}}
	A '''neutral second''' ('''n2''') is an interval that ~~spans~~ one ~~step~~ of ~~the~~ [[5L 2s\|diatonic]] ~~scale~~ with ~~a quality between major and minor~~. ~~It exists in~~ [[~~neutralization\|neutralized~~]] ~~diatonic scales as exactly one half of a~~ [[minor ~~third~~]].		A '''neutral second''' ('''n2''') is an interval that exists as exactly one half of a [[minor third]] in a variant of [[5L 2s\|diatonic]] with its original [[perfect fifth\|perfect-fifth]] generator halved. Like the [[major second]] and [[minor second]], it is considered a second, so it spans one step in diatonic-based notation, but has a quality between major and minor.

	In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to one step of the diatonic scale and one and a half steps of the chromatic scale.		In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to one step of the diatonic scale and one and a half steps of the chromatic scale.

	As a concrete [[interval region]], it is typically near 150{{cent}} in size, distinct from the [[Semitone (interval region)\|semitone]] of roughly 100{{c}} and the [[major second]] of roughly 200{{c}}. A rough tuning range for the neutral second is 130 to 170{{c}} according to [[Margo Schulter]]'s theory of interval regions. This page will consider intervals between about 120 and 170{{c}}. The outer range of this might be too extreme to call "neutral seconds", but this is done so that one can find what they're looking for easily.		As a concrete [[interval region]], it is typically near 150{{cent}} in size, distinct from the [[Semitone (interval region)\|semitone]] of roughly 100{{c}} and the [[major second]] of roughly 200{{c}}. A rough tuning range for the neutral second is 130 to 170{{c}} according to [[Margo Schulter]]'s theory of interval regions. This page will consider intervals between about 120 and 170{{c}}. The outer range of this might be too extreme to call neutral seconds, but this is done so that one can find what they're looking for easily.

	== In just intonation ==		== In just intonation ==

Jdood: fixed the link

2025-12-03T18:00:32Z

fixed the link

← Older revision		Revision as of 18:00, 3 December 2025
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	\| Complement = [[Neutral seventh]]		\| Complement = [[Neutral seventh]]
	\| Lower region = [[Semitone (interval region)\|Semitone]]		\| Lower region = [[Semitone (interval region)\|Semitone]]
	\| Higher region = [[Major_second_(interval_region)]]		\| Higher region = [[Major_second_(interval_region)\|Major second]]
	}}		}}
	A '''neutral second''' ('''n2''') is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[minor third]].		A '''neutral second''' ('''n2''') is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[minor third]].

Jdood: test

2025-12-03T17:59:37Z

test

← Older revision		Revision as of 17:59, 3 December 2025
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	\| Complement = [[Neutral seventh]]		\| Complement = [[Neutral seventh]]
	\| Lower region = [[Semitone (interval region)\|Semitone]]		\| Lower region = [[Semitone (interval region)\|Semitone]]
	\| Higher region = [[~~Major second~~]]		\| Higher region = [[Major_second_(interval_region)]]
	}}		}}
	A '''neutral second''' ('''n2''') is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[minor third]].		A '''neutral second''' ('''n2''') is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[minor third]].

FloraC: Compromise reached: restore the old structure but -specific edosteps

2025-03-14T10:59:05Z

Compromise reached: restore the old structure but -specific edosteps

← Older revision		Revision as of 10:59, 14 March 2025
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	{{Infobox interval region\|Name=Neutral second\|Cents lower=130\|Cents lower wide=120\|Cents upper=160\|Cents upper wide=170\|JI intervals=11/10, 12/11, 13/12\|MOSes=[[1L 8s]], [[1L 7s]], [[1L 6s]], [[9L 1s]], [[8L 1s]], [[7L 1s]]\|Complement=[[Neutral seventh]]\|Lower region=[[Semitone (interval region)\|Semitone]]\|Higher region=[[Major second]]}}A '''neutral second (n2)''' is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half		{{Infobox interval region
			\| Name = Neutral second
			\| Cents lower = 130
			\| Cents lower wide = 120
			\| Cents upper = 160
			\| Cents upper wide = 170
			\| JI intervals = 11/10, 12/11, 13/12
			\| MOSes = [[1L 8s]], [[1L 7s]], [[1L 6s]], [[9L 1s]], [[8L 1s]], [[7L 1s]]
			\| Complement = [[Neutral seventh]]
			\| Lower region = [[Semitone (interval region)\|Semitone]]
			\| Higher region = [[Major second]]
			}}
			A '''neutral second''' ('''n2''') is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[minor third]].

	~~of a [[minor third]].~~		In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to one step of the diatonic scale and one and a half steps of the chromatic scale.

	In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to ~~[[7edo\|1\7]] and [[24edo\|3\24]] (precisely~~ one step of the diatonic scale and one and a half steps of the chromatic scale).

	As a concrete [[interval region]], it is typically near 150{{cent}} in size, distinct from the [[Semitone (interval region)\|semitone]] of roughly 100{{c}} and the [[major second]] of roughly 200{{c}}. A rough tuning range for the neutral second is 130 to 170{{c}} according to [[Margo Schulter]]'s theory of interval regions. This page will consider intervals between about 120 and 170{{c}}. The outer range of this might be too extreme to call "neutral seconds", but this is done so that one can find what they're looking for easily.		As a concrete [[interval region]], it is typically near 150{{cent}} in size, distinct from the [[Semitone (interval region)\|semitone]] of roughly 100{{c}} and the [[major second]] of roughly 200{{c}}. A rough tuning range for the neutral second is 130 to 170{{c}} according to [[Margo Schulter]]'s theory of interval regions. This page will consider intervals between about 120 and 170{{c}}. The outer range of this might be too extreme to call "neutral seconds", but this is done so that one can find what they're looking for easily.
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	* The 13-limit '''(tridecimal) neutral/supraminor seconds''' are the ratios of [[14/13]] and [[13/12]], which are about 128{{c}} and 139{{c}}, respectively; 14/13 in particular can also be analyzed as a [[semitone]]. Despite that, it is also here for completeness.		* The 13-limit '''(tridecimal) neutral/supraminor seconds''' are the ratios of [[14/13]] and [[13/12]], which are about 128{{c}} and 139{{c}}, respectively; 14/13 in particular can also be analyzed as a [[semitone]]. Despite that, it is also here for completeness.

	== In ~~MOS~~ scales ==		== In mos scales ==
	Intervals between 120 and 171{{c}} generate the following [[mos~~\|MOS~~]] scales:		Intervals between 120 and 171{{c}} generate the following [[mos]] scales:

	These tables start from the last monolarge ~~MOS~~ generated by the interval range.		These tables start from the last monolarge mos generated by the interval range.

	Scales with more than 12 notes are not included.		Scales with more than 12 notes are not included.
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	\|-		\|-
	! Range		! Range
	! colspan="2" \| ~~MOS~~		! colspan="2" \| Mos
	\|-		\|-
	\| 120–133{{c}}		\| 120–133{{c}}

VectorGraphics at 10:24, 14 March 2025

2025-03-14T10:24:41Z

← Older revision		Revision as of 10:24, 14 March 2025
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	{{Infobox interval region\|Name=Neutral second\|Cents lower=130\|Cents lower wide=120\|Cents upper=160\|Cents upper wide=170\|JI intervals=11/10, 12/11, 13/12\|MOSes=[[1L 8s]], [[1L 7s]], [[1L 6s]], [[9L 1s]], [[8L 1s]], [[7L 1s]]\|Complement=[[Neutral seventh]]\|Lower region=[[~~Minor second~~]]\|Higher region=[[Major second]]}}A '''neutral second (n2)''' is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half		{{Infobox interval region\|Name=Neutral second\|Cents lower=130\|Cents lower wide=120\|Cents upper=160\|Cents upper wide=170\|JI intervals=11/10, 12/11, 13/12\|MOSes=[[1L 8s]], [[1L 7s]], [[1L 6s]], [[9L 1s]], [[8L 1s]], [[7L 1s]]\|Complement=[[Neutral seventh]]\|Lower region=[[Semitone (interval region)\|Semitone]]\|Higher region=[[Major second]]}}A '''neutral second (n2)''' is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half

	of a [[minor third]].		of a [[minor third]].

VectorGraphics at 10:12, 14 March 2025

2025-03-14T10:12:57Z

← Older revision		Revision as of 10:12, 14 March 2025
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	A '''neutral second (n2)''' is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half {{Infobox interval region\|Name=Neutral second\|Cents lower=130\|Cents lower wide=120\|Cents upper=160\|Cents upper wide=170\|JI intervals=11/10, 12/11, 13/12\|MOSes=[[1L 8s]], [[1L 7s]], [[1L 6s]], [[9L 1s]], [[8L 1s]], [[7L 1s]]\|Complement=[[Neutral seventh]]\|Lower region=[[Minor second]]\|Higher region=[[Major second]]}}of a [[minor third]].		{{Infobox interval region\|Name=Neutral second\|Cents lower=130\|Cents lower wide=120\|Cents upper=160\|Cents upper wide=170\|JI intervals=11/10, 12/11, 13/12\|MOSes=[[1L 8s]], [[1L 7s]], [[1L 6s]], [[9L 1s]], [[8L 1s]], [[7L 1s]]\|Complement=[[Neutral seventh]]\|Lower region=[[Minor second]]\|Higher region=[[Major second]]}}A '''neutral second (n2)''' is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half

			of a [[minor third]].

	In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to [[7edo\|1\7]] and [[24edo\|3\24]] (precisely one step of the diatonic scale and one and a half steps of the chromatic scale).		In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to [[7edo\|1\7]] and [[24edo\|3\24]] (precisely one step of the diatonic scale and one and a half steps of the chromatic scale).

VectorGraphics: Capitalization of MOS

2025-03-14T10:06:00Z

Capitalization of MOS

← Older revision		Revision as of 10:06, 14 March 2025
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	* The 13-limit '''(tridecimal) neutral/supraminor seconds''' are the ratios of [[14/13]] and [[13/12]], which are about 128{{c}} and 139{{c}}, respectively; 14/13 in particular can also be analyzed as a [[semitone]]. Despite that, it is also here for completeness.		* The 13-limit '''(tridecimal) neutral/supraminor seconds''' are the ratios of [[14/13]] and [[13/12]], which are about 128{{c}} and 139{{c}}, respectively; 14/13 in particular can also be analyzed as a [[semitone]]. Despite that, it is also here for completeness.

	== In ~~mos~~ scales ==		== In MOS scales ==
	Intervals between 120 and 171{{c}} generate the following [[mos]] scales:		Intervals between 120 and 171{{c}} generate the following [[mos\|MOS]] scales:

	These tables start from the last monolarge ~~mos~~ generated by the interval range.		These tables start from the last monolarge MOS generated by the interval range.

	Scales with more than 12 notes are not included.		Scales with more than 12 notes are not included.
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	\|-		\|-
	! Range		! Range
	! colspan="2" \| ~~Mos~~		! colspan="2" \| MOS
	\|-		\|-
	\| 120–133{{c}}		\| 120–133{{c}}

VectorGraphics at 10:05, 14 March 2025

2025-03-14T10:05:32Z

← Older revision		Revision as of 10:05, 14 March 2025
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	A '''neutral second (n2)''' is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[minor third]].		A '''neutral second (n2)''' is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half {{Infobox interval region\|Name=Neutral second\|Cents lower=130\|Cents lower wide=120\|Cents upper=160\|Cents upper wide=170\|JI intervals=11/10, 12/11, 13/12\|MOSes=[[1L 8s]], [[1L 7s]], [[1L 6s]], [[9L 1s]], [[8L 1s]], [[7L 1s]]\|Complement=[[Neutral seventh]]\|Lower region=[[Minor second]]\|Higher region=[[Major second]]}}of a [[minor third]].

	In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to [[7edo\|1\7]] and [[24edo\|3\24]] (precisely one step of the diatonic scale and one and a half steps of the chromatic scale).		In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to [[7edo\|1\7]] and [[24edo\|3\24]] (precisely one step of the diatonic scale and one and a half steps of the chromatic scale).

FloraC: The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition

2025-03-14T09:55:39Z

The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition

← Older revision		Revision as of 09:55, 14 March 2025
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	A '''neutral second (n2)'''~~, as a concrete [[~~interval ~~region]], is typically near 150{{cent}} in size, distinct from~~ the [[~~Semitone (interval region)~~\|~~semitone~~]] ~~of roughly 100{{c}}~~ and ~~the~~ [[~~major second~~]] of ~~roughly 200{{c}}. A rough tuning range for the neutral second is 130 to 170{{c}} according to~~ [[~~Margo Schulter~~]]~~'s theory of interval regions~~.		A '''neutral second (n2)''' is an interval that spans one step of the [[5L 2s\|diatonic]] scale with a quality between major and minor. It exists in [[neutralization\|neutralized]] diatonic scales as exactly one half of a [[minor third]].

	In ~~the~~ [[~~5L 2s\|diatonic~~]] ~~scale~~, a neutral second is ~~an interval that spans one step with a quality between major~~ and ~~minor. It exists in~~ [[~~neutralization~~\|~~neutralized~~]] diatonic ~~scales as exactly~~ one half of ~~a [[minor third]]~~.		In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to [[7edo\|1\7]] and [[24edo\|3\24]] (precisely one step of the diatonic scale and one and a half steps of the chromatic scale).

	In [[~~just intonation~~]], an interval ~~may be classified as a~~ neutral second ~~if it~~ is ~~reasonably mapped~~ to ~~one step~~ of ~~the diatonic scale and one and a half steps of the chromatic scale~~.		As a concrete [[interval region]], it is typically near 150{{cent}} in size, distinct from the [[Semitone (interval region)\|semitone]] of roughly 100{{c}} and the [[major second]] of roughly 200{{c}}. A rough tuning range for the neutral second is 130 to 170{{c}} according to [[Margo Schulter]]'s theory of interval regions. This page will consider intervals between about 120 and 170{{c}}. The outer range of this might be too extreme to call "neutral seconds", but this is done so that one can find what they're looking for easily.

	This page will consider intervals between about 120 and 170{{c}}. The outer range of this might be too extreme to call "neutral seconds", but this is done so that one can find what they're looking for easily.

	== In just intonation ==		== In just intonation ==
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	* The 13-limit '''(tridecimal) neutral/supraminor seconds''' are the ratios of [[14/13]] and [[13/12]], which are about 128{{c}} and 139{{c}}, respectively; 14/13 in particular can also be analyzed as a [[semitone]]. Despite that, it is also here for completeness.		* The 13-limit '''(tridecimal) neutral/supraminor seconds''' are the ratios of [[14/13]] and [[13/12]], which are about 128{{c}} and 139{{c}}, respectively; 14/13 in particular can also be analyzed as a [[semitone]]. Despite that, it is also here for completeness.

	== In ~~MOS~~ scales ==		== In mos scales ==
	Intervals between 120 and 171{{c}} generate the following [[mos~~\|MOS~~]] scales:		Intervals between 120 and 171{{c}} generate the following [[mos]] scales:

	These tables start from the last monolarge ~~MOS~~ generated by the interval range.		These tables start from the last monolarge mos generated by the interval range.

	Scales with more than 12 notes are not included.		Scales with more than 12 notes are not included.
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	\|-		\|-
	! Range		! Range
	! colspan="2" \| ~~MOS~~		! colspan="2" \| Mos
	\|-		\|-
	\| 120–133{{c}}		\| 120–133{{c}}