Neutral second: Difference between revisions

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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 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.

~~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.

== In just intonation ==

=== By prime 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 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}}.

* 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 5-limit '''acute minor second''' or '''large limma''' is a ratio of [[27/25]], and is about 133{{c}}.

== In mos scales ==

* The 7-limit '''septimal neutral second''' is a ratio of [[35/32]], and is about 155{{c}}.

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.

** 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 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 ==

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.

Scales with more than 12 notes are not included.

{| class="wikitable"

|-

! Range

! colspan="2" | ~~MOS~~

! colspan="2" | Mos

|-

| 120–133{{c}}

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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&nbsp;second]]|Higher region=[[Major&nbsp;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 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.
-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.
 == In just intonation ==
 === By prime 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 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}}.
+* 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 5-limit '''acute minor second''' or '''large limma''' is a ratio of [[27/25]], and is about 133{{c}}.
+== In mos scales ==
-* The 7-limit '''septimal neutral second''' is a ratio of [[35/32]], and is about 155{{c}}.
+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.
-** 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 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 ==
-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.
-Scales with more than 12 notes are not included.
 {| class="wikitable"
 |-
 ! Range
-! colspan="2" | MOS
+! colspan="2" | Mos
 |-
 | 120–133{{c}}