Neutral second: Difference between revisions
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A '''neutral second (n2 | {{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. | |||
In [[just intonation]], an interval may be classified as a neutral second if it is reasonably mapped to | 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 | 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 == | ||
=== By prime limit === | === By prime limit === | ||
The [[3-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 | * 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. | |||
== In 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. | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Range | ! Range | ||
! colspan="2" | | ! colspan="2" | Mos | ||
|- | |- | ||
| 120–133{{c}} | | 120–133{{c}} | ||
| Line 34: | Line 43: | ||
|- | |- | ||
| 150–171{{c}} | | 150–171{{c}} | ||
| | | [[1L 6s]] | ||
| | | [[7L 1s]] | ||
|} | |} | ||
{{Navbox intervals}} | {{Navbox intervals}} | ||