Neutral second
A neutral second (n2) is an interval that spans one step of the diatonic scale with a quality between major and minor. It exists in 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 1\7 and 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 ¢ in size, distinct from the semitone of roughly 100 ¢ and the major second of roughly 200 ¢. A rough tuning range for the neutral second is 130 to 170 ¢ according to Margo Schulter's theory of interval regions.
In just intonation
By prime limit
The 3-limit and 5-limit do not have simple neutral seconds, so we start with the 7-limit:
- The 7-limit septimal neutral second
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In moment-of-symmetry scales
Intervals between 120 and 171 ¢ generate the following MOS scales:
These tables start from the last monolarge MOS generated by the interval range.
MOSes with more than 12 notes are not included.
| Range | MOS | |
|---|---|---|
| 120–133 ¢ | 1L 8s | 9L 1s |
| 133–150 ¢ | 1L 7s | 8L 1s |
| 150–171 ¢ | 1L 6s | 7L 1s |
| V • T • EInterval regions | |
|---|---|
| Seconds and thirds | Comma and diesis • Semitone • Neutral second • Major second • (Interseptimal second-third) • Minor third • Neutral third • Major third |
| Fourths and fifths | (Interseptimal third-fourth) • Perfect fourth • (Semiaugmented fourth) • Tritone • (Semidiminished fifth) • Perfect fifth • (Interseptimal fifth-sixth) |
| Sixths and sevenths | Minor sixth • Neutral sixth • Major sixth • (Interseptimal sixth-seventh) • Minor seventh • Neutral seventh • Major seventh • Octave |