Neutral second

A neutral second (n2) is an interval that exists as exactly one half of a minor third in a variant of diatonic with its original 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.

← Semitone

Neutral second

Major second →

Name	Neutral second
Lower bound	120¢ – 130¢
Upper bound	160¢ – 170¢
Generated MOSes	1L 8s, 1L 7s, 1L 6s, 9L 1s, 8L 1s, 7L 1s
Example JI intervals
Intervals	11/10 (165¢) 12/11 (150.6¢) 13/12 (138.6¢)
Related regions
Complement	Neutral seventh

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 ¢ 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. This page will consider intervals between about 120 and 170 ¢. 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 ¢.
• The 7-limit septimal neutral second is a ratio of 35/32, and is about 155 ¢.
  • There is also a 7-limit swetismic neutral second, which is a ratio of 49/45, and is about 147 ¢.
• The 11-limit (undecimal) neutral/submajor seconds are the ratios of 12/11 and 11/10, which are about 151 ¢ and 165 ¢, 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 ¢ and 139 ¢, 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 ¢ 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.

Range	Mos
120–133 ¢	1L 8s	9L 1s
133–150 ¢	1L 7s	8L 1s
150–171 ¢	1L 6s	7L 1s