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. This page will consider intervals between about 120 and 170 cents.

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 cents.
• The 7-limit septimal neutral second is a ratio of 35/32, and is about 155 cents.
• The 11-limit (undecimal) neutral/submajor seconds are the ratios of 12/11 and 11/10, which are about 151 cents and 165 cents, 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 cents and 139 cents, respectively; 14/13 in particular can also be analyzed as a semitone. Despite that, it is also here for completeness.

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