Neutral third

In music theory, a neutral interval is an interval that is neither a major nor minor, but instead in between. For example, in equal temperament, a major third is 400 cents, a minor third is 300 cents, and a neutral third is 350 cents. A neutral interval inverts to a neutral interval. For example, the inverse of a neutral third is a neutral sixth.

Roughly, neutral intervals are a quarter tone sharp from minor intervals and a quarter tone flat from major intervals. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, the intervals are closer together.

minor neutral major
seconds D ≊ Dhalf flat D
thirds E ≊ Ehalf flat E
sixths A ≊ Ahalf flat A
sevenths B ≊ Bhalf flat B


Neutral second
Inverseneutral seventh
Interval class~1+12
Just interval11:10 or 12:11[1]
12-Tone equal temperament100 or 200
24-Tone equal temperament150
Just intonation165 or 151
Neutral second on C Play.

A neutral second or medium second is an interval wider than a minor second and narrower than a major second. Three distinct intervals may be termed neutral seconds:

The equal-tempered neutral is found in some traditional Arabic music (see also Arab tone system). Because the equal tempered neutral second is essentially a semitone (minor second) plus a quarter-tone, they may be considered three-quarter tones in the quarter tone scale.

In equal temperament

Approximations to the 12:11 and 11:10 neutral seconds can be found in a number of equally tempered tuning systems. 11:10 is very closely matched by 22-ET, whereas 12:11 is matched by 24-ET, 31-ET and 41-ET. 72-ET matches both intervals closely and is also the smallest widely used equal temperament that uniquely matches both intervals. Tuning systems that temper out the comma of 121:120 do not distinguish between the two intervals. 17-ET has a neutral second between 12:11 and 13:12, and a neutral third between 16:13 and 11:9.


Neutral seventh
Inverseneutral second
Other names-
Interval class~1+12
Just interval11:6,[1] 64:35,[2] or 24:13
12-Tone equal temperament1000 or 1100
24-Tone equal temperament1050
Just intonation1049, 1045, or 1061
Neutral seventh on C Play.

A neutral seventh is a musical interval wider than a minor seventh play but narrower than a major seventh play. Four distinct intervals may be termed neutral sevenths:

These intervals are all within about 12 cents of each other and are difficult for most people to distinguish.

A neutral seventh can be formed by stacking a neutral third together with a perfect fifth. Based on its positioning in the harmonic series, the undecimal neutral seventh implies a root one perfect fifth below the lower of the two notes.

See also


  1. ^ a b Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0-8247-4714-3. 3/4-tone, undecimal neutral second and 21/4-tone, undecimal neutral seventh.
  2. ^ Haluska (2003), p.?. Septimal neutral seventh.
  3. ^ a b Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0-89579-507-8.