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.
|Just interval||11:10 or 12:11|
|Equal temperament||100 or 200|
|24 equal temperament||150|
|Just intonation||165 or 151|
The equal-tempered neutral is found in some traditional Arab 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.
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.
|Just interval||11:6, 64:35, or 24:13|
|Equal temperament||1000 or 1100|
|24 equal temperament||1050|
|Just intonation||1049, 1045, or 1061|
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 third implies a root one perfect fifth below the lower of the two notes.