Neutral sixth

A neutral sixth is a musical interval wider than a minor sixth  play  but narrower than a major sixth  play . Three distinct intervals may be termed neutral sixths:

The undecimal neutral sixth has a ratio of 18:11 between the frequencies of the two tones, or about 852.59 cents.  play 

A tridecimal neutral sixth has a ratio of 13:8 between the frequencies of the two tones, or about 840.53 cents. This is the smallest neutral sixth, and occurs infrequently in music, as little music utilizes the 13th harmonic.  play 

An equal-tempered neutral sixth is 850 cents, a hair narrower than the 18:11 ratio. It is an equal-tempered quarter tone exactly half way between the equal-tempered minor and major sixths, and half of an equal-tempered perfect eleventh (octave plus fourth).  play 

These intervals are all within about 12 cents of each other and are difficult for most people to distinguish. Neutral sixths are roughly a quarter tone sharp from 12 equal temperament minor sixths and a quarter tone flat from 12-ET major sixths. 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.