A neutral sixth is a musical interval wider than a minor sixth

Minor sixth

-Subminor sixth:In music, a subminor sixth or septimal sixth is an interval that is noticeably narrower than a minor sixth but noticeably wider than a diminished sixth.The sub-minor sixth is an interval of a 14:9 ratio or alternately 11:7....

  but narrower than a major sixth

Major sixth

In classical music from Western culture, a sixth is a musical interval encompassing six staff positions , and the major sixth is one of two commonly occurring sixths. It is qualified as major because it is the largest of the two...

 . 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.

• 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
  Harmonic
  A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...
  
  .

• An equal-tempered
  Equal temperament
  An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
  
   neutral sixth is characterized by a difference in 850 cents
  Cent (music)
  The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
  
   between the two tones, a hair narrower than the 18:11 ratio, and exactly half of an equal-tempered perfect eleventh (octave plus fourth).

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

Quarter tone

A quarter tone , is a pitch halfway between the usual notes of a chromatic scale, an interval about half as wide as a semitone, which is half a whole tone....

 flat from 12 equal temperament minor sixths and a quarter tone sharp from 12-ET major sixths. In just intonation, as well as in tunings such as 31-ET

31 equal temperament

In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO , , is the tempered scale derived by dividing the octave into 31 equal-sized steps...

, 41-ET

41 equal temperament

In music, 41 equal temperament, often abbreviated 41-tET, 41-EDO, or 41-ET, is the tempered scale derived by dividing the octave into 41 equally-sized steps . Each step represents a frequency ratio of 21/41, or 29.27 cents , an interval close in size to the septimal comma. 41-ET can be seen as a...

, or 72-ET

72 equal temperament

In music, 72 equal temperament, called twelfth-tone, 72-tet, 72-edo, or 72-et, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps...

, which more closely approximate just intonation, the intervals are closer together.

A neutral sixth can be formed by subtracting a neutral second

Neutral second

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

 from a minor seventh

Minor seventh

In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions , and the minor seventh is one of two commonly occurring sevenths. The minor quality specification identifies it as being the smallest of the two: the minor seventh spans ten semitones, the...

. Based on its positioning in the harmonic series, the undecimal neutral sixth implies a root

Root (chord)

In music theory, the root of a chord is the note or pitch upon which a triadic chord is built. For example, the root of the major triad C-E-G is C....

one minor seventh above the higher of the two notes.