A neutral seventh is a musical interval wider than 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...

  but narrower than a major seventh

Major seventh

In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions , and the major seventh is one of two commonly occurring sevenths. It is qualified as major because it is the larger of the two...

 . Four distinct intervals may be termed neutral sevenths:

• A septimal neutral seventh has a ratio of 64:35 or about 1045 cents.

• The just undecimal neutral seventh has a ratio of 11:6 between the frequencies of the two tones, or about 1049 cents . Alternately, 13:7 or about 1071.7 cents.

• A tridecimal neutral seventh has a ratio of 24:13 between the frequencies of the two tones, or about 1061 cents. This is the largest neutral seventh, 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 seventh is characterized by a difference in 1050 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 larger than the 11:6 ratio, and exactly half of an equal-tempered major thirteenth (octave plus major sixth).

These intervals are all within about 12 cents and are difficult for most people to distinguish. Neutral sevenths 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....

 sharp from 12 equal temperament minor sevenths and a quarter tone flat from 12-ET major sevenths. 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 seventh can be formed by stacking a neutral third

Neutral third

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

 together with a perfect fifth

Perfect fifth

In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...

. Based on its positioning in the harmonic series, the undecimal neutral third 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 perfect fifth below the lower of the two notes.