A neutral second or medium second is a musical interval wider than a minor second

Minor second

In modern Western tonal music theory a minor second is the interval between two notes on adjacent staff positions, or having adjacent note letters, whose alterations cause them to be one semitone or half-step apart, such as B and C or C and D....

 and narrower than a major second

Major second

In Western music theory, a major second is a musical interval spanning two semitones, and encompassing two adjacent staff positions . For example, the interval from C to D is a major second, as the note D lies two semitones above C, and the two notes are notated on adjacent staff postions...

. Three distinct intervals may be termed neutral seconds:

• The intermediate neutral second, called the lesser undecimal neutral second , has a ratio between the higher-frequency
  Frequency
  Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
  
   tone to the lower-frequency tone of 12:11 and is about 150.64 cents wide, while the larger one,

• the greater undecimal neutral second , has a ratio of 11:10 between the two tones and is about 165.00 cents wide. The lesser undecimal neutral second may be derived from the harmonic series
  Harmonic series (music)
  Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
  
   as the interval between the eleventh and twelfth harmonics. The greater undecimal neutral second may be derived from the harmonic series
  Harmonic series (music)
  Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
  
   as the interval between the tenth and eleventh harmonics.

• 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 second is characterized by a difference in 150 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 smaller than a ratio of frequencies between the two tones of 12:11, and exactly half of an equal-tempered minor third.

Roughly speaking, then, neutral seconds are 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 minor seconds and a quarter tone flat from major seconds. The equal-tempered neutral second may be found in the quarter tone scale and in some traditional Arab music

Arab music

Arabic music or Arab music is the music of the Arab World, including several genres and styles of music ranging from Arabic classical to Arabic pop music and from secular to sacred music....

 (see also Arab tone system

Arab tone system

The modern Arab tone system, or system of musical tuning, is based upon the theoretical division of the octave into twenty-four equal divisions or 24-tone equal temperament , the distance between each successive note being a quarter tone . Each tone has its own name not repeated in different...

). Because neutral seconds are essentially a semitone (minor second) plus a quarter-tone, they may be considered three-quarter tones.

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

22 equal temperament

In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the tempered scale derived by dividing the octave into 22 equal steps . Each step represents a frequency ratio of 21/22, or 54.55 cents ....

, whereas 12:11 is matched by 24-ET

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....

, 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...

 and 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...

. 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...

 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

Comma (music)

In music theory, a comma is a minute interval, the difference resulting from tuning one note two different ways. The word "comma" used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F tuned using the D-based Pythagorean tuning...

of 121:120 do not distinguish between the two intervals.