A
neutral second or
medium second is a musical interval wider than a minor second and narrower than a
major secondA major second , also called a whole step or a whole tone, is a musical interval that occurs between the first and second degrees of a major scale, the tonic and the supertonic. The major second is abbreviated as M2; its inversion is the minor seventh...
. 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 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 , possesses a ratio of 11:10 between the two tones and is about 165.00 cents wide.
A
neutral second or
medium second is a musical interval wider than a minor second and narrower than a
major secondA major second , also called a whole step or a whole tone, is a musical interval that occurs between the first and second degrees of a major scale, the tonic and the supertonic. The major second is abbreviated as M2; its inversion is the minor seventh...
. 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 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 , possesses 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
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 seriesPitched 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 is a musical temperament, or a system of tuning in which every pair of adjacent notes has an identical frequency ratio. In equal temperament tunings, an interval — usually the octave — is divided into a series of equal steps...
neutral second is characterized by a difference in 150 centsThe cent is a logarithmic unit of measure used for musical intervals. Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive...
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 toneA quarter tone is an interval about half as wide as a semitone, which is half a whole tone.Many composers are known for having written music including quarter tones or the quarter tone scale, first proposed by 19th-century music theorist Mikha'il Mishaqah , including: Pierre Boulez, Julián...
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 musicArabic music or Arab music includes several genres and styles of music ranging from Arabic classical to Arabic pop music and from secular to sacred music....
(see also
Arab tone systemThe 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-ETIn 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-ETA quarter tone is an interval about half as wide as a semitone, which is half a whole tone.Many composers are known for having written music including quarter tones or the quarter tone scale, first proposed by 19th-century music theorist Mikha'il Mishaqah , including: Pierre Boulez, Julián...
,
31-ETIn music, 31 equal temperament , which can be abbreviated 31-TET, 31-EDO, 31-ET, is the tempered scale derived by dividing the octave into 31 equal-sized steps...
and
41-ETIn 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...
.
72-ETIn 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
commaIn music theory, a comma is a small or very small interval between two enharmonic notes tuned in different ways. For example, an A flat tuned as a major third below C in just intonation, and a G sharp tuned as a major third above E, will not be exactly the same note...
of 121:120 do not distinguish between the two intervals.