music theory Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...

, a neutral interval is an interval that is neither a major nor minor, but instead in between. For example, in

equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...

, a

major third In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Forte, Allen (1979). ''Tonal Harmony in Concept and P ...

is 400 cents, a

minor third In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two com ...

is 300 cents, and a neutral third is 350 cents. A neutral interval inverts to a neutral interval. For example, the inverse of a neutral third is a neutral sixth. Roughly, neutral intervals are a

quarter tone A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, a ...

sharp from minor intervals and a quarter tone flat from major intervals. In just intonation, as well as in tunings such as 31-ET, 41-ET, or

72-ET 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 (equal frequency ratios). Each step represents a frequency ...

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

Neutral second In music theory, a neutral interval is an interval that is neither a major nor minor, but instead in between. For example, in equal temperament, a major third is 400 cents, a minor third is 300 cents, and a neutral third is 350 cents. A neutral ...

Neutral third A neutral third is a musical interval wider than a minor third but narrower than a major third , named by Jan Pieter Land in 1880. Land makes reference to the neutral third attributed to Zalzal (8th c.), described by Al-Farabi (10th c.) as ...

Neutral sixth A neutral sixth is a musical interval wider than a minor sixth but narrower than a major sixth . Three distinct intervals may be termed neutral sixths: * The ''undecimal neutral sixth'' has a ratio of 18:11 between the frequencies of the tw ...

* Neutral seventh

Second

A neutral second or medium second is an interval wider than a

minor second A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...

and narrower than a

major second In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more deta ...

. 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 of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

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 as the interval between the

eleventh In music or music theory, an eleventh is the note eleven scale degrees from the root of a chord and also the interval between the root and the eleventh. The interval can be also described as a compound fourth, spanning an octave plus a f ...

and twelfth harmonics. The greater undecimal neutral second may be derived from the harmonic series as the interval between the tenth and eleventh harmonics. * An ''

equal-tempered An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, w ...

neutral second'' is characterized by a difference in 150 cents 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. The equal-tempered neutral is found in some traditional

Arabic music Arabic music or Arab music ( ar, الموسيقى العربية, al-mūsīqā al-ʿArabīyyah) is the music of the Arab world with all its diverse music styles and genres. Arabic countries have many rich and varied styles of music and also man ...

(see also

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 (24-TET), the distance between each successive note being a quarter tone ( ...

). Because the equal tempered neutral second is essentially a semitone (minor second) plus a quarter-tone, they may be considered three-quarter tones in the

quarter tone scale A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, a ...

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, whereas 12:11 is matched by 24-ET, 31-ET and 41-ET.

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 The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline ...

of 121:120 do not distinguish between the two intervals. 17-ET has a neutral second between 12:11 and 13:12, and a neutral third between 16:13 and 11:9.

Seventh

A neutral seventh is a musical interval wider than a

minor seventh In music theory, a minor seventh is one of two musical intervals that span seven staff positions. It is ''minor'' because it is the smaller of the two sevenths, spanning ten semitones. The major seventh spans eleven. For example, the interval f ...

but narrower than a

major seventh In music from Western culture, a seventh is a musical interval encompassing seven staff positions (see Interval number for more details), and the major seventh is one of two commonly occurring sevenths. It is qualified as ''major'' because it i ...

. 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 Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

of the two tones,Andrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p.131. . or about 1049 cents . Alternately, 13:7 or about 1071.7 cents . * A ''tridecimal neutral seventh'' has a ratio of 24:13 between the

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 A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...

. * An ''

neutral seventh'' is characterized by a difference in 1050 cents 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 of each other and are difficult for most people to distinguish. A neutral seventh can be formed by stacking a

neutral third A neutral third is a musical interval wider than a minor third but narrower than a major third , named by Jan Pieter Land in 1880. Land makes reference to the neutral third attributed to Zalzal (8th c.), described by Al-Farabi (10th c.) as ...

together with a

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval fro ...

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

root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the sur ...

one perfect fifth below the lower of the two notes.

References

{{Intervals Neutral intervals Quarter tones

Second

In equal temperament

Seventh

See also

References