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; the name has been taken over by Alois Hába. Three distinct intervals may be termed neutral thirds:


 * The undecimal neutral third has a ratio of 11:9 between the frequencies of the two tones, or about 347.41 cents.
 * A tridecimal neutral third has a ratio of 16:13 between the frequencies of the two tones, or about 359.47 cents.  This is the largest neutral third, and occurs infrequently in music, as little music utilizes the 13th harmonic.
 * An equal-tempered neutral third is characterized by a difference in 350 cents between the two tones, a hair wider than the 11:9 ratio, and exactly half of an equal-tempered perfect fifth.

These intervals are all within about 12 cents and are difficult for most people to distinguish by ear. Neutral thirds are roughly a quarter tone sharp from 12 equal temperament minor thirds and a quarter tone flat from 12-ET major thirds. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, the intervals are closer together.

A neutral third can be formed by stacking a neutral second together with a whole tone. Zalzal's wosta, a neutral third of 354.55 cents, may be constructed through the addition of a whole tone and a three quarter tone: 9:8 x 12:11 = 27:22.

Neutral thirds expressed in the form of a ratio of two whole numbers can also be considered as the interval between the harmonics of the same order. For instance, an undecimal neutral third, with a ratio of 11:9, is the interval between harmonics 11 and 9. The fundamental is then four octaves and a tone (9:1) below the lower of the two tones, or four octaves and a narrow fourth (11:1) below the higher of the two tones – or, if octaves are neglected, a tone (9:8) below the lower note and a narrow fourth (11:8) below the higher one.

A triad formed by two neutral thirds is neither major nor minor, thus the neutral thirds triad is ambiguous. While it is not found in twelve tone equal temperament it is found in others such as the quarter tone scale and 31-tet.

In infants' song
Infants experiment with singing, and a few studies of individual infants' singing found that neutral thirds regularly arise in their improvisations. In two separate case studies of the progression and development of these improvisations, neutral thirds were found to arise in infants' songs after major and minor seconds and thirds, but before intervals smaller than a semitone and also before intervals as large as a perfect fourth or larger.

In modern classical Western music
The neutral third has been used by a number of modern composers, including Charles Ives, James Tenney, and Gayle Young.

In traditional music
The equal-tempered neutral third may be found in the quarter tone scale and in some traditional Arab music (see also Arab tone system). Undecimal neutral thirds appear in traditional Georgian music. Neutral thirds are also found in American folk music.

In contemporary popular music
Blue notes (a note found in country music, blues, and some rock music) on the third note of a scale can be seen as a variant of a neutral third with the tonic, as they fall in between a major third and a minor third. Similarly the blue note on the seventh note of the scale can be seen as a neutral third with the dominant. Unlike most classical music, blue notes do not have exact values.

In equal temperaments
Two steps of seven-tone equal temperament form an interval of 342.8571 cents, which is within 5 cents of 347.4079 for the undecimal (11:9) neutral third. This is an equal temperament in reasonably common use, at least in the form of "near seven equal", as it is a tuning used for Thai music as well as the Ugandan Chopi tradition of music.

The neutral third also has good approximations in other commonly used equal temperaments including 24-ET (7 steps, 350 cents ) and similarly by all multiples of 24 equal steps such as 48-ET and 72-ET, 31-ET (9 steps, 348.39), 34-ET (10 steps, 352.941 cents ), 41-ET (12 steps, 351.22 cents ), and slightly less closely by 53-ET (15 steps, 339.62 cents ).

Close approximations to the tridecimal neutral third (16:13) appear in 53-ET and 72-ET. Both of these temperaments distinguish between the tridecimal (16:13) and undecimal (11:9) neutral thirds. All the other tuning systems mentioned above fail to distinguish between these intervals; they temper out the comma 144:143.