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Neutral third

A neutral third,, is a musical interval wider than a minor third but narrower than a major third. It is called the neutral third in 24-Tone Equal Temperament, and the submajor third, or the superminor third, in Just Intonation. It was named neutral third by Jan Pieter Land in 1880. Land makes reference to the neutral third attributed to Zalzal, described by Al-Farabi as corresponding to a ratio of 27:22 and by Avicenna as 39:32. The Zalzalian third may have been a mobile interval.

Occurrence in human music
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 Claudius Ptolemy describes an "even diatonic" tuning which uses two justly tuned neutral thirds in Harmonikon built off the 12:11 and 11:10 neutral seconds in compound intervals with 9:8 and 10:9 whole tones, forming the intervals: (12/11)*(9/8) = 27/22, (11/10)*(10/9) = 11/9. The latter of these is an interval found in the harmonic series as the interval between partials 9 and 11. 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. == In equal temperaments ==
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. == See also ==
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