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Neutral third

Neutral third
Inverse neutral sixth
Other names -
Abbreviation n3
Semitones ~3½
Interval class ~3½
Just interval 11:9,[1] 27:22,[2] or 16:13[3]
Equal temperament 350
Just intonation 347, 355, or 359

A neutral third is a musical interval wider than a minor third About this sound play  but narrower than a major third About this sound play . Three distinct intervals may be termed neutral thirds:

  • A tridecimal neutral third About this sound play  has a ratio of 16:13 between the frequencies of the two tones, or about 359.47 cents.[5] This is the largest neutral third, and occurs infrequently in music, as little music utilizes the 13th harmonic.

These intervals are all within about 12 cents and are difficult for most people to distinguish. 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. Based on its positioning in the harmonic series, the undecimal neutral third implies a root one whole tone below the lower of the two notes.

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 About this sound Play  and 31-tet About this sound Play .

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.[6]

In modern classical music

The neutral third has been used by a number of modern composers, including Charles Ives, James Tenney, and Gayle Young.[7]

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.[8] Neutral thirds are also found in American folk music.[9]

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.[citation needed]

In equal temperaments

Two steps of seven equal take you to 342.8571 cents which is within 5 cents of 347.4079 for the undecimal (11:9) neutral third.[10] This is an ET 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.[11] See Equal temperaments in ethnomusicology.

It also has good approximations in other commonly used ETs including 24-ET (7 steps, 350 cents[12]) and similarly by all multiples of 24 equal steps such as 48-ET[13] and 72-ET,[14] 31-ET (9 steps, 349.39),[15] 34-ET (10 steps, 352.941 cents[16]), 41-ET (12 steps, 351.22 cents[17]), and slightly less closely by 53-ET (15 steps, 339.62 cents[18]).

Close approximations to the tridecimal neutral third (16:13) appear in 53-ET [18] and 72-ET.[14] 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; this can be interpreted as tempering out the comma 144:143.

See also


  1. ^ Haluska, (2003) p.xxiii. Undecimal neutral third.
  2. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0-8247-4714-3. Neutral third, Zalzal's wosta.
  3. ^ Haluska (2003), p.xxiv. Tridecimal neutral third.
  4. ^ Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0-89579-507-8. "Super-Major Second".
  5. ^ [1] Jan Haluska, The Mathematical Theory of Tone Systems, CRC (2004).
  6. ^ [2] Nettl, Bruno "Infant Musical Development and Primitive Music" Southwestern Journal of Anthropology, Vol. 12, No. 1, pp. 87-91. (Spring, 1956)
  7. ^ [3] Young, Gayle "The Pitch Organization of Harmonium for James Tenney", Perspectives of New Music, Vol. 26, No. 2. pp. 204-212 (Summer, 1988)
  8. ^ Society for the Study of Caucasia (1994). The Annual of the Society for the Study of Caucasia. The Society. p. 93. Retrieved 14 April 2011. 
  9. ^ [4] Boswell, George W. "The Neutral Tone as a Function of Folk-Song Text", Yearbook of the International Folk Music Council, Vol. 2, 1970, pp. 127-132 (1970)
  10. ^ Xenharmonic wiki 7-edo
  11. ^ Morton, David (1980). "The Music of Thailand", Musics of Many Cultures, p.70. May, Elizabeth, ed. ISBN 0-520-04778-8.
  12. ^ Xenharmonic wiki 24 edo
  13. ^ Xenharmonic wiki 48 edo
  14. ^ a b Xenharmonic wiki 72 edo
  15. ^ Xenharmonic wiki 31 edo
  16. ^ Xenharmonic wiki 34 edo
  17. ^ Xenharmonic wiki 41 edo
  18. ^ a b Xenharmonic wiki 53 edo