Neutral third
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A neutral third is a musical interval between a minor third and a major third. Three distinct intervals may be termed neutral thirds:
- A tridecimal neutral third has a ratio of 16:13 between the frequencies of the two tones, or about 359.47 cents.[1] 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 350.00 cents between the two tones, a hair larger than a ratio of frequencies between the two tones of 11:9.
- The undecimal neutral third has a ratio of 11:9 between the frequencies of the two tones, or about 347.41 cents.
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 minor thirds and a quarter tone flat from major thirds.
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.
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[edit] Occurrence in human music
[edit] 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.[2]
[edit] In modern classical music
The neutral third has been used by a number of modern composers, including Charles Ives, James Tenney, and Gayle Young.[3]
[edit] 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.[citation needed] Neutral thirds are also found in American folk music.[4]
[edit] In equal temperaments
Although there are no neutral thirds in any of the commonly used equally tempered tuning systems with less than 24 divisions of the octave, just neutral thirds are very closely approximated by all the commonly used equally-tempered tuning systems with larger numbers of division in the octave, including 24-ET, 31-ET, 34-ET, 41-ET, 72-ET, and slightly less closely by 53-ET.
Close approximations to the tridecimal neutral third 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; this can be interpreted as tempering out the comma 144:143.
[edit] See also
[edit] References
- ^ [1] Jan Haluska, The Mathematical Theory of Tone Systems, CRC (2004).
- ^ [2] Nettl, Bruno "Infant Musical Development and Primitive Music" Southwestern Journal of Anthropology, Vol. 12, No. 1, pp. 87-91. (Spring, 1956)
- ^ [3] Young, Gayle "The Pitch Organization of Harmonium for James Tenney", Perspectives of New Music, Vol. 26, No. 2. pp. 204-212 (Summer, 1988)
- ^ [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)
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