Neutral third

Neutral Third

Inverse	neutral sixth
Name
Other names	-
Abbreviation	n3
Size
Semitones	~3½
Interval class	~3½
Just interval	11:9[1], 27:22[2], or 16:13[3]
Cents
Equal temperament	300 or 400
24 equal temperament	350
Just intonation	347, 355, or 359

Neutral third on C  Play (help·info).

A neutral third is a musical interval wider than a minor third  play (help·info) but narrower than a major third  play (help·info). Three distinct intervals may be termed neutral thirds:

• The undecimal neutral third has a ratio of 11:9^[4] between the frequencies of the two tones, or about 347.41 cents  play (help·info).

• A tridecimal neutral third  play (help·info) 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.

• An equal-tempered neutral third  play (help·info) 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. 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  Play (help·info) and 31-tet  Play (help·info).

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

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.

See also

• List of musical intervals
• Microtonal music

References

1. ^ Haluska, (2003) p.xxiii. Undecimal neutral third.
2. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0824747143. 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 0895795078. "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. http://books.google.com/books?id=YbYWAQAAMAAJ. 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)