A neutral third is a musical interval wider than a minor thirdplayⓘ but narrower than a major thirdplayⓘ, named by Jan Pieter Land in 1880.[4] Land makes reference to the neutral third attributed to Zalzal (8th c.), described by Al-Farabi (10th c.) as corresponding to a ratio of 27:22 (354.5 cents) and by Avicenna (Ibn Sina, 11th c.) as 39:32 (342.5 cents).[5] The Zalzalian third may have been a mobile interval.
Three distinct intervals may be termed neutral thirds:[6]
The undecimal neutral third has a ratio of 11:9[7] between the frequencies of the two tones, or about 347.41 cents playⓘ. This ratio is the mathematical mediant of the major third 5/4 and the minor third 6/5, and as such, has the property that if harmonic notes of frequency f and (11/9) f are played together, the beat frequency of the 5th harmonic of the lower pitch against the 4th of the upper, i.e. , is the same as the beat frequency of the 6th harmonic of the lower pitch against the 5th of the upper, i.e. . In this sense, it is the unique ratio which is equally well-tuned as a major and minor third.
A tridecimal neutral thirdplayⓘ has a ratio of 16:13 between the frequencies of the two tones, or about 359.47 cents.[3] This is the largest neutral third, and occurs infrequently in music, as little music utilizes the 13th harmonic. It is the mediant of the septimal major third 9/7 and septimal minor third 7/6, and as such, enjoys an analogous property with regard to the beating of the corresponding harmonics as above. That is, .
An equal-tempered neutral thirdplayⓘ is characterized by a difference of 350 cents between the two tones, slightly 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.
In addition to the above examples, a square root neutral third can be characterized by a ratio of between two frequencies, being exactly half of a just perfect fifth of 3/2 and measuring about 350.98 cents. Such a definition stems from the two thirds traditionally making a fifth-based triad.
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ⓘ and 31-tet Playⓘ.
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.[8]
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.
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 temperamentsEdit
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.[12] 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.[13]
The neutral third also has good approximations in other commonly used equal temperaments including 24-ET (7 steps, 350 cents[14]) and similarly by all multiples of 24 equal steps such as 48-ET[15] and 72-ET,[16]31-ET (9 steps, 348.39),[17]34-ET (10 steps, 352.941 cents[18]), 41-ET (12 steps, 351.22 cents[19]), and slightly less closely by 53-ET (15 steps, 339.62 cents[20]).
Close approximations to the tridecimal neutral third (16:13) appear in 53-ET[20] and 72-ET.[16] 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.
^ abHaluska (2003), p. xxiv. Tridecimal neutral third.
^J. P. Land, Over de toonladders der Arabische muziek, 1880; Recherches sur l'histoire de la gamme arabe, 1884. See Hermann von Helmholtz, On the Sensations of Tone, (Alexander John Ellis, trans.) (3rd ed., 1895), p. 281, note † (addition by Ellis).
^Liberty Manik (1969). Das Arabische Tonsystem im Mittelalter (Leiden: Brill, 1969), 46–49.
^Alois Hába, Neue Harmonielehre des diatonischen, chromatischen, Viertel-, Drittel-, Sechstel- und Zwölftel-Tonsystems (Leipzig: Fr. Kistner & C.F.W. Sigel, 1927), 143. [ISBN unspecified]. Cited in Skinner, Miles Leigh (2007). Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky, p. 25. ProQuest. ISBN9780542998478.
^Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p. 131. ISBN0-89579-507-8. "Super-Major Second".
^Young, Gayle. "The Pitch Organization of Harmonium for James Tenney", Perspectives of New Music, vol. 26, no. 2. pp. 204–212 (Summer 1988) JSTOR 833190
^Aronson, Howard I., ed. (1994). The Annual of the Society for the Study of Caucasia. Society for the Study of Caucasia. p. 93. Retrieved 14 April 2011.
^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) JSTOR 767430
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A neutral third is a musical interval wider than a minor third play but narrower than a major third play named by Jan Pieter Land in 1880 4 Land makes reference to the neutral third attributed to Zalzal 8th c described by Al Farabi 10th c as corresponding to a ratio of 27 22 354 5 cents and by Avicenna Ibn Sina 11th c as 39 32 342 5 cents 5 The Zalzalian third may have been a mobile interval Neutral thirdInverseneutral sixthNameOther names Abbreviationn3SizeSemitones 3 Interval class 3 Just interval11 9 1 27 22 1 2 or 16 13 3 Cents24 equal temperament350Just intonation347 355 or 359 source source source Neutral third on C source source source 27 22Neutral thirdThree distinct intervals may be termed neutral thirds 6 The undecimal neutral third has a ratio of 11 9 7 between the frequencies of the two tones or about 347 41 cents play This ratio is the mathematical mediant of the major third 5 4 and the minor third 6 5 and as such has the property that if harmonic notes of frequency f and 11 9 f are played together the beat frequency of the 5th harmonic of the lower pitch against the 4th of the upper i e 5 f 4 11 9 f 1 9 f displaystyle 5f 4 11 9 f 1 9 f is the same as the beat frequency of the 6th harmonic of the lower pitch against the 5th of the upper i e 6 f 5 11 9 f 1 9 f 1 9 f displaystyle 6f 5 11 9 f 1 9 f 1 9 f In this sense it is the unique ratio which is equally well tuned as a major and minor third A tridecimal neutral third play has a ratio of 16 13 between the frequencies of the two tones or about 359 47 cents 3 This is the largest neutral third and occurs infrequently in music as little music utilizes the 13th harmonic It is the mediant of the septimal major third 9 7 and septimal minor third 7 6 and as such enjoys an analogous property with regard to the beating of the corresponding harmonics as above That is 7 f 6 16 13 f 9 f 7 16 13 f 5 13 f displaystyle 7f 6 16 13 f 9f 7 16 13 f 5 13 f An equal tempered neutral third play is characterized by a difference of 350 cents between the two tones slightly 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 In addition to the above examples a square root neutral third can be characterized by a ratio of 3 2 displaystyle sqrt 3 2 between two frequencies being exactly half of a just perfect fifth of 3 2 and measuring about 350 98 cents Such a definition stems from the two thirds traditionally making a fifth based triad 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 and 31 tet Play Contents 1 Occurrence in human music 1 1 In infants song 1 2 In modern classical Western music 1 3 In traditional music 1 4 In contemporary popular music 2 In equal temperaments 3 See also 4 ReferencesOccurrence in human music EditIn infants song Edit 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 8 In modern classical Western music Edit The neutral third has been used by a number of modern composers including Charles Ives James Tenney and Gayle Young 9 In traditional music Edit 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 10 Neutral thirds are also found in American folk music 11 In contemporary popular music Edit 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 EditTwo 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 12 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 13 The neutral third also has good approximations in other commonly used equal temperaments including 24 ET 7 steps 350 cents 14 and similarly by all multiples of 24 equal steps such as 48 ET 15 and 72 ET 16 31 ET 9 steps 348 39 17 34 ET 10 steps 352 941 cents 18 41 ET 12 steps 351 22 cents 19 and slightly less closely by 53 ET 15 steps 339 62 cents 20 Close approximations to the tridecimal neutral third 16 13 appear in 53 ET 20 and 72 ET 16 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 EditList of pitch intervals Microtonal musicReferences Edit a b Haluska Jan 2003 The Mathematical Theory of Tone Systems p xxiii ISBN 0 8247 4714 3 Undecimal neutral third and Zalzal s wosta Neutral third scales on Xenharmonic Wiki a b Haluska 2003 p xxiv Tridecimal neutral third J P Land Over de toonladders der Arabische muziek 1880 Recherches sur l histoire de la gamme arabe 1884 See Hermann von Helmholtz On the Sensations of Tone Alexander John Ellis trans 3rd ed 1895 p 281 note addition by Ellis Liberty Manik 1969 Das Arabische Tonsystem im Mittelalter Leiden Brill 1969 46 49 Alois Haba Neue Harmonielehre des diatonischen chromatischen Viertel Drittel Sechstel und Zwolftel Tonsystems Leipzig Fr Kistner amp C F W Sigel 1927 143 ISBN unspecified Cited in Skinner Miles Leigh 2007 Toward a Quarter tone Syntax Analyses of Selected Works by Blackwood Haba Ives and Wyschnegradsky p 25 ProQuest ISBN 9780542998478 Andrew Horner Lydia Ayres 2002 Cooking with Csound Woodwind and Brass Recipes p 131 ISBN 0 89579 507 8 Super Major Second Nettl Bruno Infant Musical Development and Primitive Music Southwestern Journal of Anthropology vol 12 no 1 pp 87 91 Spring 1956 JSTOR 3628859 Young Gayle The Pitch Organization of Harmonium for James Tenney Perspectives of New Music vol 26 no 2 pp 204 212 Summer 1988 JSTOR 833190 Aronson Howard I ed 1994 The Annual of the Society for the Study of Caucasia Society for the Study of Caucasia p 93 Retrieved 14 April 2011 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 JSTOR 767430 7edo on Xenharmonic Wiki Morton David 1980 The Music of Thailand Musics of Many Cultures p 70 May Elizabeth ed ISBN 0 520 04778 8 24edo on Xenharmonic Wiki 48edo on Xenharmonic Wiki a b 72edo on Xenharmonic Wiki 31edo on Xenharmonic Wiki 34edo on Xenharmonic Wiki 41edo on Xenharmonic Wiki a b 53edo on Xenharmonic Wiki Retrieved from https en wikipedia org w index php title Neutral third amp oldid 1177890461, wikipedia, wiki, book, books, library,
