Quarter tone
From Wikipedia, the free encyclopedia
A quarter tone 
play (help·info) is an interval about half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone.
Many composers are known for having written music including quarter tones or the quarter tone scale, first proposed by 19th-century music theorist Mikha'il Mishaqah (Touma 1996, p. 16), including: Pierre Boulez, Julián Carrillo, Mildred Couper, Alberto Ginastera, Gérard Grisey, Alois Hába, Charles Ives, Tristan Murail, Krzysztof Penderecki, Giacinto Scelsi, Tui St. George Tucker, Ivan Alexandrovich Wyschnegradsky, Iannis Xenakis (see List of quarter tone pieces).
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[edit] Types of quarter tones
The term quarter tone can refer to a number of different intervals, all very close in size. In the quarter tone scale, also called 24 tone equal temperament (24-TET), the quarter tone is 50 cents, or a frequency ratio of 21/24 or 1.0293, and divides the octave into 24 equal steps. In this scale the quarter tone is the smallest step. A semitone is thus made of two steps, and three steps make a three-quarter tone play (help·info) or neutral second, half of a minor third.
In just intonation the quarter tone can be represented as 36:35 or 33:32, approximately half the semitone of 16:15 or 25:24. The ratio of 36:35 is only 1.23 cents narrower than a 24-TET quarter tone. This just ratio is also the difference between a minor third (6:5) and septimal minor third (7:6).
Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems. 22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET has an interval of 45.28 cents, slightly smaller. 72-TET also has equally-tempered quarter-tones, and indeed contains 3 quarter tone scales, since 72 is divisible by 24.
Composer Ben Johnston, to accommodate the just septimal quarter tone, uses a small "7" as an accidental to indicate a note is lowered 49 cents, or an upside down "∠" to indicate a note is raised 49 cents,[2] or a ratio of 36/35.[3] Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33/32, or 53 cents.[3]
[edit] Playing quarter tones on musical instruments
Because many musical instruments manufactured today are designed for the 12-tone scale, not all are usable for playing quarter tones. Sometimes special playing techniques must be used.
Conventional musical instruments which can play quarter tones include
- Synthesizers (if design permits)
- Fretless string instruments (on fretted string instruments it is possible with bending or special tuning)
- Slide brass instruments (trombone)
- Valved brass instruments (trumpet, horn, tuba)
- Woodwind instruments, using special fingering or bending.
- Harmonica
- Harp
- Pianos, if specially tuned
- Pitched percussion instruments
Experimental instruments have been built to play in quarter tones, for example a quarter tone clarinet by Fritz Schüller (1883-1977) of Markneukirchen.
Other instruments can be used to play quarter tones when using audio signal processing effects such as pitch shifting.
Pairs of conventional instruments tuned a quarter tone apart can be used to play some quarter tone music. Indeed, "quarter tone pianos" have been built which consist essentially of two pianos stacked one above the other in a single case, one tuned a quarter tone higher than the other.
[edit] Music of the Middle East
While the use of quarter tones in Western music is a more recent and experimental phenomenon, these and other microtonal intervals have been an important part of the music of the Arab world, Iran (Persia), Turkey, Assyria, Kurdistan and neighboring lands and areas for many centuries.
Many Arabic maqamat contain intervals of three-quarter tone size; a short list of these follows.[4]
- Bayati play (help·info)
- بياتي
- D E
F G A B♭ C D
- D E
- بياتي
- Hussayni
- Siga play (help·info)
- سيكاه
- E F G A B C D E
- E
- سيكاه
- Rast play (help·info)
- راست
- C D E F G A B C
- with a B♭ replacing the B in the descending scale
- with a B♭ replacing the B
- C D E
- راست
- ‘Ajam
The medieval philosopher and scientist Al-Farabi described a number of intervals in his work in music, including a number of quarter tones.
Assyrian/Syriac Church scale:
- 1 - Qadmoyo (Bayati)
- 2 - Trayono (Hussayni)
- 3 - Tlithoyo (Segah)
- 4 - Rbi‘oyo (Rast)
- 5 - Hmishoyo
- 6 - Shtithoyo (‘Ajam)
- 7 - Shbi‘oyo
- 8 - Tminoyo
[edit] Quarter tone scale
Known as gadwal in Arabic[5], the quarter tone scale was developed in the Middle East in the eighteenth century and many of the first detailed writings in the nineteenth century Syria describe the scale as being of 24 equal tones[6] The invention of the scale is attributed to Mikhail Mishaqa whose work Essay on the Art of Music for the Emir Shihāb (al-Risāla al-shihābiyya fi 'l-ṣinā‘a al-mūsīqiyya) is devoted to the topic but also makes clear his teacher Sheikh Muhammad al-‘Attār (1764-1828) was one of many already familiar with the concept.[7]
The quarter tone scale may be primarily considered a theoretical construct in Arabic music. The quarter tone gives musicians a "conceptual map" which with to discuss and compare intervals by number of quarter tones and this may be one of the reasons it accompanies a renewed interest in theory, with instruction in music theory being a mainstream requirement since that period.[6]
Previously pitches of a mode where chosen from a scale consisting of seventeen tones, developed by Safi 'I-Din al-Urmawi in the thirteenth century.[7]
[edit] In popular music
The Japanese multi-instrumentalist and experimental musical instrument builder Yuichi Onoue developed a 24-TET quarter tone tuning on his guitar.[8]
[edit] Greek tetrachords
The enharmonic genus of the tetrachord described by the Greek Archytas[cite this quote] consists of two quarter tones and a major third.
[edit] Interval size in equal temperament
Here are the sizes of some common intervals in a 24-note equally tempered scale, with the interval names proposed by Alois Hába (neutral third, etc.) and Ivan Wyschnegradsky (major fourth, etc.):
| interval name | size (steps) | size (cents) | midi | just ratio | just (cents) | midi | error |
|---|---|---|---|---|---|---|---|
| octave | 24 | 1200 | play (help·info) |
2:1 | 1200 | play (help·info) |
0 |
| semidiminished octave or [ minor octave ] | 23 | 1150 | play (help·info) |
2:1 | 1200 | play (help·info) |
−50 |
| supermajor seventh | 23 | 1150 | play (help·info) |
15:8 | 1088 | play (help·info) |
+62 |
| major seventh | 22 | 1100 | play (help·info) |
15:8 | 1088 | play (help·info) |
+12 |
| neutral seventh | 21 | 1050 | play (help·info) |
11:6 | 1049 | play (help·info) |
+1 |
| minor seventh | 20 | 1000 | play (help·info) |
16:9 | 996.09 | play (help·info) |
+3.91 |
| supermajor sixth/subminor seventh | 19 | 950 | play (help·info) |
16:9 | 996.09 | play (help·info) |
−46.09 |
| major sixth | 18 | 900 | play (help·info) |
5:3 | 884 | play (help·info) |
+16 |
| neutral sixth | 17 | 850 | play (help·info) |
11:9 | 852.59 | play (help·info) |
−2.59 |
| minor sixth | 16 | 800 | play (help·info) |
8:5 | 814 | play (help·info) |
−14 |
| subminor sixth | 15 | 750 | play (help·info) |
14:9 | 764.9 | play (help·info) |
−14.9 |
| perfect fifth | 14 | 700 | play (help·info) |
3:2 | 701.95 | play (help·info) |
−1.95 |
| minor fifth | 13 | 650 | play (help·info) |
10:7 | 617 | play (help·info) |
+33 |
| tritone | 12 | 600 | play (help·info) |
7:5 | 582.51 | play (help·info) |
+17.49 |
| undecimal tritone or semi-augmented fourth | 11 | 550 | play (help·info) |
11:8 | 551.32 | play (help·info) |
−1.32 |
| perfect fourth | 10 | 500 | play (help·info) |
4:3 | 498.05 | play (help·info) |
+1.95 |
| tridecimal major third | 9 | 450 | play (help·info) |
13:10 | 454.21 | play (help·info) |
−4.21 |
| septimal major third | 9 | 450 | play (help·info) |
9:7 | 435.08 | play (help·info) |
+14.92 |
| major third | 8 | 400 | play (help·info) |
5:4 | 386.31 | play (help·info) |
+13.69 |
| undecimal neutral third | 7 | 350 | play (help·info) |
11:9 | 347.41 | play (help·info) |
+2.59 |
| minor third | 6 | 300 | play (help·info) |
6:5 | 315.64 | play (help·info) |
−15.64 |
| septimal minor third | 5 | 250 | play (help·info) |
7:6 | 266.88 | play (help·info) |
−16.88 |
| tridecimal minor third | 5 | 250 | play (help·info) |
15:13 | 247.74 | play (help·info) |
+2.26 |
| septimal whole tone or supermajor second | 5 | 250 | play (help·info) |
8:7 | 231.17 | play (help·info) |
+18.83 |
| whole tone, major tone | 4 | 200 | play (help·info) |
9:8 | 203.91 | play (help·info) |
−3.91 |
| neutral second, lesser undecimal | 3 | 150 | play (help·info) |
12:11 | 150.64 | play (help·info) |
−0.64 |
| diatonic semitone, just | 2 | 100 | play (help·info) |
16:15 | 111.73 | play (help·info) |
−11.73 |
| septimal quarter tone, subminor second/[ major prime ] | 1 | 50 | play (help·info) |
36:35 | 48.77 | play (help·info) |
+1.23 |
Moving from 12-TET to 24-TET does not improve the matches to any intervals in the harmonic series, but it adds a number of new intervals not available in 12-TET. New intervals matched particularly closely include the neutral second, neutral third, and (11:8) ratio, or the 11th harmonic. The septimal minor third and septimal major third are approximated rather poorly; the (13:10) and (15:13) ratios, involving the 13th harmonic, are matched very closely. Overall, 24-TET can be viewed as matching the 11th harmonic more closely than the 7th.
[edit] See also
[edit] Notes
- ^ a b Boatwright, Howard (1971). "Ives' Quarter-Tone Impressions", p.8-9. Perspectives on American Composers, p.3-12, Boretz & Cone, eds.
- ^ Douglas Keislar; Easley Blackwood; John Eaton; Lou Harrison; Ben Johnston; Joel Mandelbaum; William Schottstaedt. p.193. "Six American Composers on Nonstandard Tunnings", Perspectives of New Music, Vol. 29, No. 1. (Winter, 1991), pp. 176-211.
- ^ a b Fonville, John (Summer, 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters", p.114, Perspectives of New Music, Vol. 29, No. 2, pp. 106-137.
- ^ Spector, Johanna (May 1970). "Classical 'Ud Music in Egypt with Special Reference to Maqamat" (GIF). Ethnomusicology 14 (2): 243–257. doi:. http://www.jstor.org/view/00141836/ap030019/03a00040/0. Retrieved 2006-09-08.
- ^ "Classical 'Ud Music in Egypt with Special Reference to Maqamat", p.246. Johanna Spector. Ethnomusicology, Vol. 14, No. 2. (May, 1970), pp. 243-257.
- ^ a b Marcus, Scott (1993)."The Interface between Theory and Practice: Intonation in Arab Music", Asian Music, Vol. 24, No. 2. (Spring - Summer, 1993), pp. 39-58.
- ^ a b Maalouf, Shireen (2003). "Mikhii'il Mishiiqa: Virtual Founder of the Twenty-Four Equal Quartertone Scale", Journal of the American Oriental Society, Vol. 123, No. 4. (Oct. - Dec., 2003), pp. 835-840.
- ^ Yuichi Onoue on hypercustom.com
[edit] References
- Bartolozzi, Bruno (1967). New Sounds for Woodwind. London, New York: Oxford University Press.
- Caravan, Ronald R. (1979). Preliminary Exercises and Etudes in Contemporary Techniques for Clarinet: Introductory Material for the Study of Multiphonics, Quarter Tones, and Timbre Variation. [Oswego, N.Y.]: Ethos Publications.
- Ellis, Don (1975). Quarter Tones: A Text with Musical Examples, Exercises and Etudes. Plainview, N.Y.: Harold Branch Pub. Co.
- MacDonald, John (1822). A Treatise on the Harmonic System Arising from the Vibrations of the Aliquot Divisions of Strings According to the Gradual Progress of the Notes from the Middle, to the Remote Extremes: Explaining Simply, by Curved Delineations, the Manner in Which the Harmonic Tones, Half and Quarter Notes, Are Generated and Produced on Every Corresponding Part of the String; and under a Copious Explanatory Description Illustrated by Musical and Appropriate Plates, Giving an Easy and Familiar Adaptation of the Whole to the Purposes of Composition and Instrumental Music, and More Particularly, to the Practice of the Violin, Tenor, Violoncello and Double Bass, on All the Strings, and in Every Compass of These Instruments, by Every Practical Mode of Execution; with Some Musical Animadversions Introductory of the General Subject, Briefly Alluding to the Rise and Progress of Music, and to the Corrections of Temperament: and Stating Various Improvements of Instruments, Experimentally Ascertained: Concluding with an Application or Two of the Principle of Musical Notes, to Purposes of Utility, and a Reference to Terms Less Generally Noticed. London: Printed for the Author, and Sold by T. Preston.
- Möllendorff, Willi, and Joe Monzo (2001). Music with Quarter-Tones: Experiences at the Bichromatic Harmonium. [United States]: J. Monzo.
- Touma, Habib Hassan (1996). The Music of the Arabs, trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.
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