Quartertone

A quarter tone whole tone.


Many composers are known for having written music including quarter tones or the quarter tone scale (24 equal temperament), first proposed by 19th-century music theorist Mikha'il Mishaqah,[1] including: Pierre Boulez, Julián Carrillo, Mildred Couper, Alberto Ginastera, Gérard Grisey, Alois Hába, Ljubica Marić, Charles Ives, Tristan Murail, Krzysztof Penderecki, Giacinto Scelsi, Karlheinz Stockhausen, Tui St. George Tucker, Ivan Alexandrovich Wyschnegradsky, and Iannis Xenakis (see List of quarter tone pieces).

Types of quarter tones


The term quarter tone can refer to a number of different intervals, all very close in size. For example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments (e.g., D–E).minor third.

In just intonation the quarter tone can be represented by the septimal quarter tone, 36:35 (48.77 cents), or as 33:32 (53.27 cents), 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

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 that cannot play quarter tones (except by using special techniques—see below) include

Conventional musical instruments that can play quarter tones include

  • Electronic instruments:
  • Fretless string instruments, such as fretless guitars, ouds members of the huqin family of instruments, and members of the violin family
  • String instruments with movable frets (such as the sitar)
  • Specially-fretted string instruments
  • Wind instruments whose main means of tone-control is a slide, such as trombones, the tromboon, and slide whistles
  • Specially keyed woodwind instruments
  • Valved brass instruments with extra, quarter-tone valves
  • Pitched percussion instruments, when tuning permits (e.g., timpani), or using special techniques

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.

Music of the Middle East

While the use of quarter tones in modern Western music is a more recent and experimental phenomenon, these and other microtonal intervals have been an important part of the music of Iran (Persia), the Arab world, Armenia, 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.[6]

  1. Shoor (Bayati) )
    شور (بیاتی)
    D E F G A B C D
  2. Rast )
    راست
    C D E C
    with a B replacing the B in the descending scale
  3. Sabba )
    صبا
    D E F G A B C D
  4. Siga )
    سيكاه
    E
  5. ‘Ajam
  6. Hussayni

The Islamic philosopher and scientist Al-Farabi described a number of intervals in his work in music, including a number of quarter tones.

Assyrian/Syriac Church Music Scale:[7]

  • 1 - Qadmoyo (Bayati)
  • 2 - Trayono (Hussayni)
  • 3 - Tlithoyo (Segah)
  • 4 - Rbi‘oyo (Rast)
  • 5 - Hmishoyo
  • 6 - Shtithoyo (‘Ajam)
  • 7 - Shbi‘oyo
  • 8 - Tminoyo

Quarter tone scale


Known as gadwal in Arabic,[8] 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.[9] 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.[10]

The quarter tone scale may be primarily considered a theoretical construct in Arabic music. The quarter tone gives musicians a "conceptual map" with which 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.[9]

Previously, pitches of a mode were chosen from a scale consisting of seventeen tones, developed by Safi 'I-Din al-Urmawi in the thirteenth century.[10]

In popular music

The Japanese multi-instrumentalist and experimental musical instrument builder Yuichi Onoue developed a 24-TET quarter tone tuning on his guitar.[11] Norwegian guitarist Ronni Le Tekrø of the band TNT used a quarter-step guitar on the band's third studio album, Intuition.

Ancient Greek tetrachords

The enharmonic genus of the Greek tetrachord consisted of a ditone or an approximate major third and a semitone which was divided into two microtones. Aristoxenos, Didymos and others presented the semitone as being divided into two approximate quarter tone intervals of about the same size, while other ancient Greek theorists described the microtones resulting from dividing the semitone of the enharmonic genus as unequal in size (i.e., one smaller than a quarter tone and one larger) .[12]

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 ) 2:1 1200.00 ) 0.00
semidiminished octave 23 1150 ) 2:1 1200.00 ) −50.00
supermajor seventh 23 1150 ) 35:18 1151.23 −1.23
major seventh 22 1100 ) 15:8 1088.27 ) +11.73
neutral seventh 21 1050 ) 11:6 1049.36 ) +0.64
minor seventh 20 1000 ) 16:9 996.09 ) +3.91
supermajor sixth/subminor seventh 19 950 ) 7:4 968.83 ) −18.83
major sixth 18 900 ) 5:3 884.36 ) +15.64
neutral sixth 17 850 ) 18:11 852.59 ) −2.59
minor sixth 16 800 ) 8:5 813.69 ) −13.69
subminor sixth 15 750 ) 14:9 764.92 ) −14.92
perfect fifth 14 700 ) 3:2 701.95 ) −1.95
minor fifth 13 650 ) 16:11 648.68 ) +1.32
lesser septimal tritone 12 600 ) 7:5 582.51 ) +17.49
major fourth 11 550 ) 11:8 551.32 ) −1.32
perfect fourth 10 500 ) 4:3 498.05 ) +1.95
tridecimal major third 9 450 ) 13:10 454.21 ) −4.21
septimal major third 9 450 ) 9:7 435.08 ) +14.92
major third 8 400 ) 5:4 386.31 ) +13.69
undecimal neutral third 7 350 ) 11:9 347.41 ) +2.59
minor third 6 300 ) 6:5 315.64 ) −15.64
septimal minor third 5 250 ) 7:6 266.88 ) −16.88
tridecimal minor third 5 250 ) 15:13 247.74 ) +2.26
septimal whole tone 5 250 ) 8:7 231.17 ) +18.83
whole tone, major tone 4 200 ) 9:8 203.91 ) −3.91
whole tone, minor tone 4 200 10:9 182.40 +17.60
neutral second, greater undecimal 3 150 ) 11:10 165.00 ) −15.00
neutral second, lesser undecimal 3 150 ) 12:11 150.64 ) −0.64
15:14 semitone 2 100 ) 15:14 119.44 −19.44
diatonic semitone, just 2 100 ) 16:15 111.73 ) −11.73
21:20 semitone 2 100 ) 21:20 84.47 ) +15.53
28:27 semitone 1 50 ) 28:27 62.96 ) −12.96
septimal quarter tone 1 50 ) 36:35 48.77 ) +1.23

Moving from 12-TET to 24-TET allows the better approximation of a number of intervals. 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.

See also

References

Further reading

  • Bartolozzi, Bruno (1967). New Sounds for Woodwind. London, New York: Oxford University Press.
  • Bousted, Donald (2002). "Microtonality, the Recorder and the Quarter-Tone Recorder Manual". The Recorder Magazine 22, no. 3 (Fall): 99–102.
  • Bousted, Donald (2005). "Next Step Quarter-Tone Resources: Melody". The Recorder Magazine 25, no. 3 (Fall): 88–91.
  • 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.
  • Rees, Carla (2007). "Eva Kingma and the Quarter-Tone Flute". Pan: The Flute Magazine 26, no. 4:23-29.
  • Rewoldt, Todd (2000). "Altissimo Quarter-Tones for the Alto Saxophone". Saxophone Symposium 25:56–69.

External links

  • "quarter-tone / 24-edo", TonalSoft.com.

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