Quarter tone

A quarter tone is an interval about half as wide (aurally, or logarithmically) as a semitone, which is half a whole tone.

Trumpet with 3 normal valves and a quartering on the extension valve (right).

Trumpet with 3 normal valves and a quartering on the extension valve (right).

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

Contents

  • 1 Types of quarter tones
  • 2 Playing quarter tones on musical instruments
  • 3 Music of the Middle East
    • 3.1 Quarter tone scale
  • 4 Greek tetrachords
  • 5 Interval size in equal temperament
  • 6 Notes
  • 7 References

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. 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  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.

Playing quarter tones on musical instruments

A quarter tone clarinet by Fritz Schüller.

A quarter tone clarinet by Fritz Schüller.

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)
  • Woodwind instruments, using special fingering or bending.
  • Harmonica
  • Flute
  • Clarinet
  • Saxophone
  • Harp

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 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, Turkey, Iran, 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.[1] (Note: Due to the lack of widespread support for Unicode quarter tone characters, a regular flat symbol is used with a strikethrough. The proper form has a short diagonal stroke through the stem, not a straight stroke through the bowl. )

  1. Bayati play 

بياتي

D E F G A B C D

  1. Hussayni
  2. Siga play 

سيكاه

E F G A B C D E

  1. Rast play 

راست

C D E F G A B C

with a B replacing the B in the descending scale

  1. ‘Ajam

صبا

D E F G A B C D

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

Quarter tone scale

The quarter tone scale was developed in the Middle East in the eighteen century and many of the first detailed writings in the nineteenth century Syria describe the scale as being of 24 equal tones[2] 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-inā‘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.[3]

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.[2]

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.[3]

Greek tetrachords

The enharmonic genus of the tetrachord described by the Greek Archytas consists of two quarter tones and a major third.

Interval size in equal temperament

Here are the sizes of some common intervals in a 24-note equally tempered scale:

interval name

size (steps)

size (cents)

midi

just ratio

just (cents)

midi

difference

perfect fifth

14

700.00

play 

3:2

701.95

play 

1.95

tritone

12

600

play 

7:5

582.51

play 

-17.49

eleventh harmonic

11

550.00

play 

11:8

551.32

play 

1.32

perfect fourth

10

500

play 

4:3

498.05

play 

-1.95

tridecimal major third

9

450.00

13:10

454.21

play 

4.21

septimal major third

9

450.00

play 

9:7

435.08

play 

-14.92

major third

8

400.00

play 

5:4

386.31

play 

-13.69

undecimal neutral third

7

350.00

play 

11:9

347.41

play 

-2.59

minor third

6

300.00

play 

6:5

315.64

play 

15.64

septimal minor third

5

250.00

7:6

266.88

play 

16.88

tridecimal minor third

5

250.00

15:13

247.74

play 

-2.26

septimal whole tone

5

250.00

play 

8:7

231.17

play 

-18.83

whole tone, major tone

4

200.00

play 

9:8

203.91

play 

3.91

neutral second, lesser undecimal

3

150.00

play 

11:10

150.64

play 

0.64

diatonic semitone, just

2

100.00

play 

16:15

111.73

play 

11.73

septimal quarter tone, just

1

50.00

play 

36:35

48.77

play 

-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.

Notes

  1. ^ Spector, Johanna (May 1970). "Classical 'Ud Music in Egypt with Special Reference to Maqamat" (GIF). Ethnomusicology 14 (2): 243–257. doi:10.2307/849799. Retrieved on 2006-09-08. 
  2. ^ 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.
  3. ^ 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.

References

  • Habib Hassan Touma (1996). The Music of the Arabs, trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.
 
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