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.

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 (see List of quarter tone pieces).

[edit] Types of quarter tones

Composer Charles Ives chose the chord above as good possibility for a "fundamental" chord in the quarter tone scale, akin not to the tonic but to the major chord of traditional tonality.^[1] Play (help·info)

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 2^1/24 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

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.

[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] (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 (help·info)

   بياتي

   D E♭ F G A B♭ C D

2. Hussayni
3. Siga play (help·info)

   سيكاه

   E♭ F G A B♭ C D E♭

4. Rast play (help·info)

   راست

   C D E♭ F G A B♭ C

   with a B♭ replacing the B♭ in the descending scale

5. ‘Ajam

• Sabba play (help·info)

  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

[edit] Quarter tone scale

Composer Charles Ives chose the chord above as good possibility for a "secondary" chord in the quarter tone scale, akin to the minor chord of traditional tonality. He considered that it may be built upon any degree of the quarter tone scale.^[1] Play (help·info)

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

• Temperament
• Microtonal music
• List of quarter tone pieces
• List of meantone intervals

[edit] Notes

[edit] References

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

[edit] Links

• About 24-EDO and persian music