A quarter tone , is a pitch halfway between the usual notes of a chromatic scale, 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,[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).
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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♭).[3] 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 approximately 1.0293, and divides the octave into 24 equal steps (equal temperament). 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 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,[4] or a ratio of 36/35.[5] Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33/32, or 53 cents.[5]
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 cannot play quarter tones (except by using special techniques—see below) include
Conventional musical instruments which can play quarter tones include
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.
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 the Iran (Persia), 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]
The persian 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]:
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]
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 Tekro of the band TNT (band) used a quarter-step guitar on the band's third studio album, Intuition.
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]
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 | ||
| lesser septimal tritone | 12 | 600 | 7:5 | 582.51 | +17.49 | ||
| undecimal tritone or semi-augmented 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 | −8.42 | ||
| 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.
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