A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.
Quarter tones have their roots in the music of the Middle East and more specifically in Persian traditional music. However, the first evidenced proposal of the equally-tempered quarter tone scale, or 24 equal temperament, was made by 19th-century music theorists Heinrich Richter in 1823 and Mikhail Mishaqa about 1840. Composers who have written music using this scale include: Igor Markevitch, Pierre Boulez, Julián Carrillo, Mildred Couper, George Enescu, Alberto Ginastera, Gérard Grisey, Alois Hába, Thomas Heberer Ljubica Marić, Charles Ives, Tristan Murail, Krzysztof Penderecki, Giacinto Scelsi, Ammar El Sherei, Karlheinz Stockhausen, Tui St. George Tucker, Ivan Wyschnegradsky, Iannis Xenakis, and Seppe Gebruers (See List of quarter tone pieces.)
Types
Equal-tempered tuning systems
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♭). In the quarter-tone scale, also called 24-tone equal temperament (24-TET), the quarter tone is 50 cents, or a frequency ratio of 24√2 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. The 8-TET scale is composed of three-quarter tones. Four steps make a whole tone. 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 22.642 cents, which doubled makes up for over 90% the spectral range of a quarter tone. 72-TET also has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24. The smallest interval in 31 equal temperament (the "diesis" of 38.71 cents) is half a chromatic semitone, one-third of a diatonic semitone and one-fifth of a whole tone, so it may function as a quarter tone, a fifth-tone or a sixth-tone.
Just intonation tuning systems In just intonation the quarter tone can be represented by the septimal quarter tone, 36:35 (48.77 cents), or by the undecimal quarter tone (i.e. the thirty-third harmonic), 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). 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 "7" () to indicate a note is raised 49 cents, or a ratio of 36:35. Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33:32, or 53 cents. The Maneri-Sims notation system designed for 72-et uses the accidentals and for a quarter tone (36:35 or 48.77 cents) up and down.
Playing quarter tones
A quarter tone clarinet was built by Fritz Schüller (1883–1977) of Markneukirchen, and a quarter tone mechanism for flutes by Eva Kingma.
Music of the Middle East
Many Persian dastgah and Arabic maqamat contain intervals of three-quarter tone size; a short list of these follows.
Bayati (بیاتی): D E F G A B♭ C D
Rast (راست): C D E F G A B C (ascending) C B A G F E D C (descending)
Saba (صبا): D E F G♭ A B♭ C D♭
Segah (سه گاه): E F G A B C D E
‘Ajam (عجم) Hoseyni 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:
Qadmoyo (Bayati) Trayono (Hussayni) Tlithoyo (Segah) Rbiʿoyo (Rast) Hmishoyo Shtithoyo (ʿAjam) Shbiʿoyo Tminoyo
Quarter-tone scale Known as gadwal in Arabic, 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. The invention of the scale is attributed to Mishaqa who wrote a book devoted to the topic but made clear that his teacher, Sheikh Muhammad al-Attar (1764–1828), was one among many already familiar with the concept.
The quarter tone scale may be primarily a theoretical construct in Arabic music. The quarter tone gives musicians a "conceptual map" they can use 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 a mainstream requirement since that period. Previously, pitches of a mode were chosen from a scale consisting of seventeen tones, developed by Safi al-Din al-Urmawi in the thirteenth century.
Composer Charles Ives chose the chord C–D–F–G–B♭ 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 Here is the secondary "minor" and its "first inversion":
In popular Western music
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