page_title: Quarter tone
section_title: Equal-tempered tuning systems
hierarchical_section_title: Quarter tone / Types of quarter tones / Equal-tempered tuning systems
caption_attribution_description: English: Subminor seventh on C: B=A. 19 quarter-tones.
context_page_description: A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide 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 tone has its roots in the music of the Middle East and more specifically in Persian traditional music. However, the first evidenced proposal of quarter tones, or the quarter-tone scale, was made by 19th-century music theorists Heinrich Richter in 1823 and Mikha'il Mishaqah about 1840. Composers who have written music using this scale include: Pierre Boulez, Julián Carrillo, Mildred Couper, George Enescu, Alberto Ginastera, Gérard Grisey, Alois Hába, Ljubica Marić, Charles Ives, Tristan Murail, Krzysztof Penderecki, Giacinto Scelsi, Ammar El Sherei, Karlheinz Stockhausen, Tui St. George Tucker, Ivan Alexandrovich Wyschnegradsky, and Iannis Xenakis.
context_section_description: 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 play  or neutral second, half of a minor third. The 8-TET scale is composed of three-quarter tones (Play ). Four steps make a whole tone play .
  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 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.
caption: The "subminor seventh": Bthree quarter flat=Ahalf sharp, 19 quarter tones. It approximates the harmonic seventh, B7♭. Maneri-Sims notation: BSims flagged arrow up.svg♭
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