A septimal quarter tone (in

music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

) is an interval with the ratio of 36:35, which is the difference between the

septimal minor third Septimal may refer to: *Septimal chromatic semitone, the interval 21:20, about 84.47 cents *Septimal comma, a small musical interval in just intonation divisible by 7 *Septimal diatonic semitone, the interval 15:14, about 119.44 cents *S ...

and the Just

minor third In music theory, a minor third is a interval (music), musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval (music)#Number, interval numb ...

, or about 48.77 cents wide. The name derives from the interval being the

7-limit 7-limit or septimal tunings and intervals are musical instrument tunings that have a limit of seven: the largest prime factor contained in the interval ratios between pitches is seven. Thus, for example, 50:49 is a 7-limit interval, but 14 ...

approximation of a

quarter tone A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (orally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, a ...

. The septimal quarter tone can be viewed either as a musical interval in its own right, or as a

comma The comma is a punctuation mark that appears in several variants in different languages. Some typefaces render it as a small line, slightly curved or straight, but inclined from the vertical; others give it the appearance of a miniature fille ...

; if it is tempered out in a given tuning system, the distinction between the two different types of minor thirds is lost. The septimal quarter tone may be derived from the harmonic series as the interval between the thirty-fifth and thirty-sixth harmonics. Composer Ben Johnston uses a small seven ("") as an accidental to indicate a note is lowered by 36/35 (≈49 cents), or an upside-down seven ("") to indicate a note is raised by the same amount."Ben Johnston's Extended Just Intonation – A Guide for Interpreters",

John Fonville John Fonville is a flutist and composer. Fonville specializes in extended techniques on the flute, especially microtonality, and performs on instruments including a complete set of quarter tone ( Kingma system) flutes.Maneri-Sims notation system designed for

72-et In music, 72 equal temperament, called twelfth-tone, 72 TET, 72 EDO, or 72 ET, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps (equal frequency ratios). Each step ...

uses the accidentals and for a quarter tone (36:35 or 48.77 cents) up and down. The septimal quarter tone is tempered out by

twelve-tone equal temperament 12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (\sqrt 2/math> ≈ 1.05946). That resul ...

, but not in any of 19-TET, 22-TET,

24-TET A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (orally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, an ...

, or

31-TET In music, 31 equal temperament, which can also be abbreviated (31 tone ) or (equal division of the octave), also known as tricesimoprimal, is the musical temperament, tempered scale derived by dividing the octave into 31 equally-p ...

. 22-TET and

offer a very close match to the septimal quarter tone. The septimal quarter tone is the difference between the 9:5 just

minor seventh In music theory, a minor seventh is one of two musical intervals that span seven staff positions. It is ''minor'' because it is the smaller of the two sevenths, spanning ten semitones. The major seventh spans eleven. For example, the interval ...

and the

harmonic seventh The harmonic seventh interval, also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969 cent (music), cents). This is about 32 cents narrower, with a more stable and consonant sound, than a ...

References

{{Intervals, state=expanded 7-limit tuning and intervals Commas (music) Quarter tones 0036:0035