Septimal quarter tone
Encyclopedia
A septimal quarter-tone (in music
) is an interval
with the ratio of 36:35 , which is the difference between the septimal minor third
and the Just minor third
, or about 48.77 cents wide. The name derives from the interval being the 7-limit approximation of a quarter tone
. The septimal quarter-tone can be viewed either as a musical interval in its own right, or as a comma
; 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 "7" as an accidental to indicate a note is lowered 49 cents, or an upside down "ㄥ" to indicate a note is raised 49 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.
The septimal quarter-tone is tempered out by twelve-tone equal temperament, but not in any of 19-TET, 22-TET, 24-TET, or 31-TET. 22-TET and 24-TET offer a very close match to the septimal quarter-tone.
The septimal quarter-tone is the difference between the just minor seventh
and the harmonic seventh
.
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
) is an interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
with the ratio of 36:35 , which is the difference between the septimal minor third
Septimal minor third
In music, the septimal minor third , also called the subminor third, is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5...
and the Just minor third
Minor third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...
, or about 48.77 cents wide. The name derives from the interval being the 7-limit approximation of a quarter tone
Quarter tone
A quarter tone , is a pitch halfway between the usual notes of a chromatic scale, an interval about half as wide as a semitone, which is half a whole tone....
. The septimal quarter-tone can be viewed either as a musical interval in its own right, or as a comma
Septimal comma
A septimal comma is a small musical interval in just intonation that contains the number seven in its prime factorization. There is more than one such interval, so the term septimal comma is ambiguous, but it most commonly refers to the interval 64/63....
; 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
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
as the interval between the thirty-fifth and thirty-sixth harmonics.
Composer Ben Johnston uses a small "7" as an accidental to indicate a note is lowered 49 cents, or an upside down "ㄥ" to indicate a note is raised 49 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.
The septimal quarter-tone is tempered out by twelve-tone equal temperament, but not in any of 19-TET, 22-TET, 24-TET, or 31-TET. 22-TET and 24-TET offer a very close match to the septimal quarter-tone.
The septimal quarter-tone is the difference between the just minor seventh
Minor seventh
In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions , and the minor seventh is one of two commonly occurring sevenths. The minor quality specification identifies it as being the smallest of the two: the minor seventh spans ten semitones, the...
and the harmonic seventh
Harmonic seventh
The harmonic seventh interval , also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio . This is somewhat narrower than and is "sweeter in quality" than an "ordinary" minor seventh, which has a just-intonation ratio of 9:5 , or an equal-temperament ratio of...
.