Septimal semicomma
Encyclopedia
In music, the ratio 126/125 is called the septimal semicomma . It is also called the starling comma after its use in starling temperament, as well as the small septimal comma. It is equal to approximately 13.79 cents
.
Factored into primes it is:
Or as simple just intervals:
Thus it is the difference between three minor third
s of 6/5 plus a septimal minor third
of 7/6 and an octave (2/1). This comma is important to certain tuning systems, such as septimal meantone temperament
.
A diminished seventh chord
consisting of three minor thirds and a subminor third making up an octave is possible in such systems. This characteristic feature of these tuning systems is known as the septimal semicomma diminished seventh chord.
and 31 equal temperament
, but not in 22 equal temperament
, 34 equal temperament
, 41 equal temperament
, or 53 equal temperament
.
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
.
Factored into primes it is:
Or as simple just intervals:
Thus it is the difference between three 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...
s of 6/5 plus a 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...
of 7/6 and an octave (2/1). This comma is important to certain tuning systems, such as septimal meantone temperament
Septimal meantone temperament
In music, septimal meantone temperament, also called standard septimal meantone or simply septimal meantone, refers to the tempering of 7-limit musical intervals by a meantone temperament tuning in the range from fifths flattened by the amount of fifths for 12 equal temperament to those as flat as...
.
A diminished seventh chord
Diminished seventh chord
A diminished seventh chord is a four note chord that comprises a diminished triad plus the interval of a diminished seventh above the root. Thus it is , or enharmonically , of any major scale; for example, C diminished-seventh would be , or enharmonically...
consisting of three minor thirds and a subminor third making up an octave is possible in such systems. This characteristic feature of these tuning systems is known as the septimal semicomma diminished seventh chord.
In equal temperament
It is tempered out in 19 equal temperament19 equal temperament
In music, 19 equal temperament, called 19-TET, 19-EDO, or 19-ET, is the tempered scale derived by dividing the octave into 19 equal steps . Each step represents a frequency ratio of 21/19, or 63.16 cents...
and 31 equal temperament
31 equal temperament
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO , , is the tempered scale derived by dividing the octave into 31 equal-sized steps...
, but not in 22 equal temperament
22 equal temperament
In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the tempered scale derived by dividing the octave into 22 equal steps . Each step represents a frequency ratio of 21/22, or 54.55 cents ....
, 34 equal temperament
34 equal temperament
In musical theory, 34 equal temperament, also referred to as 34-tet, 34-edo or 34-et, is the tempered tuning derived by dividing the octave into 34 equal-sized steps...
, 41 equal temperament
41 equal temperament
In music, 41 equal temperament, often abbreviated 41-tET, 41-EDO, or 41-ET, is the tempered scale derived by dividing the octave into 41 equally-sized steps . Each step represents a frequency ratio of 21/41, or 29.27 cents , an interval close in size to the septimal comma. 41-ET can be seen as a...
, or 53 equal temperament
53 equal temperament
In music, 53 equal temperament, called 53-TET, 53-EDO, or 53-ET, is the tempered scale derived by dividing the octave into 53 equal steps . Each step represents a frequency ratio of 21/53, or 22.6415 cents , an interval sometimes called the Holdrian comma.- History :Theoretical interest in this...
.