Septimal semicomma

In music, the septimal semicomma, a seven-limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents (play^ⓘ).^{[citation needed]} It is also called the small septimal comma^[1] and the starling comma after its use in starling temperament.

Factored into primes it is: ${\displaystyle 2*3^{2}*5^{-3}*7}$

Or as simple just intervals: ${\displaystyle (6/5)^{3}*(7/6)*(2/1)^{-1}}$

Thus it is the difference between three minor thirds 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.

In equal temperament[edit]

It is tempered out in 19 equal temperament and 31 equal temperament, but not in 22 equal temperament, 34 equal temperament, 41 equal temperament, or 53 equal temperament.

References[edit]