Septimal semicomma

In music, the ratio 126/125 is called the septimal semicomma (Audio|Septimal semicomma on C.mid|play). 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: $2*3^2*5^\{-3\}*7$

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

Thus it is the difference between three minor thirds of 6/5 and 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".

See also

Septimal meantone temperament