Septimal semicomma

In music, the septimal semicomma, a seven-limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents ({{Audio|Septimal semicomma on C.mid|play}}).{{Citation needed|date=December 2011}} It is also called the small septimal commaHaluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. {{ISBN|978-0-8247-4714-5}}. and the starling comma after its use in starling temperament.

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 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.