# Septimal semicomma

Septimal semicomma as difference between 3 just minor thirds plus 1 septimal minor third and 1 octaves.

In music, the septimal semicomma, a seven-limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents ( ).[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: $2*3^2*5^{-3}*7$

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.

## In equal temperament

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.

## Sources

1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 978-0-8247-4714-5.