Millioctave

The millioctave (moct) is a unit of measurement for musical intervals. As is expected from the prefix milli-, a millioctave is defined as 1/1000 of an octave. From this it follows that one millioctave is equal to the ratio 2^1/1000, the 1000th root of 2, or approximately 1.0006934 (play^ⓘ).

Given two frequencies a and b, the measurement of the interval between them in millioctaves can be calculated by

${\displaystyle n=1000\log _{2}\left({\frac {a}{b}}\right)\approx 3322\log _{10}\left({\frac {a}{b}}\right)}$

Likewise, if you know a note b and the number n of millioctaves in the interval, then the other note a may be calculated by:

${\displaystyle a=b\times 2^{\frac {n}{1000}}}$

Like the more common cent, the millioctave is a linear measure of intervals, and thus the size of intervals can be calculated by adding their millioctave values, instead of multiplication, which is necessary for calculations of frequencies.

A millioctave is exactly 1.2 cents.