The Milli octave ( mO ) is a measure of the size of musical intervals. An octave is subdivided into 1000 mO.
It applies (see interval):
Now, assuming for the octave, that it consists of 1000 mO gives:
From then follow:
Like the more common Centmaß is the Milli octave so that a linear measure for intervals, ie a means to add size information of intervals instead of multiplying them, as it is necessary for frequency ratios.
A Milli octave corresponds to exactly 1.2 cents.
History and Significance
The Milli octave was introduced in 1903 by the German physicist Arthur von Oettingen in his essay The dual system of harmony. But already in 1871 discussed George Biddell Airy in On Sound and Atmospheric Vibrations with the Mathematical Elements of Music the proposal of John Frederick William Herschel, a 1000 division of the octave.
Compared to the Centmaß the Milli octave has never prevail. However, it is occasionally used to this day by authors who want to avoid the obvious association of information with equal- cent intervals.