An interval measurement which simply divides the octave (2:1 ratio) into 1000 logarithmically-equal parts.
A millioctave is thus calculated as the 1000th root of 2, or 2(1/1000), with a ratio of approximately 1:1.000693387. It is an irrational number, equal to exactly 1.2 (= 11/5) cents.
The formula for calculating the millioctave-value of any ratio is:
millioctaves = log10r * [1000 / log10(2)] or millioctaves = log2r * 1000
where r is the ratio.
Cents are almost universally used today as a small logarithmic measurement to compare interval sizes, however, certain authors prefer not to use the usual 12edo scale as a basis for comparison, and thus prefer millioctaves.
The most prominent use of millioctaves is perhaps in Mark Lindley / Ronald Turner-Smith, Mathematical Models of Musical Scales (1993).