# Millioctave

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The millioctave (moct) is a unit of interval size that divides the octave (2/1) into 1000 logarithmically equal parts. So, the millioctave can be defined as a frequency ratio of the 1000th root of 2, or 20.001. Its independence from the "classical"/"standard" 12edo tuning, and its similarity to other metric/SI units, have led some ethnomusicologists and microtonalists to prefer it over similar measures such as cents. However, others note that it naturally favors 10edo and its multiples, just as cents favor 12edo and its multiples.

## History

The millioctave (German abbreviation mO) was introduced by the German physicist Arthur von Oettingen in his book Das duale Harmoniesystem (1913).

## Usage convention

In this wiki, the cent is the preferred unit for interval sizes and differences, approximations, etc., and alternative units are usually tolerated only when the good reasons are obvious. But it cannot be ruled out that there are also a few places where the use of millioctaves as opposed to cents proves advantageous in terms of clarity and comprehensibility.

## Conversion

• To convert a just interval (n/d) to millioctaves (m), use the formula m = 1000 * log2(n/d) .
• Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .
• 1 moct is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 moct.