Millioctave

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The millioctave (mO) is a logarithmic interval size measure. which divides the octave (2/1) into 1000 logarithmically equal parts. Its independence from the "classical"/"standard" 12edo tuning, and its similarity to other metric/SI units, have led some 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.

When comparing the approximations of just intervals between different systems, mO values can be used equally well as cent values. Also the absolute size of commas can be given in millioctave steps.

1 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001.

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 mO is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 mO.

Links

http://en.wikipedia.org/wiki/Millioctave

Other interval size measures