Millioctave: Difference between revisions

The '''millioctave''' ('''moct''') is a [[unit of interval size]] that divides the [[octave]] (2/1) into [[1000edo|1000 logarithmically equal parts]]. So, the millioctave can be defined as a frequency ratio of the 1000th root of 2, or 2^0.001. Its independence from the "classical"/"standard" [[12edo]] tuning, and its similarity to other metric/[[wikipedia:International System of Units|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.  

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

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.

* To convert a just interval (n/d) to millioctaves (m), use the formula m = 1000 * log<span style="font-size: 80%; vertical-align: sub;">2</span>(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.

[[Category:Interval size measures]]

[[Category:Terms]]

[[Category:1000edo]]