  # millioctave / m8ve / μ8ve / moct / μoct

[Joe Monzo]

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).

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### millioctaves calculator

Ratio may be entered as fraction or floating-point decimal number.
(value must be greater than 1)

For EDOs (equal-temperaments), type: "a/b" (without quotes)
where "a" = EDO degree and "b" = EDO cardinality.
(value must be less than 1)

Enter ratio: = millioctaves

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