millioctave

(m8ve, μ8ve; moct, μoct)

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 = log₁₀(ratio) * [1000 / log₁₀(2)]

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 it of which I'm aware is in Mark Lindley / Ronald Turner-Smith, Mathematical Models of Musical Scales (1993).

[from Joe Monzo, JustMusic: A New Harmony]

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