  # sk, 612-edo

[Joe Monzo]

A small unit of interval measurement, noted first by Gene Ward Smith in the 1960s, used by him as an interval measurement, and named by him in 2007 as a sort of abbreviation of skhisma, an interval to which it is very close in size.

A sk divides the octave into 612 equal parts. Its use is valuable because it has extremely low error for the 5-limit just-intonation ratios, thus obviating the need for decimal places in measuring those intervals logarithmically.

The sk is therefore calculated as the 612th root of 2, or 2(1/311), with a ratio of approximately 1:1.00113323505844. It is an irrational number.

A sk is:

• exactly 1 49/51 (= 1.9607843137254901... = ~ 2 ) cents,

The formula for calculating the sk-value of any ratio r is: sks = log10(r) * [ 612 / log10(2) ] or sks = log2(r) * 612

A sk represents one degree of 612-edo tuning.

Another useful feature of the sk is that 612 is a multiple of 12, therefore the sk is an exact divisor of the 12-edo semitone. The 12-edo semitone is exactly 51 sks.

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### sks 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: = sks

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