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:
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.