User:Eliora/Standard deviation
Standard deviation is a way of assessing harmonic strength.
Null hypothesis
An interval which consists of edosteps is an irrational number, which occasionally comes close rational numbers. Null hypothesis is therefore that a typical interval is dissonant.
Center for measurement
Therefore, counting the null hypothesis above, we assume 50% of error on edostep to be the center of our measuring, and an exact landing on the edostep by JI interval (which never happens) as infinitely away from the center of the error curve. Since it never happens, this means every interval approximation is finite number of standard deviations away.
12edo
Assume we want to measure the strength of 3/2 in 12edo this way. The value is 701.955c just. First, take the center - 750 cents. Then take the two semitone borders - 700 and 800 cents.
Since the difference between just and 12edo fifth is 1.955 cent, we take two-tailed z-score of 1.955 / 50, or alternately single-tailed z-score for 1.955 / 100.
The value is 2.063, which means that 12edo represents the expected consonance of 3/2 with about two standard deviations away from the average dissonant irrational sound a random edostep interval will make.