A small unit of interval measurement, noted first by Gene Ward Smith in 1969, and suggested as an interval measurement by Joe Monzo in April 2007. (See Yahoo tuning group message 71213 [Sun Apr 15, 2007 2:45 pm PST].)
A gene divides the octave into 311 equal parts. Its use is valuable because it has very low error for the just-intonation ratios thru the 41-prime-limit, thus obviating the need for decimal places in measuring those intervals logarithmically.
The gene is therefore calculated as the 311th root of 2, or 2(1/311), with a ratio of approximately 1:1.00223125462134. It is an irrational number.
A gene is:
The formula for calculating the gene-value of any ratio r is: genes = log10(r) * [ 311 / log10(2) ] or genes = log2(r) * 311
A gene represents one degree of 311-edo tuning.
The 12-edo semitone is exactly 25 11/12 (= 25.91,6...) genes.