StaticcompareCompares multiple tuning systems against JI reference intervals. Returns a comparison table with cent errors for each interval in each tuning.
Array of tuning systems to compare.
JI ratios to compare (e.g., [[3,2], [5,4]] = P5 and M3).
StaticdetectDetects wolf intervals: single instances of an interval that stand out from the other
intervals of the same number of steps. For each step count k, the typical size (median
over all starting degrees) is taken as meant to be the nearest consonance (6/5, 5/4,
4/3, 3/2, 8/5, 5/3) when within threshold of it; an instance more than threshold
away from that consonance is a wolf (Pythagorean tuning's G#–Eb fifth). Equal
temperaments have none.
The tuning system to audit.
Error threshold in cents (default 20: Pythagorean tuning's wolf fifth is a Pythagorean comma, 23.5¢, short).
Array of { interval (step count), from (starting step), errorCents (from the consonance) }.
Distance from the just consonance it stands for, in cents.
Step the out-of-tune interval starts on.
Size of the interval in steps of the tuning.
StaticgetReturns definitions of common musical commas, with cents to three decimals.
ratioText is exact. The Mercator comma (3^53/2^84) is beyond Number precision:
its ratio is the nearest doubles and its cents are computed from the exponents.
Size in cents, to three decimals.
'Syntonic comma', 'Pythagorean comma', 'Schisma'…
As [numerator, denominator] (may lose precision for very large ratios; see ratioText).
Exact ratio as text: '81/80'.
StaticgetFinds unison vectors for a JustIntonation tuning: the known commas by which two sizes of the same interval (same number of steps, different starting notes) differ. In 5-limit JI the fifths 3/2 and 40/27, or the whole tones 9/8 and 10/9, differ by 81/80.
Static methods for comparing tuning systems against JI, detecting wolf intervals, and finding optimal EDOs.