Comparison With 31 Equal Temperament
The perfect fifth of quarter-comma meantone, expressed as a fraction of an octave, is 1/4 log2 5. This number is irrational and in fact transcendental; hence a chain of meantone fifths, like a chain of pure 3/2 fifths, never closes (i.e. never equals a chain of octaves). However, the continued fraction approximations to this irrational fraction number allow us to find equal divisions of the octave which do close; the denominators of these are 1, 2, 5, 7, 12, 19, 31, 174, 205, 789 ... From this we find that 31 quarter-comma meantone fifths come close to closing, and conversely 31 equal temperament represents a good approximation to quarter-comma meantone. See: schisma.
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