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If a tuning composed of a pythagorean chain of "5ths" is extended to 54 elements, the 54th, which can be prime-factored as 2-84 353 and thus expressed as the 2,3-monzo [-84 53 > , is ~3.61504586553314 cents higher in pitch than the starting note. Its ratio is 19,383,245,667,680,019,896,796,723 / 19,342,813,113,834,066,795,298,816, expressed in decimal form as ~1.0020903140411.
Because Mercator recognized this small anomaly (or comma, in its general meaning), it is known today as "Mercator's comma" or more simply the "mercator comma". This comma is a < vapro (i.e., is tempered-out, or vanishes) in 53ed2.
Below are some other interval measurements for the mercator-comma:
~0.036150459 (~ 1/28) 12-edo Semitone ~0.216902752 (~ 2/9) 72-edo moria ~0.903761466 (~ 9/10) savart ~1.849127501 (~1 6/7) grads ~2.199152902 (~2 1/5) 730-edo Woolhouse-units ~3.012538221 (~3) millioctaves ~3.193290515 (~3 1/5) Türk cents ~3.615045866 (~3 3/5) cents ~90.68643808 (~90 2/3) jots ~110.9476501 (~111) tuning units ~148.0722787 (~148) 12mus
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