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Encyclopedia of Microtonal Music Theory

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mercator-comma / Mercator's comma

[Joe Monzo]

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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