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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".

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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