History
Theoretical interest in this division goes back to antiquity. Ching Fang (78–37 BC), a Chinese music theorist, observed that a series of 53 just fifths is very nearly equal to 31 octaves . He calculated this difference with six-digit accuracy to be . Later the same observation was made by the mathematician and music theorist Nicholas Mercator (c. 1620–1687), who calculated this value precisely as, which is known as Mercator's comma. Mercator's comma is of such small value to begin with (≈ 3.615 cents), but 53 equal temperament flattens each fifth by only 1/53 of that comma (≈ 0.0682 cent ≈ 1/315 syntonic comma). Thus, 53 equal temperament is for all practical purposes equivalent to an extended Pythagorean tuning.
After Mercator, William Holder published a treatise in 1694 which pointed out that 53 equal temperament also very closely approximates the just major third (to within 1.4 cents), and consequently 53 equal temperament accommodates the intervals of 5-limit just intonation very well. This property of 53-TET may have been known earlier; Isaac Newton's unpublished manuscripts suggest that he had been aware of it as early as 1664–65.
Read more about this topic: 53 Equal Temperament
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