Theoretical Properties
The 53-et tuning equates to the unison, or tempers out, the intervals 32805/32768, known as the schisma, and 15625/15552, known as the kleisma. These are both 5-limit intervals, involving only the primes 2, 3 and 5 in their factorization, and the fact that 53-et tempers out both characterizes it completely as a 5-limit temperament: it is the only regular temperament tempering out both of these intervals, or commas, a fact which seems to have first been recognized by Japanese music theorist Shohé Tanaka. Because it tempers these out, 53-et can be used for both schismatic temperament, tempering out the schisma, and Hanson temperament (also called kleismic), tempering out the kleisma.
The interval of 7/4 is 4.8 cents sharp in 53-et, and using it for 7-limit harmony means that the septimal kleisma, the interval 225/224, is also tempered out.
Read more about this topic: 53 Equal Temperament
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