53 equal temperament
In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps. Each step represents a frequency ratio of 2¹⁄⁵³, or 22.6415 cents, an interval sometimes called the Holdrian comma. 53-EDO is a tuning of equal temperament in which the tempered perfect fifth is 701.89 cents wide, as shown in Figure 1. The 53-EDO 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-EDO can be used for both schismatic temperament, tempering out the schisma, and Hanson temperament, tempering out the kleisma.
