# sixth-tone / 1/6-tone / 6th-tone

[Joe Monzo]

Calculated as the 36th root of 2 -- 36√2, or 2(1/36) -- an irrational proportion with the approximate ratio of 1: 1.019440643702, and an interval size of exactly 331/3 cents. It is the size of one degree, and thus the basic "step" size, in the 36-eq (or 36-ET) scale, also called the "sixth-tone scale" or system. The formula for calculating the sixth-tone value of any ratio is: 1/6-tones = log10r * [ 36 / log102] or 1/6-tones = log2r * 36, where r is the ratio.

One of the most famous advocates of this system was Ferrucio Busoni, in his Sketch for a New Aesthetic of Music [1907]. On Busoni's encouragement, Alois Hába began composing in 36-ET, and both Busoni and Hába had keyboard instruments built in the 1920s which could be played in this tuning.

A 1/6-tone is equal to exactly two 72edo moria, and is also the size of the quomma, one of the basic intervals in the blackjack, canasta, and studloco scales of the miracle family of temperaments.

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