6th-tone, sixth-tone, 1/6-tone

Calculated as the 36th root of 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 = log₁₀(ratio) * [ 36 / log₁₀(2) ]

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.

[from Joe Monzo, JustMusic: A New Harmony]

---

(to download a zip file of the entire Dictionary, click here)

For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here

I welcome feedback about this webpage: corrections, improvements, good links. Let me know if you don't understand something. return to the Microtonal Dictionary index return to my home page return to the Sonic Arts home page