3ed11/9

Revision as of 11:47, 29 June 2025 by Squib (talk | contribs) (not sure if this merits moving the page)

3 equal divisions of 11/9 (abbreviated 3ed11/9) is a nonoctave tuning system that divides the interval of 11/9 into 3 equal parts of about 116 ¢ each. Each step represents a frequency ratio of (11/9)1/3, or the cube root of 11/9.

← 2ed11/9 3ed11/9 4ed11/9 →
Prime factorization 3 (prime)
Step size 115.803 ¢ 
Octave 10\3ed11/9 (1158.03 ¢)
(semiconvergent)
Twelfth 16\3ed11/9 (1852.84 ¢)
(semiconvergent)
Consistency limit 3
Distinct consistency limit 3

6 steps of this temperament is an extremely close approximation of 81:121, having only 0.3% relative error. 11 steps is obviously 81:169, so 81:121:169 is well approximated, which represents the approximate 2:3:4 created by overtones of chimes.[1]

A simpler name for it is 3ed11/9.