3ed11/9

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3ed11/9

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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

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.

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 (9²:11²:13²) is well approximated, which represents the approximate 2:3:4 created by overtones of chimes.

9²:11²:13²:17² is also very well approximated, but 9²:15² has around 25% relative error.

A simpler name for it is 3ed11/9.

Todo: format, add values

Approximation of odd square harmonics relative to 9²

1²:9²

3²:9²

5²:9²

7²:9²

9²:9²

11²:9²

13²:9²

15²:9²

17²:9²

19²:9²

Approximation of odd square harmonics

3²

5²

7²

9²

11²

13²

15²

17²

19²