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.

11 steps of this temperament is an extremely close approximation of 9²:13², having only 0.5% relative error. 6 steps is exactly 9²:11² (since 3 steps is 9:11), so 9²:11²:13² (81:121:169) 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.

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