3ed11/9: Difference between revisions
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m Squib moved page 11ed169/81 to 3ed11/9: far simpler and clearer name for essentially the same thing Tags: Mobile edit Mobile web edit Advanced mobile edit |
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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.<ref>[https://en.wikipedia.org/wiki/Strike_tone#Tuning_a_bell Wikipedia | ''Strike tone'']</ref> | |||
9²:11²:13²:17² is also very well approximated, but 9²:15² has around 25% relative error. | 9²:11²:13²:17² is also very well approximated, but 9²:15² has around 25% relative error. | ||
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===Approximation of odd square harmonics relative to 9²=== | ===Approximation of odd square harmonics relative to 9²=== | ||
Revision as of 22:14, 19 July 2025
| ← 2ed11/9 | 3ed11/9 | 4ed11/9 → |
(semiconvergent)
(semiconvergent)
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.[1]
9²:11²:13²:17² is also very well approximated, but 9²:15² has around 25% relative error.
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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