3ed11/9: Difference between revisions
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not sure if this merits moving the page Tags: Mobile edit Mobile web edit Advanced mobile edit |
going to move to 3ed11/9 next if i can figure out how Tags: Mobile edit Mobile web edit Advanced mobile edit |
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{{ED intro}} | {{ED intro}} | ||
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.<ref>[https://en.wikipedia.org/wiki/Strike_tone#Tuning_a_bell Wikipedia | ''Strike tone'']</ref> | 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.<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. | |||
A simpler name for it is 3ed11/9. | A simpler name for it is 3ed11/9. | ||
{{todo|inline=1|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 | |||
Revision as of 22:06, 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.
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.[1]
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.
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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