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
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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>
11 steps of this temperament is an extremely close approximation of :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.


A simpler name for it is 3ed11/9.
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===Approximation of odd square harmonics relative to 9²===
===Approximation of odd square harmonics relative to 9²===