3ed11/9: Difference between revisions

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 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>
-²:11²:13²:17² is also very well approximated, but 9²:15² has around 25% relative error.
+²:11²:13²:17²:23² is also very well approximated.
-{{todo|inline=1|format|add values}}
 ===Approximation of odd square harmonics relative to 9²===
-²:9²
+{{todo|inline=1|formatting}}
-²:9²
-²:9²
-²:9²
-²:9²
-²:9²
-²:9²
-²:9²
-²:9²
+ratio | steps | relative error | absolute error
-²:9²
+²:9² | -66 | -30.4% | -35.2¢
+²:9² | -33 | -15.2% | -17.6¢
-===Approximation of odd square harmonics===
+²:9² | -18 | -42.5% | -49.3¢
-²
+²:9² | -8 | -48.6% | -56.3¢
-²
+²:9² | 0 | 0% | 0¢
-²
+²:9² | 6 | 0% | 0¢
-²
+²:9² | 11 | -0.51% | -0.59¢
-²
+²:9² | 15 | -27.4% | -32.1¢
-²
+²:9² | 19 | -1.6% | -1.8¢
-²
+²:9² | 22 | -34.2% | -39.5¢
-²
+²:9² | 25 | -33.4% | -38.7¢
-²
+²:9² | 28 | -5.4% | -6.3¢