7/4: Difference between revisions
m →Approximations: minor cleanup |
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== Approximations == | == Approximations == | ||
[[EDO]]s containing good approximations of the interval 7:4 are (pre-ordered by [[relative error]]): | [[EDO]]s (up to 200) containing good approximations<ref>absolute error < 7 cents and relative error < 7 rc </ref> of the interval 7:4 are (pre-ordered by magnitude of [[relative error]]): | ||
{| class="wikitable sortable | {| class="wikitable sortable right-1 center-2 right-3 right-4" | ||
|- | |- | ||
! [[EDO]] | ! [[EDO]] | ||
! | ! class="unsortable" | deg\edo | ||
! | ! Absolute <br> error ([[Cent|¢]]) | ||
! class="unsortable" | Prominent Multiples | ! Relative <br> error ([[Relative cent|r¢]]) | ||
! class="unsortable" | Prominent multiples <ref>Multiples up to 200edo with approximation better then 7rc off</ref> | |||
|- | |- | ||
| [[26edo]] | | [[109edo|109]] | ||
| 0. | | 88\109 | ||
| 0. | | +0.0186 | ||
| [[78edo]] | | +0.1687 | ||
| | |||
|- | |||
| [[135edo|135]] | |||
| 109\135 | |||
| -0.0630 | |||
| -0.7086 | |||
|- | |||
| [[26edo|26]] | |||
| 21\26 | |||
| -0.4049 | |||
| -0.8772 | |||
| [[52edo|42\52]], [[78edo|63\78]], [[104edo|84\104]], [[130edo|105\130]], [[156edo|126\156]], 147\182 | |||
|- | |||
| [[83edo|83]] | |||
| 67\83 | |||
| +0.1512 | |||
| +1.0459 | |||
| [[166edo|134\166]] | |||
|- | |- | ||
| [[ | | [[192edo|192]] | ||
| 0. | | 155\192 | ||
| 1. | | +0.0759 | ||
| [[ | | +1.2145 | ||
| [[161edo|130\161]] | |||
|- | |- | ||
| [[57edo]] | | [[57edo|57]] | ||
| 0. | | 46\57 | ||
| 1.9231 | | +0.4049 | ||
| | | +1.9231 | ||
| [[114edo|92\114]], [[171edo|138\171]] | |||
|- | |- | ||
| [[ | | [[187edo|187]] | ||
| | | 151\187 | ||
| 2. | | -0.1581 | ||
| -2.4630 | |||
| | | | ||
|- | |- | ||
| [[ | | [[31edo|31]] | ||
| | | 25\31 | ||
| | | +1.0839 | ||
| [[ | | +2.8003 | ||
| [[62edo|50\62]] | |||
|- | |- | ||
| [[ | | [[140edo|140]] | ||
| | | 113\140 | ||
| | | +0.2545 | ||
| +2.9689 | |||
| | | | ||
|- | |- | ||
| [[ | | [[21edo|21]] | ||
| | | 17\21 | ||
| 4. | | -2.6026 | ||
| -4.5547 | |||
| | | | ||
|- | |- | ||
| [[ | | [[88edo|88]] | ||
| | | 71\88 | ||
| | | +0.6441 | ||
| | | +4.7233 | ||
| | |||
|- | |- | ||
| [[ | | [[197edo|197]] | ||
| | | 159\197 | ||
| | | +0.2980 | ||
| +4.8920 | |||
| | | | ||
|- | |- | ||
| [[ | | [[47edo|47]] | ||
| | | 38\47 | ||
| | | -1.3868 | ||
| -5.4319 | |||
|- | |||
| | | | ||
|- | |- | ||
| [[ | | [[73edo|73]] | ||
| 1. | | 59\73 | ||
| | | -1.0371 | ||
| -6.3091 | |||
| | | | ||
|- | |- | ||
| [[ | | [[36edo|36]] | ||
| | | 29\36 | ||
| | | +2.1592 | ||
| +6.4777 | |||
| | | | ||
|- | |- | ||
| [[ | | [[145edo|145]] | ||
| | | 117\145 | ||
| | | +0.5500 | ||
| +6.6464 | |||
| | | | ||
|} | |} | ||
<references/> | |||
== See also == | == See also == | ||