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== Approximations ==
== Approximations ==


[[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]]):
Following [[EDO]]s (up to 200) contain good approximations<ref>absolute error < 7 cents and relative error < 7 rc</ref> of the interval 7:4. Errors are given by magnitude, the arrows in the table show if the EDO representation is sharp (&uarr;) or flat (&darr;).


{| class="wikitable sortable right-1 center-2 right-3 right-4"
{| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"
|-
|-
! [[EDO]]
! [[EDO]]
Line 70: Line 70:
! Absolute <br> error ([[Cent|¢]])
! Absolute <br> error ([[Cent|¢]])
! Relative <br> error ([[Relative cent|r¢]])
! Relative <br> error ([[Relative cent|r¢]])
! &#8597;
! class="unsortable" | Prominent multiples <ref>Multiples up to 200edo with approximation better then 7rc off</ref>
! class="unsortable" | Prominent multiples <ref>Multiples up to 200edo with approximation better then 7rc off</ref>
|-
|-
| [[109edo|109]]
| [[21edo|21]]
| 88\109
| 17\21
| +0.0186
| 2.6026
| +0.1687
| 4.5547
|
| &uarr;
|-
| [[135edo|135]]
| 109\135
| -0.0630
| -0.7086
|
|
|-
|-
| [[26edo|26]]
| [[26edo|26]]
| 21\26
| 21\26
| -0.4049
| 0.4049
| -0.8772
| 0.8772
| &uarr;
| [[52edo|42\52]], [[78edo|63\78]], [[104edo|84\104]], [[130edo|105\130]], [[156edo|126\156]], 147\182
| [[52edo|42\52]], [[78edo|63\78]], [[104edo|84\104]], [[130edo|105\130]], [[156edo|126\156]], 147\182
|-
|-
| [[83edo|83]]
| [[31edo|31]]
| 67\83
| 25\31
| +0.1512
| 1.0839
| +1.0459
| 2.8003
| [[166edo|134\166]]
| &darr;
| [[62edo|50\62]]
|-
| [[36edo|36]]
| 29\36
| 2.1592
| 6.4777
| &uarr;
|
|-
|-
| [[192edo|192]]
| [[47edo|47]]
| 155\192
| 38\47
| +0.0759
| 1.3868
| +1.2145
| 5.4319
| [[161edo|130\161]]
| &uarr;
|
|-
|-
| [[57edo|57]]
| [[57edo|57]]
| 46\57
| 46\57
| +0.4049
| 0.4049
| +1.9231
| 1.9231
| &darr;
| [[114edo|92\114]], [[171edo|138\171]]
| [[114edo|92\114]], [[171edo|138\171]]
|-
|-
| [[187edo|187]]
| [[73edo|73]]
| 151\187
| 59\73
| -0.1581
| 1.0371
| -2.4630
| 6.3091
| &uarr;
|
|
|-
|-
| [[31edo|31]]
| [[83edo|83]]
| 25\31
| 67\83
| +1.0839
| 0.1512
| +2.8003
| 1.0459
| [[62edo|50\62]]
| &darr;
| [[166edo|134\166]]
|-
|-
| [[140edo|140]]
| [[88edo|88]]
| 113\140
| 71\88
| +0.2545
| 0.6441
| +2.9689
| 4.7233
| &darr;
|
|
|-
|-
| [[21edo|21]]
| [[109edo|109]]
| 17\21
| 88\109
| -2.6026
| 0.0186
| -4.5547
| 0.1687
| &darr;
|
|
|-
|-
| [[88edo|88]]
| [[135edo|135]]
| 71\88
| 109\135
| +0.6441
| 0.0630
| +4.7233
| 0.7086
| &uarr;
|
|
|-
|-
| [[197edo|197]]
| [[140edo|140]]
| 159\197
| 113\140
| +0.2980
| 0.2545
| +4.8920
| 2.9689
| &darr;
|
|
|-
|-
| [[47edo|47]]
| [[145edo|145]]
| 38\47
| 117\145
| -1.3868
| 0.5500
| -5.4319
| 6.6464
|
| &darr;
|-
|-
| [[73edo|73]]
| [[187edo|187]]
| 59\73
| 151\187
| -1.0371
| 0.1581
| -6.3091
| 2.4630
| &uarr;
|
|
|-
|-
| [[36edo|36]]
| [[192edo|192]]
| 29\36
| 155\192
| +2.1592
| 0.0759
| +6.4777
| 1.2145
|
| &darr;
| [[161edo|130\161]]
|-
|-
| [[145edo|145]]
| [[197edo|197]]
| 117\145
| 159\197
| +0.5500
| 0.2980
| +6.6464
| 4.8920
| &darr;
|
|
|}
|}
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