|
|
| Line 13: |
Line 13: |
| As 11/7 is 22/21 (about 80.5¢) above the perfect fifth, it can be resolved down by a step from 11/7 to 3/2. | | As 11/7 is 22/21 (about 80.5¢) above the perfect fifth, it can be resolved down by a step from 11/7 to 3/2. |
|
| |
|
| == Approximations by edos == | | == Approximation == |
| | | {{Interval_Edo_Approximation | 11/7}} |
| Following [[edo]]s (up to 200) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 11/7. Errors are given by magnitude, the arrows in the table show if the edo representation is sharp (↑) or flat (↓).
| |
| | |
| {| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"
| |
| |-
| |
| ! [[Edo]]
| |
| ! class="unsortable" | deg\edo
| |
| ! Absolute <br> error ([[Cent|¢]])
| |
| ! Relative <br> error ([[Relative cent|r¢]])
| |
| ! ↕
| |
| ! class="unsortable" | Equally acceptable multiples <ref>Super EDOs up to 200 within the same error tolerance</ref>
| |
| |-
| |
| | [[20edo|20]] || 13\20 || 2.4920 || 4.1534 || ↓ ||
| |
| |-
| |
| | [[23edo|23]] || 15\23 || 0.1167 || 0.2236 || ↑ || [[46edo|30\46]], [[69edo|45\69]], [[92edo|60\92]], [[115edo|75\115]], [[138edo|90\138]], [[161edo|105\161]], [[184edo|120\184]]
| |
| |-
| |
| | [[26edo|26]] || 17\26 || 2.1233 || 4.6006 || ↑ ||
| |
| |-
| |
| | [[43edo|43]] || 28\43 || 1.0967 || 3.9298 || ↓ ||
| |
| |-
| |
| | [[49edo|49]] || 32\49 || 1.1814 || 4.8242 || ↑ ||
| |
| |-
| |
| | [[66edo|66]] || 43\66 || 0.6739 || 3.7062 || ↓ ||
| |
| |-
| |
| | [[72edo|72]] || 47\72 || 0.8413 || 5.0478 || ↑ ||
| |
| |-
| |
| | [[89edo|89]] || 58\89 || 0.4696 || 3.4826 || ↓ || [[178edo|116\178]]
| |
| |-
| |
| | [[95edo|95]] || 62\95 || 0.6659 || 5.2714 || ↑ ||
| |
| |-
| |
| | [[112edo|112]] || 73\112 || 0.3492 || 3.2590 || ↓ ||
| |
| |-
| |
| | [[118edo|118]] || 77\118 || 0.5588 || 5.4950 || ↑ ||
| |
| |-
| |
| | [[135edo|135]] || 88\135 || 0.2698 || 3.0354 || ↓ ||
| |
| |-
| |
| | [[141edo|141]] || 92\141 || 0.4867 || 5.7186 || ↑ ||
| |
| |-
| |
| | [[158edo|158]] || 103\158 || 0.2136 || 2.8118 || ↓ ||
| |
| |-
| |
| | [[164edo|164]] || 107\164 || 0.4348 || 5.9422 || ↑ ||
| |
| |-
| |
| | [[181edo|181]] || 118\181 || 0.1716 || 2.5882 || ↓ ||
| |
| |-
| |
| | [[187edo|187]] || 122\187 || 0.3957 || 6.1658 || ↑ ||
| |
| |}
| |
|
| |
|
| <references/> | | <references/> |