11/7: Difference between revisions
+FJS name; cleanup; expansion |
added another table of EDO approximations, but is it really helpful? |
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11/7 is [[22/21]] (about 80.5¢) above the [[3/2]] perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2. | 11/7 is [[22/21]] (about 80.5¢) above the [[3/2]] perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2. | ||
== Approximations by EDOs == | |||
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/> | |||
== See also == | == See also == | ||