5/4: Difference between revisions
Change name from "just" to "classic" in accordance with others |
another table of EDO approximations |
||
| Line 13: | Line 13: | ||
In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated here melodically in singing into a resonant [http://udderbot.wikispaces.com/home udderbot] (from the fundamental up to 5 and then noodling between 5 and 4). | In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated here melodically in singing into a resonant [http://udderbot.wikispaces.com/home udderbot] (from the fundamental up to 5 and then noodling between 5 and 4). | ||
== 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 5/4. 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> | |||
|- | |||
| [[25edo|25]] || 8\25 || 2.3137 || 4.8202 || ↓ || | |||
|- | |||
| [[28edo|28]] || 9\28 || 0.5994 || 1.3987 || ↓ || [[56edo|18\56]], [[84edo|27\84]], [[112edo|36\112]], [[140edo|45\140]], | |||
|- | |||
| [[31edo|31]] || 10\31 || 0.7831 || 2.0229 || ↑ || [[62edo|20\62]], [[93edo|30\93]], | |||
|- | |||
| [[34edo|34]] || 11\34 || 1.9216 || 5.4445 || ↑ || | |||
|- | |||
| [[53edo|53]] || 17\53 || 1.4081 || 6.2189 || ↓ || | |||
|- | |||
| [[59edo|59]] || 19\59 || 0.1270 || 0.6242 || ↑ || [[118edo|38\118]], [[177edo|57\177]], | |||
|- | |||
| [[87edo|87]] || 28\87 || 0.1068 || 0.7744 || ↓ || [[174edo|56\174]], | |||
|- | |||
| [[90edo|90]] || 29\90 || 0.3530 || 2.6471 || ↑ || [[180edo|58\180]], | |||
|- | |||
| [[115edo|115]] || 37\115 || 0.2268 || 2.1731 || ↓ || | |||
|- | |||
| [[121edo|121]] || 39\121 || 0.4631 || 4.6701 || ↑ || | |||
|- | |||
| [[143edo|143]] || 46\143 || 0.2997 || 3.5718 || ↓ || | |||
|- | |||
| [[146edo|146]] || 47\146 || 0.0123 || 0.1502 || ↓ || | |||
|- | |||
| [[149edo|149]] || 48\149 || 0.2635 || 3.2714 || ↑ || | |||
|- | |||
| [[152edo|152]] || 49\152 || 0.5284 || 6.6930 || ↑ || | |||
|- | |||
| [[171edo|171]] || 55\171 || 0.3488 || 4.9704 || ↓ || | |||
|- | |||
| [[199edo|199]] || 64\199 || 0.3841 || 6.3691 || ↓ || | |||
|} | |||
<references/> | |||
== See also == | == See also == | ||
* [[8/5]] – its [[octave complement]] | * [[8/5]] – its [[octave complement]] | ||
* [[6/5]] – its [[fifth complement]] | * [[6/5]] – its [[fifth complement]] | ||