3/2: Difference between revisions
m Don't know why this page and /just perfect fifth/ are separate but let's make it obvious |
table of EDO approximations added; brought 94edo to my attention |
||
| Line 13: | Line 13: | ||
'''3/2''' is the [[frequency ratio]] of the [[just perfect fifth]]. What tunes it well, is one of variants of [[12edo]] or [[17edo]] (such as [[24edo]], [[34edo]] and 36edo). Other edos tune it well too (5, 7, 29, 41, 53, 200). But not all edos are like this. 35edo is great for 2, 5, 7, 9, 11 and 17 but fails on 3. | '''3/2''' is the [[frequency ratio]] of the [[just perfect fifth]]. What tunes it well, is one of variants of [[12edo]] or [[17edo]] (such as [[24edo]], [[34edo]] and 36edo). Other edos tune it well too (5, 7, 29, 41, 53, 200). But not all edos are like this. 35edo is great for 2, 5, 7, 9, 11 and 17 but fails on 3. | ||
== 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 3/2. 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> | |||
|- | |||
| [[12edo|12]] || 7\12 || 1.9550 || 1.9550 || ↓ || [[24edo|14\24]], [[36edo|21\36]] | |||
|- | |||
| [[17edo|17]] || 10\17 || 3.9274 || 5.5637 || ↑ || | |||
|- | |||
| [[29edo|29]] || 17\29 || 1.4933 || 3.6087 || ↑ || | |||
|- | |||
| [[41edo|41]] || 24\41 || 0.4840 || 1.6537 || ↑ || [[82edo|48\82]], [[123edo|72\123]], [[164edo|96\164]] | |||
|- | |||
| [[53edo|53]] || 31\53 || 0.0682 || 0.3013 || ↓ || [[106edo|62\106]], [[159edo|93\159]] | |||
|- | |||
| [[65edo|65]] || 38\65 || 0.4165 || 2.2563 || ↓ || [[130edo|76\130]], [[195edo|114\195]] | |||
|- | |||
| [[70edo|70]] || 41\70 || 0.9021 || 5.2625 || ↑ || | |||
|- | |||
| [[77edo|77]] || 45\77 || 0.6563 || 4.2113 || ↓ || | |||
|- | |||
| [[89edo|89]] || 52\89 || 0.8314 || 6.1663 || ↓ || | |||
|- | |||
| [[94edo|94]] || 55\94 || 0.1727 || 1.3525 || ↑ || [[188edo|110\188]] | |||
|- | |||
| [[111edo|111]] || 65\111 || 0.7477 || 6.9162 || ↑ || | |||
|- | |||
| [[118edo|118]] || 69\118 || 0.2601 || 2.5575 || ↓ || | |||
|- | |||
| [[135edo|135]] || 79\135 || 0.2672 || 3.0062 || ↑ || | |||
|- | |||
| [[142edo|142]] || 83\142 || 0.5466 || 6.4675 || ↓ || | |||
|- | |||
| [[147edo|147]] || 86\147 || 0.0858 || 1.0512 || ↑ || | |||
|- | |||
| [[171edo|171]] || 100\171 || 0.2006 || 2.8588 || ↓ || | |||
|- | |||
| [[176edo|176]] || 103\176 || 0.3177 || 4.6600 || ↑ || | |||
|- | |||
| [[183edo|183]] || 107\183 || 0.3157 || 4.8138 || ↓ || | |||
|- | |||
| [[200edo|200]] || 117\200 || 0.0450 || 0.7500 || ↑ || | |||
|- | |||
|} | |||
<references/> | |||
== See also == | == See also == | ||
* [[Gallery of Just Intervals]] | * [[Gallery of Just Intervals]] | ||
* [[4/3]] – its [[octave complement]] | * [[4/3]] – its [[octave complement]] | ||