5/4: Difference between revisions

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== Approximations by EDOs ==

Following [[EDO]]s (up to 200, and also ~~730~~) 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 (↓).

Following [[EDO]]s (up to 200, and also 643) 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"

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! Relative <br> error ([[Relative cent|r¢]])

! ↕

! class="unsortable" | Equally acceptable multiples <ref>Super EDOs up to 200 ~~(and 730)~~ within the same error tolerance</ref>

! 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]],

| [[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]],

| [[31edo|31]] || 10\31 || 0.7831 || 2.0229 || ↑ || [[62edo|20\62]], [[93edo|30\93]]

|-

| [[34edo|34]] || 11\34 || 1.9216 || 5.4445 || ↑ ||

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| [[53edo|53]] || 17\53 || 1.4081 || 6.2189 || ↓ ||

|-

| [[59edo|59]] || 19\59 || 0.1270 || 0.6242 || ↑ || [[118edo|38\118]], [[177edo|57\177]],

| [[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]],

| [[87edo|87]] || 28\87 || 0.1068 || 0.7744 || ↓ || [[174edo|56\174]]

|-

| [[90edo|90]] || 29\90 || 0.3530 || 2.6471 || ↑ || [[180edo|58\180]],

| [[90edo|90]] || 29\90 || 0.3530 || 2.6471 || ↑ || [[180edo|58\180]]

|-

| [[115edo|115]] || 37\115 || 0.2268 || 2.1731 || ↓ ||

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| [[199edo|199]] || 64\199 || 0.3841 || 6.3691 || ↓ ||

|-

| [[~~730edo~~|~~730~~]] || ~~235~~\~~730~~ || 0.~~0123~~ || 0.~~7509~~ || &~~darr~~; ||

| [[643edo|643]] || 207\643 || 0.0004 || 0.0235 || ↑ ||

|}

@@ Line 16: / Line 16: @@
 == Approximations by EDOs ==
-Following [[EDO]]s (up to 200, and also 730) 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 (&uarr;) or flat (&darr;).
+Following [[EDO]]s (up to 200, and also 643) 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 (&uarr;) or flat (&darr;).
 {| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"
@@ Line 25: / Line 25: @@
 ! Relative <br> error ([[Relative cent|r¢]])
 ! &#8597;
-! class="unsortable" | Equally acceptable multiples <ref>Super EDOs up to 200 (and 730) within the same error tolerance</ref>
+! 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 || &darr; ||
 |-
-|  [[28edo|28]]  ||  9\28  || 0.5994 || 1.3987 || &darr; || [[56edo|18\56]], [[84edo|27\84]], [[112edo|36\112]], [[140edo|45\140]],
+|  [[28edo|28]]  ||  9\28  || 0.5994 || 1.3987 || &darr; || [[56edo|18\56]], [[84edo|27\84]], [[112edo|36\112]], [[140edo|45\140]]
 |-
-|  [[31edo|31]]  || 10\31  || 0.7831 || 2.0229 || &uarr; || [[62edo|20\62]], [[93edo|30\93]],
+|  [[31edo|31]]  || 10\31  || 0.7831 || 2.0229 || &uarr; || [[62edo|20\62]], [[93edo|30\93]]
 |-
 |  [[34edo|34]]  || 11\34  || 1.9216 || 5.4445 || &uarr; ||
@@ Line 37: / Line 37: @@
 |  [[53edo|53]]  || 17\53  || 1.4081 || 6.2189 || &darr; ||
 |-
-|  [[59edo|59]]  || 19\59  || 0.1270 || 0.6242 || &uarr; || [[118edo|38\118]], [[177edo|57\177]],
+|  [[59edo|59]]  || 19\59  || 0.1270 || 0.6242 || &uarr; || [[118edo|38\118]], [[177edo|57\177]]
 |-
-|  [[87edo|87]]  || 28\87  || 0.1068 || 0.7744 || &darr; || [[174edo|56\174]],
+|  [[87edo|87]]  || 28\87  || 0.1068 || 0.7744 || &darr; || [[174edo|56\174]]
 |-
-|  [[90edo|90]]  || 29\90  || 0.3530 || 2.6471 || &uarr; || [[180edo|58\180]],
+|  [[90edo|90]]  || 29\90  || 0.3530 || 2.6471 || &uarr; || [[180edo|58\180]]
 |-
 | [[115edo|115]] || 37\115 || 0.2268 || 2.1731 || &darr; ||
@@ Line 59: / Line 59: @@
 | [[199edo|199]] || 64\199 || 0.3841 || 6.3691 || &darr; ||
 |-
-| [[730edo|730]] || 235\730 || 0.0123 || 0.7509 || &darr; ||
+| [[643edo|643]] || 207\643 || 0.0004 || 0.0235 || &uarr; ||
 |}