270edo: Difference between revisions

Line 79:

| 0.1028

| 2.31

|-

| style="border-top: double;" | 2.3.5.7.11.13.17

| style="border-top: double;" | 676/675, 715/714, 936/935, 1001/1000, 1225/1224, 4096/4095

| style="border-top: double;" | {{mapping| 270 428 627 758 934 999 1104 }}

| style="border-top: double;" | -0.0799

| style="border-top: double;" | 0.1718

| style="border-top: double;" | 3.86

|-

| 2.3.5.7.11.13.17.19

| 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1225/1224, 1331/1330

| {{mapping| 270 428 627 758 934 999 1104 1147 }}

| -0.0777

| 0.1608

| 3.62

|-

| 2.3.5.7.11.13.17.19.23

| 460/459, 529/528, 676/675, 715/714, 736/735, 936/935, 1001/1000, 1216/1215

| {{mapping| 270 428 627 758 934 999 1104 1147 1221 }}

| -0.0296

| 0.2037

| 4.58

|}

* 270et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 11- and 13-limit. It is the first ~~past~~ [[72edo|72]] ~~with a lower~~ 11-limit ~~relative error,~~ and ~~the first past~~ [[224edo|224]] ~~with a lower~~ 13-limit ~~relative error~~. The next equal temperament that does better in terms of either absolute ~~error~~ or relative error in the 11-limit is [[342edo|342]], and in the 13-limit, [[494edo|494]].

* 270et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 11- and 13-limit. It is the first to beat [[72edo|72]] in the 11-limit and [[224edo|224]] in the 13-limit. The next equal temperament that does better in terms of either absolute or relative error in the 11-limit is [[342edo|342]], and in the 13-limit, [[494edo|494]].

* It is even more prominent in the 2.3.5.7.11.13.19 subgroup. Not until [[552edo|552]] do we reach a better equal temperament in terms of absolute error, and not until [[2190edo|2190]] do we reach one in terms of relative error.

* It is also prominent in the 17-, 19-, and 23-limit, where it has lower absolute errors than any previous equal temperaments, despite inconsistency in the corresponding odd limits.

@@ Line 79: / Line 79: @@
 | 0.1028
 | 2.31
+|-
+| style="border-top: double;" | 2.3.5.7.11.13.17
+| style="border-top: double;" | 676/675, 715/714, 936/935, 1001/1000, 1225/1224, 4096/4095
+| style="border-top: double;" | {{mapping| 270 428 627 758 934 999 1104 }}
+| style="border-top: double;" | -0.0799
+| style="border-top: double;" | 0.1718
+| style="border-top: double;" | 3.86
+|-
+| 2.3.5.7.11.13.17.19
+| 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1225/1224, 1331/1330
+| {{mapping| 270 428 627 758 934 999 1104 1147 }}
+| -0.0777
+| 0.1608
+| 3.62
+|-
+| 2.3.5.7.11.13.17.19.23
+| 460/459, 529/528, 676/675, 715/714, 736/735, 936/935, 1001/1000, 1216/1215
+| {{mapping| 270 428 627 758 934 999 1104 1147 1221 }}
+| -0.0296
+| 0.2037
+| 4.58
 |}
-* 270et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 11- and 13-limit. It is the first past [[72edo|72]] with a lower 11-limit relative error, and the first past [[224edo|224]] with a lower 13-limit relative error. The next equal temperament that does better in terms of either absolute error or relative error in the 11-limit is [[342edo|342]], and in the 13-limit, [[494edo|494]].
+* 270et has lower [[Tenney-Euclidean temperament measures #TE simple badness|relative errors]] than any previous equal temperaments in the 11- and 13-limit. It is the first to beat [[72edo|72]] in the 11-limit and [[224edo|224]] in the 13-limit. The next equal temperament that does better in terms of either absolute or relative error in the 11-limit is [[342edo|342]], and in the 13-limit, [[494edo|494]].
 * It is even more prominent in the 2.3.5.7.11.13.19 subgroup. Not until [[552edo|552]] do we reach a better equal temperament in terms of absolute error, and not until [[2190edo|2190]] do we reach one in terms of relative error.
 * It is also prominent in the 17-, 19-, and 23-limit, where it has lower absolute errors than any previous equal temperaments, despite inconsistency in the corresponding odd limits.