User:FloraC/Sequence of equal temperaments by error/Supplement: Difference between revisions

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-This just occurred to me when doing the temperament measures table for [[31edo]]. All GPVs (and only GPVs) are accounted. How I did it: [[Patent val/Properties]].
+For a method to iterate thru all GPVs, see [[Patent val/Properties]]. GPVs starting with a zero are excluded as they would meddle with the results.
-* 3-limit: {{EDOs| 1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867 }}…
+The '''tier''' of an equal temperament is defined as the number of GPVs before it that is tuned more efficient than it.
-* 5-limit: {{EDOs| 1, 1c, 2c, 2, 3, 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296 }}…
-* 7-limit: {{EDOs| 1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355 }}…
-* 11-limit: {{EDOs| 1ce, 2cde, 2, 3de, 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691 }}…
-* 13-limit: {{EDOs| 2cde, 2f, 3, 3de, 3def, 4ef, 5e, 7, 8d, 9, 12f, 19e, 19, 27e, 31, 41, 53, 58, 72, 224, 270, 494, 1506, 2190, 2684, 5585, 6079, 14618 }}…
-* 17-limit: {{EDOs| 4ef, 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203 }}…
-* 19-limit: {{EDOs| 7, 8d, 8dhh, 9g, 9, 12f, 19egh, 26, 27eg, 46, 72, 217, 270, 581, 742, 1178, 1578, 2000, 2460, 3395, 8269, 8539, 16808, 20203 }}…
-* 23-limit: {{EDOs| 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808 }}…
-* 29-limit: {{EDOs| 26i, 46, 58hi, 80, 140, 159, 183, 243e, 311, 954hj, 1578, 16808 }}…
-* 31-limit: {{EDOs| 46, 99efk, 103h, 183, 190g, 217, 311, 954hj, 4501, 16808 }}…
-* 37-limit: {{EDOs| 80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808 }}…
-* sqrt (2).sqrt (3).5.7.11.13: {{EDOs| 10e, 10, 34d, 58, 72, 270, 2684, 13112 }}…
+; 3-limit:
-* sqrt (2).sqrt (3).5.7.11.13.17: {{EDOs| 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808 }}…
+: {{EDOs| 1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867 }}…
+; 5-limit:
+: {{EDOs| 1, 1c, 2c, 2, 3, 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296 }}…
+; 7-limit:
+: {{EDOs| 1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355 }}…
+; 11-limit:
+: {{EDOs| 1ce, 2cde, 2, 3de, 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691 }}…
+; 13-limit:
+: {{EDOs| 2cde, 2f, 3, 3de, 3def, 4ef, 5e, 7, 8d, 9, 12f, 19e, 19, 27e, 31, 41, 53, 58, 72, 224, 270, 494, 1506, 2190, 2684, 5585, 6079, 14618 }}…
+; 17-limit:
+: {{EDOs| 4ef, 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203 }}…
+; 19-limit:
+: {{EDOs| 7, 8d, 8dhh, 9g, 9, 12f, 19egh, 26, 27eg, 46, 72, 217, 270, 581, 742, 1178, 1578, 2000, 2460, 3395, 8269, 8539, 16808, 20203 }}…
+; 23-limit:
+: {{EDOs| 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808 }}…
+; 29-limit:
+: {{EDOs| 26i, 46, 58hi, 80, 140, 159, 183, 243e, 311, 954hj, 1578, 16808 }}…
+; 31-limit:
+: {{EDOs| 46, 99efk, 103h, 183, 190g, 217, 311, 954hj, 4501, 16808 }}…
+; 7-limit:
+: {{EDOs| 80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808 }}…
+; sqrt (2).sqrt (3).5.7.11.13 subgroup:
+: {{EDOs| 10e, 10, 34d, 58, 72, 270, 2684, 13112 }}…
+; sqrt (2).sqrt (3).5.7.11.13.17 subgroup:
+: {{EDOs| 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808 }}…