The Archipelago: Difference between revisions
m Final cleanup |
Edo lists reviewed |
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| Line 20: | Line 20: | ||
{{val| 0 0 0 0 1 0 }} | {{val| 0 0 0 0 1 0 }} | ||
{{Val list|legend=1| 5, 9, 10, 15, 19, 24, 29, 43, 53, 58, 72, 87, 111, 121, 130, 183, 940 }} | {{Val list|legend=1| 5, 9, 10, 14cf, 15, 19, 24, 29, 34d, 43, 49f, 53, 58, 72, 87, 111, 121, 130, 183, 198, 270, 940, 1210f }} | ||
[[Optimal patent val]]: [[940edo]] | [[Optimal patent val]]: [[940edo|940]] | ||
== Rank-4 temperaments == | == Rank-4 temperaments == | ||
| Line 32: | Line 32: | ||
[[Mapping]]: [{{val| 1 0 0 0 4 -1 }}, {{val| 0 2 0 0 -3 3 }}, {{val| 0 0 1 0 2 1 }}, {{val| 0 0 0 1 -1 0 }}] | [[Mapping]]: [{{val| 1 0 0 0 4 -1 }}, {{val| 0 2 0 0 -3 3 }}, {{val| 0 0 1 0 2 1 }}, {{val| 0 0 0 1 -1 0 }}] | ||
{{Val list|legend=1| 15, 19, 29, 43, 53, 58, 72, 87, 111, 130, 183, 198, 270, 940 }} | {{Val list|legend=1| 14cf, 15, 19, 29, 39df, 43, 53, 58, 72, 87, 111, 130, 183, 198, 270, 940, 1210f }} | ||
=== 49/48 === | === 49/48 === | ||
| Line 43: | Line 41: | ||
[[Mapping]]: [{{val| 1 0 0 2 0 -1 }}, {{val| 0 2 0 1 0 3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 0 1 0 }}] | [[Mapping]]: [{{val| 1 0 0 2 0 -1 }}, {{val| 0 2 0 1 0 3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 0 1 0 }}] | ||
{{Val list|legend=1| 5, 9, 10, 15, 19, 24 }} | {{Val list|legend=1| 5, 9, 10, 14cf, 15, 19, 24, 29, 38df, 53d, 67cddef, 105cdddeefff }} | ||
=== 1716/1715 === | === 1716/1715 === | ||
| Line 52: | Line 50: | ||
[[Mapping]]: [{{val| 1 0 0 0 -1 -1 }}, {{val| 0 2 0 0 -5 3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 1 3 0 }}] | [[Mapping]]: [{{val| 1 0 0 0 -1 -1 }}, {{val| 0 2 0 0 -5 3 }}, {{val| 0 0 1 0 0 1 }}, {{val| 0 0 0 1 3 0 }}] | ||
{{Val list|legend=1| 58, 72 | {{Val list|legend=1| 58, 72, 121, 130, 193, 198, 270, 940, 1210f }} | ||
=== 364/363 === | === 364/363 === | ||
| Line 61: | Line 59: | ||
[[Mapping]]: [{{val| 1 0 0 -1 0 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 2 1 0 }}] | [[Mapping]]: [{{val| 1 0 0 -1 0 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 2 1 0 }}] | ||
{{Val list|legend=1| | {{Val list|legend=1| 14cf, 15, 23deff, 24, 29, 34d, 43, 49f, 58, 72, 87, 121, 130, 193, 217, 289, 338e, 410e }} | ||
=== 351/350 === | === 351/350 === | ||
| Line 70: | Line 68: | ||
[[Mapping]]: [{{val| 1 0 0 -2 0 -1 }}, {{val| 0 2 0 9 0 3 }}, {{val| 0 0 1 -1 0 1 }}, {{val| 0 0 0 0 1 0 }}] | [[Mapping]]: [{{val| 1 0 0 -2 0 -1 }}, {{val| 0 2 0 9 0 3 }}, {{val| 0 0 1 -1 0 1 }}, {{val| 0 0 0 0 1 0 }}] | ||
{{Val list|legend=1| 19, 53, 58, 72 | {{Val list|legend=1| 14cf, 19, 24, 34d, 53, 58, 72, 111, 130, 183, 313, 462f }} | ||
=== 352/351 === | === 352/351 === | ||
| Line 79: | Line 77: | ||
[[Mapping]]: [{{val| 1 0 0 0 -6 -1 }}, {{val| 0 2 0 0 9 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 0 0 }}] | [[Mapping]]: [{{val| 1 0 0 0 -6 -1 }}, {{val| 0 2 0 0 9 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 0 0 }}] | ||
{{Val list|legend=1| 29, | {{Val list|legend=1| 10, 19e, 24, 29, 34d, 53, 58, 87, 111, 121, 140, 198, 459b, 517bcdf, 657bdf }} | ||
=== 540/539 === | === 540/539 === | ||
| Line 88: | Line 86: | ||
[[Mapping]]: [{{val| 1 0 0 0 2 -1 }}, {{val| 0 2 0 0 6 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 -2 0 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 -1 }}, {{val| 0 2 0 0 6 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 -2 0 }}] | ||
{{Val list|legend=1| 9, 19, 53, 58 | {{Val list|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49f, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }} | ||
=== 847/845 === | === 847/845 === | ||
| Line 97: | Line 95: | ||
[[Mapping]]: [{{val| 1 0 0 0 -1 -1 }}, {{val| 0 2 0 0 3 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 2 -1 0 }}] | [[Mapping]]: [{{val| 1 0 0 0 -1 -1 }}, {{val| 0 2 0 0 3 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 2 -1 0 }}] | ||
{{Val list|legend=1| | {{Val list|legend=1| 24d, 29, 38df, 49f, 53, 58, 87, 111, 140, 198, 347, 487e, 545c }} | ||
== Rank-3 temperaments == | == Rank-3 temperaments == | ||
| Line 184: | Line 182: | ||
[[Mapping]]: [{{val| 1 0 0 13 -9 1 }}, {{val| 0 2 0 -7 4 3 }}, {{val| 0 0 1 -2 4 1 }}] | [[Mapping]]: [{{val| 1 0 0 13 -9 1 }}, {{val| 0 2 0 -7 4 3 }}, {{val| 0 0 1 -2 4 1 }}] | ||
{{Val list|legend=1| 34, 43, 53, 87, 130, 183, 217, 270, 940 }} | {{Val list|legend=1| 34, 43, 53, 87, 130, 183, 217, 270, 940, 1210f }} | ||
[[Badness]]: 0.604 × 10<sup>-3</sup> | [[Badness]]: 0.604 × 10<sup>-3</sup> | ||
| Line 204: | Line 202: | ||
== Rank-2 temperaments == | == Rank-2 temperaments == | ||
Rank two temperaments tempering out 676/675 include the 13-limit versions of [[ | Rank two temperaments tempering out 676/675 include the 13-limit versions of [[Ragismic microtemperaments #Hemiennealimmal|hemiennealimmal]], [[Breedsmic temperaments #Harry|harry]], [[Kleismic family #Tritikleismic|tritikleismic]], [[Kleismic family #Catakleismic|catakleimsic]], [[Marvel temperaments #Negri|negri]], [[Hemifamity temperaments #Mystery|mystery]], [[Hemifamity temperaments #Buzzard|buzzard]], [[Kleismic family #Quadritikleismic|quadritikleismic]]. | ||
It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 18 in hemiennealimmal, 6 in harry, 9 in tritikleismic, 3 in catakleismic, 2 in negri, 2 in buzzard, 12 in quadritikleismic. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to [[29edo | It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 18 in hemiennealimmal, 6 in harry, 9 in tritikleismic, 3 in catakleismic, 2 in negri, 2 in buzzard, 12 in quadritikleismic. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to [[29edo]] alone. | ||
=== Decitonic aka decoid === | === Decitonic aka decoid === | ||
| Line 219: | Line 217: | ||
[[POTE generator]]: ~15/13 = 248.917 | [[POTE generator]]: ~15/13 = 248.917 | ||
{{Val list|legend=1| 130, 270, 940, 1210f | {{Val list|legend=1| 130, 270, 940, 1210f }} | ||
[[Badness]]: 0.013475 | [[Badness]]: 0.013475 | ||
| Line 338: | Line 336: | ||
[[Comma list]]: 676/675 | [[Comma list]]: 676/675 | ||
[[Sval]] [[map]]: [ | [[Sval]] [[map]]: [{{val| 1 0 0 -1 }}, {{val| 0 2 0 3 }}, {{val| 0 0 1 1 }}] | ||
{{Val list|legend=1| 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 }} | {{Val list|legend=1| 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 }} | ||