The Archipelago: Difference between revisions

m Final cleanup
Edo lists reviewed
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 }}
 
[[Optimal patent val]]: [[940edo]]


=== 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, 77, 121, 130, 140, 149, 198, 212, 270 }}
{{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| 9, 15, 29, 43, 58, 72, 87, 121, 130 }}
{{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, 77, 111, 130 }}
{{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, 34, 53, 58, 63, 77, 87, 111, 121 }}
{{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, 63, 72, 111, 121, 183 }}
{{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| 9, 29, 53, 58, 87, 111, 140, 149, 198 }}
{{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 [[Ragismic_microtemperaments|hemiennealimmal]], [[Breedsmic_temperaments|harry]], [[Kleismic_family|tritikleismic]], [[Kleismic_family|catakleimsic]], [[Marvel_temperaments|negri]], [[Hemifamity_temperaments|mystery]], [[Hemifamity_temperaments|buzzard]], [[Kleismic_family|quadritikleismic]].
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|29EDO]] alone.
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, 1480cf }}
{{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]]: [&lt;1 0 0 -1|, &lt;0 2 0 3|, &lt;0 0 1 1|]
[[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 }}