The Archipelago: Difference between revisions

Line 176:

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|29EDO]] alone.

==Decitonic==

==Decitonic (aka Decoid)==

~~Commas~~: 676/675, 1001/1000, 1716/1715, 4225/4224

[[Comma list]]: 676/675, 1001/1000, 1716/1715, 4225/4224

[[Mapping]]: [<10 0 47 36 98 37|, <0 2 -3 -1 -8 0|]

[[POTE_tuning|POTE generator]]: ~15/13 = 248.917

~~Map: [<10 0 47 36 98 37~~|~~, <0 2 -3 -~~1 ~~-8 0~~|]

~~EDOs~~: ~~130, 270, 940, 1480~~

[[Badness]]: 0.013475

~~Badness~~: ~~0.0135~~

==Avicenna==

[[Comma list]]: 676/675, 1001/1000, 3025/3024, 4096/4095

~~==Avicenna==~~

[[Mapping]]: [<3 2 8 16 9 8|, <0 8 -3 -22 4 9|]

~~Commas~~: ~~676/675~~, ~~1001/1000, 3025/3024, 4096/4095~~

[[POTE_tuning|POTE generator]]: ~13/12 = 137.777

~~Map: [<3 2 8 16 9 8~~|~~, <0 8 -3 -22 4 9~~|]

~~EDOs:~~ 87, 183, 270

Badness: 0.~~0156~~

[[Badness]]: 0.015557

=Subgroup temperaments=

@@ Line 176: / Line 176: @@
 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]].
-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|29EDO]] alone.
-==Decitonic==
+==Decitonic (aka Decoid)==
-Commas: 676/675, 1001/1000, 1716/1715, 4225/4224
+{{see also|Breedsmic temperaments#Decoid}}
+[[Comma list]]: 676/675, 1001/1000, 1716/1715, 4225/4224
+[[Mapping]]: [&lt;10 0 47 36 98 37|, &lt;0 2 -3 -1 -8 0|]
 [[POTE_tuning|POTE generator]]: ~15/13 = 248.917
-Map: [&lt;10 0 47 36 98 37|, &lt;0 2 -3 -1 -8 0|]
+{{Val list|legend=1| 130, 270, 940, 1210f, 1480cf }}
-EDOs: 130, 270, 940, 1480
+[[Badness]]: 0.013475
-Badness: 0.0135
+==Avicenna==
+[[Comma list]]: 676/675, 1001/1000, 3025/3024, 4096/4095
-==Avicenna==
+[[Mapping]]: [&lt;3 2 8 16 9 8|, &lt;0 8 -3 -22 4 9|]
-Commas: 676/675, 1001/1000, 3025/3024, 4096/4095
 [[POTE_tuning|POTE generator]]: ~13/12 = 137.777
-Map: [&lt;3 2 8 16 9 8|, &lt;0 8 -3 -22 4 9|]
+{{Val list|legend=1| 87, 183, 270 }}
-EDOs: 87, 183, 270
-Badness: 0.0156
+[[Badness]]: 0.015557
 =Subgroup temperaments=