The Archipelago: Difference between revisions

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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 (aka ~~Decoid)~~ ===

=== Decitonic aka decoid ===

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

Subgroup: 2.3.5.7.11.13

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

[[Comma list]]: 676/675, 1001/1000, 1716/1715, 4096/4095

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

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

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

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=== Avicenna ===

Subgroup: 2.3.5.7.11.13

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

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

[[Mapping]]: [{{val| 3 2 8 16 9 8 }}, {{val| 0 8 -3 -22 4 9 }}]

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

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

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=== Tertiathirds ===

Subgroup: 2.3.5.7.11.13

[[Comma list]]: 676/675, 1716/1715, 3025/3024, 4225/4224

[[Mapping]]: [~~<~~1 -4 2 -6 -9 -5|~~, <~~0 52 3 82 116 81|]

[[Mapping]]: [{{val| 1 -4 2 -6 -9 -5 }}, {{val| 0 52 3 82 116 81 }}]

[[~~POTE_tuning|~~POTE generator]]: ~14/13 = 128.8902

[[POTE generator]]: ~14/13 = 128.8902

{{Val list|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}

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==== 17-limit ====

Subgroup: 2.3.5.7.11.13.17

Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224

Mapping: [~~<~~1 -4 2 -6 -9 -5 -3|~~, <~~0 52 3 82 116 81 66|]

Mapping: [{{val| 1 -4 2 -6 -9 -5 -3 }}, {{val| 0 52 3 82 116 81 66 }}]

POTE generator: ~14/13 = 128.8912

@@ Line 192: / Line 192: @@
 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 (aka Decoid) ===
+=== Decitonic aka decoid ===
-{{see also|Breedsmic temperaments#Decoid}}
+{{see also| Breedsmic temperaments #Decoid}}
-[[Comma list]]: 676/675, 1001/1000, 1716/1715, 4225/4224
+Subgroup: 2.3.5.7.11.13
-[[Mapping]]: [&lt;10 0 47 36 98 37|, &lt;0 2 -3 -1 -8 0|]
+[[Comma list]]: 676/675, 1001/1000, 1716/1715, 4096/4095
-[[POTE_tuning|POTE generator]]: ~15/13 = 248.917
+[[Mapping]]: [{{val| 10 0 47 36 98 37 }}, {{val| 0 2 -3 -1 -8 0 }}]
+[[POTE generator]]: ~15/13 = 248.917
 {{Val list|legend=1| 130, 270, 940, 1210f, 1480cf }}
@@ Line 206: / Line 208: @@
 === Avicenna ===
-{{see also|Landscape microtemperaments#Avicenna}}
+{{see also| Landscape microtemperaments #Avicenna }}
+Subgroup: 2.3.5.7.11.13
 [[Comma list]]: 676/675, 1001/1000, 3025/3024, 4096/4095
-[[Mapping]]: [&lt;3 2 8 16 9 8|, &lt;0 8 -3 -22 4 9|]
+[[Mapping]]: [{{val| 3 2 8 16 9 8 }}, {{val| 0 8 -3 -22 4 9 }}]
-[[POTE_tuning|POTE generator]]: ~13/12 = 137.777
+[[POTE generator]]: ~13/12 = 137.777
 {{Val list|legend=1| 87, 183, 270 }}
@@ Line 219: / Line 223: @@
 === Tertiathirds ===
-{{see also|Wizmic microtemperaments#Tertiathirds}}
+{{see also| Wizmic microtemperaments #Tertiathirds }}
+Subgroup: 2.3.5.7.11.13
 [[Comma list]]: 676/675, 1716/1715, 3025/3024, 4225/4224
-[[Mapping]]: [&lt;1 -4 2 -6 -9 -5|, &lt;0 52 3 82 116 81|]
+[[Mapping]]: [{{val| 1 -4 2 -6 -9 -5 }}, {{val| 0 52 3 82 116 81 }}]
-[[POTE_tuning|POTE generator]]: ~14/13 = 128.8902
+[[POTE generator]]: ~14/13 = 128.8902
 {{Val list|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
@@ Line 232: / Line 238: @@
 ==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
 Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224
-Mapping: [&lt;1 -4 2 -6 -9 -5 -3|, &lt;0 52 3 82 116 81 66|]
+Mapping: [{{val| 1 -4 2 -6 -9 -5 -3 }}, {{val| 0 52 3 82 116 81 66 }}]
 POTE generator: ~14/13 = 128.8912