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Semicomma family: Difference between revisions

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m Spell 1\1 in decimal; note the badness metric being used; misc. cleanup
+CTE tunings and error maps (1/2)
Line 12: Line 12:
: mapping generators: ~2, ~75/64
: mapping generators: ~2, ~75/64


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~75/64 = 271.627
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~75/64 = 271.670
: [[error map]]: {{val| 0.000 -0.264 -1.324 }}
* [[POTE]]: ~2 = 1200.000, ~75/64 = 271.627
: error map: {{val| 0.000 -0.564 -1.195 }}


[[Tuning ranges]]:
[[Tuning ranges]]:
Line 45: Line 49:
{{Multival|legend=1| 7 -3 8 -21 -7 27 }}
{{Multival|legend=1| 7 -3 8 -21 -7 27 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/6 = 271.509
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~7/6 = 271.513
: [[error map]]: {{val| 0.000 -1.364 -0.853 +3.278 }}
* [[POTE]]: ~2 = 1200.000, ~7/6 = 271.509
: error map: {{val| 0.000 -1.394 -0.840 +3.243 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 51: Line 59:
: {{monzo list| 1 0 0 0 | 14/11 0 -7/11 7/11 | 27/11 0 3/11 -3/11 | 27/11 0 -8/11 8/11 }}
: {{monzo list| 1 0 0 0 | 14/11 0 -7/11 7/11 | 27/11 0 3/11 -3/11 | 27/11 0 -8/11 8/11 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5
* 9-odd-limit: ~7/6 = {{monzo| 3/17 2/17 -1/17 }}
* [[9-odd-limit]]: ~7/6 = {{monzo| 3/17 2/17 -1/17 }}
: {{monzo list| 1 0 0 0 | 21/17 14/17 -7/17 0 | 42/17 -6/17 3/17 0 | 41/17 16/17 -8/17 0 }}
: {{monzo list| 1 0 0 0 | 21/17 14/17 -7/17 0 | 42/17 -6/17 3/17 0 | 41/17 16/17 -8/17 0 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5
Line 74: Line 82:
Mapping: {{mapping| 1 0 3 1 3 | 0 7 -3 8 2 }}
Mapping: {{mapping| 1 0 3 1 3 | 0 7 -3 8 2 }}


{{Multival|legend=1| 7 -3 8 2 -21 -7 -21 27 15 -22 }}
Wedgie: {{multival| 7 -3 8 2 -21 -7 -21 27 15 -22 }}


Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.426
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/6 = 271.560
* POTE: ~2 = 1200.000, ~7/6 = 271.426


Minimax tuning:
Minimax tuning:
Line 98: Line 108:
Mapping: {{mapping| 1 0 3 1 3 8 | 0 7 -3 8 2 -19 }}
Mapping: {{mapping| 1 0 3 1 3 8 | 0 7 -3 8 2 -19 }}


Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.546
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/6 = 271.556
* POTE: ~2 = 1200.000, ~7/6 = 271.546


Tuning ranges:
Tuning ranges:
Line 104: Line 116:
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 275.659]
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 275.659]


{{Optimal ET sequence|legend=0| 22, 31, 53, 84e, 137e }}
{{Optimal ET sequence|legend=0| 22, 31, 53, 84e }}


Badness (Smith): 0.019718
Badness (Smith): 0.019718
Line 115: Line 127:
Mapping: {{mapping| 1 0 3 1 3 3 | 0 7 -3 8 2 3 }}
Mapping: {{mapping| 1 0 3 1 3 3 | 0 7 -3 8 2 3 }}


Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.301
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/6 = 271.747
* POTE: ~2 = 1200.000, ~7/6 = 271.301


{{Optimal ET sequence|legend=0| 9, 22, 31f }}
{{Optimal ET sequence|legend=0| 9, 22, 31f }}
Line 128: Line 142:
Mapping: {{mapping| 1 0 3 1 3 1 | 0 7 -3 8 2 12 }}
Mapping: {{mapping| 1 0 3 1 3 1 | 0 7 -3 8 2 12 }}


Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.088
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/6 = 271.163
* POTE: ~2 = 1200.000, ~7/6 = 271.088


Tuning ranges:
Tuning ranges:
Line 134: Line 150:
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 281.691]
* 13- and 15-odd-limit diamond tradeoff: ~7/6 = [266.871, 281.691]


{{Optimal ET sequence|legend=0| 22f, 31 }}
{{Optimal ET sequence|legend=0| 9, 22f, 31 }}


Badness (Smith): 0.019931
Badness (Smith): 0.019931


==== Doublethink ====
==== Doublethink ====
Doublethink is a weak extension of orwell to the 13-limit. It splits the generator of ~7/6 into two [[13/12]]~[[14/13]]'s by tempering out their difference, [[169/168]].
Doublethink is a weak extension of orwell to the 13-limit. It splits the generator of ~7/6 into two [[13/12]]~[[14/13]]'s by tempering out their difference, [[169/168]]. Its ploidacot is alpha-tetradecacot.  


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 147: Line 163:
Mapping: {{mapping| 1 0 3 1 3 2 | 0 14 -6 16 4 15 }}
Mapping: {{mapping| 1 0 3 1 3 2 | 0 14 -6 16 4 15 }}


Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 135.723
Optimal tunings:
* CTE: ~2 = 1200.000, ~13/12 = 135.811
* POTE: ~2 = 1200.000, ~13/12 = 135.723


Tuning ranges:
Tuning ranges:
Line 153: Line 171:
* 13- and 15-odd-limit diamond tradeoff: ~13/12 = [128.298, 138.573]
* 13- and 15-odd-limit diamond tradeoff: ~13/12 = [128.298, 138.573]


{{Optimal ET sequence|legend=0| 9, 35bd, 44, 53, 62, 115ef, 168eef }}
{{Optimal ET sequence|legend=0| 9, 35bd, 44, 53, 62, 115ef }}


Badness (Smith): 0.027120
Badness (Smith): 0.027120
Line 164: Line 182:
Mapping: {{mapping| 1 0 3 1 -4 | 0 7 -3 8 33 }}
Mapping: {{mapping| 1 0 3 1 -4 | 0 7 -3 8 33 }}


Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 271.288
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/6 = 271.316
* POTE: ~2 = 1200.000, ~7/6 = 271.288


Tuning ranges:
Tuning ranges:
Line 170: Line 190:
* 11-odd-limit diamond tradeoff: ~7/6 = [266.871, 272.514]
* 11-odd-limit diamond tradeoff: ~7/6 = [266.871, 272.514]


{{Optimal ET sequence|legend=0| 31, 84, 115, 376b, 491bd, 606bde }}
{{Optimal ET sequence|legend=0| 22e, 31, 84, 115 }}


Badness (Smith): 0.031438
Badness (Smith): 0.031438
Line 181: Line 201:
Mapping: {{mapping| 1 7 0 9 17 | 0 -14 6 -16 -35 }}
Mapping: {{mapping| 1 7 0 9 17 | 0 -14 6 -16 -35 }}


Optimal tuning (POTE): ~2 = 1200.000, ~55/36 = 735.752
: mapping generators: ~2, ~72/55


{{Optimal ET sequence|legend=0| 31, 106, 137, 442bd }}
Optimal tunings:
* CTE: ~2 = 1200.000, ~55/36 = 735.754
* POTE: ~2 = 1200.000, ~55/36 = 735.752
 
{{Optimal ET sequence|legend=0| 31, 75e, 106, 137 }}


Badness (Smith): 0.038377
Badness (Smith): 0.038377
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