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[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000, ~16875/16384 = 55.3052
* [[WE]]: ~2 = 1199.8082{{c}}, ~16875/16384 = 55.2840{{c}}
* [[POTE]]: ~2 = 1200.000, ~16875/16384 = 55.293
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16875/16384 = 55.2961{{c}}


{{Optimal ET sequence|legend=1| 21, 22, 43, 65, 152, 217, 586, 803 }}
{{Optimal ET sequence|legend=1| 21, 22, 43, 65, 152, 217, 586, 803 }}


[[Badness]] (Smith): 0.083778
[[Badness]] (Sintel): 1.965


{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
Line 50: Line 50:
Mapping: {{Mapping| 1 2 2 3 | 0 -9 7 10 }}
Mapping: {{Mapping| 1 2 2 3 | 0 -9 7 10 }}


Optimal tuning (CTE): ~2 = 1200.0000, ~33/32 = 55.2760
Optimal tunings:
* WE: ~2 = 1199.7406{{c}}, ~33/32 = 55.2653{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2770{{c}}


{{Optimal ET sequence|legend=1| 21, 22, 43, 65, 87, 152, 369, 521e }}
{{Optimal ET sequence|legend=0| 21, 22, 43, 65, 87, 152, 369, 521e }}


Badness: 0.0107
Badness (Sintel): 0.335


{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
Line 79: Line 81:
Mapping: {{mapping| 1 2 2 3 5 | 0 -9 7 10 -1 }}
Mapping: {{mapping| 1 2 2 3 5 | 0 -9 7 10 -1 }}


Optimal tuning (CTE): ~2 = 1200.000, ~32/31 = 55.276
Optimal tunings:
* WE: ~2 = 1199.8050{{c}}, ~32/31 = 55.2669{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~32/31 = 55.2759{{c}}


{{Optimal ET sequence|legend=0| 21, 22, 43, 65, 87, 152, 369, 521e, 673e }}
{{Optimal ET sequence|legend=0| 21, 22, 43, 65, 87, 152, 369, 521e, 673e }}
Line 129: Line 133:
{{Mapping|legend=1| 1 2 2 4 | 0 -9 7 -26 }}
{{Mapping|legend=1| 1 2 2 4 | 0 -9 7 -26 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~28/27 = 55.122
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9190{{c}}, ~28/27 = 55.1186{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/27 = 55.1242{{c}}


{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}
{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}


[[Badness]] (Smith): 0.088746
[[Badness]] (Sintel): 2.246


=== 11-limit ===
=== 11-limit ===
Line 142: Line 148:
Mapping: {{mapping| 1 2 2 4 3 | 0 -9 7 -26 10 }}
Mapping: {{mapping| 1 2 2 4 3 | 0 -9 7 -26 10 }}


Optimal tuning (POTE): ~2 = 1200.000, ~28/27 = 55.126
Optimal tunings:
* WE: ~2 = 1199.9480{{c}}, ~28/27 = 55.1241{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 55.1271{{c}}


{{Optimal ET sequence|legend=0| 22, 65, 87, 196, 283 }}
{{Optimal ET sequence|legend=0| 22, 65, 87, 196, 283 }}


Badness (Smith): 0.035844
Badness (Sintel): 1.185


{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
Line 171: Line 179:
Mapping: {{mapping| 1 2 2 4 3 2 | 0 -9 7 -26 10 37 }}
Mapping: {{mapping| 1 2 2 4 3 2 | 0 -9 7 -26 10 37 }}


Optimal tuning (POTE): ~2 = 1200.000, ~28/27 = 55.138
Optimal tunings:
* WE: ~2 = 1199.9926{{c}}, ~28/27 = 55.1378{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~28/27 = 55.1382{{c}}


{{Optimal ET sequence|legend=0| 22, 65, 87, 283 }}
{{Optimal ET sequence|legend=0| 22, 65, 87, 283 }}


Badness (Smith): 0.031366
Badness (Sintel): 1.296


== Alphaquarter ==
== Alphaquarter ==
Line 189: Line 199:
{{Mapping|legend=1| 1 2 2 0 | 0 -9 7 61 }}
{{Mapping|legend=1| 1 2 2 0 | 0 -9 7 61 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~16128/15625 = 55.243
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7349{{c}}, ~16128/15625 = 55.2306{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16128/15625 = 55.2405{{c}}


{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}
{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}


[[Badness]] (Smith): 0.116594
[[Badness]] (Sintel): 2.951


=== 11-limit ===
=== 11-limit ===
Line 202: Line 214:
Mapping: {{mapping| 1 2 2 0 3 | 0 -9 7 61 10 }}
Mapping: {{mapping| 1 2 2 0 3 | 0 -9 7 61 10 }}


Optimal tuning (POTE): ~2 = 1200.000, ~33/32 = 55.243
Optimal tunings:
* WE: ~2 = 1199.7229{{c}}, ~33/32 = 55.2303{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2407{{c}}


{{Optimal ET sequence|legend=0| 65d, 87, 152, 239, 391 }}
{{Optimal ET sequence|legend=0| 65d, 87, 152, 239, 391 }}


Badness (Smith): 0.029638
Badness (Sintel): 0.980


{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
Line 231: Line 245:
Mapping: {{mapping| 1 2 2 0 3 2 | 0 -9 7 61 10 37 }}
Mapping: {{mapping| 1 2 2 0 3 2 | 0 -9 7 61 10 37 }}


Optimal tuning (POTE): ~2 = 1200.000, ~33/32 = 55.236
Optimal tunings:
* WE: ~2 = 1199.6491{{c}}, ~33/32 = 55.2200{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.2328{{c}}


{{Optimal ET sequence|legend=0| 65d, 87, 152f, 239f }}
{{Optimal ET sequence|legend=0| 65d, 87, 152f, 239f }}


Badness (Smith): 0.025344
Badness (Sintel): 1.047


== Escapist ==
== Escapist ==
Line 249: Line 265:
{{Mapping|legend=1| 1 2 2 3 | 0 -9 7 -4 }}
{{Mapping|legend=1| 1 2 2 3 | 0 -9 7 -4 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~49/48 = 55.327
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.9926{{c}}, ~49/48 = 55.2809{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 55.3479{{c}}


{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}
{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}


[[Badness]] (Smith): 0.077950
[[Badness]] (Sintel): 1.973


=== 11-limit ===
=== 11-limit ===
Line 262: Line 280:
Mapping: {{mapping| 1 2 2 3 3 | 0 -9 7 -4 10 }}
Mapping: {{mapping| 1 2 2 3 3 | 0 -9 7 -4 10 }}


Optimal tuning (POTE): ~2 = 1200.000, ~33/32 = 55.354
Optimal tunings:
* WE: ~2 = 1199.0859{{c}}, ~33/32 = 55.3117{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.3574{{c}}


{{Optimal ET sequence|legend=0| 21, 22, 43, 65d }}
{{Optimal ET sequence|legend=0| 21, 22, 43, 65d }}


Badness (Smith): 0.036700
Badness (Sintel): 1.213


{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
Line 291: Line 311:
Mapping: {{mapping| 1 2 2 3 3 3 | 0 -9 7 -4 10 15 }}
Mapping: {{mapping| 1 2 2 3 3 3 | 0 -9 7 -4 10 15 }}


Optimal tuning (POTE): ~2 = 1200.000, ~26/25 = 55.550
Optimal tunings:
* WE: ~2 = 1199.5949{{c}}, ~33/32 = 55.5317{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 55.5480{{c}}


{{Optimal ET sequence|legend=0| 21, 22, 43 }}
{{Optimal ET sequence|legend=0| 21, 22, 43 }}


Badness (Smith): 0.035261
Badness (Sintel): 1.457


= Weak extensions =
= Weak extensions =
Line 320: Line 342:
{{Mapping|legend=1| 2 4 4 7 | 0 -9 7 -15 }}
{{Mapping|legend=1| 2 4 4 7 | 0 -9 7 -15 }}


: mapping generators: ~343/243, ~16875/16384
: mapping generators: ~343/243, ~405/392


[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~16875/16384 = 55.320
[[Optimal tuning]]s:
* [[WE]]: ~343/243 = 599.8762{{c}}, ~405/392 = 55.3089{{c}}
* [[CWE]]: ~343/243 = 600.0000{{c}}, ~405/392 = 55.3273{{c}}


{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}
{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}


[[Badness]] (Smith): 0.059241
[[Badness]] (Sintel): 1.499


=== 11-limit ===
=== 11-limit ===
Line 335: Line 359:
Mapping: {{mapping| 2 4 4 7 6 | 0 -9 7 -15 10 }}
Mapping: {{mapping| 2 4 4 7 6 | 0 -9 7 -15 10 }}


Optimal tuning (POTE): ~99/70 = 600.000, ~33/32 = 55.304
Optimal tunings:
* WE: ~99/70 = 599.8383{{c}}, ~33/32 = 55.2895{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~33/32 = 55.3081{{c}}


{{Optimal ET sequence|legend=0| 22, 86, 108, 130, 152, 282 }}
{{Optimal ET sequence|legend=0| 22, 86, 108, 130, 152, 282 }}


Badness (Smith): 0.024619
Badness (Sintel): 0.814


{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
Line 364: Line 390:
Mapping: {{mapping| 2 4 4 7 6 11 | 0 -9 7 -15 10 -39 }}
Mapping: {{mapping| 2 4 4 7 6 11 | 0 -9 7 -15 10 -39 }}


Optimal tuning (POTE): ~99/70 = 600.000, ~33/32 = 55.325
Optimal tunings:
* WE: ~99/70 = 599.8331{{c}}, ~33/32 = 55.3093{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~33/32 = 55.3295{{c}}


{{Optimal ET sequence|legend=0| 22f, 108f, 130, 282 }}
{{Optimal ET sequence|legend=0| 22f, 108f, 130, 282 }}


Badness (Smith): 0.022887
Badness (Sintel): 0.946


==== Septisuperquad ====
==== Septisuperquad ====
Line 379: Line 407:
Mapping: {{mapping| 2 4 4 7 6 5 | 0 -9 7 -15 10 26 }}
Mapping: {{mapping| 2 4 4 7 6 5 | 0 -9 7 -15 10 26 }}


Optimal tuning (POTE): ~55/39 = 600.000, ~33/32 = 55.359
Optimal tunings:
* WE: ~55/39 = 599.9152{{c}}, ~33/32 = 55.3509{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~33/32 = 55.3584{{c}}


{{Optimal ET sequence|legend=0| 22, 108, 130 }}
{{Optimal ET sequence|legend=0| 22, 108, 130 }}


Badness (Smith): 0.033038
Badness (Sintel): 1.365


== Arch ==
== Arch ==
Line 397: Line 427:
: mapping generators: ~2, ~64/63
: mapping generators: ~2, ~64/63


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~64/63 = 27.668
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9246{{c}}, ~64/63 = 27.6662{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~64/63 = 27.6676{{c}}


{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347, 824c, 1171c, 1518cd }}
{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347, 824c, 1171c, 1518cd }}


[[Badness]] (Smith): 0.094345
[[Badness]] (Sintel): 2.388


=== 11-limit ===
=== 11-limit ===
Line 410: Line 442:
Mapping: {{mapping| 1 2 2 2 3 | 0 -18 14 35 20 }}
Mapping: {{mapping| 1 2 2 2 3 | 0 -18 14 35 20 }}


Optimal tuning (POTE): ~2 = 1200.000, ~64/63 = 27.663
Optimal tunings:
* WE: ~2 = 1199.8347{{c}}, ~64/63 = 27.6590{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/63 = 27.6617{{c}}


{{Optimal ET sequence|legend=0| 43, 87, 130, 217, 347e, 911cde }}
{{Optimal ET sequence|legend=0| 43, 87, 130, 217, 347e, 911cde }}


Badness (Smith): 0.036541
Badness (Sintel): 1.208


{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
{| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"
Line 439: Line 473:
Mapping: {{mapping| 1 2 2 2 3 4 | 0 -18 14 35 20 -13 }}
Mapping: {{mapping| 1 2 2 2 3 4 | 0 -18 14 35 20 -13 }}


Optimal tuning (POTE): ~2 = 1200.000, ~64/63 = 27.660
Optimal tunings:
* WE: ~2 = 1199.8733{{c}}, ~64/63 = 27.6569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~64/63 = 27.6594{{c}}


{{Optimal ET sequence|legend=0| 43, 87, 130, 217, 347e, 564e }}
{{Optimal ET sequence|legend=0| 43, 87, 130, 217, 347e, 564e }}


Badness (Smith): 0.019504
Badness (Sintel): 0.806


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Escapade family| ]] <!-- main article -->
[[Category:Escapade family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Escapade_family"