Meantone family: Difference between revisions
→Sharptone: A bit more description as to why sharptone only works in 5edo. |
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| Line 20: | Line 20: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 697.214 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.214{{c}} | ||
: [[error map]]: {{val| 0 -4.741 +2.544 }} | : [[error map]]: {{val| 0 -4.741 +2.544 }} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 696.239 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.239{{c}} | ||
: [[error map]]: {{val| 0 -5.716 -1.359 }} | : [[error map]]: {{val| 0 -5.716 -1.359 }} | ||
| Line 35: | Line 35: | ||
{{Optimal ET sequence|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b }} | {{Optimal ET sequence|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b }} | ||
[[Badness]]: 0.007381 | [[Badness]] (Smith): 0.007381 | ||
=== Extensions === | === Extensions === | ||
| Line 74: | Line 74: | ||
* ''[[Plutus]]'' (+15/14) → [[Very low accuracy temperaments #Plutus|Very low accuracy temperaments]] | * ''[[Plutus]]'' (+15/14) → [[Very low accuracy temperaments #Plutus|Very low accuracy temperaments]] | ||
* [[Godzilla]] (+49/48) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]] | * [[Godzilla]] (+49/48) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]] | ||
* | * [[Mothra]] (+1029/1024) → [[Gamelismic clan #Mothra|Gamelismic clan]] | ||
* ''[[Mohaha]]'' (+121/120) → [[Rastmic clan #Mohaha|Rastmic clan]] | * ''[[Mohaha]]'' (+121/120) → [[Rastmic clan #Mohaha|Rastmic clan]] | ||
| Line 93: | Line 93: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 696.952 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.952{{c}} | ||
: [[error map]]: {{val| 0 -5.003 +1.495 +0.695 }} | : [[error map]]: {{val| 0 -5.003 +1.495 +0.695 }} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 696.495 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.495{{c}} | ||
: [[error map]]: {{val| 0 -5.460 -0.334 -3.877 }} | : [[error map]]: {{val| 0 -5.460 -0.334 -3.877 }} | ||
| Line 112: | Line 112: | ||
{{Optimal ET sequence|legend=1| 12, 19, 31, 81, 112b, 143b }} | {{Optimal ET sequence|legend=1| 12, 19, 31, 81, 112b, 143b }} | ||
[[Badness]]: 0.013707 | [[Badness]] (Smith): 0.013707 | ||
=== Undecimal meantone (huygens) === | === Undecimal meantone (huygens) === | ||
| Line 127: | Line 127: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.168 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.168{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.967 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.967{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 143: | Line 143: | ||
{{Optimal ET sequence|legend=0| 12, 19e, 31, 105, 136b }} | {{Optimal ET sequence|legend=0| 12, 19e, 31, 105, 136b }} | ||
Badness: 0.017027 | Badness (Smith): 0.017027 | ||
; Music | ; Music | ||
| Line 156: | Line 156: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.855 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.855{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.642 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.642{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 165: | Line 165: | ||
{{Optimal ET sequence|legend=0| 12f, 19e, 31 }} | {{Optimal ET sequence|legend=0| 12f, 19e, 31 }} | ||
Badness: 0.018048 | Badness (Smith): 0.018048 | ||
===== Meantonic ===== | ===== Meantonic ===== | ||
| Line 177: | Line 177: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.649 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.649{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.377 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.377{{c}} | ||
{{Optimal ET sequence|legend=0| 12fg, 19eg, 31, 50e }} | {{Optimal ET sequence|legend=0| 12fg, 19eg, 31, 50e }} | ||
Badness: 0.019037 | Badness (Smith): 0.019037 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 192: | Line 192: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.555 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.555{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.273 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.273{{c}} | ||
{{Optimal ET sequence|legend=0| 12fghh, 19egh, 31, 50e }} | {{Optimal ET sequence|legend=0| 12fghh, 19egh, 31, 50e }} | ||
Badness: 0.017846 | Badness (Smith): 0.017846 | ||
===== Meantoid ===== | ===== Meantoid ===== | ||
| Line 209: | Line 209: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.036 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.036{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.448 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.448{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 19eg, 31g }} | {{Optimal ET sequence|legend=0| 12f, 19eg, 31g }} | ||
Badness: 0.019433 | Badness (Smith): 0.019433 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 224: | Line 224: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.216 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.216{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.394 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.394{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 19egh, 31gh }} | {{Optimal ET sequence|legend=0| 12f, 19egh, 31gh }} | ||
Badness: 0.017437 | Badness (Smith): 0.017437 | ||
===== Huygens ===== | ===== Huygens ===== | ||
| Line 241: | Line 241: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.908 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.908{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.003 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.003{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 31 }} | {{Optimal ET sequence|legend=0| 12f, 31 }} | ||
Badness: 0.019982 | Badness (Smith): 0.019982 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 256: | Line 256: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.931 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.931{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.140 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.140{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 31 }} | {{Optimal ET sequence|legend=0| 12f, 31 }} | ||
Badness: 0.018047 | Badness (Smith): 0.018047 | ||
==== Grosstone ==== | ==== Grosstone ==== | ||
| Line 273: | Line 273: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.258 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.258{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.264 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.264{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 286: | Line 286: | ||
{{Optimal ET sequence|legend=0| 12, 31, 43, 74 }} | {{Optimal ET sequence|legend=0| 12, 31, 43, 74 }} | ||
Badness: 0.025899 | Badness (Smith): 0.025899 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 296: | Line 296: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.300 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.300{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.335 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.335{{c}} | ||
{{Optimal ET sequence|legend=0| 12, 31, 43, 74g }} | {{Optimal ET sequence|legend=0| 12, 31, 43, 74g }} | ||
Badness: 0.020889 | Badness (Smith): 0.020889 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
| Line 311: | Line 311: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.327 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.327{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.380 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.380{{c}} | ||
{{Optimal ET sequence|legend=0| 12, 31, 43, 74gh }} | {{Optimal ET sequence|legend=0| 12, 31, 43, 74gh }} | ||
Badness: 0.017611 | Badness (Smith): 0.017611 | ||
==== Meridetone ==== | ==== Meridetone ==== | ||
| Line 328: | Line 328: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.516 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.516{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.529 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.529{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 337: | Line 337: | ||
{{Optimal ET sequence|legend=0| 12f, 31f, 43 }} | {{Optimal ET sequence|legend=0| 12f, 31f, 43 }} | ||
Badness: 0.026421 | Badness (Smith): 0.026421 | ||
===== Meridetonic ===== | ===== Meridetonic ===== | ||
| Line 347: | Line 347: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.508 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.508{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.514 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.514{{c}} | ||
{{Optimal ET sequence|legend=0| 12fg, 31fg, 43 }} | {{Optimal ET sequence|legend=0| 12fg, 31fg, 43 }} | ||
Badness: 0.027706 | Badness (Smith): 0.027706 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 362: | Line 362: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.485 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.485{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.481 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.481{{c}} | ||
{{Optimal ET sequence|legend=0| 12fghh, 31fgh, 43 }} | {{Optimal ET sequence|legend=0| 12fghh, 31fgh, 43 }} | ||
Badness: 0.025315 | Badness (Smith): 0.025315 | ||
===== Meridetoid ===== | ===== Meridetoid ===== | ||
| Line 377: | Line 377: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.610 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.610{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.376 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.376{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 31fg, 43g }} | {{Optimal ET sequence|legend=0| 12f, 31fg, 43g }} | ||
Badness: 0.027518 | Badness (Smith): 0.027518 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 392: | Line 392: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.701 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.701{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.316 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.316{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 19effgh, 31fgh, 43gh }} | {{Optimal ET sequence|legend=0| 12f, 19effgh, 31fgh, 43gh }} | ||
Badness: 0.023613 | Badness (Smith): 0.023613 | ||
===== Sauveuric ===== | ===== Sauveuric ===== | ||
| Line 407: | Line 407: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.538 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.538{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.644 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.644{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 43 }} | {{Optimal ET sequence|legend=0| 12f, 43 }} | ||
Badness: 0.023881 | Badness (Smith): 0.023881 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 422: | Line 422: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.555 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.555{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.715 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.715{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 43 }} | {{Optimal ET sequence|legend=0| 12f, 43 }} | ||
Badness: 0.020540 | Badness (Smith): 0.020540 | ||
==== Hemimeantone ==== | ==== Hemimeantone ==== | ||
| Line 439: | Line 439: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~26/15 = 948.611 | * CTE: ~2 = 1200.000{{c}}, ~26/15 = 948.611{{c}} | ||
* POTE: ~2 = 1200.000, ~26/15 = 948.465 | * POTE: ~2 = 1200.000{{c}}, ~26/15 = 948.465{{c}} | ||
{{Optimal ET sequence|legend=0| 19e, 43, 62 }} | {{Optimal ET sequence|legend=0| 19e, 43, 62 }} | ||
Badness: 0.031433 | Badness (Smith): 0.031433 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 454: | Line 454: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~26/15 = 948.617 | * CTE: ~2 = 1200.000{{c}}, ~26/15 = 948.617{{c}} | ||
* POTE: ~2 = 1200.000, ~26/15 = 948.477 | * POTE: ~2 = 1200.000{{c}}, ~26/15 = 948.477{{c}} | ||
{{Optimal ET sequence|legend=0| 19eg, 43, 62 }} | {{Optimal ET sequence|legend=0| 19eg, 43, 62 }} | ||
Badness: 0.023380 | Badness (Smith): 0.023380 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
| Line 469: | Line 469: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~19/11 = 948.609 | * CTE: ~2 = 1200.000{{c}}, ~19/11 = 948.609{{c}} | ||
* POTE: ~2 = 1200.000, ~19/11 = 948.473 | * POTE: ~2 = 1200.000{{c}}, ~19/11 = 948.473{{c}} | ||
{{Optimal ET sequence|legend=0| 19egh, 43, 62 }} | {{Optimal ET sequence|legend=0| 19egh, 43, 62 }} | ||
Badness: 0.018952 | Badness (Smith): 0.018952 | ||
==== Semimeantone ==== | ==== Semimeantone ==== | ||
| Line 486: | Line 486: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~55/39 = 600.000, ~3/2 = 697.168 | * CTE: ~55/39 = 600.000{{c}}, ~3/2 = 697.168{{c}} | ||
* POTE: ~55/39 = 600.000, ~3/2 = 697.005 | * POTE: ~55/39 = 600.000{{c}}, ~3/2 = 697.005{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 38deefff, 50eff, 62, 136b }} | {{Optimal ET sequence|legend=0| 12f, 38deefff, 50eff, 62, 136b }} | ||
Badness: 0.040668 | Badness (Smith): 0.040668 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 501: | Line 501: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~3/2 = 697.174 | * CTE: ~17/12 = 600.000{{c}}, ~3/2 = 697.174{{c}} | ||
* POTE: ~17/12 = 600.000, ~3/2 = 696.927 | * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 696.927{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 50eff, 62, 136bg }} | {{Optimal ET sequence|legend=0| 12f, 50eff, 62, 136bg }} | ||
Badness: 0.031491 | Badness (Smith): 0.031491 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
| Line 516: | Line 516: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~3/2 = 697.187 | * CTE: ~17/12 = 600.000{{c}}, ~3/2 = 697.187{{c}} | ||
* POTE: ~17/12 = 600.000, ~3/2 = 696.906 | * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 696.906{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 50eff, 62 }} | {{Optimal ET sequence|legend=0| 12f, 50eff, 62 }} | ||
Badness: 0.024206 | Badness (Smith): 0.024206 | ||
=== Meanpop === | === Meanpop === | ||
| Line 537: | Line 537: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.531 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.531{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.434 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.434{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 553: | Line 553: | ||
{{Optimal ET sequence|legend=0| 12e, 19, 31, 81, 112b }} | {{Optimal ET sequence|legend=0| 12e, 19, 31, 81, 112b }} | ||
Badness: 0.021543 | Badness (Smith): 0.021543 | ||
; Music | ; Music | ||
| Line 567: | Line 567: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.356 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.356{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.211 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.211{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 580: | Line 580: | ||
{{Optimal ET sequence|legend=0| 19, 31, 50, 81 }} | {{Optimal ET sequence|legend=0| 19, 31, 50, 81 }} | ||
Badness: 0.020883 | Badness (Smith): 0.020883 | ||
===== Meanpoppic ===== | ===== Meanpoppic ===== | ||
| Line 590: | Line 590: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.351 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.351{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.194 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.194{{c}} | ||
{{Optimal ET sequence|legend=0| 19g, 31, 50, 81, 131bd }} | {{Optimal ET sequence|legend=0| 19g, 31, 50, 81, 131bd }} | ||
Badness: 0.019953 | Badness (Smith): 0.019953 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 605: | Line 605: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.347 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.347{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.188 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.188{{c}} | ||
{{Optimal ET sequence|legend=0| 19gh, 31, 50, 81 }} | {{Optimal ET sequence|legend=0| 19gh, 31, 50, 81 }} | ||
Badness: 0.017791 | Badness (Smith): 0.017791 | ||
===== Meanpoid ===== | ===== Meanpoid ===== | ||
| Line 620: | Line 620: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.439 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.439{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.408 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.408{{c}} | ||
{{Optimal ET sequence|legend=0| 19, 31 }} | {{Optimal ET sequence|legend=0| 19, 31 }} | ||
Badness: 0.022870 | Badness (Smith): 0.022870 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 635: | Line 635: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.484 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.484{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.499 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.499{{c}} | ||
{{Optimal ET sequence|legend=0| 12ef, 19, 31 }} | {{Optimal ET sequence|legend=0| 12ef, 19, 31 }} | ||
Badness: 0.020488 | Badness (Smith): 0.020488 | ||
==== Meanplop ==== | ==== Meanplop ==== | ||
| Line 650: | Line 650: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.283 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.283{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.202 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.202{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 659: | Line 659: | ||
{{Optimal ET sequence|legend=0| 12e, 19, 31f }} | {{Optimal ET sequence|legend=0| 12e, 19, 31f }} | ||
Badness: 0.027666 | Badness (Smith): 0.027666 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 669: | Line 669: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.407 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.407{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.414 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.414{{c}} | ||
{{Optimal ET sequence|legend=0| 12e, 19 }} | {{Optimal ET sequence|legend=0| 12e, 19 }} | ||
Badness: 0.026836 | Badness (Smith): 0.026836 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 684: | Line 684: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.473 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.473{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.497 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.497{{c}} | ||
{{Optimal ET sequence|legend=0| 12e, 19 }} | {{Optimal ET sequence|legend=0| 12e, 19 }} | ||
Badness: 0.023540 | Badness (Smith): 0.023540 | ||
===== Meanploid ===== | ===== Meanploid ===== | ||
| Line 699: | Line 699: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.661 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.661{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.415 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.415{{c}} | ||
{{Optimal ET sequence|legend=0| 12e, 19g, 31fg }} | {{Optimal ET sequence|legend=0| 12e, 19g, 31fg }} | ||
Badness: 0.026094 | Badness (Smith): 0.026094 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 714: | Line 714: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 697.016 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.016{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.583 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.583{{c}} | ||
{{Optimal ET sequence|legend=0| 12e, 19gh, 31fgh }} | {{Optimal ET sequence|legend=0| 12e, 19gh, 31fgh }} | ||
Badness: 0.023104 | Badness (Smith): 0.023104 | ||
=== Meanenneadecal === | === Meanenneadecal === | ||
| Line 731: | Line 731: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.153 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.153{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.250 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.250{{c}} | ||
Tuning ranges: | Tuning ranges: | ||
| Line 740: | Line 740: | ||
{{Optimal ET sequence|legend=0| 7d, 12, 19, 31e }} | {{Optimal ET sequence|legend=0| 7d, 12, 19, 31e }} | ||
Badness: 0.021423 | Badness (Smith): 0.021423 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 750: | Line 750: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.098 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.098{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.146 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.146{{c}} | ||
{{Optimal ET sequence|legend=0| 7df, 12f, 19, 31e }} | {{Optimal ET sequence|legend=0| 7df, 12f, 19, 31e }} | ||
Badness: 0.021182 | Badness (Smith): 0.021182 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 765: | Line 765: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.216 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.216{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.575 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.575{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 19, 31e }} | {{Optimal ET sequence|legend=0| 12f, 19, 31e }} | ||
Badness: 0.022980 | Badness (Smith): 0.022980 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 780: | Line 780: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.277 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.277{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.706 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.706{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 19, 31e }} | {{Optimal ET sequence|legend=0| 12f, 19, 31e }} | ||
Badness: 0.020293 | Badness (Smith): 0.020293 | ||
===== Meanenneadecoid ===== | ===== Meanenneadecoid ===== | ||
| Line 795: | Line 795: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.450 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.450{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.025 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.025{{c}} | ||
{{Optimal ET sequence|legend=0| 7dfg, 12f, 19g }} | {{Optimal ET sequence|legend=0| 7dfg, 12f, 19g }} | ||
Badness: 0.020171 | Badness (Smith): 0.020171 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 810: | Line 810: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.793 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.793{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.121 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.121{{c}} | ||
{{Optimal ET sequence|legend=0| 7dfgh, 12f, 19gh }} | {{Optimal ET sequence|legend=0| 7dfgh, 12f, 19gh }} | ||
Badness: 0.018045 | Badness (Smith): 0.018045 | ||
==== Vincenzo ==== | ==== Vincenzo ==== | ||
| Line 825: | Line 825: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 695.790 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 695.790{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 695.060 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 695.060{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 12, 19 }} | {{Optimal ET sequence|legend=0| 7d, 12, 19 }} | ||
Badness: 0.024763 | Badness (Smith): 0.024763 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 840: | Line 840: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.011 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.011{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 695.858 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 695.858{{c}} | ||
{{Optimal ET sequence|legend=0| 12, 19 }} | {{Optimal ET sequence|legend=0| 12, 19 }} | ||
Badness: 0.025535 | Badness (Smith): 0.025535 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 855: | Line 855: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.120 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.120{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.131 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.131{{c}} | ||
{{Optimal ET sequence|legend=0| 12, 19 }} | {{Optimal ET sequence|legend=0| 12, 19 }} | ||
Badness: 0.022302 | Badness (Smith): 0.022302 | ||
===== Vincenzoid ===== | ===== Vincenzoid ===== | ||
| Line 870: | Line 870: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.412 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.412{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 695.358 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 695.358{{c}} | ||
{{Optimal ET sequence|legend=0| 7dg, 12, 19g }} | {{Optimal ET sequence|legend=0| 7dg, 12, 19g }} | ||
Badness: 0.022099 | Badness (Smith): 0.022099 | ||
====== 19-limit ====== | ====== 19-limit ====== | ||
| Line 885: | Line 885: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.950 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.950{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 695.725 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 695.725{{c}} | ||
{{Optimal ET sequence|legend=0| 7dgh, 12, 19gh }} | {{Optimal ET sequence|legend=0| 7dgh, 12, 19gh }} | ||
Badness: 0.019904 | Badness (Smith): 0.019904 | ||
==== Meanundec ==== | ==== Meanundec ==== | ||
| Line 900: | Line 900: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 695.620 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 695.620{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.254 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.254{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 12f, 19f }} | {{Optimal ET sequence|legend=0| 7d, 12f, 19f }} | ||
Badness: 0.024243 | Badness (Smith): 0.024243 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 915: | Line 915: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.279 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.279{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.586 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.586{{c}} | ||
{{Optimal ET sequence|legend=0| 7dg, 12f }} | {{Optimal ET sequence|legend=0| 7dg, 12f }} | ||
Badness: 0.021400 | Badness (Smith): 0.021400 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
| Line 930: | Line 930: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.849 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.849{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 698.118 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 698.118{{c}} | ||
{{Optimal ET sequence|legend=0| 7dgh, 12f }} | {{Optimal ET sequence|legend=0| 7dgh, 12f }} | ||
Badness: 0.018996 | Badness (Smith): 0.018996 | ||
=== Meanundeci === | === Meanundeci === | ||
| Line 947: | Line 947: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.702 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.702{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 694.689 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 694.689{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 12e, 19e }} | {{Optimal ET sequence|legend=0| 7d, 12e, 19e }} | ||
Badness: 0.031539 | Badness (Smith): 0.031539 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 962: | Line 962: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.241 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.241{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 694.764 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 694.764{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 12e, 19e }} | {{Optimal ET sequence|legend=0| 7d, 12e, 19e }} | ||
Badness: 0.026288 | Badness (Smith): 0.026288 | ||
=== Bimeantone === | === Bimeantone === | ||
| Line 981: | Line 981: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~63/44 = 600.000, ~3/2 = 696.520 | * CTE: ~63/44 = 600.000{{c}}, ~3/2 = 696.520{{c}} | ||
* POTE: ~63/44 = 600.000, ~3/2 = 696.016 | * POTE: ~63/44 = 600.000{{c}}, ~3/2 = 696.016{{c}} | ||
{{Optimal ET sequence|legend=0| 12, 26de, 38d, 50 }} | {{Optimal ET sequence|legend=0| 12, 26de, 38d, 50 }} | ||
Badness: 0.038122 | Badness (Smith): 0.038122 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 996: | Line 996: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~55/39 = 600.000, ~3/2 = 696.341 | * CTE: ~55/39 = 600.000{{c}}, ~3/2 = 696.341{{c}} | ||
* POTE: ~55/39 = 600.000, ~3/2 = 695.836 | * POTE: ~55/39 = 600.000{{c}}, ~3/2 = 695.836{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 26deff, 38df, 50 }} | {{Optimal ET sequence|legend=0| 12f, 26deff, 38df, 50 }} | ||
Badness: 0.028817 | Badness (Smith): 0.028817 | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
| Line 1,011: | Line 1,011: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~3/2 = 696.353 | * CTE: ~17/12 = 600.000{{c}}, ~3/2 = 696.353{{c}} | ||
* POTE: ~17/12 = 600.000, ~3/2 = 695.783 | * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 695.783{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 38df, 50 }} | {{Optimal ET sequence|legend=0| 12f, 38df, 50 }} | ||
Badness: 0.022666 | Badness (Smith): 0.022666 | ||
==== 19-limit ==== | ==== 19-limit ==== | ||
| Line 1,026: | Line 1,026: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~3/2 = 696.384 | * CTE: ~17/12 = 600.000{{c}}, ~3/2 = 696.384{{c}} | ||
* POTE: ~17/12 = 600.000, ~3/2 = 695.752 | * POTE: ~17/12 = 600.000{{c}}, ~3/2 = 695.752{{c}} | ||
{{Optimal ET sequence|legend=0| 12f, 26deff, 38df, 50 }} | {{Optimal ET sequence|legend=0| 12f, 26deff, 38df, 50 }} | ||
Badness: 0.017785 | Badness (Smith): 0.017785 | ||
=== Trimean === | === Trimean === | ||
| Line 1,045: | Line 1,045: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/10 = 167.707 | * CTE: ~2 = 1200.000{{c}}, ~11/10 = 167.707{{c}} | ||
* POTE: ~2 = 1200.000, ~11/10 = 167.805 | * POTE: ~2 = 1200.000{{c}}, ~11/10 = 167.805{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 36d, 43, 50, 93 }} | {{Optimal ET sequence|legend=0| 7d, 36d, 43, 50, 93 }} | ||
Badness: 0.050729 | Badness (Smith): 0.050729 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,060: | Line 1,060: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/10 = 167.712 | * CTE: ~2 = 1200.000{{c}}, ~11/10 = 167.712{{c}} | ||
* POTE: ~2 = 1200.000, ~11/10 = 167.790 | * POTE: ~2 = 1200.000{{c}}, ~11/10 = 167.790{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 43, 50, 93 }} | {{Optimal ET sequence|legend=0| 7d, 43, 50, 93 }} | ||
Badness: 0.035445 | Badness (Smith): 0.035445 | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
| Line 1,075: | Line 1,075: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/10 = 167.705 | * CTE: ~2 = 1200.000{{c}}, ~11/10 = 167.705{{c}} | ||
* POTE: ~2 = 1200.000, ~11/10 = 167.786 | * POTE: ~2 = 1200.000{{c}}, ~11/10 = 167.786{{c}} | ||
{{Optimal ET sequence|legend=0| 7dg, 43, 50, 93 }} | {{Optimal ET sequence|legend=0| 7dg, 43, 50, 93 }} | ||
Badness: 0.025221 | Badness (Smith): 0.025221 | ||
== Flattone == | == Flattone == | ||
| Line 1,094: | Line 1,094: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 693.552 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 693.552{{c}} | ||
: [[error map]]: {{val| 0.000 -8.403 -12.106 -10.794 }} | : [[error map]]: {{val| 0.000 -8.403 -12.106 -10.794 }} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 693.779 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 693.779{{c}} | ||
: error map: {{val| 0.000 -8.176 -11.197 -12.838 }} | : error map: {{val| 0.000 -8.176 -11.197 -12.838 }} | ||
| Line 1,116: | Line 1,116: | ||
{{Optimal ET sequence|legend=1| 7, 19, 26, 45 }} | {{Optimal ET sequence|legend=1| 7, 19, 26, 45 }} | ||
[[Badness]]: 0.038553 | [[Badness]] (Smith): 0.038553 | ||
=== 11-limit === | === 11-limit === | ||
| Line 1,128: | Line 1,128: | ||
Optimal tuning: | Optimal tuning: | ||
* CTE: ~2 = 1200.000, ~3/2 = 693.251 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 693.251{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 693.126 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 693.126{{c}} | ||
Tuning ranges: | Tuning ranges: | ||
| Line 1,137: | Line 1,137: | ||
{{Optimal ET sequence|legend=0| 7, 19, 26, 45, 71bc, 116bcde }} | {{Optimal ET sequence|legend=0| 7, 19, 26, 45, 71bc, 116bcde }} | ||
Badness: 0.033839 | Badness (Smith): 0.033839 | ||
=== 13-limit === | === 13-limit === | ||
| Line 1,147: | Line 1,147: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 693.029 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 693.029{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 693.058 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 693.058{{c}} | ||
Tuning ranges: | Tuning ranges: | ||
| Line 1,156: | Line 1,156: | ||
{{Optimal ET sequence|legend=0| 7, 19, 26, 45f, 71bcf, 116bcdef }} | {{Optimal ET sequence|legend=0| 7, 19, 26, 45f, 71bcf, 116bcdef }} | ||
Badness: 0.022260 | Badness (Smith): 0.022260 | ||
== Flattertone == | == Flattertone == | ||
| Line 1,170: | Line 1,170: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 692.698 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 692.698{{c}} | ||
: [[error map]]: {{val| 0.000 -9.257 -15.520 +7.047 }} | : [[error map]]: {{val| 0.000 -9.257 -15.520 +7.047 }} | ||
* [[CWE]]: ~2 = 1200.000, ~3/2 = 692.048 | * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 692.048{{c}} | ||
: error map: {{val| 0.000 -9.907 -18.122 -4.012 }} | : error map: {{val| 0.000 -9.907 -18.122 -4.012 }} | ||
{{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }} | {{Optimal ET sequence|legend=1| 7d, 19d, 26, 59bcd, 85bccd }} | ||
[[Badness]]: 0.0961 | [[Badness]] (Smith): 0.0961 | ||
==== 11-limit ==== | ==== 11-limit ==== | ||
| Line 1,189: | Line 1,189: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 692.642 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 692.642{{c}} | ||
* [[CWE]]: ~2 = 1200.000, ~3/2 = 692.042 | * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 692.042{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 19d, 26, 59bcd, 85bccd }} | {{Optimal ET sequence|legend=0| 7d, 19d, 26, 59bcd, 85bccd }} | ||
| Line 1,212: | Line 1,212: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 699.622 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 699.622{{c}} | ||
: [[error map]]: {{val| 0.000 -2.333 +12.173 +31.931 }} | : [[error map]]: {{val| 0.000 -2.333 +12.173 +31.931 }} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 701.573 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.573{{c}} | ||
: error map: {{val| 0.000 -0.382 +19.979 +28.028 }} | : error map: {{val| 0.000 -0.382 +19.979 +28.028 }} | ||
| Line 1,224: | Line 1,224: | ||
{{Optimal ET sequence|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }} | {{Optimal ET sequence|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }} | ||
[[Badness]]: 0.020690 | [[Badness]] (Smith): 0.020690 | ||
=== 11-limit === | === 11-limit === | ||
| Line 1,238: | Line 1,238: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 703.334 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 703.334{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 703.254 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 703.254{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 12, 17c, 29cde }} | {{Optimal ET sequence|legend=0| 5, 12, 17c, 29cde }} | ||
Badness: 0.024180 | Badness (Smith): 0.024180 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,253: | Line 1,253: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 704.847 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 704.847{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 703.636 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 703.636{{c}} | ||
Tuning ranges: | Tuning ranges: | ||
| Line 1,262: | Line 1,262: | ||
{{Optimal ET sequence|legend=0|12f, 17c, 29cdef }} | {{Optimal ET sequence|legend=0|12f, 17c, 29cdef }} | ||
Badness: 0.024108 | Badness (Smith): 0.024108 | ||
==== Dominion ==== | ==== Dominion ==== | ||
| Line 1,272: | Line 1,272: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 704.034 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 704.034{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 704.905 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 704.905{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 12, 17c, 46cde }} | {{Optimal ET sequence|legend=0| 5, 12, 17c, 46cde }} | ||
Badness: 0.027295 | Badness (Smith): 0.027295 | ||
=== Domineering === | === Domineering === | ||
| Line 1,287: | Line 1,287: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.240 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.240{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 698.776 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 698.776{{c}} | ||
{{Optimal ET sequence|legend=0| 5e, 7, 12, 19d, 43de }} | {{Optimal ET sequence|legend=0| 5e, 7, 12, 19d, 43de }} | ||
Badness: 0.021978 | Badness (Smith): 0.021978 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,302: | Line 1,302: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 695.315 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 695.315{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 695.762 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 695.762{{c}} | ||
{{Optimal ET sequence|legend=0| 5ef, 7, 12, 19d, 31def }} | {{Optimal ET sequence|legend=0| 5ef, 7, 12, 19d, 31def }} | ||
Badness: 0.027039 | Badness (Smith): 0.027039 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 1,317: | Line 1,317: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 695.894 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 695.894{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.115 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.115{{c}} | ||
{{Optimal ET sequence|legend=0| 5ef, 7, 12, 19d, 31def }} | {{Optimal ET sequence|legend=0| 5ef, 7, 12, 19d, 31def }} | ||
Badness: 0.024539 | Badness (Smith): 0.024539 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
| Line 1,332: | Line 1,332: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.139 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.139{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.217 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.217{{c}} | ||
{{Optimal ET sequence|legend=0| 5ef, 7, 12, 19d, 31def }} | {{Optimal ET sequence|legend=0| 5ef, 7, 12, 19d, 31def }} | ||
Badness: 0.020398 | Badness (Smith): 0.020398 | ||
==== Dominatrix ==== | ==== Dominatrix ==== | ||
| Line 1,347: | Line 1,347: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 694.840 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 694.840{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 698.544 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 698.544{{c}} | ||
{{Optimal ET sequence|legend=0| 5e, 7, 12f, 19df }} | {{Optimal ET sequence|legend=0| 5e, 7, 12f, 19df }} | ||
Badness: 0.018289 | Badness (Smith): 0.018289 | ||
=== Domination === | === Domination === | ||
| Line 1,362: | Line 1,362: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 703.268 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 703.268{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 705.004 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 705.004{{c}} | ||
{{Optimal ET sequence|legend=0| 5e, 12e, 17c, 46cd }} | {{Optimal ET sequence|legend=0| 5e, 12e, 17c, 46cd }} | ||
Badness: 0.036562 | Badness (Smith): 0.036562 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,377: | Line 1,377: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 703.719 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 703.719{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 705.496 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 705.496{{c}} | ||
{{Optimal ET sequence|legend=0| 5e, 12e, 17c }} | {{Optimal ET sequence|legend=0| 5e, 12e, 17c }} | ||
Badness: 0.027435 | Badness (Smith): 0.027435 | ||
=== Arnold === | === Arnold === | ||
| Line 1,392: | Line 1,392: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 698.546 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 698.546{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 698.491 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 698.491{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 7, 12e }} | {{Optimal ET sequence|legend=0| 5, 7, 12e }} | ||
Badness: 0.026141 | Badness (Smith): 0.026141 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,407: | Line 1,407: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 695.929 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 695.929{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.743 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.743{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 7, 12ef, 19def }} | {{Optimal ET sequence|legend=0| 5, 7, 12ef, 19def }} | ||
Badness: 0.023300 | Badness (Smith): 0.023300 | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
| Line 1,422: | Line 1,422: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.683 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.683{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.978 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.978{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 7, 12ef, 19def }} | {{Optimal ET sequence|legend=0| 5, 7, 12ef, 19def }} | ||
Badness: 0.024535 | Badness (Smith): 0.024535 | ||
==== 19-limit ==== | ==== 19-limit ==== | ||
| Line 1,437: | Line 1,437: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 696.996 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.996{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 697.068 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.068{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 7, 12ef, 19def }} | {{Optimal ET sequence|legend=0| 5, 7, 12ef, 19def }} | ||
Badness: 0.021098 | Badness (Smith): 0.021098 | ||
== Sharptone == | == Sharptone == | ||
| Line 1,456: | Line 1,456: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.732 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.732{{c}} | ||
: [[error map]]: {{val| 0.000 +1.777 +28.614 -57.630 }} | : [[error map]]: {{val| 0.000 +1.777 +28.614 -57.630 }} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 700.140 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.140{{c}} | ||
: error map: {{val| 0.000 -1.815 +14.245 -68.407 }} | : error map: {{val| 0.000 -1.815 +14.245 -68.407 }} | ||
{{Optimal ET sequence|legend=1| 5, 7d, 12d }} | {{Optimal ET sequence|legend=1| 5, 7d, 12d }} | ||
[[Badness]]: 0.024848 | [[Badness]] (Smith): 0.024848 | ||
=== Meanertone === | === Meanertone === | ||
| Line 1,473: | Line 1,473: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 702.730 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 702.730{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 696.615 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.615{{c}} | ||
{{Optimal ET sequence|legend=0| 5, 7d, 12de }} | {{Optimal ET sequence|legend=0| 5, 7d, 12de }} | ||
Badness: 0.025167 | Badness (Smith): 0.025167 | ||
== Supermean == | == Supermean == | ||
| Line 1,488: | Line 1,488: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.811 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 703.811{{c}} | ||
: [[error map]]: {{val| 0.000 +1.856 +28.929 -11.665 }} | : [[error map]]: {{val| 0.000 +1.856 +28.929 -11.665 }} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 704.889 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.889{{c}} | ||
: error map: {{val| 0.000 +2.934 +33.242 +4.507 }} | : error map: {{val| 0.000 +2.934 +33.242 +4.507 }} | ||
{{Optimal ET sequence|legend=1| 5d, 12d, 17c, 29c }} | {{Optimal ET sequence|legend=1| 5d, 12d, 17c, 29c }} | ||
[[Badness]]: 0.134204 | [[Badness]] (Smith): 0.134204 | ||
=== 11-limit === | === 11-limit === | ||
| Line 1,505: | Line 1,505: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 704.016 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 704.016{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 705.096 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 705.096{{c}} | ||
{{Optimal ET sequence|legend=0| 5de, 12de, 17c, 29c }} | {{Optimal ET sequence|legend=0| 5de, 12de, 17c, 29c }} | ||
Badness: 0.063262 | Badness (Smith): 0.063262 | ||
=== 13-limit === | === 13-limit === | ||
| Line 1,520: | Line 1,520: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 704.121 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 704.121{{c}} | ||
* POTE: ~2 = 1200.000, ~3/2 = 705.094 | * POTE: ~2 = 1200.000{{c}}, ~3/2 = 705.094{{c}} | ||
{{Optimal ET sequence|legend=0| 5de, 12de, 17c, 29c }} | {{Optimal ET sequence|legend=0| 5de, 12de, 17c, 29c }} | ||
Badness: 0.040324 | Badness (Smith): 0.040324 | ||
== Mohajira == | == Mohajira == | ||
| Line 1,541: | Line 1,541: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~128/105 = 348.437 | * [[CTE]]: ~2 = 1200.000{{c}}, ~128/105 = 348.437{{c}} | ||
: [[error map]]: {{val| 0.000 -5.080 +1.186 -1.637 }} | : [[error map]]: {{val| 0.000 -5.080 +1.186 -1.637 }} | ||
* [[POTE]]: ~2 = 1200.000, ~128/105 = 348.415 | * [[POTE]]: ~2 = 1200.000{{c}}, ~128/105 = 348.415{{c}} | ||
: error map: {{val| 0.000 -5.125 +1.005 -1.390 }} | : error map: {{val| 0.000 -5.125 +1.005 -1.390 }} | ||
| Line 1,560: | Line 1,560: | ||
{{Optimal ET sequence|legend=1| 7, 24, 31 }} | {{Optimal ET sequence|legend=1| 7, 24, 31 }} | ||
[[Badness]]: 0.055714 | [[Badness]] (Smith): 0.055714 | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
| Line 1,572: | Line 1,572: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/9 = 348.561 | * CTE: ~2 = 1200.000{{c}}, ~11/9 = 348.561{{c}} | ||
* POTE: ~2 = 1200.000, ~11/9 = 348.477 | * POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.477{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 1,586: | Line 1,586: | ||
{{Optimal ET sequence|legend=0| 7, 24, 31 }} | {{Optimal ET sequence|legend=0| 7, 24, 31 }} | ||
Badness: 0.026064 | Badness (Smith): 0.026064 | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
| Line 1,598: | Line 1,598: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/9 = 348.587 | * CTE: ~2 = 1200.000{{c}}, ~11/9 = 348.587{{c}} | ||
* POTE: ~2 = 1200.000, ~11/9 = 348.558 | * POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.558{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 24, 31 }} | {{Optimal ET sequence|legend=0| 7, 24, 31 }} | ||
Badness: 0.023388 | Badness (Smith): 0.023388 | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
| Line 1,615: | Line 1,615: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/9 = 348.735 | * CTE: ~2 = 1200.000{{c}}, ~11/9 = 348.735{{c}} | ||
* POTE: ~2 = 1200.000, ~11/9 = 348.736 | * POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.736{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 24, 31 }} | {{Optimal ET sequence|legend=0| 7, 24, 31 }} | ||
Badness: 0.020576 | Badness (Smith): 0.020576 | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
| Line 1,632: | Line 1,632: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/9 = 348.821 | * CTE: ~2 = 1200.000{{c}}, ~11/9 = 348.821{{c}} | ||
* POTE: ~2 = 1200.000, ~11/9 = 348.810 | * POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.810{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 24, 31, 55 }} | {{Optimal ET sequence|legend=0| 7, 24, 31, 55 }} | ||
Badness: 0.017302 | Badness (Smith): 0.017302 | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
| Line 1,651: | Line 1,651: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~25/21 = 350.352 | * [[CTE]]: ~2 = 1200.000{{c}}, ~25/21 = 350.352{{c}} | ||
: [[error map]]: {{val| 0.000 -1.250 +16.505 -14.245 }} | : [[error map]]: {{val| 0.000 -1.250 +16.505 -14.245 }} | ||
* [[POTE]]: ~2 = 1200.000, ~25/21 = 350.586 | * [[POTE]]: ~2 = 1200.000{{c}}, ~25/21 = 350.586{{c}} | ||
: error map: {{val| 0.000 -0.784 +18.370 -11.214 }} | : error map: {{val| 0.000 -0.784 +18.370 -11.214 }} | ||
{{Optimal ET sequence|legend=1| 7d, 17c, 24 }} | {{Optimal ET sequence|legend=1| 7d, 17c, 24 }} | ||
[[Badness]]: 0.077734 | [[Badness]] (Smith): 0.077734 | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
| Line 1,670: | Line 1,670: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/9 = 350.347 | * CTE: ~2 = 1200.000{{c}}, ~11/9 = 350.347{{c}} | ||
* POTE: ~2 = 1200.000, ~11/9 = 350.565 | * POTE: ~2 = 1200.000{{c}}, ~11/9 = 350.565{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 17c, 24 }} | {{Optimal ET sequence|legend=0| 7d, 17c, 24 }} | ||
| Line 1,677: | Line 1,677: | ||
Badness: 0.036207 | Badness: 0.036207 | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales (Smith): [[mohaha7]], [[mohaha10]] | ||
=== 13-limit === | === 13-limit === | ||
| Line 1,687: | Line 1,687: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/9 = 350.365 | * CTE: ~2 = 1200.000{{c}}, ~11/9 = 350.365{{c}} | ||
* POTE: ~2 = 1200.000, ~11/9 = 350.745 | * POTE: ~2 = 1200.000{{c}}, ~11/9 = 350.745{{c}} | ||
{{Optimal ET sequence|legend=0| 7d, 17c, 24, 41c }} | {{Optimal ET sequence|legend=0| 7d, 17c, 24, 41c }} | ||
| Line 1,694: | Line 1,694: | ||
Badness: 0.028738 | Badness: 0.028738 | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales (Smith): [[mohaha7]], [[mohaha10]] | ||
== Liese == | == Liese == | ||
| Line 1,710: | Line 1,710: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~10/7 = 632.783 | * [[CTE]]: ~2 = 1200.000{{c}}, ~10/7 = 632.783{{c}} | ||
: [[error map]]: {{val| 0.000 -3.606 +7.084 -8.212 }} | : [[error map]]: {{val| 0.000 -3.606 +7.084 -8.212 }} | ||
* [[POTE]]: ~2 = 1200.000, ~10/7 = 632.406 | * [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 632.406{{c}} | ||
: error map: {{val| 0.000 -4.738 +2.554 -12.363 }} | : error map: {{val| 0.000 -4.738 +2.554 -12.363 }} | ||
| Line 1,724: | Line 1,724: | ||
{{Optimal ET sequence|legend=1| 17c, 19, 55, 74d }} | {{Optimal ET sequence|legend=1| 17c, 19, 55, 74d }} | ||
[[Badness]]: 0.046706 | [[Badness]] (Smith): 0.046706 | ||
=== Liesel === | === Liesel === | ||
| Line 1,734: | Line 1,734: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~10/7 = 632.812 | * CTE: ~2 = 1200.000{{c}}, ~10/7 = 632.812{{c}} | ||
* POTE: ~2 = 1200.000, ~10/7 = 633.073 | * POTE: ~2 = 1200.000{{c}}, ~10/7 = 633.073{{c}} | ||
{{Optimal ET sequence|legend=0| 17c, 19, 36 }} | {{Optimal ET sequence|legend=0| 17c, 19, 36 }} | ||
Badness: 0.040721 | Badness (Smith): 0.040721 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,749: | Line 1,749: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~10/7 = 632.925 | * CTE: ~2 = 1200.000{{c}}, ~10/7 = 632.925{{c}} | ||
* POTE: ~2 = 1200.000, ~10/7 = 633.042 | * POTE: ~2 = 1200.000{{c}}, ~10/7 = 633.042{{c}} | ||
{{Optimal ET sequence|legend=0| 17c, 19, 36, 91ceef }} | {{Optimal ET sequence|legend=0| 17c, 19, 36, 91ceef }} | ||
Badness: 0.027304 | Badness (Smith): 0.027304 | ||
=== Elisa === | === Elisa === | ||
| Line 1,764: | Line 1,764: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~10/7 = 633.317 | * CTE: ~2 = 1200.000{{c}}, ~10/7 = 633.317{{c}} | ||
* POTE: ~2 = 1200.000, ~10/7 = 633.061 | * POTE: ~2 = 1200.000{{c}}, ~10/7 = 633.061{{c}} | ||
{{Optimal ET sequence|legend=0| 17c, 19e, 36e }} | {{Optimal ET sequence|legend=0| 17c, 19e, 36e }} | ||
Badness: 0.041592 | Badness (Smith): 0.041592 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,779: | Line 1,779: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~10/7 = 633.370 | * CTE: ~2 = 1200.000{{c}}, ~10/7 = 633.370{{c}} | ||
* POTE: ~2 = 1200.000, ~10/7 = 632.991 | * POTE: ~2 = 1200.000{{c}}, ~10/7 = 632.991{{c}} | ||
{{Optimal ET sequence|legend=0| 17c, 19e, 36e }} | {{Optimal ET sequence|legend=0| 17c, 19e, 36e }} | ||
Badness: 0.026922 | Badness (Smith): 0.026922 | ||
=== Lisa === | === Lisa === | ||
| Line 1,794: | Line 1,794: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~10/7 = 631.981 | * CTE: ~2 = 1200.000{{c}}, ~10/7 = 631.981{{c}} | ||
* POTE: ~2 = 1200.000, ~10/7 = 631.370 | * POTE: ~2 = 1200.000{{c}}, ~10/7 = 631.370{{c}} | ||
{{Optimal ET sequence|legend=0| 17cee, 19 }} | {{Optimal ET sequence|legend=0| 17cee, 19 }} | ||
Badness: 0.054829 | Badness (Smith): 0.054829 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,809: | Line 1,809: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~10/7 = 632.093 | * CTE: ~2 = 1200.000{{c}}, ~10/7 = 632.093{{c}} | ||
* POTE: ~2 = 1200.000, ~10/7 = 631.221 | * POTE: ~2 = 1200.000{{c}}, ~10/7 = 631.221{{c}} | ||
{{Optimal ET sequence|legend=0| 17cee, 19 }} | {{Optimal ET sequence|legend=0| 17cee, 19 }} | ||
Badness: 0.036144 | Badness (Smith): 0.036144 | ||
== Superpine == | == Superpine == | ||
| Line 1,828: | Line 1,828: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~35/32 = 167.279 | * [[CTE]]: ~2 = 1200.000{{c}}, ~35/32 = 167.279{{c}} | ||
: [[error map]]: {{val| 0.000 -3.793 +6.336 +5.804 }} | : [[error map]]: {{val| 0.000 -3.793 +6.336 +5.804 }} | ||
* [[CWE]]: ~2 = 1200.000, ~35/32 = 167.256 | * [[CWE]]: ~2 = 1200.000{{c}}, ~35/32 = 167.256{{c}} | ||
: error map: {{val| 0.000 -3.723 +6.613 +5.503 }} | : error map: {{val| 0.000 -3.723 +6.613 +5.503 }} | ||
{{Optimal ET sequence|legend=1| 7, 36, 43, 79c }} | {{Optimal ET sequence|legend=1| 7, 36, 43, 79c }} | ||
[[Badness]]: 0.137 | [[Badness]] (Smith): 0.137 | ||
=== 11-limit === | === 11-limit === | ||
| Line 1,845: | Line 1,845: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/10 = 167.407 | * CTE: ~2 = 1200.000{{c}}, ~11/10 = 167.407{{c}} | ||
* CWE: ~2 = 1200.000, ~11/10 = 167.338 | * CWE: ~2 = 1200.000{{c}}, ~11/10 = 167.338{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 36, 43 }} | {{Optimal ET sequence|legend=0| 7, 36, 43 }} | ||
Badness: 0.0576 | Badness (Smith): 0.0576 | ||
=== 13-limit === | === 13-limit === | ||
| Line 1,860: | Line 1,860: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~11/10 = 167.427 | * CTE: ~2 = 1200.000{{c}}, ~11/10 = 167.427{{c}} | ||
* CWE: ~2 = 1200.000, ~11/10 = 167.396 | * CWE: ~2 = 1200.000{{c}}, ~11/10 = 167.396{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 36, 43 }} | {{Optimal ET sequence|legend=0| 7, 36, 43 }} | ||
Badness: 0.0368 | Badness (Smith): 0.0368 | ||
== Lithium == | == Lithium == | ||
| Line 1,879: | Line 1,879: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~56/45 = 400.000, ~3/2 = 695.827 (~15/14 = 104.173) | * [[CTE]]: ~56/45 = 400.000{{c}}, ~3/2 = 695.827{{c}} (~15/14 = 104.173{{c}}) | ||
: [[error map]]: {{val| 0.000 -6.128 -3.007 +6.135 }} | : [[error map]]: {{val| 0.000 -6.128 -3.007 +6.135 }} | ||
* [[CWE]]: ~56/45 = 400.000, ~3/2 = 695.141 {~15/14 = 104.859) | * [[CWE]]: ~56/45 = 400.000{{c}}, ~3/2 = 695.141{{c}} {~15/14 = 104.859{{c}}) | ||
: error map: {{val| 0.000 -6.814 -5.748 +2.022 }} | : error map: {{val| 0.000 -6.814 -5.748 +2.022 }} | ||
{{Optimal ET sequence|legend=1| 12, 33cd, 45, 57 }} | {{Optimal ET sequence|legend=1| 12, 33cd, 45, 57 }} | ||
[[Badness]]: 0.0692 | [[Badness]] (Smith): 0.0692 | ||
== Squares == | == Squares == | ||
| Line 1,902: | Line 1,902: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~9/7 = 425.695 | * [[CTE]]: ~2 = 1200.000{{c}}, ~9/7 = 425.695{{c}} | ||
: [[error map]]: {{val| 0.000 -4.734 +2.570 -0.079 }} | : [[error map]]: {{val| 0.000 -4.734 +2.570 -0.079 }} | ||
* [[POTE]]: ~2 = 1200.000, ~9/7 = 425.942 | * [[POTE]]: ~2 = 1200.000{{c}}, ~9/7 = 425.942{{c}} | ||
: error map: {{val| 0.000 -5.721 -1.378 -2.300 }} | : error map: {{val| 0.000 -5.721 -1.378 -2.300 }} | ||
| Line 1,916: | Line 1,916: | ||
{{Optimal ET sequence|legend=1| 14c, 17c, 31, 169b, 200b }} | {{Optimal ET sequence|legend=1| 14c, 17c, 31, 169b, 200b }} | ||
[[Badness]]: 0.045993 | [[Badness]] (Smith): 0.045993 | ||
Scales: [[skwares8]], [[skwares11]], [[skwares14]] | Scales: [[skwares8]], [[skwares11]], [[skwares14]] | ||
| Line 1,928: | Line 1,928: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~9/7 = 425.599 | * CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.599{{c}} | ||
* POTE: ~2 = 1200.000, ~9/7 = 425.957 | * POTE: ~2 = 1200.000{{c}}, ~9/7 = 425.957{{c}} | ||
{{Optimal ET sequence|legend=0| 14c, 17c, 31, 130bee, 169beee }} | {{Optimal ET sequence|legend=0| 14c, 17c, 31, 130bee, 169beee }} | ||
Badness: 0.021636 | Badness (Smith): 0.021636 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 1,943: | Line 1,943: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~9/7 = 425.578 | * CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.578{{c}} | ||
* POTE: ~2 = 1200.000, ~9/7 = 425.550 | * POTE: ~2 = 1200.000{{c}}, ~9/7 = 425.550{{c}} | ||
{{Optimal ET sequence|legend=0| 14c, 17c, 31, 79cf }} | {{Optimal ET sequence|legend=0| 14c, 17c, 31, 79cf }} | ||
Badness: 0.025514 | Badness (Smith): 0.025514 | ||
==== Squad ==== | ==== Squad ==== | ||
| Line 1,958: | Line 1,958: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~9/7 = 425.297 | * CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.297{{c}} | ||
* POTE: ~2 = 1200.000, ~9/7 = 425.752 | * POTE: ~2 = 1200.000{{c}}, ~9/7 = 425.752{{c}} | ||
{{Optimal ET sequence|legend=0| 14cf, 17c, 31f }} | {{Optimal ET sequence|legend=0| 14cf, 17c, 31f }} | ||
Badness: 0.026877 | Badness (Smith): 0.026877 | ||
==== Agora ==== | ==== Agora ==== | ||
| Line 1,973: | Line 1,973: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~9/7 = 425.870 | * CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.870{{c}} | ||
* POTE: ~2 = 1200.000, ~9/7 = 426.276 | * POTE: ~2 = 1200.000{{c}}, ~9/7 = 426.276{{c}} | ||
{{Optimal ET sequence|legend=0| 14cf, 31, 45ef, 76e }} | {{Optimal ET sequence|legend=0| 14cf, 31, 45ef, 76e }} | ||
Badness: 0.024522 | Badness (Smith): 0.024522 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 1,988: | Line 1,988: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~9/7 = 425.919 | * CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.919{{c}} | ||
* POTE: ~2 = 1200.000, ~9/7 = 426.187 | * POTE: ~2 = 1200.000{{c}}, ~9/7 = 426.187{{c}} | ||
{{Optimal ET sequence|legend=0| 14cf, 31 }} | {{Optimal ET sequence|legend=0| 14cf, 31 }} | ||
Badness: 0.022573 | Badness (Smith): 0.022573 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
| Line 2,003: | Line 2,003: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~9/7 = 425.984 | * CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.984{{c}} | ||
* POTE: ~2 = 1200.000, ~9/7 = 426.225 | * POTE: ~2 = 1200.000{{c}}, ~9/7 = 426.225{{c}} | ||
{{Optimal ET sequence|legend=0| 14cf, 31 }} | {{Optimal ET sequence|legend=0| 14cf, 31 }} | ||
Badness: 0.018839 | Badness (Smith): 0.018839 | ||
=== Cuboctahedra === | === Cuboctahedra === | ||
| Line 2,018: | Line 2,018: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~9/7 = 425.899 | * CTE: ~2 = 1200.000{{c}}, ~9/7 = 425.899{{c}} | ||
* POTE: ~2 = 1200.000, ~9/7 = 425.993 | * POTE: ~2 = 1200.000{{c}}, ~9/7 = 425.993{{c}} | ||
{{Optimal ET sequence|legend=0| 31, 107b, 138b, 169be, 200be }} | {{Optimal ET sequence|legend=0| 31, 107b, 138b, 169be, 200be }} | ||
Badness: 0.056826 | Badness (Smith): 0.056826 | ||
== Jerome == | == Jerome == | ||
| Line 2,037: | Line 2,037: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~54/49 = 139.371 | * [[CTE]]: ~2 = 1200.000{{c}}, ~54/49 = 139.371{{c}} | ||
: [[error map]]: {{val| 0.000 -5.098 +1.114 +6.774 }} | : [[error map]]: {{val| 0.000 -5.098 +1.114 +6.774 }} | ||
* [[POTE]]: ~2 = 1200.000, ~54/49 = 139.343 | * [[POTE]]: ~2 = 1200.000{{c}}, ~54/49 = 139.343{{c}} | ||
: error map: {{val| 0.000 -5.238 +0.553 +6.577 }} | : error map: {{val| 0.000 -5.238 +0.553 +6.577 }} | ||
{{Optimal ET sequence|legend=1| 17c, 26, 43 }} | {{Optimal ET sequence|legend=1| 17c, 26, 43 }} | ||
[[Badness]]: 0.108656 | [[Badness]] (Smith): 0.108656 | ||
=== 11-limit === | === 11-limit === | ||
| Line 2,054: | Line 2,054: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~12/11 = 139.349 | * CTE: ~2 = 1200.000{{c}}, ~12/11 = 139.349{{c}} | ||
* POTE: ~2 = 1200.000, ~12/11 = 139.428 | * POTE: ~2 = 1200.000{{c}}, ~12/11 = 139.428{{c}} | ||
{{Optimal ET sequence|legend=0| 17c, 26, 43 }} | {{Optimal ET sequence|legend=0| 17c, 26, 43 }} | ||
Badness: 0.047914 | Badness (Smith): 0.047914 | ||
=== 13-limit === | === 13-limit === | ||
| Line 2,069: | Line 2,069: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~13/12 = 139.369 | * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.369{{c}} | ||
* POTE: ~2 = 1200.000, ~13/12 = 139.387 | * POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.387{{c}} | ||
{{Optimal ET sequence|legend=0| 17c, 26, 43 }} | {{Optimal ET sequence|legend=0| 17c, 26, 43 }} | ||
Badness: 0.029285 | Badness (Smith): 0.029285 | ||
=== 17-limit === | === 17-limit === | ||
| Line 2,084: | Line 2,084: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~13/12 = 139.334 | * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.334{{c}} | ||
* POTE: ~2 = 1200.000, ~13/12 = 139.362 | * POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.362{{c}} | ||
{{Optimal ET sequence|legend=0| 17cg, 26, 43 }} | {{Optimal ET sequence|legend=0| 17cg, 26, 43 }} | ||
Badness: 0.020878 | Badness (Smith): 0.020878 | ||
=== 19-limit === | === 19-limit === | ||
| Line 2,099: | Line 2,099: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~13/12 = 139.296 | * CTE: ~2 = 1200.000{{c}}, ~13/12 = 139.296{{c}} | ||
* POTE: ~2 = 1200.000, ~13/12 = 139.313 | * POTE: ~2 = 1200.000{{c}}, ~13/12 = 139.313{{c}} | ||
{{Optimal ET sequence|legend=0| 17cgh, 26, 43, 69 }} | {{Optimal ET sequence|legend=0| 17cgh, 26, 43, 69 }} | ||
Badness: 0.018229 | Badness (Smith): 0.018229 | ||
== Meantritone == | == Meantritone == | ||
| Line 2,116: | Line 2,116: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~7/5 = 580.568 | * [[CTE]]: ~2 = 1200.000{{c}}, ~7/5 = 580.568{{c}} | ||
: [[error map]]: {{val| 0.000 -4.795 +2.325 +0.381 }} | : [[error map]]: {{val| 0.000 -4.795 +2.325 +0.381 }} | ||
* [[POTE]]: ~2 = 1200.000, ~7/5 = 580.766 | * [[POTE]]: ~2 = 1200.000{{c}}, ~7/5 = 580.766{{c}} | ||
: error map: {{val| 0.000 -5.785 -1.634 -3.380 }} | : error map: {{val| 0.000 -5.785 -1.634 -3.380 }} | ||
{{Optimal ET sequence|legend=1| 29cd, 31, 188bcd, 219bbcd }} | {{Optimal ET sequence|legend=1| 29cd, 31, 188bcd, 219bbcd }} | ||
[[Badness]]: 0.082239 | [[Badness]] (Smith): 0.082239 | ||
=== 11-limit === | === 11-limit === | ||
| Line 2,133: | Line 2,133: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~7/5 = 580.482 | * CTE: ~2 = 1200.000{{c}}, ~7/5 = 580.482{{c}} | ||
* POTE: ~2 = 1200.000, ~7/5 = 580.647 | * POTE: ~2 = 1200.000{{c}}, ~7/5 = 580.647{{c}} | ||
{{Optimal ET sequence|legend=0| 29cde, 31 }} | {{Optimal ET sequence|legend=0| 29cde, 31 }} | ||
Badness: 0.042869 | Badness (Smith): 0.042869 | ||
== Injera == | == Injera == | ||
| Line 2,154: | Line 2,154: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 695.330 (~21/20 = 95.330) | * [[CTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}}) | ||
: [[error map]]: {{val| 0.000 -6.625 -4.993 +12.495 }} | : [[error map]]: {{val| 0.000 -6.625 -4.993 +12.495 }} | ||
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 694.375 (~21/20 = 94.375) | * [[POTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 694.375{{c}} (~21/20 = 94.375{{c}}) | ||
: error map: {{val| 0.000 -7.580 -8.813 +8.675 }} | : error map: {{val| 0.000 -7.580 -8.813 +8.675 }} | ||
| Line 2,166: | Line 2,166: | ||
{{Optimal ET sequence|legend=1| 12, 26, 38 }} | {{Optimal ET sequence|legend=1| 12, 26, 38 }} | ||
[[Badness]]: 0.031130 | [[Badness]] (Smith): 0.031130 | ||
; Music | ; Music | ||
| Line 2,179: | Line 2,179: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~3/2 = 694.098 (~21/20 = 94.098) | * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.098{{c}} (~21/20 = 94.098{{c}}) | ||
* POTE: ~7/5 = 600.000, ~3/2 = 692.840 (~21/20 = 92.840) | * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.840{{c}} (~21/20 = 92.840{{c}}) | ||
Tuning ranges: | Tuning ranges: | ||
| Line 2,188: | Line 2,188: | ||
{{Optimal ET sequence|legend=0| 12, 26 }} | {{Optimal ET sequence|legend=0| 12, 26 }} | ||
Badness: 0.023124 | Badness (Smith): 0.023124 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 2,198: | Line 2,198: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~3/2 = 693.806 (~21/20 = 93.806) | * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.806{{c}} (~21/20 = 93.806{{c}}) | ||
* POTE: ~7/5 = 600.000, ~3/2 = 692.673 (~21/20 = 92.673) | * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.673{{c}} (~21/20 = 92.673{{c}}) | ||
Tuning ranges: | Tuning ranges: | ||
| Line 2,207: | Line 2,207: | ||
{{Optimal ET sequence|legend=0| 12f, 14cf, 26 }} | {{Optimal ET sequence|legend=0| 12f, 14cf, 26 }} | ||
Badness: 0.021565 | Badness (Smith): 0.021565 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
| Line 2,217: | Line 2,217: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~3/2 = 693.852 (~21/20 = 93.852) | * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.852{{c}} (~21/20 = 93.852{{c}}) | ||
* POTE: ~7/5 = 600.000, ~3/2 = 692.487 (~21/20 = 92.487) | * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.487{{c}} (~21/20 = 92.487{{c}}) | ||
{{Optimal ET sequence|legend=0| 12f, 14cf, 26 }} | {{Optimal ET sequence|legend=0| 12f, 14cf, 26 }} | ||
Badness: 0.018358 | Badness (Smith): 0.018358 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
| Line 2,232: | Line 2,232: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~3/2 = 694.031 (~21/20 = 94.031) | * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.031{{c}} (~21/20 = 94.031{{c}}) | ||
* POTE: ~7/5 = 600.000, ~3/2 = 692.299 (~21/20 = 92.299) | * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 692.299{{c}} (~21/20 = 92.299{{c}}) | ||
{{Optimal ET sequence|legend=0| 12f, 14cf, 26 }} | {{Optimal ET sequence|legend=0| 12f, 14cf, 26 }} | ||
Badness: 0.015118 | Badness (Smith): 0.015118 | ||
==== Enjera ==== | ==== Enjera ==== | ||
| Line 2,247: | Line 2,247: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~3/2 = 693.088 (~21/20 = 93.088) | * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 693.088{{c}} (~21/20 = 93.088{{c}}) | ||
* POTE: ~7/5 = 600.000, ~3/2 = 694.121 (~21/20 = 94.121) | * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.121{{c}} (~21/20 = 94.121{{c}}) | ||
{{Optimal ET sequence|legend=0| 10cdeef, 12f }} | {{Optimal ET sequence|legend=0| 10cdeef, 12f }} | ||
Badness: 0.026542 | Badness (Smith): 0.026542 | ||
=== Injerous === | === Injerous === | ||
| Line 2,262: | Line 2,262: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~3/2 = 694.619 (~21/20 = 94.619) | * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 694.619{{c}} (~21/20 = 94.619{{c}}) | ||
* POTE: ~7/5 = 600.000, ~3/2 = 690.548 (~21/20 = 90.548) | * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 690.548{{c}} (~21/20 = 90.548{{c}}) | ||
{{Optimal ET sequence|legend=0| 12e, 14c, 26e, 40cee }} | {{Optimal ET sequence|legend=0| 12e, 14c, 26e, 40cee }} | ||
Badness: 0.038577 | Badness (Smith): 0.038577 | ||
=== Lahoh === | === Lahoh === | ||
| Line 2,277: | Line 2,277: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~3/2 = 695.330 (~21/20 = 95.330) | * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 695.330{{c}} (~21/20 = 95.330{{c}}) | ||
* POTE: ~7/5 = 600.000, ~3/2 = 699.001 (~21/20 = 99.001) | * POTE: ~7/5 = 600.000{{c}}, ~3/2 = 699.001{{c}} (~21/20 = 99.001{{c}}) | ||
{{Optimal ET sequence|legend=0| 10cd, 12 }} | {{Optimal ET sequence|legend=0| 10cd, 12 }} | ||
Badness: 0.043062 | Badness (Smith): 0.043062 | ||
=== Teff === | === Teff === | ||
| Line 2,298: | Line 2,298: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~11/8 = 552.331 (~33/32 = 47.669) | * CTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.331{{c}} (~33/32 = 47.669{{c}}) | ||
* POTE: ~7/5 = 600.000, ~11/8 = 552.530 (~33/32 = 47.470) | * POTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.530{{c}} (~33/32 = 47.470{{c}}) | ||
{{Optimal ET sequence|legend=0| 24d, 26, 50d }} | {{Optimal ET sequence|legend=0| 24d, 26, 50d }} | ||
Badness: 0.070689 | Badness (Smith): 0.070689 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 2,313: | Line 2,313: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~11/8 = 552.297 (~33/32 = 47.703) | * CTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.297{{c}} (~33/32 = 47.703{{c}}) | ||
* POTE: ~7/5 = 600.000, ~11/8 = 552.532 (~33/32 = 47.468) | * POTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.532{{c}} (~33/32 = 47.468{{c}}) | ||
{{Optimal ET sequence|legend=0| 24d, 26, 50d }} | {{Optimal ET sequence|legend=0| 24d, 26, 50d }} | ||
Badness: 0.040047 | Badness (Smith): 0.040047 | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
| Line 2,328: | Line 2,328: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~11/8 = 552.249 (~34/33 = 47.751) | * CTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.249{{c}} (~34/33 = 47.751{{c}}) | ||
* POTE: ~7/5 = 600.000, ~11/8 = 552.656 (~34/33 = 47.344) | * POTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.656{{c}} (~34/33 = 47.344{{c}}) | ||
{{Optimal ET sequence|legend=0| 24d, 26 }} | {{Optimal ET sequence|legend=0| 24d, 26 }} | ||
Badness: 0.029499 | Badness (Smith): 0.029499 | ||
==== 19-limit ==== | ==== 19-limit ==== | ||
| Line 2,343: | Line 2,343: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~7/5 = 600.000, ~11/8 = 552.107 (~34/33 = 47.893) | * CTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.107{{c}} (~34/33 = 47.893{{c}}) | ||
* POTE: ~7/5 = 600.000, ~11/8 = 552.638 (~34/33 = 47.362) | * POTE: ~7/5 = 600.000{{c}}, ~11/8 = 552.638{{c}} (~34/33 = 47.362{{c}}) | ||
{{Optimal ET sequence|legend=0| 24d, 26 }} | {{Optimal ET sequence|legend=0| 24d, 26 }} | ||
Badness: 0.023133 | Badness (Smith): 0.023133 | ||
== Pombe == | == Pombe == | ||
| Line 2,362: | Line 2,362: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~735/512 = 600.000, ~48/35 = 551.845 (~36/35 = 48.155) | * [[CTE]]: ~735/512 = 600.000{{c}}, ~48/35 = 551.845{{c}} (~36/35 = 48.155{{c}}) | ||
: [[error map]]: {{val| 0.000 -5.645 -1.075 -9.600 }} | : [[error map]]: {{val| 0.000 -5.645 -1.075 -9.600 }} | ||
* [[POTE]]: ~735/512 = 600.000, ~48/35 = 552.221 (~36/35 = 48.779) | * [[POTE]]: ~735/512 = 600.000{{c}}, ~48/35 = 552.221{{c}} (~36/35 = 48.779{{c}}) | ||
: error map: {{val| 0.000 -6.229 -3.411 -8.140 }} | : error map: {{val| 0.000 -6.229 -3.411 -8.140 }} | ||
{{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }} | {{Optimal ET sequence|legend=1| 24, 26, 50, 126bcd, 176bcdd, 226bbcdd }} | ||
[[Badness]]: 0.116104 | [[Badness]] (Smith): 0.116104 | ||
=== 11-limit === | === 11-limit === | ||
| Line 2,379: | Line 2,379: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~99/70 = 600.000, ~11/8 = 551.843 (~36/35 = 48.157) | * CTE: ~99/70 = 600.000{{c}}, ~11/8 = 551.843{{c}} (~36/35 = 48.157{{c}}) | ||
* POTE: ~99/70 = 600.000, ~11/8 = 552.093 (~36/35 = 47.907) | * POTE: ~99/70 = 600.000{{c}}, ~11/8 = 552.093{{c}} (~36/35 = 47.907{{c}}) | ||
{{Optimal ET sequence|legend=0| 24, 26, 50 }} | {{Optimal ET sequence|legend=0| 24, 26, 50 }} | ||
Badness: 0.052099 | Badness (Smith): 0.052099 | ||
=== 13-limit === | === 13-limit === | ||
| Line 2,394: | Line 2,394: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~99/70 = 600.000, ~11/8 = 551.848 (~36/35 = 48.152) | * CTE: ~99/70 = 600.000{{c}}, ~11/8 = 551.848{{c}} (~36/35 = 48.152{{c}}) | ||
* POTE: ~99/70 = 600.000, ~11/8 = 552.150 (~36/35 = 47.850) | * POTE: ~99/70 = 600.000{{c}}, ~11/8 = 552.150{{c}} (~36/35 = 47.850{{c}}) | ||
{{Optimal ET sequence|legend=0| 24, 26, 50 }} | {{Optimal ET sequence|legend=0| 24, 26, 50 }} | ||
Badness: 0.031039 | Badness (Smith): 0.031039 | ||
=== 17-limit === | === 17-limit === | ||
| Line 2,409: | Line 2,409: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~11/8 = 551.793 (~36/35 = 48.207) | * CTE: ~17/12 = 600.000{{c}}, ~11/8 = 551.793{{c}} (~36/35 = 48.207{{c}}) | ||
* POTE: ~17/12 = 600.000, ~11/8 = 552.158 (~36/35 = 47.842) | * POTE: ~17/12 = 600.000{{c}}, ~11/8 = 552.158{{c}} (~36/35 = 47.842{{c}}) | ||
{{Optimal ET sequence|legend=0| 24, 26, 50 }} | {{Optimal ET sequence|legend=0| 24, 26, 50 }} | ||
Badness: 0.021260 | Badness (Smith): 0.021260 | ||
=== 19-limit === | === 19-limit === | ||
| Line 2,424: | Line 2,424: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~11/8 = 551.660 (~36/35 = 48.340) | * CTE: ~17/12 = 600.000{{c}}, ~11/8 = 551.660{{c}} (~36/35 = 48.340{{c}}) | ||
* POTE: ~17/12 = 600.000, ~11/8 = 552.120 (~36/35 = 47.880) | * POTE: ~17/12 = 600.000{{c}}, ~11/8 = 552.120{{c}} (~36/35 = 47.880{{c}}) | ||
{{Optimal ET sequence|legend=0| 24, 26, 50 }} | {{Optimal ET sequence|legend=0| 24, 26, 50 }} | ||
Badness: 0.016548 | Badness (Smith): 0.016548 | ||
== Orphic == | == Orphic == | ||
| Line 2,441: | Line 2,441: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2401/1728 = 600.000, ~343/288 = 324.275 (~7/6 = 275.725) | * [[CTE]]: ~2401/1728 = 600.000{{c}}, ~343/288 = 324.275{{c}} (~7/6 = 275.725{{c}}) | ||
: [[error map]]: {{val| 0.000 -4.854 +2.091 +4.000 }} | : [[error map]]: {{val| 0.000 -4.854 +2.091 +4.000 }} | ||
* [[POTE]]: ~2401/1728 = 600.000, ~343/288 = 324.206 (~7/6 = 275.794) | * [[POTE]]: ~2401/1728 = 600.000{{c}}, ~343/288 = 324.206{{c}} (~7/6 = 275.794{{c}}) | ||
: error map: {{val| 0.000 -5.131 +0.983 +3.792 }} | : error map: {{val| 0.000 -5.131 +0.983 +3.792 }} | ||
{{Optimal ET sequence|legend=1| 26, 48c, 74 }} | {{Optimal ET sequence|legend=1| 26, 48c, 74 }} | ||
[[Badness]]: 0.258825 | [[Badness]] (Smith): 0.258825 | ||
=== 11-limit === | === 11-limit === | ||
| Line 2,458: | Line 2,458: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~363/256 = 600.000, ~77/64 = 324.276 (~7/6 = 275.724) | * CTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.276{{c}} (~7/6 = 275.724{{c}}) | ||
* POTE: ~363/256 = 600.000, ~77/64 = 324.238 (~7/6 = 275.762) | * POTE: ~363/256 = 600.000{{c}}, ~77/64 = 324.238{{c}} (~7/6 = 275.762{{c}}) | ||
{{Optimal ET sequence|legend=0| 26, 48c, 74 }} | {{Optimal ET sequence|legend=0| 26, 48c, 74 }} | ||
Badness: 0.101499 | Badness (Smith): 0.101499 | ||
=== 13-limit === | === 13-limit === | ||
| Line 2,473: | Line 2,473: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~55/39 = 600.000, ~77/64 = 324.250 (~7/6 = 275.750) | * CTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.250{{c}} (~7/6 = 275.750{{c}}) | ||
* POTE: ~55/39 = 600.000, ~77/64 = 324.226 (~7/6 = 275.774) | * POTE: ~55/39 = 600.000{{c}}, ~77/64 = 324.226{{c}} (~7/6 = 275.774{{c}}) | ||
{{Optimal ET sequence|legend=0| 26, 48c, 74 }} | {{Optimal ET sequence|legend=0| 26, 48c, 74 }} | ||
Badness: 0.053482 | Badness (Smith): 0.053482 | ||
== Cloudtone == | == Cloudtone == | ||
| Line 2,492: | Line 2,492: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~8/7 = 240.000, ~3/2 = 697.214 (~49/48 = 22.786) | * [[CTE]]: ~8/7 = 240.000{{c}}, ~3/2 = 697.214{{c}} (~49/48 = 22.786{{c}}) | ||
: [[error map]]: {{val| 0.000 -4.741 +2.544 -8.826 }} | : [[error map]]: {{val| 0.000 -4.741 +2.544 -8.826 }} | ||
* [[POTE]]: ~8/7 = 240.000, ~3/2 = 695.720 (~49/48 = 24.280) | * [[POTE]]: ~8/7 = 240.000{{c}}, ~3/2 = 695.720{{c}} (~49/48 = 24.280{{c}}) | ||
: error map: {{val| 0.000 -6.235 -3.435 -8.826 }} | : error map: {{val| 0.000 -6.235 -3.435 -8.826 }} | ||
{{Optimal ET sequence|legend=1| 5, 40c, 45, 50 }} | {{Optimal ET sequence|legend=1| 5, 40c, 45, 50 }} | ||
[[Badness]]: 0.102256 | [[Badness]] (Smith): 0.102256 | ||
=== 11-limit === | === 11-limit === | ||
| Line 2,509: | Line 2,509: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~8/7 = 240.000, ~3/2 = 697.034 (~56/55 = 22.966) | * CTE: ~8/7 = 240.000{{c}}, ~3/2 = 697.034{{c}} (~56/55 = 22.966{{c}}) | ||
* POTE: ~8/7 = 240.000, ~3/2 = 696.536 (~56/55 = 23.464) | * POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.536{{c}} (~56/55 = 23.464{{c}}) | ||
{{Optimal ET sequence|legend=0| 5, 45, 50 }} | {{Optimal ET sequence|legend=0| 5, 45, 50 }} | ||
Badness: 0.070378 | Badness (Smith): 0.070378 | ||
=== 13-limit === | === 13-limit === | ||
| Line 2,524: | Line 2,524: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~8/7 = 240.000, ~3/2 = 696.749 (~91/90 = 23.251) | * CTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.749{{c}} (~91/90 = 23.251{{c}}) | ||
* POTE: ~8/7 = 240.000, ~3/2 = 696.162 (~91/90 = 23.838) | * POTE: ~8/7 = 240.000{{c}}, ~3/2 = 696.162{{c}} (~91/90 = 23.838{{c}}) | ||
{{Optimal ET sequence|legend=0| 5, 45f, 50 }} | {{Optimal ET sequence|legend=0| 5, 45f, 50 }} | ||
Badness: 0.048829 | Badness (Smith): 0.048829 | ||
== Subgroup extensions == | == Subgroup extensions == | ||
| Line 2,546: | Line 2,546: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 697.681 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.681{{c}} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 697.867 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.867{{c}} | ||
{{Optimal ET sequence|legend=1| 5, 7, 12, 31, 43 }} | {{Optimal ET sequence|legend=1| 5, 7, 12, 31, 43 }} | ||
| Line 2,565: | Line 2,565: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 694.700 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 694.700{{c}} | ||
* [[CWE]]: ~2 = 1200.000, ~3/2 = 693.908 | * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 693.908{{c}} | ||
{{Optimal ET sequence|legend=1| 7, 12, 19, 26, 45 }} | {{Optimal ET sequence|legend=1| 7, 12, 19, 26, 45 }} | ||
[[Badness]]: 0.0104 | [[Badness]] (Smith): 0.0104 | ||
==== 2.3.5.11.13 subgroup ==== | ==== 2.3.5.11.13 subgroup ==== | ||
| Line 2,582: | Line 2,582: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 693.951 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 693.951{{c}} | ||
* CTE: ~2 = 1200.000, ~3/2 = 693.087 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 693.087{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 12, 19, 26, 45f }} | {{Optimal ET sequence|legend=0| 7, 12, 19, 26, 45f }} | ||
Badness: 0.0141 | Badness (Smith): 0.0141 | ||
=== Dequarter === | === Dequarter === | ||
| Line 2,599: | Line 2,599: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 696.039 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.039{{c}} | ||
* [[CWE]]: ~2 = 1200.000, ~3/2 = 693.121 | * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 693.121{{c}} | ||
{{Optimal ET sequence|legend=1| 5, 7, 19e, 26e }} | {{Optimal ET sequence|legend=1| 5, 7, 19e, 26e }} | ||
[[Badness]]: 0.0145 | [[Badness]] (Smith): 0.0145 | ||
==== Dreamtone ==== | ==== Dreamtone ==== | ||
| Line 2,616: | Line 2,616: | ||
Optimal tunings: | Optimal tunings: | ||
* CTE: ~2 = 1200.000, ~3/2 = 689.699 | * CTE: ~2 = 1200.000{{c}}, ~3/2 = 689.699{{c}} | ||
* CWE: ~2 = 1200.000, ~3/2 = 690.183 | * CWE: ~2 = 1200.000{{c}}, ~3/2 = 690.183{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 19eff, 26eff, 33ceeff, 40ceeff }} | {{Optimal ET sequence|legend=0| 7, 19eff, 26eff, 33ceeff, 40ceeff }} | ||
Badness: 0.0353 | Badness (Smith): 0.0353 | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||