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Meantone family: Difference between revisions

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- impractical 17- and 19-limit extensions (see talk)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
Line 22: Line 22:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.214{{c}}
* [[WE]]: ~2 = 1201.3906{{c}}, ~3/2 = 697.0455{{c}}
: [[error map]]: {{val| 0 -4.741 +2.544 }}
: [[error map]]: {{val| +1.391 -3.519 +1.868 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6512{{c}}
: error map: {{val| 0.000 -5.304 +0.291 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.214{{c}}
: error map: {{val| 0.000 -4.741 +2.544 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.239{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.239{{c}}
: [[error map]]: {{val| 0 -5.716 -1.359 }}
: error map: {{val| 0.000 -5.716 -1.359 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 37: Line 41:
{{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]] (Smith): 0.007381
[[Badness]] (Sintel): 0.173


=== Overview to extensions ===
=== Overview to extensions ===
Line 95: Line 99:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.952{{c}}
* [[WE]]: ~2 = 1201.2358{{c}}, ~3/2 = 697.2122{{c}}
: [[error map]]: {{val| +1.236 -3.507 +2.535 -0.412 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6562{{c}}
: error map: {{val| 0.000 -5.299 +0.311 -2.264 }}
<!-- * [[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{{c}}, ~3/2 = 696.495{{c}}
* [[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 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 114: Line 122:
{{Optimal ET sequence|legend=1| 12, 19, 31, 81, 112b, 143b }}
{{Optimal ET sequence|legend=1| 12, 19, 31, 81, 112b, 143b }}


[[Badness]] (Smith): 0.013707
[[Badness]] (Sintel): 0.347


=== Undecimal meantone (huygens) ===
=== Undecimal meantone (huygens) ===
Line 129: Line 137:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.168{{c}}
* WE: ~2 = 1200.7636{{c}}, ~3/2 = 697.4122{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.967{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.0315{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.168{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.967{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 145: Line 155:
{{Optimal ET sequence|legend=0| 12, 19e, 31, 105, 136b }}
{{Optimal ET sequence|legend=0| 12, 19e, 31, 105, 136b }}


Badness (Smith): 0.017027
Badness (Sintel): 0.563


; Music
; Music
Line 158: Line 168:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.855{{c}}
* WE: ~2 = 1200.8149{{c}}, ~3/2 = 697.1155{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.642{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.7085{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.855{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.642{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 167: Line 179:
{{Optimal ET sequence|legend=0| 12f, 19e, 31 }}
{{Optimal ET sequence|legend=0| 12f, 19e, 31 }}


Badness (Smith): 0.018048
Badness (Sintel): 0.746


===== Meantonic =====
===== Meantonic =====
Line 179: Line 191:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.649{{c}}
* WE: ~2 = 1201.2376{{c}}, ~3/2 = 697.0954{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.377{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.4563{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.649{{c}}
* 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 (Smith): 0.019037
Badness (Sintel): 0.970


====== 19-limit ======
====== 19-limit ======
Line 194: Line 208:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.555{{c}}
* WE: ~2 = 1201.4134{{c}}, ~3/2 = 697.0933{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.273{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.3526{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.555{{c}}
* 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 (Smith): 0.017846
Badness (Sintel): 1.09


===== Huygens =====
===== Huygens =====
Line 211: Line 227:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.908{{c}}
* WE: ~2 = 1199.5548{{c}}, ~3/2 = 696.7449{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.003{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.9823{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.908{{c}}
* 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 (Smith): 0.019982
Badness (Sintel): 1.02


====== 19-limit ======
====== 19-limit ======
Line 226: Line 244:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.931{{c}}
* WE: ~2 = 1199.0408{{c}}, ~3/2 = 696.5824{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.140{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.1061{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.931{{c}}
* 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 (Smith): 0.018047
Badness (Sintel): 1.10


==== Grosstone ====
==== Grosstone ====
Line 243: Line 263:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.258{{c}}
* WE: ~2 = 1199.9389{{c}}, ~3/2 = 697.2282{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.264{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.2627{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.258{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.264{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 256: Line 278:
{{Optimal ET sequence|legend=0| 12, 31, 43, 74 }}
{{Optimal ET sequence|legend=0| 12, 31, 43, 74 }}


Badness (Smith): 0.025899
Badness (Sintel): 1.07


===== 17-limit =====
===== 17-limit =====
Line 266: Line 288:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.300{{c}}
* WE: ~2 = 1199.5811{{c}}, ~3/2 = 697.0918{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.335{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.3303{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.300{{c}}
* 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 (Smith): 0.020889
Badness (Sintel): 1.06


===== 19-limit =====
===== 19-limit =====
Line 281: Line 305:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.327{{c}}
* WE: ~2 = 1199.2931{{c}}, ~3/2 = 696.9690{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.380{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.3736{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.327{{c}}
* 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 (Smith): 0.017611
Badness (Sintel): 1.07


==== Meridetone ====
==== Meridetone ====
Line 298: Line 324:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.516{{c}}
* WE: ~2 = 1199.9122{{c}}, ~3/2 = 697.4779{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.529{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.5241{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.516{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.529{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 307: Line 335:
{{Optimal ET sequence|legend=0| 12f, 31f, 43 }}
{{Optimal ET sequence|legend=0| 12f, 31f, 43 }}


Badness (Smith): 0.026421
Badness (Sintel): 1.09


===== Meridetonic =====
===== Meridetonic =====
Line 317: Line 345:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.508{{c}}
* WE: ~2 = 1199.9428{{c}}, ~3/2 = 697.4804{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.514{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.5113{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.508{{c}}
* 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 (Smith): 0.027706
Badness (Sintel): 1.41


====== 19-limit ======
====== 19-limit ======
Line 332: Line 362:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.485{{c}}
* WE: ~2 = 1200.0089{{c}}, ~3/2 = 697.4864{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.481{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.4815{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.485{{c}}
* 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 (Smith): 0.025315
Badness (Sintel): 1.54


===== Sauveuric =====
===== Sauveuric =====
Line 347: Line 379:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.538{{c}}
* WE: ~2 = 1199.3793{{c}}, ~3/2 = 697.2833{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.644{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.6222{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.538{{c}}
* 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 (Smith): 0.023881
Badness (Sintel): 1.22


====== 19-limit ======
====== 19-limit ======
Line 362: Line 396:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.555{{c}}
* WE: ~2 = 1199.0260{{c}}, ~3/2 = 697.1486{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 697.715{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 697.6887{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 697.555{{c}}
* 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 (Smith): 0.020540
Badness (Sintel): 1.25


==== Hemimeantone ====
==== Hemimeantone ====
Line 379: Line 415:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~26/15 = 948.611{{c}}
* WE: ~2 = 1201.0387{{c}}, ~26/15 = 949.2863{{c}}
* POTE: ~2 = 1200.000{{c}}, ~26/15 = 948.465{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 948.5065{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~26/15 = 948.611{{c}}
* 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 (Smith): 0.031433
Badness (Sintel): 1.30


===== 17-limit =====
===== 17-limit =====
Line 394: Line 432:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~26/15 = 948.617{{c}}
* WE: ~2 = 1201.0270{{c}}, ~26/15 = 949.2892{{c}}
* POTE: ~2 = 1200.000{{c}}, ~26/15 = 948.477{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 948.5169{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~26/15 = 948.617{{c}}
* 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 (Smith): 0.023380
Badness (Sintel): 1.19


===== 19-limit =====
===== 19-limit =====
Line 409: Line 449:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~19/11 = 948.609{{c}}
* WE: ~2 = 1201.0339{{c}}, ~19/11 = 949.2902{{c}}
* POTE: ~2 = 1200.000{{c}}, ~19/11 = 948.473{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~19/11 = 948.5111{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~19/11 = 948.609{{c}}
* 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 (Smith): 0.018952
Badness (Sintel): 1.15


==== Semimeantone ====
==== Semimeantone ====
Line 426: Line 468:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 600.000{{c}}, ~3/2 = 697.168{{c}}
* WE: ~55/39 = 600.3606{{c}}, ~3/2 = 697.4241{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~3/2 = 697.005{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~3/2 = 697.0545{{c}}
<!-- * CTE: ~55/39 = 600.000{{c}}, ~3/2 = 697.168{{c}}
* 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, …, 50eff, 62, 136b }}


Badness (Smith): 0.040668
Badness (Sintel): 1.68


===== 17-limit =====
===== 17-limit =====
Line 441: Line 485:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~3/2 = 697.174{{c}}
* WE: ~17/12 = 600.5426{{c}}, ~3/2 = 697.5571{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~3/2 = 696.927{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 696.9858{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~3/2 = 697.174{{c}}
* 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 (Smith): 0.031491
Badness (Sintel): 1.60


===== 19-limit =====
===== 19-limit =====
Line 456: Line 502:


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~3/2 = 697.187{{c}}
* WE: ~17/12 = 600.5959{{c}}, ~3/2 = 697.5985{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~3/2 = 696.906{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 696.9638{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~3/2 = 697.187{{c}}
* 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 (Smith): 0.024206
Badness (Sintel): 1.47


=== Meanpop ===
=== Meanpop ===
Line 477: Line 525:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.531{{c}}
* WE: ~2 = 1201.3464{{c}}, ~3/2 = 697.2159{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.434{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.4509{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.531{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.434{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 493: Line 543:
{{Optimal ET sequence|legend=0| 12e, 19, 31, 81, 112b }}
{{Optimal ET sequence|legend=0| 12e, 19, 31, 81, 112b }}


Badness (Smith): 0.021543
Badness (Sintel): 0.712


; Music
; Music
Line 507: Line 557:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.356{{c}}
* WE: ~2 = 1201.0765{{c}}, ~3/2 = 696.8361{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.211{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.2347{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.356{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.211{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 520: Line 572:
{{Optimal ET sequence|legend=0| 19, 31, 50, 81 }}
{{Optimal ET sequence|legend=0| 19, 31, 50, 81 }}


Badness (Smith): 0.020883
Badness (Sintel): 0.863


===== Meanpoppic =====
===== Meanpoppic =====
Line 530: Line 582:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.351{{c}}
* WE: ~2 = 1201.0727{{c}}, ~3/2 = 696.8168{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.194{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.2195{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.351{{c}}
* 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 (Smith): 0.019953
Badness (Sintel): 1.02


====== 19-limit ======
====== 19-limit ======
Line 545: Line 599:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.347{{c}}
* WE: ~2 = 1201.0719{{c}}, ~3/2 = 696.8101{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.188{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.2137{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.347{{c}}
* 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 (Smith): 0.017791
Badness (Sintel): 1.08


===== Meanpoid =====
===== Meanpoid =====
Line 560: Line 616:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.439{{c}}
* WE: ~2 = 1200.2768{{c}}, ~3/2 = 696.5683{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.408{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.4114{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.439{{c}}
* 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 (Smith): 0.022870
Badness (Sintel): 1.17


====== 19-limit ======
====== 19-limit ======
Line 575: Line 633:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.484{{c}}
* WE: ~2 = 1199.7905{{c}}, ~3/2 = 696.3779{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.499{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.4973{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.484{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.499{{c}} -->


{{Optimal ET sequence|legend=0| 12ef, 19, 31 }}
{{Optimal ET sequence|legend=0| 19, 31 }}


Badness (Smith): 0.020488
Badness (Sintel): 1.25


==== Meanplop ====
==== Meanplop ====
Line 590: Line 650:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.283{{c}}
* WE: ~2 = 1202.3237{{c}}, ~3/2 = 697.5502{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.202{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.2135{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.283{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.202{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 599: Line 661:
{{Optimal ET sequence|legend=0| 12e, 19, 31f }}
{{Optimal ET sequence|legend=0| 12e, 19, 31f }}


Badness (Smith): 0.027666
Badness (Sintel): 1.14


===== 17-limit =====
===== 17-limit =====
Line 609: Line 671:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.407{{c}}
* WE: ~2 = 1201.4737{{c}}, ~3/2 = 697.2690{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.414{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.4129{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.407{{c}}
* 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 (Smith): 0.026836
Badness (Sintel): 1.37


===== 19-limit =====
===== 19-limit =====
Line 624: Line 688:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.473{{c}}
* WE: ~2 = 1200.8839{{c}}, ~3/2 = 697.0104{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 696.497{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.4949{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 696.473{{c}}
* 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 (Smith): 0.023540
Badness (Sintel): 1.43


=== Meanenneadecal ===
=== Meanenneadecal ===
Retrieved from "https://en.xen.wiki/w/Meantone_family"