Gamelismic clan: Difference between revisions

Line 1,088:

Valentine tempers out [[126/125]] and [[6144/6125]] as well as 1029/1024. It has a generator of ~21/20, three of which make the slendric generator ~8/7. 21/20 can be stripped of its 2 and taken as 3 × 7/5. In this respect it resembles miracle, with a generator of 3 × 5/7, and casablanca, with a generator of 5 × 7/3. These three generators are the simplest in terms of the relationship of tetrads in the [[The Seven Limit Symmetrical Lattices|lattice of 7-limit tetrads]]. Valentine can also be described as the {{nowrap|31 & 46}} temperament, and [[77edo]], [[108edo]], or [[185edo]] make for excellent tunings, which also happen to be excellent tunings for [[starling]], the rank-3 temperament tempering out 126/125. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)1/9 as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit ~~as {{multival| 9 5 -3 7 … }}~~, tempering out 121/120 and 441/440; 46edo has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, (11/7)1/10.

Valentine tempers out [[126/125]] and [[6144/6125]] as well as 1029/1024. It has a generator of ~21/20, three of which make the slendric generator ~8/7. 21/20 can be stripped of its 2 and taken as 3 × 7/5. In this respect it resembles miracle, with a generator of 3 × 5/7, and casablanca, with a generator of 5 × 7/3. These three generators are the simplest in terms of the relationship of tetrads in the [[The Seven Limit Symmetrical Lattices|lattice of 7-limit tetrads]]. Valentine can also be described as the {{nowrap|31 & 46}} temperament, and [[77edo]], [[108edo]], or [[185edo]] make for excellent tunings, which also happen to be excellent tunings for [[starling]], the rank-3 temperament tempering out 126/125. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)1/9 as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit, tempering out 121/120 and 441/440; 46edo has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, (11/7)1/10.

[[Subgroup]]: 2.3.5

Line 1,096:

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~25/24 = 78.039

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~25/24 = 78.039

: [[error map]]: {{val| 0.000 +0.397 +3.882 }}

* [[POTE]]: ~2 = 1200.000, ~25/24 = 78.039

: error map: {{val| 0.000 -0.829 +3.201 }}

[[Badness]]: 0.122765

[[Badness]] (Smith): 0.122765

=== 7-limit ===

Line 1,111:

Line 1,115:

: mapping generators: ~2, ~21/20

~~Wedgie:~~ {{~~multival~~| 9 5 -3 -13 -30 -21 }}

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~21/20 = 77.864

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~21/20 = 77.878

: [[error map]]: {{val| 0.000 -1.057 +3.074 -2.459 }}

* [[POTE]]: ~2 = 1200.000, ~21/20 = 77.864

: error map: {{val| 0.000 -1.181 +3.005 -2.417 }}

[[Minimax tuning]]:

* [[7-odd-limit]]: ~21/20 = {{monzo| 1/6 1/12 0 -1/12 }}

: [{{monzo| 1 0 0 0 ~~}}, {{monzo~~| 5/2 3/4 0 -3/4 ~~}}, {{monzo~~| 17/6 5/12 0 -5/12 ~~}}, {{monzo~~| 5/2 -1/4 0 1/4 }}]

: {{monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 17/6 5/12 0 -5/12 | 5/2 -1/4 0 1/4 }}

: [[~~Eigenmonzo~~ basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3

: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3

* [[9-odd-limit]]: ~21/20 = {{monzo| 1/21 2/21 0 -1/21}}

: [{{monzo| 1 0 0 0 ~~}}, {{monzo~~| 10/7 6/7 0 -3/7 ~~}}, {{monzo~~| 47/21 10/21 0 -5/21 ~~}}, {{monzo~~| 20/7 -2/7 0 1/7 }}]

: {{monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 47/21 10/21 0 -5/21 | 20/7 -2/7 0 1/7 }}

: [[~~Eigenmonzo~~ basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7

: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7

[[Algebraic generator]]: smaller root of ''x''2 - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.

Line 1,127:

Line 1,135:

[[Badness]]: 0.031056

[[Badness]] (Smith): 0.031056

=== 11-limit ===

Line 1,140:

Line 1,148:

Wedgie: {{multival| 9 5 -3 7 -13 -30 -20 -21 -1 30 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~21/20 = 77.881

Optimal tunings:

* CTE: ~2 = 1200.000, ~21/20 = 77.963

* POTE: ~2 = 1200.000, ~21/20 = 77.881

Minimax tuning:

* [[11-odd-limit]]: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }}

* 11-odd-limit: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }}

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]

: eigenmonzo (unchanged-interval) basis: 2.11/7

Line 1,149:

Line 1,159:

Algebraic generator: positive root of 4''x''3 + 15''x''2 - 21, or else Gontrand2, the smallest positive root of 4''x''7 - 8''x''6 + 5.

{{Optimal ET sequence|legend=1| 15, 31, 46, 77, 262cdee, 339cdeee }}

{{Optimal ET sequence|legend=0| 15, 31, 46, 77, 262cdee, 339cdeee }}

Badness: 0.016687

Badness (Smith): 0.016687

==== Dwynwen ====

Line 1,160:

Line 1,170:

Mapping: {{mapping| 1 1 2 3 3 2 | 0 9 5 -3 7 26 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~21/20 = 78.219

Optimal tunings:

* CTE: ~2 = 1200.000, ~21/20 = 78.243

* POTE: ~2 = 1200.000, ~21/20 = 78.219

Badness: 0.023461

Badness (Smith): 0.023461

==== Lupercalia ====

Line 1,173:

Line 1,185:

Mapping: {{mapping| 1 1 2 3 3 3 | 0 9 5 -3 7 11 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~21/20 = 77.709

Optimal tunings:

* CTE: ~2 = 1200.000, ~21/20 = 77.694

* POTE: ~2 = 1200.000, ~21/20 = 77.709

{{Optimal ET sequence|legend=1| 15, 31~~, 77ff, 108eff, 139efff~~ }}

Badness: 0.021328

Badness (Smith): 0.021328

==== Valentino ====

Line 1,186:

Line 1,200:

Mapping: {{mapping| 1 1 2 3 3 5 | 0 9 5 -3 7 -20 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~21/20 = 77.958

Optimal tunings:

* CTE: ~2 = 1200.000, ~21/20 = 77.968

* POTE: ~2 = 1200.000, ~21/20 = 77.958

Badness: 0.020665

Badness (Smith): 0.020665

===== 17-limit =====

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Line 1,215:

Mapping: {{mapping| 1 1 2 3 3 5 5 | 0 9 5 -3 7 -20 -14 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~21/20 = 78.003

Optimal tunings:

* CTE: ~2 = 1200.000, ~21/20 = 78.003

* POTE: ~2 = 1200.000, ~21/20 = 78.003

{{Optimal ET sequence|legend=1| 15f, 31, 46, 77, 123e~~, 200ceg~~ }}

Badness: 0.016768

Badness (Smith): 0.016768

==== Semivalentine ====

Line 1,212:

Line 1,230:

Mapping: {{mapping| 2 2 4 6 6 7 | 0 9 5 -3 7 3 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~21/20 = 77.839

Optimal tunings:

* CTE: ~55/39 = 600.000, ~21/20 = 77.997

* POTE: ~55/39 = 600.000, ~21/20 = 77.839

Badness: 0.032749

Badness (Smith): 0.032749

==== Hemivalentine ====

Line 1,225:

Line 1,245:

Mapping: {{mapping| 1 1 2 3 3 4 | 0 18 10 -6 14 -9 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~40/39 = 39.044

Optimal tunings:

* CTE: ~2 = 1200.000, ~40/39 = 39.014

* POTE: ~2 = 1200.000, ~40/39 = 39.044

Badness: 0.047059

Badness (Smith): 0.047059

=== Hemivalentino ===

Line 1,238:

Line 1,260:

Mapping: {{mapping| 1 1 2 3 2 | 0 18 10 -6 45 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~45/44 = 38.921

Optimal tunings:

* CTE: ~2 = 1200.000, ~45/44 = 38.928

* POTE: ~2 = 1200.000, ~45/44 = 38.921

Badness: 0.061275

Badness (Smith): 0.061275

==== 13-limit ====

Line 1,251:

Line 1,275:

Mapping: {{mapping| 1 1 2 3 2 5 | 0 18 10 -6 45 -40 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~45/44 = 38.948

Optimal tunings:

* CTE: ~2 = 1200.000, ~45/44 = 38.944

* POTE: ~2 = 1200.000, ~45/44 = 38.948

Badness: 0.057919

Badness (Smith): 0.057919

==== Hemivalentoid ====

Line 1,264:

Line 1,290:

Mapping: {{mapping| 1 1 2 3 2 4 | 0 18 10 -6 45 -9 }}

Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~40/39 = 38.993

Optimal tunings:

* CTE: ~2 = 1200.000, ~40/39 = 38.946

* POTE: ~2 = 1200.000, ~40/39 = 38.993

Badness: 0.057931

Badness (Smith): 0.057931

== Unidec ==

@@ Line 1,088: / Line 1,088: @@
 {{Main| Valentine }}
-Valentine tempers out [[126/125]] and [[6144/6125]] as well as 1029/1024. It has a generator of ~21/20, three of which make the slendric generator ~8/7. 21/20 can be stripped of its 2 and taken as 3 × 7/5. In this respect it resembles miracle, with a generator of 3 × 5/7, and casablanca, with a generator of 5 × 7/3. These three generators are the simplest in terms of the relationship of tetrads in the [[The Seven Limit Symmetrical Lattices|lattice of 7-limit tetrads]]. Valentine can also be described as the {{nowrap|31 & 46}} temperament, and [[77edo]], [[108edo]], or [[185edo]] make for excellent tunings, which also happen to be excellent tunings for [[starling]], the rank-3 temperament tempering out 126/125. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)<sup>1/9</sup> as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as {{multival| 9 5 -3 7 … }}, tempering out 121/120 and 441/440; 46edo has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, (11/7)<sup>1/10</sup>.
+Valentine tempers out [[126/125]] and [[6144/6125]] as well as 1029/1024. It has a generator of ~21/20, three of which make the slendric generator ~8/7. 21/20 can be stripped of its 2 and taken as 3 × 7/5. In this respect it resembles miracle, with a generator of 3 × 5/7, and casablanca, with a generator of 5 × 7/3. These three generators are the simplest in terms of the relationship of tetrads in the [[The Seven Limit Symmetrical Lattices|lattice of 7-limit tetrads]]. Valentine can also be described as the {{nowrap|31 & 46}} temperament, and [[77edo]], [[108edo]], or [[185edo]] make for excellent tunings, which also happen to be excellent tunings for [[starling]], the rank-3 temperament tempering out 126/125. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)<sup>1/9</sup> as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit, tempering out 121/120 and 441/440; 46edo has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, (11/7)<sup>1/10</sup>.
 [[Subgroup]]: 2.3.5
@@ Line 1,096: / Line 1,096: @@
 {{Mapping|legend=1| 1 1 2 | 0 9 5 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/24 = 78.039
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, ~25/24 = 78.039
+: [[error map]]: {{val| 0.000 +0.397 +3.882 }}
+* [[POTE]]: ~2 = 1200.000, ~25/24 = 78.039
+: error map: {{val| 0.000 -0.829 +3.201 }}
 {{Optimal ET sequence|legend=1| 15, 31, 46, 77, 123 }}
-[[Badness]]: 0.122765
+[[Badness]] (Smith): 0.122765
 === 7-limit ===
@@ Line 1,111: / Line 1,115: @@
 : mapping generators: ~2, ~21/20
-Wedgie: {{multival| 9 5 -3 -13 -30 -21 }}
+{{Multival|legend=1| 9 5 -3 -13 -30 -21 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 77.864
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, ~21/20 = 77.878
+: [[error map]]: {{val| 0.000 -1.057 +3.074 -2.459 }}
+* [[POTE]]: ~2 = 1200.000, ~21/20 = 77.864
+: error map: {{val| 0.000 -1.181 +3.005 -2.417 }}
 [[Minimax tuning]]:
 * [[7-odd-limit]]: ~21/20 = {{monzo| 1/6 1/12 0 -1/12 }}
-: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
+: {{monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 17/6 5/12 0 -5/12 | 5/2 -1/4 0 1/4 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3
+: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3
 * [[9-odd-limit]]: ~21/20 = {{monzo| 1/21 2/21 0 -1/21}}
-: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
+: {{monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 47/21 10/21 0 -5/21 | 20/7 -2/7 0 1/7 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7
+: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7
 [[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.
@@ Line 1,127: / Line 1,135: @@
 {{Optimal ET sequence|legend=1| 15, 31, 46, 77, 185, 262cd }}
-[[Badness]]: 0.031056
+[[Badness]] (Smith): 0.031056
 === 11-limit ===
@@ Line 1,140: / Line 1,148: @@
 Wedgie: {{multival| 9 5 -3 7 -13 -30 -20 -21 -1 30 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 77.881
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~21/20 = 77.963
+* POTE: ~2 = 1200.000, ~21/20 = 77.881
 Minimax tuning:
-* [[11-odd-limit]]: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }}
+* 11-odd-limit: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }}
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]
 : eigenmonzo (unchanged-interval) basis: 2.11/7
@@ Line 1,149: / Line 1,159: @@
 Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.
-{{Optimal ET sequence|legend=1| 15, 31, 46, 77, 262cdee, 339cdeee }}
+{{Optimal ET sequence|legend=0| 15, 31, 46, 77, 262cdee, 339cdeee }}
-Badness: 0.016687
+Badness (Smith): 0.016687
 ==== Dwynwen ====
@@ Line 1,160: / Line 1,170: @@
 Mapping: {{mapping| 1 1 2 3 3 2 | 0 9 5 -3 7 26 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 78.219
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~21/20 = 78.243
+* POTE: ~2 = 1200.000, ~21/20 = 78.219
-{{Optimal ET sequence|legend=1| 15, 31f, 46 }}
+{{Optimal ET sequence|legend=0| 15, 31f, 46 }}
-Badness: 0.023461
+Badness (Smith): 0.023461
 ==== Lupercalia ====
@@ Line 1,173: / Line 1,185: @@
 Mapping: {{mapping| 1 1 2 3 3 3 | 0 9 5 -3 7 11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 77.709
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~21/20 = 77.694
+* POTE: ~2 = 1200.000, ~21/20 = 77.709
-{{Optimal ET sequence|legend=1| 15, 31, 77ff, 108eff, 139efff }}
+{{Optimal ET sequence|legend=0| 15, 31 }}
-Badness: 0.021328
+Badness (Smith): 0.021328
 ==== Valentino ====
@@ Line 1,186: / Line 1,200: @@
 Mapping: {{mapping| 1 1 2 3 3 5 | 0 9 5 -3 7 -20 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 77.958
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~21/20 = 77.968
+* POTE: ~2 = 1200.000, ~21/20 = 77.958
-{{Optimal ET sequence|legend=1| 15f, 31, 46, 77 }}
+{{Optimal ET sequence|legend=0| 15f, 31, 46, 77 }}
-Badness: 0.020665
+Badness (Smith): 0.020665
 ===== 17-limit =====
@@ Line 1,199: / Line 1,215: @@
 Mapping: {{mapping| 1 1 2 3 3 5 5 | 0 9 5 -3 7 -20 -14 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 78.003
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~21/20 = 78.003
+* POTE: ~2 = 1200.000, ~21/20 = 78.003
-{{Optimal ET sequence|legend=1| 15f, 31, 46, 77, 123e, 200ceg }}
+{{Optimal ET sequence|legend=0| 15f, 31, 46, 77, 123e }}
-Badness: 0.016768
+Badness (Smith): 0.016768
 ==== Semivalentine ====
@@ Line 1,212: / Line 1,230: @@
 Mapping: {{mapping| 2 2 4 6 6 7 | 0 9 5 -3 7 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 77.839
+Optimal tunings:
+* CTE: ~55/39 = 600.000, ~21/20 = 77.997
+* POTE: ~55/39 = 600.000, ~21/20 = 77.839
-{{Optimal ET sequence|legend=1| 16, 30, 46, 62, 108ef }}
+{{Optimal ET sequence|legend=0| 16, 30, 46, 62, 108ef }}
-Badness: 0.032749
+Badness (Smith): 0.032749
 ==== Hemivalentine ====
@@ Line 1,225: / Line 1,245: @@
 Mapping: {{mapping| 1 1 2 3 3 4 | 0 18 10 -6 14 -9 }}
-Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 39.044
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~40/39 = 39.014
+* POTE: ~2 = 1200.000, ~40/39 = 39.044
-{{Optimal ET sequence|legend=1| 30, 31, 61, 92f, 123f }}
+{{Optimal ET sequence|legend=0| 30, 31, 61, 92f }}
-Badness: 0.047059
+Badness (Smith): 0.047059
 === Hemivalentino ===
@@ Line 1,238: / Line 1,260: @@
 Mapping: {{mapping| 1 1 2 3 2 | 0 18 10 -6 45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.921
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~45/44 = 38.928
+* POTE: ~2 = 1200.000, ~45/44 = 38.921
-{{Optimal ET sequence|legend=1| 31, 92e, 123, 154, 185 }}
+{{Optimal ET sequence|legend=0| 31, 92e, 123, 154, 185 }}
-Badness: 0.061275
+Badness (Smith): 0.061275
 ==== 13-limit ====
@@ Line 1,251: / Line 1,275: @@
 Mapping: {{mapping| 1 1 2 3 2 5 | 0 18 10 -6 45 -40 }}
-Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.948
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~45/44 = 38.944
+* POTE: ~2 = 1200.000, ~45/44 = 38.948
-{{Optimal ET sequence|legend=1| 31, 92e, 123, 154 }}
+{{Optimal ET sequence|legend=0| 31, 123, 154 }}
-Badness: 0.057919
+Badness (Smith): 0.057919
 ==== Hemivalentoid ====
@@ Line 1,264: / Line 1,290: @@
 Mapping: {{mapping| 1 1 2 3 2 4 | 0 18 10 -6 45 -9 }}
-Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 38.993
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~40/39 = 38.946
+* POTE: ~2 = 1200.000, ~40/39 = 38.993
-{{Optimal ET sequence|legend=1| 31, 92ef, 123f }}
+{{Optimal ET sequence|legend=0| 31, 92ef }}
-Badness: 0.057931
+Badness (Smith): 0.057931
 == Unidec ==