Gamelismic family: Difference between revisions

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{{Technical data page}}~~ ~~

The '''gamelismic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[gamelisma]], 1029/1024. The head of this family, gamelismic, tempers out 1029/1024 alone in the full 7-limit, so it has the same 2.3.7-[[subgroup]] structure as [[slendric]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator.

The '''gamelismic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[gamelisma]], 1029/1024. The head of this family, gamelismic, tempers out 1029/1024 alone in the full 7-limit, so it has the same [[2.3.7 subgroup|2.3.7-subgroup]] structure as [[slendric]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator.

See [[Gamelismic clan]] for the rank-2 temperament without the last generator of gamelismic, and its various extensions.

Line 21:

: Angle (8/7, 5/4) = 90 degrees

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~8/7 = 233.6875, ~5/4 = 385.1853

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.6875, ~5/4 = 385.1853

[[Minimax tuning]]: c = 1029/1024

* [[7-odd-limit]]: 3, 5, and 7 1/4-comma flat

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

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/3.5/3

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3.5/3

* [[9-odd-limit]]: 3 1/7-comma flat, 5 and 7 2/7-comma flat

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

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5/3.9/7

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.9/7

[[TE tuning]] map: {{val| 1200.486 1901.833 2786.314 3367.676 }}

[[TE tuning|TE]] [[tuning map]]: {{val| 1200.486 1901.833 2786.314 3367.676 }}

{{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72, 118, 159, 190 }}

[[Badness]]: 0.176 × 10-3

[[Badness]] (Smith): 0.176 × 10-3

[[Projection pair]]: 3 1024/343 to 2.5.7

Line 58:

: Angle (8/7, 12/11) = 86.657 degrees

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~8/7 = 233.6884, ~5/4 = 385.1618

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.6884, ~5/4 = 385.1618

[[Minimax tuning]]: c = 1029/1024, e = 385/384

* [[11-odd-limit]]: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat

: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 39/14 4/7 1/2 -2/7 -1/2 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 39/14 4/7 -1/2 -2/7 1/2 }}]

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.11/5, 9/7

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.11/5, 9/7

{{Optimal ET sequence|legend=1| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}

[[Badness]]: 0.234 × 10-3

[[Badness]] (Smith): 0.234 × 10-3

[[Projection pair]]s: 3 1024/343 11 131072/12005 to 2.5.7

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Mapping: {{mapping| 1 1 0 3 5 6 | 0 3 0 -1 4 12 | 0 0 1 0 -1 -2 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~8/7 = 233.9128, ~5/4 = 384.7278

Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.9128, ~5/4 = 384.7278

{{Optimal ET sequence|legend=1| 15, 26, 41, 46, 72, 87, 159, 477cdf }}

{{Optimal ET sequence|legend=0| 15, 26, 41, 46, 72, 87, 159, 477cdf }}

Badness: 0.627 × 10-3

Badness (Smith): 0.627 × 10-3

Complexity spectrum: 8/7, 4/3, 11/8, 6/5, 14/11, 7/6, 10/9, 12/11, 5/4, 13/11, 9/8, 7/5, 11/9, 9/7, 18/13, 13/12, 16/15, 11/10, 15/14, 16/13, 14/13, 15/11, 13/10, 15/13

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Mapping: {{mapping| 1 1 0 3 5 -5 | 0 3 0 -1 4 -3 | 0 0 1 0 -1 4 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~8/7 = 233.6843, ~5/4 = 384.9830

Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6843, ~5/4 = 384.9830

{{Optimal ET sequence|legend=1| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }}

{{Optimal ET sequence|legend=0| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }}

Badness: 0.662 × 10-3

Badness (Smith): 0.662 × 10-3

=== Ominous ===

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Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 -10 | 0 0 1 0 -1 2 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~8/7 = 233.4088, ~5/4 = 385.3825

Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4088, ~5/4 = 385.3825

{{Optimal ET sequence|legend=1| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }}

{{Optimal ET sequence|legend=0| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }}

Badness: 0.751 × 10-3

Badness (Smith): 0.751 × 10-3

==== 17-limit ====

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: Angle (8/7, 6/5) = 98.6015

Optimal tuning (POTE): ~2 = ~~1\1~~, ~8/7 = 233.4313, ~5/4 = 385.2890

Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4313, ~5/4 = 385.2890

Minimax tuning:

* 17-odd-limit

: [{{monzo| 1 0 0 0 0 0 0 }}, {{monzo| 7/4 9/10 0 0 -3/10 -3/20 0 }}, {{monzo| 5/2 7/5 0 0 -4/5 1/10 0 }}, {{monzo| 11/4 -3/10 0 0 1/10 1/20 0 }}, {{monzo| 7/2 -1/5 0 0 2/5 -3/10 0 }}, {{monzo| 7/2 -1/5 0 0 -3/5 7/10 0 }}, {{monzo| 4 2/5 0 0 -4/5 3/5 0 }}]

: ~~eigenmonzo (~~unchanged-interval) basis: 2.11/9.13/9

: unchanged-interval (eigenmonzo) basis: 2.11/9.13/9

{{Optimal ET sequence|legend=1| 26, 31, 46, 72, 103, 149, 175f, 221ef }}

{{Optimal ET sequence|legend=0| 26, 31, 46, 72, 103, 149, 175f, 221ef }}

Badness: 0.612 × 10-3

Badness (Smith): 0.612 × 10-3

=== Momentous ===

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Mapping: {{mapping| 1 1 0 3 5 7 | 0 3 0 -4 1 -5 | 0 0 1 0 -1 -1 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~8/7 = 233.4088, ~5/4 = 385.3825

Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4088, ~5/4 = 385.3825

{{Optimal ET sequence|legend=1| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }}

{{Optimal ET sequence|legend=0| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }}

Badness: 0.832 × 10-3

Badness (Smith): 0.832 × 10-3

=== Foreboding ===

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Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 2 | 0 0 1 0 -1 1 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~8/7 = 233.3664, ~5/4 = 382.3425

Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.3664, ~5/4 = 382.3425

{{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72f, 185cf }}

{{Optimal ET sequence|legend=0| 5, 10, 15, 26, 31, 41, 72f, 185cf }}

Badness: 0.873 × 10-3

Badness (Smith): 0.873 × 10-3

=== Portannic ===

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Mapping: {{mapping| 1 1 2 3 3 4 | 0 3 0 -1 4 -1 | 0 0 3 0 -3 -1 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~8/7 = 233.6434, ~14/13 = 128.3440

Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6434, ~14/13 = 128.3440

{{Optimal ET sequence|legend=1| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}

{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}

Badness: 1.783 × 10-3

Badness (Smith): 1.783 × 10-3

==== 17-limit ====

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Mapping: {{mapping| 1 1 2 3 3 4 4 | 0 3 0 -1 4 -1 1 | 0 0 3 0 -3 -1 -1 }}

Optimal tuning (POTE): ~2 = ~~1\1~~, ~8/7 = 233.6803, ~14/13 = 128.4149

Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6803, ~14/13 = 128.4149

{{Optimal ET sequence|legend=1| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}

{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}

Badness: 1.303 × 10-3

Badness (Smith): 1.303 × 10-3

== Gamel ==

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[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~8/7 = 233.2909, ~5/4 = 384.2120

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.2909, ~5/4 = 384.2120

[[Badness]]: 0.853 × 10-3

[[Badness]] (Smith): 0.853 × 10-3

[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Gamelismic family| ]]

[[Category:Gamelismic| ]]

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
-{{Technical data page}}<br><br>
+{{Technical data page}}
-The '''gamelismic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[gamelisma]], 1029/1024. The head of this family, gamelismic, tempers out 1029/1024 alone in the full 7-limit, so it has the same 2.3.7-[[subgroup]] structure as [[slendric]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator.
+The '''gamelismic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[gamelisma]], 1029/1024. The head of this family, gamelismic, tempers out 1029/1024 alone in the full 7-limit, so it has the same [[2.3.7 subgroup|2.3.7-subgroup]] structure as [[slendric]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator.
 See [[Gamelismic clan]] for the rank-2 temperament without the last generator of gamelismic, and its various extensions.
@@ Line 21: / Line 21: @@
 : Angle (8/7, 5/4) = 90 degrees
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 233.6875, ~5/4 = 385.1853
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.6875, ~5/4 = 385.1853
 [[Minimax tuning]]: c = 1029/1024
 * [[7-odd-limit]]: 3, 5, and 7 1/4-comma flat
 : {{monzo list| 1 0 0 0 | 5/2 3/4 0 -3/4 | 5/2 -1/4 1 -3/4 | 5/2 -1/4 0 1/4 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3.5/3
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/3.5/3
 * [[9-odd-limit]]: 3 1/7-comma flat, 5 and 7 2/7-comma flat
 : {{monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 10/7 -1/7 1 -3/7 | 20/7 -2/7 0 1/7 }}
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.9/7
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.9/7
-[[TE tuning]] map: {{val| 1200.486 1901.833 2786.314 3367.676 }}
+[[TE tuning|TE]] [[tuning map]]: {{val| 1200.486 1901.833 2786.314 3367.676 }}
 {{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72, 118, 159, 190 }}
-[[Badness]]: 0.176 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.176 × 10<sup>-3</sup>
 [[Projection pair]]: 3 1024/343 to 2.5.7
@@ Line 58: / Line 58: @@
 : Angle (8/7, 12/11) = 86.657 degrees
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 233.6884, ~5/4 = 385.1618
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.6884, ~5/4 = 385.1618
 [[Minimax tuning]]: c = 1029/1024, e = 385/384
 * [[11-odd-limit]]: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 39/14 4/7 1/2 -2/7 -1/2 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 39/14 4/7 -1/2 -2/7 1/2 }}]
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.11/5, 9/7
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.11/5, 9/7
 {{Optimal ET sequence|legend=1| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}
-[[Badness]]: 0.234 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.234 × 10<sup>-3</sup>
 [[Projection pair]]s: 3 1024/343 11 131072/12005 to 2.5.7
@@ Line 80: / Line 80: @@
 Mapping: {{mapping| 1 1 0 3 5 6 | 0 3 0 -1 4 12 | 0 0 1 0 -1 -2 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.9128, ~5/4 = 384.7278
+Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.9128, ~5/4 = 384.7278
-{{Optimal ET sequence|legend=1| 15, 26, 41, 46, 72, 87, 159, 477cdf }}
+{{Optimal ET sequence|legend=0| 15, 26, 41, 46, 72, 87, 159, 477cdf }}
-Badness: 0.627 × 10<sup>-3</sup>
+Badness (Smith): 0.627 × 10<sup>-3</sup>
 Complexity spectrum: 8/7, 4/3, 11/8, 6/5, 14/11, 7/6, 10/9, 12/11, 5/4, 13/11, 9/8, 7/5, 11/9, 9/7, 18/13, 13/12, 16/15, 11/10, 15/14, 16/13, 14/13, 15/11, 13/10, 15/13
@@ Line 95: / Line 95: @@
 Mapping: {{mapping| 1 1 0 3 5 -5 | 0 3 0 -1 4 -3 | 0 0 1 0 -1 4 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6843, ~5/4 = 384.9830
+Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6843, ~5/4 = 384.9830
-{{Optimal ET sequence|legend=1| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }}
+{{Optimal ET sequence|legend=0| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }}
-Badness: 0.662 × 10<sup>-3</sup>
+Badness (Smith): 0.662 × 10<sup>-3</sup>
 === Ominous ===
@@ Line 108: / Line 108: @@
 Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 -10 | 0 0 1 0 -1 2 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4088, ~5/4 = 385.3825
+Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4088, ~5/4 = 385.3825
-{{Optimal ET sequence|legend=1| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }}
+{{Optimal ET sequence|legend=0| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }}
-Badness: 0.751 × 10<sup>-3</sup>
+Badness (Smith): 0.751 × 10<sup>-3</sup>
 ==== 17-limit ====
@@ Line 127: / Line 127: @@
 : Angle (8/7, 6/5) = 98.6015
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4313, ~5/4 = 385.2890
+Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4313, ~5/4 = 385.2890
 Minimax tuning:
 * 17-odd-limit
 : [{{monzo| 1 0 0 0 0 0 0 }}, {{monzo| 7/4 9/10 0 0 -3/10 -3/20 0 }}, {{monzo| 5/2 7/5 0 0 -4/5 1/10 0 }}, {{monzo| 11/4 -3/10 0 0 1/10 1/20 0 }}, {{monzo| 7/2 -1/5 0 0 2/5 -3/10 0 }}, {{monzo| 7/2 -1/5 0 0 -3/5 7/10 0 }}, {{monzo| 4 2/5 0 0 -4/5 3/5 0 }}]
-: eigenmonzo (unchanged-interval) basis: 2.11/9.13/9
+: unchanged-interval (eigenmonzo) basis: 2.11/9.13/9
-{{Optimal ET sequence|legend=1| 26, 31, 46, 72, 103, 149, 175f, 221ef }}
+{{Optimal ET sequence|legend=0| 26, 31, 46, 72, 103, 149, 175f, 221ef }}
-Badness: 0.612 × 10<sup>-3</sup>
+Badness (Smith): 0.612 × 10<sup>-3</sup>
 === Momentous ===
@@ Line 145: / Line 145: @@
 Mapping: {{mapping| 1 1 0 3 5 7 | 0 3 0 -4 1 -5 | 0 0 1 0 -1 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4088, ~5/4 = 385.3825
+Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.4088, ~5/4 = 385.3825
-{{Optimal ET sequence|legend=1| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }}
+{{Optimal ET sequence|legend=0| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }}
-Badness: 0.832 × 10<sup>-3</sup>
+Badness (Smith): 0.832 × 10<sup>-3</sup>
 === Foreboding ===
@@ Line 158: / Line 158: @@
 Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 2 | 0 0 1 0 -1 1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.3664, ~5/4 = 382.3425
+Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.3664, ~5/4 = 382.3425
-{{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72f, 185cf }}
+{{Optimal ET sequence|legend=0| 5, 10, 15, 26, 31, 41, 72f, 185cf }}
-Badness: 0.873 × 10<sup>-3</sup>
+Badness (Smith): 0.873 × 10<sup>-3</sup>
 === Portannic ===
@@ Line 171: / Line 171: @@
 Mapping: {{mapping| 1 1 2 3 3 4 | 0 3 0 -1 4 -1 | 0 0 3 0 -3 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6434, ~14/13 = 128.3440
+Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6434, ~14/13 = 128.3440
-{{Optimal ET sequence|legend=1| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}
+{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}
-Badness: 1.783 × 10<sup>-3</sup>
+Badness (Smith): 1.783 × 10<sup>-3</sup>
 ==== 17-limit ====
@@ Line 184: / Line 184: @@
 Mapping: {{mapping| 1 1 2 3 3 4 4 | 0 3 0 -1 4 -1 1 | 0 0 3 0 -3 -1 -1 }}
-Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6803, ~14/13 = 128.4149
+Optimal tuning (POTE): ~2 = 1200.0000, ~8/7 = 233.6803, ~14/13 = 128.4149
-{{Optimal ET sequence|legend=1| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}
+{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}
-Badness: 1.303 × 10<sup>-3</sup>
+Badness (Smith): 1.303 × 10<sup>-3</sup>
 == Gamel ==
@@ Line 197: / Line 197: @@
 {{Mapping|legend=1| 1 1 0 3 -1 | 0 3 0 -1 11 | 0 0 1 0 1 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 233.2909, ~5/4 = 384.2120
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~8/7 = 233.2909, ~5/4 = 384.2120
 {{Optimal ET sequence|legend=1| 10, 31, 41, 72 }}
-[[Badness]]: 0.853 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.853 × 10<sup>-3</sup>
 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Gamelismic family| ]] <!-- main article -->
 [[Category:Gamelismic| ]] <!-- key article -->
 [[Category:Rank 3]]