Sensamagic family: Difference between revisions

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The '''sensamagic family''' of [[rank-3 temperament]]s tempers out [[245/243]]. For a list of rank-2 temperaments, see [[Sensamagic clan]].

The '''sensamagic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the sensamagic comma, [[245/243]].

For a list of rank-2 temperaments, see [[Sensamagic clan]].

== Sensamagic ==

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: Angle (3/2, 9/7) = 86.5288°

[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 703.7424, ~9/7 = 440.9020

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.7424{{c}}, ~9/7 = 440.9020{{c}}

[[Minimax tuning]]:

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{{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}

[[Badness]]: 0.129 × 10-3

[[Badness]] (Smith): 0.129 × 10-3

[[Projection pair]]: 5 243/49 to 2.3.7

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[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 703.8004, ~9/7 = 440.9178

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}}

[[Minimax tuning]]:

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{{Optimal ET sequence|legend=1| 17, 19, 22, 41, 68, 87, 196, 283, 607bd, 694bd }}

[[Badness]]: 0.722 × 10-3

[[Badness]] (Smith): 0.722 × 10-3

[[Projection pair]]s: 5 243/49 11 896/81 to 2.3.7

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Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }}

{{Optimal ET sequence|legend=1| 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd }}

{{Optimal ET sequence|legend=0| 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd }}

Badness: 1.20 × 10-3

Badness (Smith): 1.20 × 10-3

== Sensawer ==

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[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 703.1900, ~9/7 = 441.1359

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.1900{{c}}, ~9/7 = 441.1359{{c}}

{{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 60e, 87, 302d, 389d, 476bd }}

[[Badness]]: 0.796 × 10-3

[[Badness]] (Smith): 0.796 × 10-3

=== 13-limit ===

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

{{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }}

{{Optimal ET sequence|legend=0| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }}

Badness: 0.928 × 10-3

Badness (Smith): 0.928 × 10-3

== Octarod ==

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[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 705.0464, ~9/7 = 439.5050

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 705.0464{{c}}, ~9/7 = 439.5050{{c}}

{{Optimal ET sequence|legend=1| 8d, 14c, 19, 22, 27e, 41, 104, 131e }}

[[Badness]]: 0.581 × 10-3

[[Badness]] (Smith): 0.581 × 10-3

Scales: [[octarod1]], [[octarod2]], [[octarod3]], [[octarod4]], [[octarod5]]

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[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 706.3702, ~9/7 = 442.1147

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 706.3702{{c}}, ~9/7 = 442.1147{{c}}

{{Optimal ET sequence|legend=1| 22, 46, 68, 95, 141bc, 163bc, 209bc, 350bc }}

[[Badness]]: 0.877 × 10-3

[[Badness]] (Smith): 0.877 × 10-3

=== Shrusic ===

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

{{Optimal ET sequence|legend=1| 22, 46, 211bcf, 233bcf, 257bcf, 279bcf }}

{{Optimal ET sequence|legend=0| 22, 46, 211bcf, 233bcf, 257bcf, 279bcf }}

Badness: 1.125 × 10-3

Badness (Smith): 1.125 × 10-3

== Bisector ==

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: mapping generators: ~77/54, ~3, ~9/7

[[Optimal tuning]] ([[POTE]]): ~77/54 = ~~1\2~~, ~3/2 = 703.0884, ~9/7 = 441.1060

[[Optimal tuning]] ([[POTE]]): ~77/54 = 600.0000{{c}}, ~3/2 = 703.0884{{c}}, ~9/7 = 441.1060{{c}}

{{Optimal ET sequence|legend=1| 22, 46, 68, 82e, 106de, 114, 128e }}

[[Badness]]: 1.089 × 10-3

[[Badness]] (Smith): 1.089 × 10-3

== Sensigh ==

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: mapping generators: ~2, ~9/7, ~11

Badness: 0.939 × 10-3

Badness (Smith): 0.939 × 10-3

=== 17-limit ===

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Mapping: {{mapping| 1 6 8 11 0 10 0 | 0 -7 -9 -13 0 -10 1 | 0 0 0 0 1 0 1 }}

[[Category:Temperament families]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''sensamagic family''' of [[rank-3 temperament]]s tempers out [[245/243]]. For a list of rank-2 temperaments, see [[Sensamagic clan]].
+The '''sensamagic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the sensamagic comma, [[245/243]].
+For a list of rank-2 temperaments, see [[Sensamagic clan]].
 == Sensamagic ==
@@ Line 19: / Line 21: @@
 : Angle (3/2, 9/7) = 86.5288°
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.7424, ~9/7 = 440.9020
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.7424{{c}}, ~9/7 = 440.9020{{c}}
 [[Minimax tuning]]:
@@ Line 31: / Line 33: @@
 {{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}
-[[Badness]]: 0.129 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.129 × 10<sup>-3</sup>
 [[Projection pair]]: 5 243/49 to 2.3.7
@@ Line 56: / Line 58: @@
 {{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 2 -2 | 0 0 2 -1 -1 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.8004, ~9/7 = 440.9178
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}}
 [[Minimax tuning]]:
@@ Line 65: / Line 67: @@
 {{Optimal ET sequence|legend=1| 17, 19, 22, 41, 68, 87, 196, 283, 607bd, 694bd }}
-[[Badness]]: 0.722 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.722 × 10<sup>-3</sup>
 [[Projection pair]]s: 5 243/49 11 896/81 to 2.3.7
@@ Line 76: / Line 78: @@
 Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }}
-{{Optimal ET sequence|legend=1| 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd }}
+{{Optimal ET sequence|legend=0| 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd }}
-Badness: 1.20 × 10<sup>-3</sup>
+Badness (Smith): 1.20 × 10<sup>-3</sup>
 == Sensawer ==
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 {{Mapping|legend=1| 1 0 0 0 -3 | 0 1 1 2 5 | 0 0 2 -1 -4 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.1900, ~9/7 = 441.1359
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.1900{{c}}, ~9/7 = 441.1359{{c}}
 {{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 60e, 87, 302d, 389d, 476bd }}
-[[Badness]]: 0.796 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.796 × 10<sup>-3</sup>
 === 13-limit ===
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 Mapping: {{mapping| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }}
-{{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }}
+{{Optimal ET sequence|legend=0| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }}
-Badness: 0.928 × 10<sup>-3</sup>
+Badness (Smith): 0.928 × 10<sup>-3</sup>
 == Octarod ==
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 {{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 2 0 | 0 0 2 -1 4 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 705.0464, ~9/7 = 439.5050
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 705.0464{{c}}, ~9/7 = 439.5050{{c}}
 {{Optimal ET sequence|legend=1| 8d, 14c, 19, 22, 27e, 41, 104, 131e }}
-[[Badness]]: 0.581 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.581 × 10<sup>-3</sup>
 Scales: [[octarod1]], [[octarod2]], [[octarod3]], [[octarod4]], [[octarod5]]
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 {{Mapping|legend=1| 1 0 0 0 -4 | 0 1 1 2 4 | 0 0 2 -1 3 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 706.3702, ~9/7 = 442.1147
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 706.3702{{c}}, ~9/7 = 442.1147{{c}}
 {{Optimal ET sequence|legend=1| 22, 46, 68, 95, 141bc, 163bc, 209bc, 350bc }}
-[[Badness]]: 0.877 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.877 × 10<sup>-3</sup>
 === Shrusic ===
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 Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }}
-{{Optimal ET sequence|legend=1| 22, 46, 211bcf, 233bcf, 257bcf, 279bcf }}
+{{Optimal ET sequence|legend=0| 22, 46, 211bcf, 233bcf, 257bcf, 279bcf }}
-Badness: 1.125 × 10<sup>-3</sup>
+Badness (Smith): 1.125 × 10<sup>-3</sup>
 == Bisector ==
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 : mapping generators: ~77/54, ~3, ~9/7
-[[Optimal tuning]] ([[POTE]]): ~77/54 = 1\2, ~3/2 = 703.0884, ~9/7 = 441.1060
+[[Optimal tuning]] ([[POTE]]): ~77/54 = 600.0000{{c}}, ~3/2 = 703.0884{{c}}, ~9/7 = 441.1060{{c}}
 {{Optimal ET sequence|legend=1| 22, 46, 68, 82e, 106de, 114, 128e }}
-[[Badness]]: 1.089 × 10<sup>-3</sup>
+[[Badness]] (Smith): 1.089 × 10<sup>-3</sup>
 == Sensigh ==
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 : mapping generators: ~2, ~9/7, ~11
-{{Optimal ET sequence|legend=1| 19, 27, 46, 111df, 157df }}
+{{Optimal ET sequence|legend=0| 19, 27, 46, 111df, 157df }}
-Badness: 0.939 × 10<sup>-3</sup>
+Badness (Smith): 0.939 × 10<sup>-3</sup>
 === 17-limit ===
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 Mapping: {{mapping| 1 6 8 11 0 10 0 | 0 -7 -9 -13 0 -10 1 | 0 0 0 0 1 0 1 }}
-{{Optimal ET sequence|legend=1| 19, 27, 46 }}
+{{Optimal ET sequence|legend=0| 19, 27, 46 }}
 [[Category:Temperament families]]