Septisemi temperaments: Difference between revisions

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+{{Technical data page}}
-These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/3 with 7/4, and 10/7 with 3/2.
+This is a collection of very low [[complexity]] temperaments [[tempering out]] the septimal minor semitone, [[21/20]], and hence equating 5/3 with 7/4, and 10/7 with 3/2.
-=Fluorine=
+Temperaments discussed elsewhere are:
-Commas: 21/20, 243/224
+* ''[[Mother]]'' (+16/15) → [[Father family #Mother|Father family]]
+* ''[[Sharptone]]'' (+28/27) → [[Meantone family #Sharptone|Meantone family]]
+* ''[[Pelogic]]'' (+135/128) → [[Mavila family #Pelogic|Mavila family]]
+* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]]
+* [[Beep]] (+27/25) → [[Bug family #Beep|Bug family]]
+* ''[[Deflated]]'' (+128/125) → [[Augmented family #Deflated|Augmented family]]
+* ''[[Gidorah]]'' (+144/125) → [[Gamelismic clan #Gidorah|Gamelismic clan]]
+* ''[[Oxygen]]'' (+175/162) → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]]
-POTE generator: ~3/2 = 663.059
+Considered below are fluorine and sodium.
-Map: [&lt;1 0 -7 -5|, &lt;0 1 6 5|]
+== Fluorine ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Avila]].''
-Wedgie: &lt;&lt;1 6 5 7 5 -5||
+[[Subgroup]]: 2.3.5.7
-EDOs: 9, 20bd, 29bd
+[[Comma list]]: 21/20, 243/224
-Badness: 0.0556
+{{Mapping|legend=1| 1 0 -7 -5 | 0 1 6 5 }}
+: mapping generators: ~2, ~3
-=Sodium=
+[[Optimal tuning]]s:
-Commas: 21/20, 54/49
+* [[WE]]: ~2 = 1211.420{{c}}, ~3/2 = 669.369{{c}}
+: [[error map]]: {{val| +11.420 -21.165 +18.481 -21.980 }}
+* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 665.210{{c}}
+: error map: {{val| 0.000 -36.745 +4.945 -42.777 }}
-POTE generator: ~7/6 = 320.182
+{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20bdd, 29bdd }}
-Map: [&lt;1 1 1 2|, &lt;0 2 5 3|]
+[[Badness]] (Sintel): 1.41
-Wedgie: &lt;&lt;2 5 3 3 -1 -7||
+== Sodium ==
+[[Subgroup]]: 2.3.5.7
-EDOs: 4, 11, 15b
+[[Comma list]]: 21/20, 54/49
-Badness: 0.0558
+{{Mapping|legend=1| 1 1 1 2 | 0 2 5 3 }}
+: mapping generators: ~2, ~7/6
-=Oxygen=
+[[Optimal tuning]]s:
-Commas: 21/20, 175/162
+* [[WE]]: ~2 = 1207.624{{c}}, ~7/6 = 322.216{{c}}
+: [[error map]]: {{val| +7.624 -49.898 +32.393 +13.072 }}
+* [[CWE]]: ~2 = 1200.000{{c}}, ~7/6 = 322.210{{c}}
+: error map: {{val| 0.000 -57.535 +24.737 -2.196 }}
-POTE generator: ~7/6 = 169.112
+{{Optimal ET sequence|legend=1| 4, 11 }}
-Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -2|]
+[[Badness]] (Sintel): 1.41
-Wedgie: &lt;&lt;3 5 2 1 -5 -9||
+[[Category:Temperament collections]]
+[[Category:Septisemi temperaments| ]] <!-- main article -->
-EDOs: 7d, 8
+[[Category:Rank 2]]
-Badness: 0.0599