Septisemi temperaments: Difference between revisions

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-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.
+{{Technical data page}}
+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.
-Discussed elsewhere are [[Father family #Mother|mother]], [[Dicot family #Flat|flat]], [[Bug family #Beep|beep]], [[Gamelismic clan #Gidorah|gidorah]], [[Meantone family #Sharptone|sharptone]] and [[Pelogic family #Pelogic|pelogic]].
+Temperaments discussed elsewhere are:
+* ''[[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]]
+Considered below are fluorine and sodium.
 == Fluorine ==
-=== 5-limit (Avila) ===
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Avila]].''
-Subgroup: 2.3.5
-[[Comma]]: 729/640
-[[Mapping]]: [{{val| 1 0 -7 }}, {{val| 0 1 6 }}]
-[[POTE generator]]: ~3/2 = 661.593
-{{Val list|legend=1| 2c, 7c, 9, 20b, 29b }}
-[[Badness]]: 0.181941
-=== 7-limit ===
+[[Subgroup]]: 2.3.5.7
-Subgroup: 2.3.5.7
 [[Comma list]]: 21/20, 243/224
-[[Mapping]]: [{{val| 1 0 -7 -5 }}, {{val| 0 1 6 5 }}]
+{{Mapping|legend=1| 1 0 -7 -5 | 0 1 6 5 }}
+: mapping generators: ~2, ~3
-{{Multival|legend=1| 1 6 5 7 5 -5 }}
-[[POTE generator]]: ~3/2 = 663.059
+[[Optimal tuning]]s:
+* [[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 }}
-{{Val list|legend=1| 9, 20bdd, 29bdd }}
+{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20bdd, 29bdd }}
-[[Badness]]: 0.055623
+[[Badness]] (Sintel): 1.41
 == Sodium ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 21/20, 54/49
-[[Mapping]]: [{{val| 1 1 1 2 }}, {{val| 0 2 5 3 }}]
+{{Mapping|legend=1| 1 1 1 2 | 0 2 5 3 }}
+: mapping generators: ~2, ~7/6
-{{Multival|legend=1| 2 5 3 3 -1 -7 }}
-[[POTE generator]]: ~7/6 = 320.182
-{{Val list|legend=1| 4, 11, 15b }}
-[[Badness]]: 0.055814
-== Oxygen ==
-Subgroup: 2.3.5.7
-[[Comma list]]: 21/20, 175/162
-[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -3 -5 -2 }}]
-{{Multival|legend=1| 3 5 2 1 -5 -9 }}
-[[POTE generator]]: ~7/6 = 169.112
+[[Optimal tuning]]s:
+* [[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 }}
-{{Val list|legend=1| 7d, 8 }}
+{{Optimal ET sequence|legend=1| 4, 11 }}
-[[Badness]]: 0.059866
+[[Badness]] (Sintel): 1.41
-[[Category:Regular temperament theory]]
+[[Category:Temperament collections]]
-[[Category:Temperament collection]]
+[[Category:Septisemi temperaments| ]] <!-- main article -->
-[[Category:Septisemi]]
 [[Category:Rank 2]]