Hemifamity family: Difference between revisions

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 The '''hemifamity family''' of temperaments are rank-3 temperaments tempering out [[5120/5103]].
-== Hemifamity  ==
+== Hemifamity ==
 Subgroup: 2.3.5.7
-[[Comma list]] c = 5120/5103
+[[Comma list]]: [[5120/5103]]
 [[Mapping]]: [{{val| 1 0 0 10 }}, {{val| 0 1 0 -6 }}, {{val| 0 0 1 1 }}]
@@ Line 16: / Line 16: @@
 : Angle (3/2, 10/9) = 82.112 degrees
-[[Minimax tuning]]:
+[[Minimax tuning]]: c = 5120/5103
 * [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just
 : [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 1/7 1/7 -1/7 }}, {{monzo| 0 0 1 0 }}, {{monzo| 10/7 -6/7 1/7 6/7 }}]
@@ Line 24: / Line 24: @@
 : [[Eigenmonzo]]s (unchanged intervals): 2, 5/4, 9/7
-{{Val list|legend=1| 99, 239, 292, 391, 881bd }}
+{{Val list|legend=1| 41, 53, 87, 94, 99, 239, 251, 292, 391, 881bd, 1272bcdd }}
 [[Badness]]: 0.153 × 10<sup>-3</sup>
@@ Line 30: / Line 30: @@
 [[Projection pair]]s: 7 5120/729
-=== Music  ===
+; Music
 * [http://www.archive.org/details/Choraled Choraled] [http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3 play] by [[Gene Ward Smith]]
 * [http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3 Hemifamity27] by [[Chris Vaisvil]]
-== Pele  ==
+== Pele ==
 Subgroup: 2.3.5.7.11
@@ Line 61: / Line 60: @@
 [[Projection pair]]s: 7 5120/729 11 655360/59049
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
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 * 15-odd-limit eigenmonzos (unchanged intervals): 2, 15/13, 6/5
-Vals: {{Val list| 29, 41, 46, 58, 87, 145, 232, 377cef }}
+Vals: {{val list| 29, 41, 46, 58, 87, 145, 232, 377cef }}
 Badness: 0.703 × 10<sup>-3</sup>
-== Laka  ==
+== Laka ==
 Subgroup: 2.3.5.7.11
@@ Line 88: / Line 87: @@
 : [[Eigenmonzo]]s (unchanged intervals): 2, 5/4, 14/11
-{{Val list|legend=1| 41, 53, 58, 94, 99e, 152, 555dee, 707ddee, 859bddee }}
+{{Val list|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }}
-Projection pairs: 5120/729 11 14348907/1310720
+[[Projection pair]]s: 5120/729 11 14348907/1310720
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 102: / Line 101: @@
 : [[Eigenmonzo]]s (unchanged intervals): 2, 11/8, 14/13
-=== 17-limit  ===
+Vals: {{val list| 41, 53, 58, 94, 111, 152f, 415de }}*
+<nowiki>*</nowiki> optimal patent val: [[205edo|205]]
+=== 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
@@ Line 114: / Line 117: @@
 : [[Eigenmonzo]]s (unchanged intervals): 2, 11/8, 14/13
-Vals: {{Val list| 58, 94, 111, 152f, 205 }}
+Vals: {{Val list| 58, 94, 111, 152f, 205, 263df }}
-== Akea  ==
+== Akea ==
 Subgroup: 2.3.5.7.11
@@ Line 134: / Line 137: @@
 Badness: 0.998 × 10<sup>-3</sup>
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 152: / Line 155: @@
 Map to lattice: [{{val| 0 1 3 -3 1 -2 }}, {{val| 0 0 -1 -1 2 2 }}]
-Vals: {{Val list| 34, 41, 46, 53, 87, 140, 321, 461e }}
+Vals: {{val list| 34, 41, 46, 53, 87, 140, 321, 461e }}
 Badness: 0.822 × 10<sup>-3</sup>
@@ Line 158: / Line 161: @@
 Scales: [[akea46_13]]
-== Kapo  ==
+== Lono ==
+Subgroup: 2.3.5.7.11
+[[Comma list]]: 176/175, 5120/5103
+[[Mapping]]: [{{val| 1 0 0 10 6 }}, {{val| 0 1 0 -6 -6 }}, {{val| 0 0 1 1 3 }}]
+{{Val list|legend=1| 46, 53, 58, 99, 111, 268cd }}
+[[Badness]]: 1.18 × 10<sup>-3</sup>
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 176/175, 351/350, 847/845
+Mapping: [{{val| 1 0 0 10 6 11 }}, {{val| 0 1 0 -6 -6 -9 }}, {{val| 0 0 1 1 3 3 }}]
+Vals: {{val list| 46, 53, 58, 99, 104c, 111, 268cd }}
+Badness: 0.908 × 10<sup>-3</sup>
+== Kapo ==
 Subgroup: 2.3.5.7.11
@@ Line 176: / Line 201: @@
 [[Badness]]: 0.994 × 10<sup>-3</sup>
-== Lono  ==
+== Namaka ==
-Subgroup: 2.3.5.7.11
-[[Comma list]]: 176/175, 5120/5103
-[[Mapping]]: [{{val| 1 0 0 10 6 }}, {{val| 0 1 0 -6 -6 }}, {{val| 0 0 1 1 3 }}]
-{{Val list|legend=1| 46, 53, 58, 99, 111 }}
-[[Badness]]: 1.18 × 10<sup>-3</sup>
-== Namaka  ==
 Subgroup: 2.3.5.7.11
@@ Line 198: / Line 212: @@
 [[Badness]]: 1.74 × 10<sup>-3</sup>
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 205: / Line 219: @@
 Mapping: [{{val| 1 0 0 10 -6 -1 }}, {{val| 0 2 0 -12 9 3 }}, {{val| 0 0 1 1 1 1 }}]
-Vals: {{Val list| 29, 53, 58, 87, 111, 140, 198 }}
+Vals: {{val list| 29, 53, 58, 87, 111, 140, 198 }}
 Badness: 0.781 × 10<sup>-3</sup>
@@ Line 211: / Line 225: @@
 [[Category:Regular temperament theory]]
 [[Category:Temperament family]]
-[[Category:Hemifamity]]
+[[Category:Hemifamity family| ]] <!-- main article -->
 [[Category:Rank 3]]
+[[Category:Listen]]