Breedsmic temperaments: Difference between revisions

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 Temperaments discussed elsewhere include:
 * ''[[Beatles]]'' (+64/63) → [[Archytas clan #Beatles|Archytas clan]]
+* ''[[Newt]]'' (+33554432/33480783) → [[Garischismic clan #Beatles|Garischismic clan]]
 * [[Decimal]] (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal|Dicot family]]
 * [[Squares]] (+81/80) → [[Meantone family #Squares|Meantone family]]
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 * ''[[Decoid]]'' (+67108864/66976875) → [[Quintosec family #Decoid|Quintosec family]]
 * ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic|Kleismic family]]
+* ''[[Subneutral]]'' (+274877906944/274658203125) → [[Luna family #Subneutral|Luna family]]
 * ''[[Neptune]]'' (+48828125/48771072) → [[Gammic family #Neptune|Gammic family]]
 * ''[[Tertiseptisix]]'' (+390625000/387420489) → [[Quartonic family #Tertiseptisix|Quartonic family]]
 * ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood|Whitewood family]]
-Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, newt, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].
+Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, septidiasemi, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].
 == Tertiaseptal ==
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 [[Badness]] (Sintel): 0.945
-== Newt ==
-Newt tempers out the [[garischisma]] and can be described as the {{nowrap| 41 & 270 }} temperament. It has a generator of a neutral third (0.2 cents flat of [[49/40]]) with a [[ploidacot]] signature of dicot. 41 generator steps fall short of 12 octaves by a [[schisma]]~[[aberschisma]]. From there the intervals of 5 and 7 can be derived.
-Newt continues to be significant as an [[11-limit]] temperament. The commas it tempers out include the [[lehmerisma]] (3025/3024), the [[symbiotic comma]] (19712/19683), the [[argyria]] (41503/41472), and the [[olympia]] (131072/130977). This extends into a strong [[13-limit]] temperament and eventually a strong no-17 [[19-limit]] temperament, a.k.a. '''neonewt'''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] work even better.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 2401/2400, 33554432/33480783
-{{Mapping|legend=1| 1 1 19 11 | 0 2 -57 -28 }}
-: mapping generators: ~2, ~49/40
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9315{{c}}, ~49/40 = 351.0932{{c}}
-: [[error map]]: {{val| -0.068 +0.163 +0.075 -0.188 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1141{{c}}
-: error map: {{val| 0.000 +0.273 +0.180 -0.022 }}
-{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}
-[[Badness]] (Sintel): 1.06
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 2401/2400, 3025/3024, 19712/19683
-Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}
-Optimal tunings:
-* WE: ~2 = 1199.9603{{c}}, ~49/40 = 351.1038{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1155{{c}}
-{{Optimal ET sequence|legend=0| 41, 188, 229, 270, 581, 851, 1121, 1972 }}
-Badness (Sintel): 0.643
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 2080/2079, 2401/2400, 3025/3024, 4096/4095
-Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}
-Optimal tunings:
-* WE: ~2 = 1199.9747{{c}}, ~49/40 = 351.1094{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1168{{c}}
-{{Optimal ET sequence|legend=0| 41, 229, 270, 581, 851, 2283b }}
-Badness (Sintel): 0.571
-=== 2.3.5.7.11.13.19 subgroup (neonewt) ===
-Subgroup: 2.3.5.7.11.13.19
-Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400
-Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}
-Optimal tunings:
-* WE: ~2 = 1199.9782{{c}}, ~49/40 = 351.1102{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1166{{c}}
-{{Optimal ET sequence|legend=0| 41, 229, 270, 581, 851 }}
-Badness (Sintel): 0.438
 == Septidiasemi ==
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 Badness (Sintel): 1.39
-== Subneutral ==
-{{See also| Luna family }}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 2401/2400, 274877906944/274658203125
-{{Mapping|legend=1| 1 -41 8 -5 | 0 60 -8 11 }}
-: mapping generators: ~2, ~46875/28672
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9998{{c}}, ~46875/28672 = 851.6994 (~57344/46875 = 348.3005{{c}})
-: [[error map]]: {{val| -0.000 +0.013 +0.090 -0.132 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~46875/28672 = 851.6995{{c}} (~57344/46875 = 348.3005{{c}})
-: error map: {{val| 0.000 +0.014 +0.090 -0.132 }}
-{{Optimal ET sequence|legend=1| 31, …, 348, 379, 410, 441, 1354, 1795, 2236 }}
-[[Badness]] (Sintel): 1.16
 == Maviloid ==
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 == Gorgik ==
+{{See also| Llywelynsmic clan }}
+Gorgik may be described as the {{nowrap| 21 & 37 }} temperament, with a [[ploidacot]] of 14-sheared 18-cot (or alpha-heptaseph due to a much simpler [[2.5.7 subgroup|2.5.7-subgroup]] [[restriction]]). [[58edo]] makes for a strong tuning for this temperament.
 [[Subgroup]]: 2.3.5.7