Landscape microtemperaments: Difference between revisions

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 Atomic tempers out the [[atom]], {{monzo| 161 -84 -12 }}, and in the [[7-limit]] the [[nommisma]], {{monzo| -55 30 2 1 }}, so that a stack of two [[schisma]]s gives the [[garischisma]], from which intervals of [[7/1|7]] can be derived. It may be described as the {{nowrap| 12 & 612 }} temperament, with a [[ploidacot]] signature of dodecaploid monocot.
-Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments #Hafnium|hafnium]].
+Atomic extensions discussed elsewhere include [[72nd-octave temperaments #Hafnium|hafnium]].
 [[Subgroup]]: 2.3.5.7
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 Badness (Sintel): 0.530
+==== Minutes ====
+Minutes (600e & 2460) splits the 1/12-octave period into five 1/60-octave parts.
+Subgroup: 2.3.5.7.11.13
+Comma list: 9801/9800, 151263/151250, 371293/371250, 184549376/184528125
+Mapping: {{mapping| 60 0 805 1690 2585 1173 | 0 1 7 -16 -25 -10 }}
+: mapping generators: ~2704/2673, ~3
+Optimal tunings:
+* WE: ~2704/2673 = 19.999967{{c}}, ~3/2 = 701.946866{{c}}
+* CWE: ~2704/2673 = 20.000000{{c}}, ~3/2 = 701.948111{{c}}
+{{Optimal ET sequence|legend=0| 600e, …, 1860, 2460, 6780, 9240 }}
+Badness (Sintel): 2.82
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 9801/9800, 12376/12375, 28561/28560, 151263/151250, 11275335/11275264
+Mapping: {{mapping| 60 0 805 1690 2585 1173 1957 | 0 1 7 -16 -25 -10 -18 }}
+Optimal tunings:
+* WE: ~2704/2673 = 19.999974{{c}}, ~3/2 = 701.946956{{c}}
+* CWE: ~2704/2673 = 20.000000{{c}}, ~3/2 = 701.947926{{c}}
+{{Optimal ET sequence|legend=0| 600e, …, 1860, 2460, 6780, 9240 }}
+Badness (Sintel): 1.67
+===== 19-limit =====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 9801/9800, 12376/12375, 12636/12635, 23409/23408, 28561/28560, 151263/151250
+Mapping: {{mapping| 60 60 385 730 1085 573 877 -61 | 0 1 7 -16 -25 -10 -18 9 }}
+Optimal tunings:
+* WE: ~2704/2673 = 19.999962{{c}}, ~3/2 = 701.946354{{c}}
+* CWE: ~2704/2673 = 20.000000{{c}}, ~3/2 = 701.947751{{c}}
+{{Optimal ET sequence|legend=0| 600e, 1860, 2460, 4320, 6780, 9240 }}
+Badness (Sintel): 1.50
 == Avicenna ==
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 Badness (Sintel): 0.640
-=== 2.3.5.7.11.13.19 subgroup (neozinc) ===
+==== 2.3.5.7.11.13.19 subgroup (neozinc) ====
 Subgroup: 2.3.5.7.11.13.19
@@ Line 779: / Line 827: @@
 Badness (Sintel): 0.477
+=== Neodymium ===
+Neodymium (540 & 1920) splits the period into 1/60-octave halves for prime 17.
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 9801/9800, 10648/10647, 31213/31212, 105644/105625, 196625/196608
+Mapping: {{mapping| 60 4 30 132 244 386 391 | 0 5 6 2 -2 -9 -8 }}
+: mapping generators: ~612/605, ~216/175
+Optimal tunings:
+* WE: ~612/605 = 20.0002{{c}}, ~216/175 = 364.3894{{c}}
+* CWE: ~612/605 = 20.0000{{c}}, ~216/175 = 364.3864{{c}}
+{{Optimal ET sequence|legend=0| 540, 1380, 1920, 2460, 4380, 6840e }}
+Badness (Sintel): 1.23
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 5929/5928, 6860/6859, 9801/9800, 10241/10240, 23409/23408, 89376/89375
+Mapping: {{mapping| 60 4 30 132 244 386 391 182 | 0 5 6 2 -2 -9 -8 4 }}
+Optimal tunings:
+* WE: ~612/605 = 20.0001{{c}}, ~216/175 = 364.3883{{c}}
+* CWE: ~612/605 = 20.0000{{c}}, ~216/175 = 364.3860{{c}}
+{{Optimal ET sequence|legend=0| 540, 1380, 1920, 2460, 4380, 6840e }}
+Badness (Sintel): 1.02
 == Poe ==