Landscape microtemperaments: Difference between revisions

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 Badness (Sintel): 1.50
+==== Hafnium ====
+Hafnium (1224 & 4320), named after the 72nd element, splits the 1/12-octave period into six 1/72-octave parts. Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these primes are also prescribed. In the add-37 version, [[37/22]] is mapped to exact 3\4.
+Subgroup: 2.3.5.7.11.13
+Comma list: 9801/9800, 151263/151250, 184549376/184528125, 308915776/308828625
+Mapping: {{mapping| 72 0 966 2028 3102 2777 | 0 1 -7 -16 -25 -22 }}
+: mapping generators: ~105/104, ~3
+Optimal tunings:
+* WE: ~105/104 = 16.666629{{c}}, ~3/2 = 701.945668{{c}}
+* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947388{{c}}
+{{Optimal ET sequence|legend=0| 1224, 3096e, 4320, 5544, 9864c }}
+Badness (Sintel): 4.76
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 9801/9800, 12376/12375, 151263/151250, 1713660/1713481, 97144749/97140736
+Mapping: {{mapping| 72 0 966 2028 3102 2777 979 | 0 1 -7 -16 -25 -22 -6 }}
+: mapping generators: ~105/104, ~3
+Optimal tunings:
+* WE: ~105/104 = 16.666615{{c}}, ~3/2 = 701.944968{{c}}
+* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947293{{c}}
+{{Optimal ET sequence|legend=0| 1224, 3096e, 4320, 5544, 9864c }}
+Badness (Sintel): 2.73
+===== 2.3.5.7.11.13.17.31 subgroup =====
+Subgroup: 2.3.5.7.11.13.17.31
+Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625
+Subgroup-val mapping: {{mapping| 72 0 966 2028 3102 2777 979 -328 | 0 1 -7 -16 -25 -22 -6 6 }}
+Optimal tunings:
+* WE: ~105/104 = 16.666643{{c}}, ~3/2 = 701.946542{{c}}
+* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947581{{c}}
+{{Optimal ET sequence|legend=0| 1224, 3096e, 4320, 5544 }}
+Badness (Sintel): 2.36
+===== 2.3.5.7.11.13.17.31.37 subgroup =====
+Subgroup: 2.3.5.7.11.13.17.31.37
+Comma list: 9801/9800, 10881/10880, 12376/12375, 16576/16575, 57629/57624, 93093/93092, 179712/179707
+Subgroup-val mapping: {{mapping| 72 0 966 2028 3102 2777 979 -328 3228 | 0 1 -7 -16 -25 -22 -6 6 -25 }}
+Optimal tunings:
+* WE: ~105/104 = 16.666648{{c}}, ~3/2 = 701.946549{{c}}
+* CWE: ~105/104 = 16.666667{{c}}, ~3/2 = 701.947386{{c}}
+{{Optimal ET sequence|legend=0| 1224, 3096el, 4320, 5544 }}
+Badness (Sintel): 1.98
 == Avicenna ==