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| Line 56: |
Line 56: |
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| {{Optimal ET sequence|legend=1|282, 759def, 1041, 1323, 2082de}} | | {{Optimal ET sequence|legend=1|282, 759def, 1041, 1323, 2082de}} |
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| == Hafnium ==
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| Hafnium is a period-72 temperament created by temperament-merging 4320edo and 5544edo, equal temperaments notable for their high divisibility. Named after the 72nd element.
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 9801/9800, 250047/250000, 184549376/184528125, 463373664/463203125
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| Mapping: [{{val|72 72 462 876 1302 1193}}, {{val|0 1 -7 -16 -25 -22}}]
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| Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948
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| Optimal tuning (CTE): ~3/2 = 701.948
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| {{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}}
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| ===17-limit===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 9801/9800, 12376/12375, 21879/21875, 194481/194480, 1713660/1713481, 97144749/97140736
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| Mapping: [{{val|72 72 462 876 1302 1193 547}}, {{val|0 1 -7 -16 -25 -22 -6}}]
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| Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948
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| Optimal tuning (CTE): ~3/2 = 701.948
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| {{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}}
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| ===2.3.5.7.11.13.17.31 subgroup===
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| Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed.
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| Subgroup: 2.3.5.7.11.13.17.31
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| Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625
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| Sval mapping: [{{val|72 72 462 876 1302 1193 547 356}}, {{val|0 1 -7 -16 -25 -22 -6 6}}]
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| Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948
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| Optimal tuning (CTE): ~3/2 = 701.948
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| ===2.3.5.7.11.13.17.31.37 subgroup===
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| [[37/22]] is mapped to exact three-quarters of the octave.
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| Subgroup: 2.3.5.7.11.13.17.31
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| Comma list: 10881/10880, 12376/12375, 16576/16575, 93093/93092, 954304/954261, 2737889/2737800, 126607131/126605120
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| Sval mapping: [{{val|72 72 462 876 1302 1193 547 356 378}}, {{val|0 1 -7 -16 -25 -22 -6 6 -25}}]
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| Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948
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| Optimal tuning (CTE): ~3/2 = 701.948
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| == Iridium == | | == Iridium == |