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| * ''[[Pluto]]'' (+4000/3969) → [[Octagar temperaments #Pluto|Octagar temperaments]] | | * ''[[Pluto]]'' (+4000/3969) → [[Octagar temperaments #Pluto|Octagar temperaments]] |
| * ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]] | | * ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]] |
| | * ''[[Subsedia]]'' (+65536/64827) → [[Buzzardsmic clan #Subsedia|Buzzardsmic clan]] |
| * ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]] | | * ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]] |
| * ''[[Grendel]]'' (+6144/6125) → [[Porwell temperaments #Grendel|Porwell temperaments]] | | * ''[[Grendel]]'' (+6144/6125) → [[Porwell temperaments #Grendel|Porwell temperaments]] |
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| For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]]. | | For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]]. |
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| Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer. | | Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, browser, and grazer, in the order of increasing [[badness]]. |
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| == Mirkat == | | == Mirkat == |
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| Badness (Sintel): 1.57 | | Badness (Sintel): 1.57 |
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| == Subsedia ==
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| The generator for subsedia (10 & 111) is 0.5 cents flat of [[15/14]]-wide semitone and tempers out the mirkwai comma and [[buzzardsma]]. In this temperament, three generators makes ~[[16/13]], five of them equals ~[[24/17]], twelve of them equals ~[[16/7]], sixteen of them equals ~[[3/1]], and 45 of them equals ~22/1.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 16875/16807, 65536/64827
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| {{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}
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| : mapping generators: ~2, ~15/14
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1199.2693{{c}}, ~15/14 = 118.8923{{c}}
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| : [[error map]]: {{val| -0.731 +0.322 -0.060 +1.543 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 118.9682{{c}}
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| : error map: {{val| 0.000 +1.536 +1.545 +3.556 }}
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| {{Optimal ET sequence|legend=1| 10, 91cd, 101, 111, 121, 232d }}
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| [[Badness]] (Sintel): 3.99
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 540/539, 1375/1372, 65536/64827
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| Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.2891{{c}}, ~15/14 = 118.8978{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~15/14 = 118.9662{{c}}
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| {{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}
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| Badness (Sintel): 2.21
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 352/351, 540/539, 676/675, 1375/1372
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| Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.2920{{c}}, ~15/14 = 118.8980{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~15/14 = 118.9666{{c}}
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| {{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}
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| Badness (Sintel): 1.31
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
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| Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.2648{{c}}, ~15/14 = 118.8946{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~15/14 = 118.9655{{c}}
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| {{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232dg }}
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| Badness (Sintel): 1.00
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| === 19-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
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| Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.2847{{c}}, ~15/14 = 118.8929{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~15/14 = 118.9644{{c}}
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| {{Optimal ET sequence|legend=0| 10, 111, 121, 232dg }}
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| Badness (Sintel): 1.09
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| == Hemiseptisix == | | == Hemiseptisix == |