6L 3s: Difference between revisions

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Keenan Pepper (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
968 edits
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Line 16: Line 16:
{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="10" | Generator
! colspan="6" | Generator
! | Cents
! | Cents
!1500edo
! | Comments
! | Comments
|-
|-
Line 26: Line 27:
| |  
| |  
| |  
| |  
| |  
| | 133.3̄
| |  
| | 166.6̄
| |
| |
| | 133.33
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| | 10\87
| |  
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Line 38: Line 37:
| |  
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| | 137.93…
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| | 172.41…
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| | 10\87
| | 137.93
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|-
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| | 9\78
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Line 51: Line 47:
| |  
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| | 138.46…
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| | 173.97…
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| | 9\78
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| | 138.46
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|-
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| | 8\69
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Line 64: Line 57:
| |  
| |  
| |  
| |  
| | 139.13…
| | 173.91…
| |  
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| | 8\69
| |
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| | 139.13
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|-
|-
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|15\129
|
|
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|139.53…
|174.41…
|
|-
| | 7\60
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| | 7\60
| |  
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| | 140
| | 140
| | 175
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|-
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| | 6\51
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Line 90: Line 87:
| |  
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| | 6\51
| | 141.17…
| |
| | 176.47…
| |
| |  
| |
| | 141.18
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| |  
| | 11\93
| |  
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| | 141.93…
| | 11\93
| | 177.41…
| |
| |
| |
| | 141.935
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| |  
| | 16\135
| |  
| |  
| |  
| |  
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| |  
| |  
| |  
| |  
| | 142.2̄
| |  
| | 177.7̄
| | 16\135
| |
| |
| | 142.22
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |
| |
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| |  
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| | 21\177
| | 21\177
| |  
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| | 142.37
| style="text-align:center;" |
|-
| |  
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| |  
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| |  
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| |  
| | 142.37…
| |  
| | 177.96…
| |
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| | 26\219
| | 142.47
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| |
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| | 5\42
| | 5\42
| |  
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Line 160: Line 127:
| |  
| |  
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| | 142.86
| | 142.85…
| | 178.57…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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|
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|14\117
| |  
|
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|143.58…
|179.48…
|
|-
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|9\75
|
|
|
|
|144
|180
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|-
| | 4\33
| | 4\33
| |  
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Line 172: Line 157:
| |  
| |  
| |  
| |  
| |  
| | 145.4̄5̄
| | 145.455
| | 181.8̄1̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
|
| |  
|11\90
|
|
|
|
|146.6̄
|183.3̄
|
|-
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|7\57
|
|
|
|
|147.36…
|184.21…
|
|-
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|10\81
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|
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|148.14…
|185.18…
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|-
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|13\105
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|148.57…
|185.71…
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|-
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|16\129
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|148.83…
|186.04…
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|-
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|19\153
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|149.01…
|186.27…
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|-
| | 3\24
| | 3\24
| |
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Line 187: Line 228:
| |  
| |  
| | 150
| | 150
| | 187.5
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
|
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|11\87
| |  
|
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|
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|
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|
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|151.72…
| |
|189.65…
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| | 151.71
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|-
|-
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| | 8\63
| |  
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| | 151.70…
| | 189.63…
| |  
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| | 152.38
| style="text-align:center;" |
|-
|-
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|
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|8\63
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| | 21\165
|152.38…
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|190.47…
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| | 152.73
| style="text-align:center;" |
|-
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| | 55\432
| |
| | 152.78
| style="text-align:center;" |  
|-
|-
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| |  
Line 247: Line 267:
| |  
| |  
| |  
| |  
| |  
| | 152.78…
| |  
| | 190.98…
| |
| | 89\699
| | 152.79
| style="text-align:center;" | Golden Triforce
| style="text-align:center;" | Golden Triforce
|-
|-
| |
|
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|
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|13\102
| |
|
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|
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|
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|152.94…
| | 34\267
|191.17…
| |
|
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| | 152.81
| style="text-align:center;" |
|-
| |
| |  
| |  
| |
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| | 13\102
| |  
| |  
| |  
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| | 152.94
| style="text-align:center;" |  
|-
|-
| |
| |
| |  
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| | 5\39
| | 5\39
Line 288: Line 287:
| |  
| |  
| |  
| |  
| |  
| | 153.84…
| |  
| | 192.30…
| | 153.85
| style="text-align:center;" | Triforce is around here
| style="text-align:center;" | Triforce is around here
|-
|-
| |  
|
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|
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|12\93
| |  
|
|
|
|154.83…
|193.54…
|
|-
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Line 304: Line 308:
| |  
| |  
| | 155.2
| | 155.2
| | 193.99…
| |  
| |  
|-
|-
| |  
|
|7\54
|
|
|
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|155.5̄
|194.4̄
|
|-
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|9\69
|
|
|
|
|156.52…
|195.65…
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|-
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|11\84
|
|
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|157.14…
|196.42…
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|-
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|13\99
|
|
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|157.5̄7̄
|196.9̄6̄
|
|-
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|15\114
|
|
|
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|157.89…
|197.36…
|
|-
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|17\129
|
|
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|158.13…
|197.67…
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|-
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|19\144
|
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|158.3̄
|197.91…
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|-
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|21\159
|
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|158.49…
|198.11…
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|-
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|23\174
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|158.62…
|198.27…
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|-
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|25\189
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|158.73…
|198.41…
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|-
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|27\204
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|158.82…
|198.52…
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|-
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|29\219
|
|
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|158.90…
|198.63…
|
|-
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|31\234
|
|
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|158.97…
|198.71…
|
|-
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|33\249
|
|
|
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|159.03…
|198.79…
|
|-
|
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|35\264
|
|
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|159.0̄9̄
|198.86…
|
|-
|
|
|
|37\279
|
|
|159.13…
|198.92…
|
|-
|
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|39\294
|
|159.18…
|198.97…
|
|-
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|41\309
|159.22…
|199.02…
|
|-
| | 2\15
| | 2\15
| |
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| |
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Line 317: Line 498:
| |  
| |  
| | 160
| | 160
| | 200
| style="text-align:center;" | Boundary of propriety (generators
| style="text-align:center;" | Boundary of propriety (generators


smaller than this are proper)
smaller than this are proper)
|-
|
|21\156
|
|
|
|
|161.53…
|201.92…
|
|-
|
|19\141
|
|
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|161.70…
|202.12…
|
|-
|-
| |  
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| | 17\126
| |  
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| | 161.90…
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| | 202.38…
| |
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| | 17\126
| | 161.905
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
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| | 15\111
| |  
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| | 162.16…
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| | 202.70…
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| | 15\111
| |
| | 162.16
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| |  
| | 13\96
| |  
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| |  
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| |
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| |
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| | 13\96
| |  
| |  
| |  
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| | 162.50
| | 162.50
| | 203.125
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
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| | 11\81
| |  
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| |  
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| |  
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| | 162.96…
| | 11\81
| | 203.70…
| |
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| | 162.96
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |
| |  
| |  
| | 9\66
| | 9\66
Line 383: Line 569:
| |  
| |  
| |  
| |  
| | 163.64
| | 163.6̄3̄
| | 204.5̄4̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
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| | 7\51
| | 7\51
Line 395: Line 579:
| |  
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| | 164.70…
| | 164.71
| | 205.88…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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Line 408: Line 589:
| |  
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| | 165.51…
| | 165.52
| | 206.89…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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|17\123
|
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|165.85…
|207.31…
|
|-
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| | 5\36
| | 5\36
Line 420: Line 609:
| |  
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| | 166.6̄
| |  
| | 208.3̄
| | 166.67
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 428: Line 616:
| |  
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| | 13\93
| |  
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| | 167.92…
| | 167.74
| | 209.91…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 8\57
| |  
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| | 168.42…
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| | 210.52…
| | 34\243
| |
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| | 167.9
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 457: Line 639:
| |  
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| | 168.92…
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| | 211.15…
| |
| style="text-align:center;" | L/s = e
| | 89\636
| | 167.93
| style="text-align:center;" |  
|-
|-
| |  
| |  
| | 11\78
| |  
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| | 169.23…
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| | 211.53…
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| | 55\393
| |
| | 167.94
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 14\99
| |  
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| | 169.6̄9̄
| | 21\150
| | 212.2̄1̄
| |
| |
| |
| | 168
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
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| | 17\120
| |  
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| | 8\57
| |  
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| | 170.00
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| | 212.5
| |
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| | 168.42
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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|
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|20\141
| |
|
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|
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|
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|
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|170.21…
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|212.76…
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|
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| | 168.93
| style="text-align:center;" | L/s = e
|-
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| | 11\78
| |
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| | 169.23
| style="text-align:center;" | <span style="display: block; text-align: center;">
 
</span>
|-
|-
| |  
|
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|23\162
| |  
|
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|
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|
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| | 14\99
|170.37…
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|212.96…
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|
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| | 169.70
| style="text-align:center;" |  
|-
|-
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|
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|26\183
| |  
|
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|
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|170.49…
| | 17\120
|213.11…
| |
|
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| | 170.00
| style="text-align:center;" | <span style="display: block; text-align: center;">
 
</span>
|-
|-
| |
| |
| | 3\21
| | 3\21
| |  
| |  
Line 567: Line 709:
| |  
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| | 171.42…
| |  
| | 214.28…
| | 171.43
| style="text-align:center;" | L/s = 3
| style="text-align:center;" | L/s = 3
|-
|-
Line 578: Line 719:
| |  
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| |  
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| | 172.53…
| |  
| | 215.67…
| |
| style="text-align:center;" |<span style="display: block; text-align: center;">L/s = pi</span>
| |
| | 172.54
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
|-
| |  
| |  
| | 16\111
| |  
| |  
| |  
| |  
| |  
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| |  
| |  
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| | 172.97…
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| | 216.21…
| | 16\111
| |
| |
| | 172.97
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 13\90
| |  
| |  
| |  
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| |  
| |  
| |  
| |  
| |  
| | 173.3̄
| | 13\90
| | 216.6̄
| |
| |
| |
| | 173.33
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |
| |  
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| | 10\69
| | 10\69
Line 621: Line 749:
| |  
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| | 173.91
| | 173.91…
| | 217,39…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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Line 634: Line 759:
| |  
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| | 174.36
| | 174.35…
| | 217.94…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |  
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| | 7\48
| | 7\48
| |
| |  
| |  
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Line 648: Line 770:
| |  
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| | 175.00
| | 175.00
| | 218.75
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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|
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|
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|18\123
| |  
|
|
|
|175.60…
|219.51…
|
|-
| |  
| |  
| | 11\75
| | 11\75
Line 661: Line 790:
| |  
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| | 176.00
| | 176.00
| | 220
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
|
| |  
|
|15\102
|
|
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|176.47…
|220.58…
|
|-
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|19\129
|
|
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|176.74…
|220.93…
|
|-
|
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|23\156
|
|
|
|176.92…
|221.15…
|
|-
| |  
| |  
| | 4\27
| | 4\27
Line 671: Line 829:
| |  
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| |  
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| | 177.7̄
| |  
| | 222.2̄
| | 177.78
| style="text-align:center;" | L/s = 4
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| |  
| |  
| |  
| | 17\114
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 178.94…
| |  
| | 223.68…
| | 17\114
| |
| |
| | 178.95
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| |
| |
| |
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Line 699: Line 849:
| |  
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| | 179.31
| | 179.31…
| | 224.13…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |  
| |  
| |  
| |  
| | 9\60
| | 9\60
| |
| |  
| |  
| |  
| |  
| |  
| |  
| | 180.00
| | 180.00
| | 225
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
|
| |  
|
| |  
|14\93
|
|
|
|180.64…
|225.80…
|
|-
|
|
|19\126
|
|
|
|180.95…
|226.19…
|
|-
| |  
| |  
| | 5\33
| | 5\33
Line 724: Line 889:
| |  
| |  
| |  
| |  
| |  
| | 181.8̄1̄
| | 181.82
| | 227.2̄7̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| |  
| |  
| |  
| | 26\171
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 182.45…
| |  
| | 228.07…
| |
| |
| | 26\171
| | 182.46
| style="text-align:center;" | Terrain is around here
| style="text-align:center;" | Terrain is around here
|-
|-
| |  
| |  
| |  
| |  
| | 21\138
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 182.60…
| |  
| | 228.26…
| |
| | 21\138
| |
| | 182.61
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| |  
| |  
| |  
| | 16\105
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 182.85…
| |  
| | 228.57…
| | 16\105
| |
| |
| | 182.86
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |
| |  
| |  
| |  
| |  
Line 777: Line 929:
| |  
| |  
| |  
| |  
| | 183.33
| | 183.3̄
| | 229.16̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |
| |  
| |  
| | 6\39
| | 6\39
Line 790: Line 939:
| |  
| |  
| |  
| |  
| | 184.62
| | 184.61…
| | 230.76…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|
|
|19\123
|
|
|
|185.36…
|231.70…
|
|-
|
|
|13\84
|
|
|
|185.71…
|232.14…
|
|-
|-
| |  
| |  
| | 7\45
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 186.6̄
| | 233.3̄
| |  
| |  
| | 7\45
|-
| |  
|
| |  
|
| |  
|15\96
| | 186.67
|
| |  
|
|
|187.5
|234.375
|
|-
|-
| |  
| |  
| | 8\51
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 188.23…
| |  
| | 235.29…
| | 8\51
| |
| |
| | 188.235
| |  
| |  
|-
|-
| |  
| |  
| | 9\57
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 189.47…
| | 236.84…
| |  
| |  
| |  
|-
| |  
|
| | 9\57
|
| |  
|19\120
| | 189.47
|
| |  
|
|
|190
|237.5
|
|-
|-
| |  
| |  
| | 10\63
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 190.47…
| |  
| | 238.09…
| |
| |
| | 10\63
| | 190.48
| |  
| |  
|-
|-
| | 1\6
| | 1\6
| |
| |
| |
| |
| |  
| |  
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| |  
Line 856: Line 1,030:
| |  
| |  
| | 200
| | 200
| | 250
| style="text-align:center;" |  
| style="text-align:center;" |  
|}
|}


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Revision as of 06:44, 23 August 2021

↖ 5L 2s ↑ 6L 2s 7L 2s ↗
← 5L 3s 6L 3s 7L 3s →
↙ 5L 4s ↓ 6L 4s 7L 4s ↘ 
┌╥╥┬╥╥┬╥╥┬┐
│║║│║║│║║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLs
sLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 1\9 to 1\6 (133.3 ¢ to 200.0 ¢)
Dark 1\6 to 2\9 (200.0 ¢ to 266.7 ¢)
TAMNAMS information
Name hyrulic
Prefix hyru-
Abbrev. hy
Related MOS scales
Parent 3L 3s
Sister 3L 6s
Daughters 9L 6s, 6L 9s
Neutralized 3L 6s
2-Flought 15L 3s, 6L 12s
Equal tunings
Equalized (L:s = 1:1) 1\9 (133.3 ¢)
Supersoft (L:s = 4:3) 4\33 (145.5 ¢)
Soft (L:s = 3:2) 3\24 (150.0 ¢)
Semisoft (L:s = 5:3) 5\39 (153.8 ¢)
Basic (L:s = 2:1) 2\15 (160.0 ¢)
Semihard (L:s = 5:2) 5\36 (166.7 ¢)
Hard (L:s = 3:1) 3\21 (171.4 ¢)
Superhard (L:s = 4:1) 4\27 (177.8 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)

6L 3s is a MOS pattern with period 1\3.

The tiny region between 26\171 and 281\1848 is the terrain region, giving the abitonic scale for the remarkable terrain temperament chromatic pair. If you feel that is too small a region to allocate or prefer edos of a more usual size, you can call it the region between 5/33 and 6/39, but that misses the extreme accuracy of this temperament.

For a more down-to-earth temperament, try triforce.

Generator Cents 1500edo Comments
1\9 133.3̄ 166.6̄
10\87 137.93… 172.41…
9\78 138.46… 173.97…
8\69 139.13… 173.91…
15\129 139.53… 174.41…
7\60 140 175
6\51 141.17… 176.47…
11\93 141.93… 177.41…
16\135 142.2̄ 177.7̄
21\177 142.37… 177.96…
5\42 142.85… 178.57…
14\117 143.58… 179.48…
9\75 144 180
4\33 145.4̄5̄ 181.8̄1̄
11\90 146.6̄ 183.3̄
7\57 147.36… 184.21…
10\81 148.14… 185.18…
13\105 148.57… 185.71…
16\129 148.83… 186.04…
19\153 149.01… 186.27…
3\24 150 187.5
11\87 151.72… 189.65…
151.70… 189.63…
8\63 152.38… 190.47…
152.78… 190.98… Golden Triforce
13\102 152.94… 191.17…
5\39 153.84… 192.30… Triforce is around here
12\93 154.83… 193.54…
155.2 193.99…
7\54 155.5̄ 194.4̄
9\69 156.52… 195.65…
11\84 157.14… 196.42…
13\99 157.5̄7̄ 196.9̄6̄
15\114 157.89… 197.36…
17\129 158.13… 197.67…
19\144 158.3̄ 197.91…
21\159 158.49… 198.11…
23\174 158.62… 198.27…
25\189 158.73… 198.41…
27\204 158.82… 198.52…
29\219 158.90… 198.63…
31\234 158.97… 198.71…
33\249 159.03… 198.79…
35\264 159.0̄9̄ 198.86…
37\279 159.13… 198.92…
39\294 159.18… 198.97…
41\309 159.22… 199.02…
2\15 160 200 Boundary of propriety (generators

smaller than this are proper)

21\156 161.53… 201.92…
19\141 161.70… 202.12…
17\126 161.90… 202.38…
15\111 162.16… 202.70…
13\96 162.50 203.125
11\81 162.96… 203.70…
9\66 163.6̄3̄ 204.5̄4̄
7\51 164.70… 205.88…
12\87 165.51… 206.89…
17\123 165.85… 207.31…
5\36 166.6̄ 208.3̄
167.92… 209.91…
8\57 168.42… 210.52…
168.92… 211.15… L/s = e
11\78 169.23… 211.53…
14\99 169.6̄9̄ 212.2̄1̄
17\120 170.00 212.5
20\141 170.21… 212.76…
23\162 170.37… 212.96…
26\183 170.49… 213.11…
3\21 171.42… 214.28… L/s = 3
172.53… 215.67… L/s = pi
16\111 172.97… 216.21…
13\90 173.3̄ 216.6̄
10\69 173.91… 217,39…
17\117 174.35… 217.94…
7\48 175.00 218.75
18\123 175.60… 219.51…
11\75 176.00 220
15\102 176.47… 220.58…
19\129 176.74… 220.93…
23\156 176.92… 221.15…
4\27 177.7̄ 222.2̄ L/s = 4
17\114 178.94… 223.68…
13\87 179.31… 224.13…
9\60 180.00 225
14\93 180.64… 225.80…
19\126 180.95… 226.19…
5\33 181.8̄1̄ 227.2̄7̄
26\171 182.45… 228.07… Terrain is around here
21\138 182.60… 228.26…
16\105 182.85… 228.57…
11\72 183.3̄ 229.16̄
6\39 184.61… 230.76…
19\123 185.36… 231.70…
13\84 185.71… 232.14…
7\45 186.6̄ 233.3̄
15\96 187.5 234.375
8\51 188.23… 235.29…
9\57 189.47… 236.84…
19\120 190 237.5
10\63 190.47… 238.09…
1\6 200 250
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