6L 3s: Difference between revisions

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Xenwolf (talk | contribs)
Looks broken. Also, don't push new number notation without getting consensus first. Undo revision 76766 by Moremajorthanmajor (talk)
Tag: Undo
Line 16: Line 16:
{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="6" | Generator
! colspan="10" | Generator
! | Cents
! | Cents
!1500edo
! | Comments
! | Comments
|-
|-
Line 27: Line 26:
| |  
| |  
| |  
| |  
| | 133.3̄
| |  
| | 166.
| |  
| |
| |
| | 133.33
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 10\87
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| | 137.93
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|-
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Line 37: Line 52:
| |  
| |  
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| | 137.93…
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| | 172.41…
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| | 9\78
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| | 138.46
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|-
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| | 9\78
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Line 47: Line 64:
| |  
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| | 138.46…
| | 173.97…
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|-
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| | 8\69
| | 8\69
| |  
| |  
| |  
| |  
| | 139.13
| |
|-
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| | 139.13…
| | 173.91…
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|-
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|15\129
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|
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|139.53…
|174.41…
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| | 7\60
| |  
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| | 7\60
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| | 140
| | 140
| | 175
| |  
| |  
|-
|-
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| | 6\51
| | 6\51
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Line 86: Line 95:
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| |  
| | 141.18
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
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| | 11\93
| |  
| |  
| | 141.17…
| |  
| | 176.47…
| |  
| | 141.935
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| |  
| | 11\93
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| | 141.93…
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| | 177.41…
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| | 16\135
| |
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| | 142.22
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| |  
| | 16\135
| |  
| |  
| |  
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| |  
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| | 142.2̄
| |  
| | 177.
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| | 21\177
| |
| | 142.37
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 21\177
| |  
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| | 142.37…
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| | 177.96…
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| | 26\219
| | 142.47
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 5\42
| | 5\42
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Line 127: Line 160:
| |  
| |  
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| | 142.85…
| | 142.86
| | 178.57…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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|14\117
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|143.58…
|179.48…
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|-
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|9\75
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|144
|180
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|-
| | 4\33
| | 4\33
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Line 157: Line 172:
| |  
| |  
| |  
| |  
| | 145.4̄5̄
| |  
| | 181.8̄1̄
| | 145.455
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
|
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|11\90
| |  
|
|
|
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|146.6̄
|183.3̄
|
|-
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|7\57
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|147.36…
|184.21…
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|-
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|10\81
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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 228: Line 187:
| |  
| |  
| | 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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|151.72…
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|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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|8\63
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|152.38…
| | 21\165
|190.47…
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| | 152.73
| style="text-align:center;" |
|-
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| | 55\432
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| | 152.78
| style="text-align:center;" |  
|-
|-
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Line 267: Line 247:
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| | 152.78…
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| | 190.98…
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| | 89\699
| | 152.79
| style="text-align:center;" | Golden Triforce
| style="text-align:center;" | Golden Triforce
|-
|-
|
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|13\102
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|152.94…
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|191.17…
| | 34\267
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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 287: Line 288:
| |  
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| | 153.84…
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| | 192.30…
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| | 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
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|
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|154.83…
|193.54…
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|-
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Line 308: Line 304:
| |  
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| | 155.2
| | 155.2
| | 193.99…
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|-
|-
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|7\54
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|155.5̄
|194.4̄
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|-
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|9\69
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|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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|13\99
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|157.5̄7̄
|196.9̄6̄
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|-
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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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|19\144
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|158.3̄
|197.91…
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|21\159
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|158.49…
|198.11…
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|23\174
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|158.62…
|198.27…
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|25\189
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|158.73…
|198.41…
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|27\204
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|158.82…
|198.52…
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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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|-
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|35\264
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|159.0̄9̄
|198.86…
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|-
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|37\279
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|159.13…
|198.92…
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|-
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|39\294
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|159.18…
|198.97…
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|41\309
|159.22…
|199.02…
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| | 2\15
| | 2\15
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Line 498: Line 317:
| |  
| |  
| | 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)
|-
|-
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|21\156
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|161.53…
|201.92…
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|-
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|19\141
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|161.70…
|202.12…
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|-
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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
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| | 162.16
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 13\96
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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
| | 11\81
Line 558: Line 370:
| |  
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| | 162.96
| | 162.96…
| | 203.70…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 9\66
| | 9\66
Line 569: Line 383:
| |  
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| | 163.6̄3̄
| | 163.64
| | 204.5̄4̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 7\51
| | 7\51
Line 579: Line 395:
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| | 164.70…
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| | 205.88…
| | 164.71
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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Line 589: Line 408:
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| | 165.51…
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| | 206.89…
| | 165.52
| 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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|-
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| | 5\36
| | 5\36
Line 609: Line 420:
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| | 166.6̄
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| | 208.
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| | 166.67
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 616: Line 428:
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| | 13\93
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| | 167.92…
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| | 209.91…
| | 167.74
| 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…
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| | 34\243
| |
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| | 167.9
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 639: Line 457:
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| | 168.92…
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| | 211.15…
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| style="text-align:center;" | L/s = e
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| | 89\636
| | 167.93
| style="text-align:center;" |  
|-
|-
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| | 11\78
| |  
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| | 169.23…
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| | 211.53…
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| | 55\393
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| | 167.94
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 14\99
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| | 169.6̄9̄
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| | 212.2̄1̄
| | 21\150
| |
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| | 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
| | 168.42
| | 212.5
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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|20\141
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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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|170.37…
| | 14\99
|212.96…
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| | 169.70
| style="text-align:center;" |  
|-
|-
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|26\183
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|170.49…
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|213.11…
| | 17\120
|
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| | 170.00
| style="text-align:center;" | <span style="display: block; text-align: center;">
 
</span>
|-
|-
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| | 3\21
| | 3\21
| |  
| |  
Line 709: Line 567:
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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 719: Line 578:
| |  
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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>
|-
|-
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| | 16\111
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| | 172.97…
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| | 216.21…
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| | 16\111
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| | 172.97
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 13\90
| | 13\90
Line 738: Line 608:
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| | 173.33
| | 173.
| | 216.6̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| |
| |
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| |  
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| | 10\69
| | 10\69
Line 749: Line 621:
| |  
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| | 173.91…
| | 173.91
| | 217,39…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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Line 759: Line 634:
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| | 174.35…
| | 174.36
| | 217.94…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| |
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| | 7\48
| | 7\48
| |
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Line 770: Line 648:
| |  
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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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|18\123
| |  
|
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|
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|175.60…
|219.51…
|
|-
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| | 11\75
| | 11\75
Line 790: Line 661:
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| | 176.00
| | 176.00
| | 220
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
|
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|
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|15\102
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|176.47…
|220.58…
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|-
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|19\129
|
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|176.74…
|220.93…
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|-
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|23\156
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|176.92…
|221.15…
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|-
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| | 4\27
| | 4\27
Line 829: Line 671:
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| | 177.7̄
| |  
| | 222.
| |  
| | 177.78
| style="text-align:center;" | L/s = 4
| style="text-align:center;" | L/s = 4
|-
|-
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Line 838: Line 686:
| |  
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| | 178.95
| | 178.94…
| | 223.68…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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Line 849: Line 699:
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| | 179.31…
| | 179.31
| | 224.13…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
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| | 9\60
| | 9\60
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| | 180.00
| | 180.00
| | 225
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
|
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|
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|14\93
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|
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|180.64…
|225.80…
|
|-
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|19\126
|
|
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|180.95…
|226.19…
|
|-
| |  
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| | 5\33
| | 5\33
Line 889: Line 724:
| |  
| |  
| |  
| |  
| | 181.8̄1̄
| |  
| | 227.2̄7̄
| | 181.82
| 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;" |  
|-
|-
| |
| |
| |
| |
| |
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Line 918: Line 764:
| |  
| |  
| |  
| |  
| |
| | 182.86
| | 182.85…
| | 228.57…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |
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| |  
Line 929: Line 777:
| |  
| |  
| |  
| |  
| | 183.
| | 183.33
| | 229.16̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |
| |
| |
| |  
| |  
| | 6\39
| | 6\39
Line 939: Line 790:
| |  
| |  
| |  
| |  
| | 184.61…
| | 184.62
| | 230.76…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
|
| |  
|
| |  
|19\123
| |  
|
| |  
|
| |  
|
| |  
|185.36…
| | 7\45
|231.70…
| |  
|
| |  
|-
| |  
|
| | 186.67
|
| |  
|13\84
|
|
|
|185.71…
|232.14…
|
|-
|-
| |  
| |  
| | 7\45
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 186.6̄
| |  
| | 233.
| |  
| | 8\51
| |
| |
| | 188.235
| |  
| |  
|-
|-
|
|
|15\96
|
|
|
|187.5
|234.375
|
|-
| |  
| |  
| | 8\51
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 188.23…
| | 235.29…
| |  
| |  
|-
| |
| |  
| |  
| | 9\57
| | 9\57
| |  
| |  
| | 189.47
| |
|-
| |  
| |  
| |  
| |  
| |  
| |  
| | 189.47…
| | 236.84…
| |  
| |  
|-
|
|
|19\120
|
|
|
|190
|237.5
|
|-
| |  
| |  
| | 10\63
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 190.47…
| | 10\63
| | 238.09…
| | 190.48
| |  
| |  
|-
|-
| | 1\6
| | 1\6
| |
| |
| |
| |
| |  
| |  
| |  
| |  
Line 1,030: Line 856:
| |  
| |  
| | 200
| | 200
| | 250
| style="text-align:center;" |  
| style="text-align:center;" |  
|}
|}


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

Revision as of 07:17, 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 ¢)
ViewTalkEdit

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 Comments
1\9 133.33
10\87 137.93
9\78 138.46
8\69 139.13
7\60 140
6\51 141.18
11\93 141.935
16\135 142.22
21\177 142.37
26\219 142.47
5\42 142.86
4\33 145.455
3\24 150
151.71
8\63 152.38
21\165 152.73
55\432 152.78
89\699 152.79 Golden Triforce
34\267 152.81
13\102 152.94
5\39 153.85 Triforce is around here
155.2
2\15 160 Boundary of propriety (generators

smaller than this are proper)

17\126 161.905
15\111 162.16
13\96 162.50
11\81 162.96
9\66 163.64
7\51 164.71
12\87 165.52
5\36 166.67
13\93 167.74
34\243 167.9
89\636 167.93
55\393 167.94
21\150 168
8\57 168.42
168.93 L/s = e
11\78 169.23

14\99 169.70
17\120 170.00

3\21 171.43 L/s = 3
172.54 L/s = pi
16\111 172.97
13\90 173.33
10\69 173.91
17\117 174.36
7\48 175.00
11\75 176.00
4\27 177.78 L/s = 4
17\114 178.95
13\87 179.31
9\60 180.00
5\33 181.82
26\171 182.46 Terrain is around here
21\138 182.61
16\105 182.86
11\72 183.33
6\39 184.62
7\45 186.67
8\51 188.235
9\57 189.47
10\63 190.48
1\6 200