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5L 7s: Difference between revisions

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== Scale tree ==
== Scale tree ==
{| class="wikitable"
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
|-
! colspan="8" | Generator
| 7\12 || || || || || || 700.000 || 1 || 1 || 2.000 ||  
! | in cents
! | Comments
|-
|-
| style="text-align:center;" | 5\12
| || || || || || 38\65 || 701.539 || 6 || 5 || 1.200 || Photia
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 500
| |
|-
|-
| |
| || || || || 31\53 || || 701.887 || 5 || 4 || 1.250 || Helmholtz
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 37\89
| style="text-align:center;" | 498.876
| |
|-
|-
| |
| || || || || || 55\94 || 702.128 || 9 || 7 || 1.286 || Garibaldi
| |
| |
| |
| |
| |
| style="text-align:center;" | 32\77
| |
| style="text-align:center;" | 498.702
| |
|-
|-
| |
| || || || 24\41 || || || 702.409 || 4 || 3 || 1.333 || Andromeda
| |
| |
| |
| |
| style="text-align:center;" | 27\65
| |
| |
| style="text-align:center;" | 498.462
| style="text-align:center;" | Photia
|-
|-
| |
| || || || || || 65\111 || 702.703 || 11 || 8 || 1.375 ||
| |
| |
| |
| |
| |
| style="text-align:center;" | 49\118
| |
| style="text-align:center;" | 498.305
| style="text-align:center;" | Helmholtz/Pontiac/Nestoria
|-
|-
| |
| || || || || 41\70 || || 702.857 || 7 || 5 || 1.400 ||
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 71\171
| style="text-align:center;" | 498.246
| style="text-align:center;" | Helmholtz/Pontiac/Nestoria
|-
|-
| |
| || || || || || 58\99 || 703.030 || 10 || 7 || 1.428 || Undecental
| |
| |
| |
| style="text-align:center;" | 22\53
| |
| |
| |
| style="text-align:center;" | 498.113
| style="text-align:center;" | Helenus
|-
|-
| |
| || || 17\29 || || || || 703.448 || 3 || 2 || 1.500 || L/s = 3/2 Edson
| |
| |
| |
| |
| style="text-align:center;" | 39\94
| |
| |
| style="text-align:center;" | 497.872
| style="text-align:center;" | Garibaldi
|-
|-
| |
| || || || || || 61\104 || 703.846 || 11 || 7 || 1.571 ||
| |
| |
| style="text-align:center;" | 17\41
| |
| |
| |
| |
| style="text-align:center;" | 497.591
| style="text-align:center;" | Cassandra
|-
|-
| |
| || || || || 44\75 || || 704.000 || 8 || 5 || 1.600 ||
| |
| |
| |
| |
| style="text-align:center;" | 46\111
| |
| |
| style="text-align:center;" | 497.297
| |
|-
|-
| |
| || || || || || 71\121 || 704.132 || 13 || 8 || 1.625 || Golden parapyth
| |
| |
| |
| style="text-align:center;" | 29\70
| |
| |
| |
| style="text-align:center;" | 497.143
| style="text-align:center;" | Undecental
|-
|-
| |
| || || || 27\46 || || || 704.348 || 5 || 3 || 1.667 || Leapday
| |
| |
| |
| |
| style="text-align:center;" | 41\99
| |
| |
| style="text-align:center;" | 496.97
| style="text-align:center;" | Undecental
|-
|-
| |
| || || || || || 64\109 || 704.587 || 12 || 7 || 1.714 ||
| |
| style="text-align:center;" | 12\29
| |
| |
| |
| |
| |
| style="text-align:center;" | 496.552
| style="text-align:center;" | Optimum rank range (L/s=3/2)
 
Edson
|-
|-
| |
| || || || || 37\63 || || 704.762 || 7 || 4 || 1.750 ||
| |
| |
| |
| |
| style="text-align:center;" | 43\104
| |
| |
| style="text-align:center;" | 496.154
| |
|-
|-
| |  
| || || || || || 47\80 || 705.000 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 496.157
| style="text-align:center;" | L/s = pi/2
|-
|-
| |
| || 10\17 || || || || || 705.882 || 2 || 1 || 2.000 || Basic p-chromatic<br>(Generators smaller than this are proper)
| |
| |
| |
| style="text-align:center;" | 31\75
| |
| |
| |
| style="text-align:center;" | 496
| |
|-
|-
| |  
| || || || || || 43\73 || 706.849 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 495.904
| style="text-align:center;" | L/s = phi
|-
|-
| |
| || || || || 33\56 || || 707.143 || 7 || 3 || 2.333 || Supra
| |
| |
| |
| |
| style="text-align:center;" | 50\121
| |
| |
| style="text-align:center;" | 495.868
| style="text-align:center;" | Leapday/[[Peppermint-24|Peppermint]]/Pepperoni
|-
|-
| |
| || || || || || 56\95 || 707.368 || 12 || 5 || 2.400 ||
| |
| |
| style="text-align:center;" | 19\46
| |
| |
| |
| |
| style="text-align:center;" | 495.652
| style="text-align:center;" | Leapday
|-
|-
| |
| || || || 23\39 || || || 707.692 || 5 || 2 || 2.500 || Quasisupra
| |
| |
| |
| |
| style="text-align:center;" | 45\109
| |
| |
| style="text-align:center;" | 495.413
| |
|-
|-
| |  
| || || || || || 59\100 || 708.000 || 13 || 5 || 2.600 ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 495.325
| style="text-align:center;" | L/s = sqrt(3)
|-
|-
| |
| || || || || 36\61 || || 708.197 || 8 || 3 || 2.667 ||
| |
| |
| |
| style="text-align:center;" | 26\63
| |
| |
| |
| style="text-align:center;" | 495.238
| |
|-
|-
| |
| || || || || || 49\83 || 708.434 || 11 || 4 || 2.750 ||
| |
| |
| |
| |
| style="text-align:center;" | 33\80
| |
| |
| style="text-align:center;" | 495
| |
|-
|-
| |
| || || 13\22 || || || || 709.091 || 3 || 1 || 3.000 || L/s = 3/1 Suprapyth
| style="text-align:center;" | 7\17
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 494.118
| style="text-align:center;" | Boundary of propriety (generators larger than this are proper)
 
Supraphon
|-
|-
| |
| || || || || || 42\71 || 709.859 || 10 || 3 || 3.333 ||
| |
| |
| |
| |
| style="text-align:center;" | 30\73
| |
| |
| style="text-align:center;" | 493.151
| |
|-
|-
| |
| || || || || 29\49 || || 710.204 || 7 || 2 || 3.500 || Superpyth
| |
| |
| |
| style="text-align:center;" | 23\56
| |
| |
| |
| style="text-align:center;" | 492.857
| |
|-
|-
| |
| || || || || || 45\76 || 710.526 || 11 || 3 || 3.667 ||
| |
| |
| |
| |
| style="text-align:center;" | 39\95
| |
| |
| style="text-align:center;" | 492.632
| |
|-
|-
| |
| || || || 16\27 || || || 711.111 || 4 || 1 || 4.000 ||
| |
| |
| style="text-align:center;" | 16\39
| |
| |
| |
| |
| style="text-align:center;" | 492.308
| |
|-
|-
| |
| || || || || || 35\59 || 711.864 || 9 || 2 || 4.500 ||
| |
| |
| |
| |
| style="text-align:center;" | 41\100
| |
| |
| style="text-align:center;" | 492
| |
|-
|-
| |  
| || || || || 19\32 || || 712.500 || 5 || 1 || 5.000 ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 491.946
| style="text-align:center;" | L/s = phi+1
|-
|-
| |
| || || || || || 22\37 || 713.514 || 6 || 1 || 6.000 ||
| |
| |
| |
| style="text-align:center;" | 25\61
| |
| |
| |
| style="text-align:center;" | 491.803
| |
|-
|-
| |
| 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 491.655
| style="text-align:center;" | L/s = e
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 34\83
| |  
| |  
| style="text-align:center;" | 491.566
| |
|-
| |
| |
| style="text-align:center;" | 9\22
| |
| |
| |
| |
| |
| style="text-align:center;" | 490.909
| style="text-align:center;" | Suprapyth/Supra
|-
| |
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 490.569
| style="text-align:center;" | L/s = pi
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 29\71
| |
| |
| style="text-align:center;" | 490.141
| |
|-
| |
| |
| |
| |
| style="text-align:center;" | 20\49
| |
| |
| |
| style="text-align:center;" | 489.796
| style="text-align:center;" | Superpyth
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 31\76
| |
| |
| style="text-align:center;" | 489.474
| |
|-
| |
| |
| |
| style="text-align:center;" | 11\27
| |
| |
| |
| |
| style="text-align:center;" | 488.889
| style="text-align:center;" | Archy
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 24\59
| |
| |
| style="text-align:center;" | 488.136
| |
|-
| |
| |
| |
| |
| style="text-align:center;" | 13\32
| |
| |
| |
| style="text-align:center;" | 487.500
| |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 15\37
| |
| |
| style="text-align:center;" | 486.486
| |
|-
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 17\42
| |
| style="text-align:center;" | 485.714
| |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 19\47
| style="text-align:center;" | 485.106
| |
|-
| style="text-align:center;" | 2\5
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 480.000
| |
|}
|}


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