12L 5s: Difference between revisions

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This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between [[24/19|24/19]] and [[32/25|32/25]], thus its generator is a perfect fourth between 7/17edo (494.412) and 5/12edo (500 cents).
This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between [[24/19|24/19]] and [[32/25|32/25]], thus its generator is a perfect fourth between 7/17edo (494.412) and 5/12edo (500 cents).


{| class="wikitable"
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
|-
| | 7/17
| 7\17 || || || || || || 494.412 || 1 || 1 || 1.000 ||
| |  
| |  
| |  
| |  
| | 494.412
|-
|-
| |  
| || || || || || 40\97 || 494.845 || 6 || 5 || 1.200 ||  
| |  
| |  
| |  
| | 33/80
| | 495
|-
|-
| |  
| || || || || 33\80 || || 495.000 || 5 || 4 || 1.250 ||
| |  
| |  
| | 26/63
| |  
| | 495,238
|-
|-
| |  
| || || || || || 59\143 || 495.105 || 9 || 7 || 1.286 ||
| |  
| |  
| |  
| | 45/109
| | 495.412
|-
|-
| |  
| || || || 26\63 || || || 495.238 || 4 || 3 || 1.333 || Leapfrog
| |  
| | 19/46
| |  
| |  
| | 495.625
|-
|-
| |  
| || || || || || 71\172 || 495.349 || 11 || 8 || 1.375 ||
| |  
| |  
| |  
| |  
| | 495.807
|-
|-
| |  
| || || || || 45\109 || || 495.413 || 7 || 5 || 1.400 || Leapweek
| |  
| |  
| |  
| | 50/121
| | 495.868
|-
|-
| |  
| || || || || || 64\155 || 495.484 || 10 || 7 || 1.428 ||
| |  
| |  
| |  
| |  
| | 495.904
|-
|-
| |  
| || || 19\46 || || || || 495.652 || 3 || 2 || 1.500 || L/s = 3/2
| |  
| |  
| | 31/75
| |  
| | 496
|-
|-
| |  
| || || || || || 69\167 || 495.808 || 11 || 7 || 1.571 || Leapday
| |  
| |  
| |  
| |  
| | 496.123
|-
|-
| |  
| || || || || 50\121 || || 495.868 || 8 || 5 || 1.600 ||
| |  
| |  
| |  
| | 43/104
| | 496.154
|-
|-
| |  
| || || || || || 81\196 || 495.918 || 13 || 8 || 1.625 || Golden neogothic
| | 12/29
| |  
| |  
| |  
| | 496.552
|-
|-
| |  
| || || || 31\75 || || || 496.000 || 5 || 3 || 1.667 ||
| |  
| |  
| |  
| | 41/99
| | 496.97
|-
|-
| |  
| || || || || || 74\179 || 496.089 || 12 || 7 || 1.714 ||
| |  
| |  
| | 29/70
| |  
| | 497.143
|-
|-
| |  
| || || || || 43\104 || || 496.154 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| |  
| | 497.254
|-
|-
| |  
| || || || || || 55\133 || 496.241 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| | 46/111
| | 497.297
|-
|-
| |  
| || 12\29 || || || || || 496.552 || 2 || 1 || 2.000 || Basic 12L 5s<br>(Generators smaller than this are proper)
| |  
| |  
| |  
| |  
| | 497.342
|-
|-
| |  
| || || || || || 53\128 || 496.875 || 9 || 4 || 2.250 ||
| |  
| | 17/41
| |  
| |  
| | 497.561
|-
|-
| |  
| || || || || 41\99 || || 496.970 || 7 || 3 || 2.333 || Undecental
| |  
| |  
| |  
| |  
| | 497.658
|-
|-
| |  
| || || || || || 70\169 || 497.041 || 12 || 5 || 2.400 || Argent tuning
| |  
| |  
| |  
| | 39/94
| | 497.872
|-
|-
| |  
| || || || 29\70 || || || 497.143 || 5 || 2 || 2.500 ||
| |  
| |  
| | 22/53
| |  
| | 498.113
|-
|-
| |  
| || || || || || 75\181 || 497.238 || 13 || 5 || 2.600 || Unnamed golden tuning
| |  
| |  
| |  
| | 27/65
| | 498,4615
|-
|-
| | 5/12
| || || || || 46\111 || || 497.297 || 8 || 3 || 2.667 ||
| |  
|-
| |  
| || || || || || 63\152 || 497.368 || 11 || 4 || 2.750 || Kwai
| |  
|-
| |  
| || || 17\41 || || || || 497.561 || 3 || 1 || 3.000 || L/s = 3/1, garibaldi/andromeda
| | 500
|-
| || || || || || 56\135 || 497.778 || 10 || 3 || 3.333 ||
|-
| || || || || 39\94 || || 497.872 || 7 || 2 || 3.500 || Garibaldi/cassandra
|-
| || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||
|-
| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi/helenus
|-
| || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || Pontiac
|-
| || || || || 27\65 || || 498.462 || 5 || 1 || 5.000 || Photia
|-
| || || || || || 32\77 || 498.701 || 6 || 1 || 6.000 || Grackle↓
|-
| 5\12 || || || || || || 500.000 || 1 || 0 || → inf ||
|}
|}

Revision as of 07:07, 18 May 2021

This MOS separates its small steps by intervals of 3L-2L-2L-3L-2L. Its major third of -4 generators approximates an interval between 24/19 and 32/25, thus its generator is a perfect fourth between 7/17edo (494.412) and 5/12edo (500 cents).

Scale tree

Generator Cents L s L/s Comments
7\17 494.412 1 1 1.000
40\97 494.845 6 5 1.200
33\80 495.000 5 4 1.250
59\143 495.105 9 7 1.286
26\63 495.238 4 3 1.333 Leapfrog
71\172 495.349 11 8 1.375
45\109 495.413 7 5 1.400 Leapweek
64\155 495.484 10 7 1.428
19\46 495.652 3 2 1.500 L/s = 3/2
69\167 495.808 11 7 1.571 Leapday
50\121 495.868 8 5 1.600
81\196 495.918 13 8 1.625 Golden neogothic
31\75 496.000 5 3 1.667
74\179 496.089 12 7 1.714
43\104 496.154 7 4 1.750
55\133 496.241 9 5 1.800
12\29 496.552 2 1 2.000 Basic 12L 5s
(Generators smaller than this are proper)
53\128 496.875 9 4 2.250
41\99 496.970 7 3 2.333 Undecental
70\169 497.041 12 5 2.400 Argent tuning
29\70 497.143 5 2 2.500
75\181 497.238 13 5 2.600 Unnamed golden tuning
46\111 497.297 8 3 2.667
63\152 497.368 11 4 2.750 Kwai
17\41 497.561 3 1 3.000 L/s = 3/1, garibaldi/andromeda
56\135 497.778 10 3 3.333
39\94 497.872 7 2 3.500 Garibaldi/cassandra
61\147 497.959 11 3 3.667
22\53 498.113 4 1 4.000 Garibaldi/helenus
49\118 498.305 9 2 4.500 Pontiac
27\65 498.462 5 1 5.000 Photia
32\77 498.701 6 1 6.000 Grackle↓
5\12 500.000 1 0 → inf
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