6L 3s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
+link to scala file, +category
New scale tree
Line 19: Line 19:


== Scale tree ==
== Scale tree ==
{| class="wikitable"
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
|-
! colspan="10" | Generator
| 1\9 || || || || || || 133.333 || 1 || 1 || 1.000 ||  
! | Cents
! | Comments
|-
|-
| | 1\9
| || || || || || 6\51 || 141.176 || 6 || 5 || 1.200 ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |
| | 133.33
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 5\42 || || 142.857 || 5 || 4 || 1.250 ||
| |  
| |  
| |  
| |  
| |  
| |
| |  
| |  
| | 10\87
| | 137.93
| |  
|-
|-
| |  
| || || || || || 9\75 || 144.000 || 9 || 7 || 1.286 ||
| |  
| |  
| |  
| |  
| |  
| |
| |
| | 9\78
| |  
| | 138.46
| |  
|-
|-
| |  
| || || || 4\33 || || || 145.455 || 4 || 3 || 1.333 ||
| |  
| |  
| |  
| |  
| |  
| |
| | 8\69
| |  
| |  
| | 139.13
| |  
|-
|-
| |  
| || || || || || 11\90 || 146.667 || 11 || 8 || 1.375 ||  
| |  
| |  
| |  
| |  
| |
| | 7\60
| |  
| |  
| |  
| | 140
| |  
|-
|-
| |  
| || || || || 7\57 || || 147.368 || 7 || 5 || 1.400 ||
| |  
| |  
| |  
| |
| | 6\51
| |  
| |  
| |  
| |  
| | 141.18
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 10\81 || 148.148 || 10 || 7 || 1.428 ||
| |  
| |  
| |  
| |  
| |
| | 11\93
| |  
| |  
| |  
| | 141.935
| style="text-align:center;" |  
|-
|-
| |  
| || || 3\24 || || || || 150.000 || 3 || 2 || 1.500 ||  
| |  
| |  
| |  
| |  
| |  
| |
| | 16\135
| |  
| |  
| | 142.22
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 11\87 || 151.724 || 11 || 7 || 1.571 || Hemimist
| |  
| |  
| |  
| |  
| |  
| |
| |  
| | 21\177
| |  
| | 142.37
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 8\63 || || 152.381 || 8 || 5 || 1.600 ||
| |  
| |  
| |  
| |  
| |  
| |
| |  
| |  
| | 26\219
| | 142.47
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 13\102 || 152.911 || 13 || 8 || 1.625 || Unnamed golden tuning<br>Triforce (optimal around here)
| |  
| |  
| |  
| | 5\42
| |  
| |
| |
| |  
| |  
| | 142.86
| style="text-align:center;" |  
|-
|-
| |  
| || || || 5\39 || || || 153.846 || 5 || 3 || 1.667 ||
| |  
| |  
| | 4\33
| |  
| |  
| |  
| |
| |  
| |  
| | 145.455
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 12\93 || 154.839 || 12 || 7 || 1.714 ||
| |  
| | 3\24
| |  
| |  
| |
| |
| |  
| |  
| |  
| | 150
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 7\54 || || 155.556 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| |  
| |  
| |
| |
| |  
| |  
| | 151.71
| |  
|-
|-
| |  
| || || || || || 9\69 || 156.522 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| | 8\63
| |  
| |
| |
| |  
| |  
| | 152.38
| style="text-align:center;" |  
|-
|-
| |  
| || 2\15 || || || || || 160.000 || 2 || 1 || 2.000 || Basic hyrulic
| |  
| |  
| |  
| |  
| |  
| | 21\165
| |
| |  
| |  
| | 152.73
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 9\66 || 163.636 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| |  
| |  
| |
| |  
| | 55\432
| |  
| | 152.78
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 7\51 || || 164.706 || 7 || 3 || 2.333 ||
| |  
| |  
| |  
| |  
| |  
| |
| |  
| |  
| | 89\699
| | 152.79
| style="text-align:center;" | Golden Triforce
|-
|-
| |  
| || || || || || 12\87 || 165.517 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| |  
| |  
| |
| | 34\267
| |  
| |  
| | 152.81
| style="text-align:center;" |  
|-
|-
| |  
| || || || 5\36 || || || 166.667 || 5 || 2 || 2.500 ||  
| |  
| |  
| |  
| |  
| | 13\102
| |
| |
| |  
| |  
| | 152.94
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 13\93 || 167.742 || 13 || 5 || 2.600 || Unnamed golden tuning
| |  
| |  
| | 5\39
| |  
| |  
| |  
| |  
| |
| |
| | 153.85
| style="text-align:center;" | Triforce is around here
|-
|-
| |  
| || || || || 8\57 || || 168.421 || 8 || 3 || 2.667 ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |
| | 155.2
| |  
|-
|-
| |  
| || || || || || 11\78 || 169.231 || 11 || 4 || 2.750 ||
| | 2\15
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 160
| style="text-align:center;" | Boundary of propriety (generators
 
smaller than this are proper)
|-
|-
| |  
| || || 3\21 || || || || 171.439 || 3 || 1 || 3.000 ||  
| |  
| |  
| |  
| |  
| |  
| |
| |  
| |  
| | 17\126
| | 161.905
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 10\69 || 173.913 || 10 || 3 || 3.333 ||
| |  
| |  
| |  
| |  
| |  
| |
| |  
| | 15\111
| |  
| | 162.16
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 7\48 || || 175.000 || 7 || 2 || 3.500 ||
| |  
| |  
| |  
| |  
| |  
| |
| | 13\96
| |  
| |  
| | 162.50
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 11\75 || 176.000 || 11 || 3 || 3.667 ||
| |  
| |  
| |  
| |
| |
| | 11\81
| |  
| |  
| |  
| | 162.96
| style="text-align:center;" |  
|-
|-
| |  
| || || || 4\27 || || || 177.778 || 4 || 1 || 4.000 ||
| |  
| |  
| |  
| |  
| | 9\66
| |
| |
| |  
| |  
| | 163.64
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 9\60 || 180.000 || 9 || 2 || 4.500 ||
| |  
| |  
| |  
| | 7\51
| |  
| |
| |
| |  
| |  
| | 164.71
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 5\33 || || 181.818 || 5 || 1 || 5.000 ||  
| |  
| |  
| |  
| |
| | 12\87
| |  
| |  
| |  
| |  
| | 165.52
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 6\39 || 184.615 || 6 || 1 || 6.000 || Mirkat
| |  
| |  
| | 5\36
| |  
| |  
| |
| |
| |  
| |  
| | 166.67
| style="text-align:center;" |  
|-
|-
| |
| 1\6 || || || || || || 200.000 || 1 || 0 || → inf ||
| |
| |
| |
| |
| | 13\93
| |
| |
| |
| |
| | 167.74
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 34\243
| |
| |
| | 167.9
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 89\636
| | 167.93
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 55\393
| |
| | 167.94
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 21\150
| |
| |
| |
| | 168
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 8\57
| |
| |
| |
| |
| |
| | 168.42
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 168.93
| style="text-align:center;" | L/s = e
|-
| |
| |
| |
| |
| |
| | 11\78
| |
| |
| |
| |
| | 169.23
| style="text-align:center;" | <span style="display: block; text-align: center;">
 
</span>
|-
| |
| |
| |
| |
| |
| |
| | 14\99
| |
| |
| |
| | 169.70
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 17\120
| |
| |
| | 170.00
| style="text-align:center;" | <span style="display: block; text-align: center;">
 
</span>
|-
| |
| |
| | 3\21
| |
| |
| |
| |
| |
| |
| |
| | 171.43
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 172.54
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| |
| |
| |
| |
| |
| |
| |
| | 16\111
| |
| |
| | 172.97
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 13\90
| |
| |
| |
| | 173.33
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 10\69
| |
| |
| |
| |
| | 173.91
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 17\117
| |
| |
| |
| | 174.36
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 7\48
| |
| |
| |
| |
| |
| | 175.00
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 11\75
| |
| |
| |
| |
| | 176.00
| style="text-align:center;" |
|-
| |
| |
| |
| | 4\27
| |
| |
| |
| |
| |
| |
| | 177.78
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| |
| |
| |
| | 17\114
| |
| |
| | 178.95
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 13\87
| |
| |
| |
| | 179.31
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 9\60
| |
| |
| |
| |
| | 180.00
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 5\33
| |
| |
| |
| |
| |
| | 181.82
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 26\171
| | 182.46
| style="text-align:center;" | Terrain is around here
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 21\138
| |
| | 182.61
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 16\105
| |
| |
| | 182.86
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 11\72
| |
| |
| |
| | 183.33
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 6\39
| |  
| |  
| |  
| |  
| | 184.62
| style="text-align:center;" |  
|-
| |
| |
| |
| |
| |
| |
| | 7\45
| |
| |
| |
| | 186.67
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 8\51
| |
| |
| | 188.235
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 9\57
| |
| | 189.47
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 10\63
| | 190.48
| |
|-
| | 1\6
| |  
| |  
| |
| |
| |
| |
| |
| |
| |
| | 200
| style="text-align:center;" |  
|}
|}


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:Hyrulic| ]] <!-- main article -->
[[Category:Hyrulic| ]] <!-- main article -->

Revision as of 13:44, 3 March 2022

↖ 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.

Scales

Scale tree

Generator Cents L s L/s Comments
1\9 133.333 1 1 1.000
6\51 141.176 6 5 1.200
5\42 142.857 5 4 1.250
9\75 144.000 9 7 1.286
4\33 145.455 4 3 1.333
11\90 146.667 11 8 1.375
7\57 147.368 7 5 1.400
10\81 148.148 10 7 1.428
3\24 150.000 3 2 1.500
11\87 151.724 11 7 1.571 Hemimist
8\63 152.381 8 5 1.600
13\102 152.911 13 8 1.625 Unnamed golden tuning
Triforce (optimal around here)
5\39 153.846 5 3 1.667
12\93 154.839 12 7 1.714
7\54 155.556 7 4 1.750
9\69 156.522 9 5 1.800
2\15 160.000 2 1 2.000 Basic hyrulic
9\66 163.636 9 4 2.250
7\51 164.706 7 3 2.333
12\87 165.517 12 5 2.400
5\36 166.667 5 2 2.500
13\93 167.742 13 5 2.600 Unnamed golden tuning
8\57 168.421 8 3 2.667
11\78 169.231 11 4 2.750
3\21 171.439 3 1 3.000
10\69 173.913 10 3 3.333
7\48 175.000 7 2 3.500
11\75 176.000 11 3 3.667
4\27 177.778 4 1 4.000
9\60 180.000 9 2 4.500
5\33 181.818 5 1 5.000
6\39 184.615 6 1 6.000 Mirkat
1\6 200.000 1 0 → inf
Retrieved from "https://en.xen.wiki/index.php?title=6L_3s&oldid=88939"