8L 6s: Difference between revisions

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== Scale properties ==
== Scale properties ==
{{TAMNAMS use}}
{{TAMNAMS use}}
{{MOS data}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}


== Scale tree ==
== Scale tree ==
Line 13: Line 21:
| 13/7 = Hedgehog is optimal around here
| 13/7 = Hedgehog is optimal around here
| 13/6 = Urchin is around here
| 13/6 = Urchin is around here
| 11/5 = Gwazy, Bisupermajor are around here
| 11/5 = Gwazy and Bisupermajor are around here
}}
}}


{{stub}}
{{stub}}

Latest revision as of 14:08, 5 May 2025

↖ 7L 5s ↑ 8L 5s 9L 5s ↗
← 7L 6s 8L 6s 9L 6s →
↙ 7L 7s ↓ 8L 7s 9L 7s ↘
Scale structure
Step pattern LLsLsLsLLsLsLs
sLsLsLLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 5\14 to 3\8 (428.6 ¢ to 450.0 ¢)
Dark 1\8 to 2\14 (150.0 ¢ to 171.4 ¢)
TAMNAMS information
Related to 6L 2s (ekic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 6L 2s
Sister 6L 8s
Daughters 14L 8s, 8L 14s
Neutralized 2L 12s
2-Flought 22L 6s, 8L 20s
Equal tunings
Equalized (L:s = 1:1) 5\14 (428.6 ¢)
Supersoft (L:s = 4:3) 18\50 (432.0 ¢)
Soft (L:s = 3:2) 13\36 (433.3 ¢)
Semisoft (L:s = 5:3) 21\58 (434.5 ¢)
Basic (L:s = 2:1) 8\22 (436.4 ¢)
Semihard (L:s = 5:2) 19\52 (438.5 ¢)
Hard (L:s = 3:1) 11\30 (440.0 ¢)
Superhard (L:s = 4:1) 14\38 (442.1 ¢)
Collapsed (L:s = 1:0) 3\8 (450.0 ¢)
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8L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 6 small steps, with a period of 4 large steps and 3 small steps that repeats every 600.0 ¢, or twice every octave. 8L 6s is a child scale of 6L 2s, expanding it by 6 tones. Generators that produce this scale range from 428.6 ¢ to 450 ¢, or from 150 ¢ to 171.4 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 8L 6s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 85.7 ¢
Major 1-mosstep M1ms L 85.7 ¢ to 150.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 150.0 ¢ to 171.4 ¢
Augmented 2-mosstep A2ms 2L 171.4 ¢ to 300.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 150.0 ¢ to 257.1 ¢
Major 3-mosstep M3ms 2L + s 257.1 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 300.0 ¢ to 342.9 ¢
Major 4-mosstep M4ms 3L + s 342.9 ¢ to 450.0 ¢
5-mosstep Diminished 5-mosstep d5ms 2L + 3s 300.0 ¢ to 428.6 ¢
Perfect 5-mosstep P5ms 3L + 2s 428.6 ¢ to 450.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 450.0 ¢ to 514.3 ¢
Major 6-mosstep M6ms 4L + 2s 514.3 ¢ to 600.0 ¢
7-mosstep Perfect 7-mosstep P7ms 4L + 3s 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 600.0 ¢ to 685.7 ¢
Major 8-mosstep M8ms 5L + 3s 685.7 ¢ to 750.0 ¢
9-mosstep Perfect 9-mosstep P9ms 5L + 4s 750.0 ¢ to 771.4 ¢
Augmented 9-mosstep A9ms 6L + 3s 771.4 ¢ to 900.0 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 750.0 ¢ to 857.1 ¢
Major 10-mosstep M10ms 6L + 4s 857.1 ¢ to 900.0 ¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 900.0 ¢ to 942.9 ¢
Major 11-mosstep M11ms 7L + 4s 942.9 ¢ to 1050.0 ¢
12-mosstep Diminished 12-mosstep d12ms 6L + 6s 900.0 ¢ to 1028.6 ¢
Perfect 12-mosstep P12ms 7L + 5s 1028.6 ¢ to 1050.0 ¢
13-mosstep Minor 13-mosstep m13ms 7L + 6s 1050.0 ¢ to 1114.3 ¢
Major 13-mosstep M13ms 8L + 5s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 8L + 6s 1200.0 ¢

Generator chain

Generator chain of 8L 6s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
10 Augmented 1-mosdegree A1md Augmented 8-mosdegree A8md
9 Augmented 3-mosdegree A3md Augmented 10-mosdegree A10md
8 Augmented 5-mosdegree A5md Augmented 12-mosdegree A12md
7 Augmented 0-mosdegree A0md Augmented 7-mosdegree A7md
6 Augmented 2-mosdegree A2md Augmented 9-mosdegree A9md
5 Major 4-mosdegree M4md Major 11-mosdegree M11md
4 Major 6-mosdegree M6md Major 13-mosdegree M13md
3 Major 1-mosdegree M1md Major 8-mosdegree M8md
2 Major 3-mosdegree M3md Major 10-mosdegree M10md
1 Perfect 5-mosdegree P5md Perfect 12-mosdegree P12md
0 Perfect 0-mosdegree
Perfect 7-mosdegree		 P0md
P7md		 Perfect 7-mosdegree
Perfect 14-mosdegree		 P7md
P14md
−1 Perfect 2-mosdegree P2md Perfect 9-mosdegree P9md
−2 Minor 4-mosdegree m4md Minor 11-mosdegree m11md
−3 Minor 6-mosdegree m6md Minor 13-mosdegree m13md
−4 Minor 1-mosdegree m1md Minor 8-mosdegree m8md
−5 Minor 3-mosdegree m3md Minor 10-mosdegree m10md
−6 Diminished 5-mosdegree d5md Diminished 12-mosdegree d12md
−7 Diminished 7-mosdegree d7md Diminished 14-mosdegree d14md
−8 Diminished 2-mosdegree d2md Diminished 9-mosdegree d9md
−9 Diminished 4-mosdegree d4md Diminished 11-mosdegree d11md
−10 Diminished 6-mosdegree d6md Diminished 13-mosdegree d13md

Modes

Scale degrees of the modes of 8L 6s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
12|0(2) 1 LLsLsLsLLsLsLs Perf. Maj. Aug. Maj. Maj. Perf. Maj. Perf. Maj. Aug. Maj. Maj. Perf. Maj. Perf.
10|2(2) 6 LsLLsLsLsLLsLs Perf. Maj. Perf. Maj. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Maj. Perf. Maj. Perf.
8|4(2) 4 LsLsLLsLsLsLLs Perf. Maj. Perf. Maj. Min. Perf. Maj. Perf. Maj. Perf. Maj. Min. Perf. Maj. Perf.
6|6(2) 2 LsLsLsLLsLsLsL Perf. Maj. Perf. Maj. Min. Perf. Min. Perf. Maj. Perf. Maj. Min. Perf. Min. Perf.
4|8(2) 7 sLLsLsLsLLsLsL Perf. Min. Perf. Maj. Min. Perf. Min. Perf. Min. Perf. Maj. Min. Perf. Min. Perf.
2|10(2) 5 sLsLLsLsLsLLsL Perf. Min. Perf. Min. Min. Perf. Min. Perf. Min. Perf. Min. Min. Perf. Min. Perf.
0|12(2) 3 sLsLsLLsLsLsLL Perf. Min. Perf. Min. Min. Dim. Min. Perf. Min. Perf. Min. Min. Dim. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 6s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\14 428.571 171.429 1:1 1.000 Equalized 8L 6s
38\106 430.189 169.811 8:7 1.143
33\92 430.435 169.565 7:6 1.167
61\170 430.588 169.412 13:11 1.182
28\78 430.769 169.231 6:5 1.200
79\220 430.909 169.091 17:14 1.214
51\142 430.986 169.014 11:9 1.222
74\206 431.068 168.932 16:13 1.231
23\64 431.250 168.750 5:4 1.250
87\242 431.405 168.595 19:15 1.267
64\178 431.461 168.539 14:11 1.273
105\292 431.507 168.493 23:18 1.278
41\114 431.579 168.421 9:7 1.286
100\278 431.655 168.345 22:17 1.294
59\164 431.707 168.293 13:10 1.300
77\214 431.776 168.224 17:13 1.308
18\50 432.000 168.000 4:3 1.333 Supersoft 8L 6s
85\236 432.203 167.797 19:14 1.357
67\186 432.258 167.742 15:11 1.364
116\322 432.298 167.702 26:19 1.368
49\136 432.353 167.647 11:8 1.375
129\358 432.402 167.598 29:21 1.381
80\222 432.432 167.568 18:13 1.385
111\308 432.468 167.532 25:18 1.389
31\86 432.558 167.442 7:5 1.400
106\294 432.653 167.347 24:17 1.412
75\208 432.692 167.308 17:12 1.417
119\330 432.727 167.273 27:19 1.421
44\122 432.787 167.213 10:7 1.429
101\280 432.857 167.143 23:16 1.438
57\158 432.911 167.089 13:9 1.444
70\194 432.990 167.010 16:11 1.455
13\36 433.333 166.667 3:2 1.500 Soft 8L 6s
73\202 433.663 166.337 17:11 1.545
60\166 433.735 166.265 14:9 1.556
107\296 433.784 166.216 25:16 1.562
47\130 433.846 166.154 11:7 1.571 Pogo is around here
128\354 433.898 166.102 30:19 1.579
81\224 433.929 166.071 19:12 1.583
115\318 433.962 166.038 27:17 1.588
34\94 434.043 165.957 8:5 1.600
123\340 434.118 165.882 29:18 1.611
89\246 434.146 165.854 21:13 1.615
144\398 434.171 165.829 34:21 1.619
55\152 434.211 165.789 13:8 1.625
131\362 434.254 165.746 31:19 1.632
76\210 434.286 165.714 18:11 1.636
97\268 434.328 165.672 23:14 1.643
21\58 434.483 165.517 5:3 1.667 Semisoft 8L 6s
92\254 434.646 165.354 22:13 1.692
71\196 434.694 165.306 17:10 1.700
121\334 434.731 165.269 29:17 1.706
50\138 434.783 165.217 12:7 1.714 Echidna is around here
129\356 434.831 165.169 31:18 1.722
79\218 434.862 165.138 19:11 1.727
108\298 434.899 165.101 26:15 1.733
29\80 435.000 165.000 7:4 1.750
95\262 435.115 164.885 23:13 1.769
66\182 435.165 164.835 16:9 1.778
103\284 435.211 164.789 25:14 1.786
37\102 435.294 164.706 9:5 1.800
82\226 435.398 164.602 20:11 1.818
45\124 435.484 164.516 11:6 1.833
53\146 435.616 164.384 13:7 1.857 Hedgehog is optimal around here
8\22 436.364 163.636 2:1 2.000 Basic 8L 6s
Scales with tunings softer than this are proper
51\140 437.143 162.857 13:6 2.167 Urchin is around here
43\118 437.288 162.712 11:5 2.200 Gwazy and Bisupermajor are around here
78\214 437.383 162.617 20:9 2.222
35\96 437.500 162.500 9:4 2.250
97\266 437.594 162.406 25:11 2.273
62\170 437.647 162.353 16:7 2.286
89\244 437.705 162.295 23:10 2.300
27\74 437.838 162.162 7:3 2.333
100\274 437.956 162.044 26:11 2.364
73\200 438.000 162.000 19:8 2.375
119\326 438.037 161.963 31:13 2.385
46\126 438.095 161.905 12:5 2.400
111\304 438.158 161.842 29:12 2.417
65\178 438.202 161.798 17:7 2.429
84\230 438.261 161.739 22:9 2.444
19\52 438.462 161.538 5:2 2.500 Semihard 8L 6s
87\238 438.655 161.345 23:9 2.556
68\186 438.710 161.290 18:7 2.571
117\320 438.750 161.250 31:12 2.583
49\134 438.806 161.194 13:5 2.600
128\350 438.857 161.143 34:13 2.615
79\216 438.889 161.111 21:8 2.625
109\298 438.926 161.074 29:11 2.636
30\82 439.024 160.976 8:3 2.667
101\276 439.130 160.870 27:10 2.700
71\194 439.175 160.825 19:7 2.714
112\306 439.216 160.784 30:11 2.727
41\112 439.286 160.714 11:4 2.750
93\254 439.370 160.630 25:9 2.778
52\142 439.437 160.563 14:5 2.800
63\172 439.535 160.465 17:6 2.833
11\30 440.000 160.000 3:1 3.000 Hard 8L 6s
58\158 440.506 159.494 16:5 3.200
47\128 440.625 159.375 13:4 3.250
83\226 440.708 159.292 23:7 3.286
36\98 440.816 159.184 10:3 3.333
97\264 440.909 159.091 27:8 3.375
61\166 440.964 159.036 17:5 3.400
86\234 441.026 158.974 24:7 3.429
25\68 441.176 158.824 7:2 3.500
89\242 441.322 158.678 25:7 3.571
64\174 441.379 158.621 18:5 3.600
103\280 441.429 158.571 29:8 3.625
39\106 441.509 158.491 11:3 3.667
92\250 441.600 158.400 26:7 3.714
53\144 441.667 158.333 15:4 3.750
67\182 441.758 158.242 19:5 3.800
14\38 442.105 157.895 4:1 4.000 Superhard 8L 6s
59\160 442.500 157.500 17:4 4.250
45\122 442.623 157.377 13:3 4.333
76\206 442.718 157.282 22:5 4.400
31\84 442.857 157.143 9:2 4.500
79\214 442.991 157.009 23:5 4.600
48\130 443.077 156.923 14:3 4.667
65\176 443.182 156.818 19:4 4.750
17\46 443.478 156.522 5:1 5.000
54\146 443.836 156.164 16:3 5.333
37\100 444.000 156.000 11:2 5.500
57\154 444.156 155.844 17:3 5.667
20\54 444.444 155.556 6:1 6.000
43\116 444.828 155.172 13:2 6.500
23\62 445.161 154.839 7:1 7.000
26\70 445.714 154.286 8:1 8.000
3\8 450.000 150.000 1:0 → ∞ Collapsed 8L 6s
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