7L 8s: Difference between revisions
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Mos intro, infobox mos |
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{{Infobox MOS}} | {{Infobox MOS}} | ||
{{MOS intro}} | |||
It is notable for supporting [[Porcupine]], of the [[Porcupine_family|porcupine family]]. | |||
== Scale properties == | |||
{{TAMNAMS use}} | |||
=== Intervals === | |||
{{MOS intervals}} | |||
{{MOS | === Generator chain === | ||
{{MOS genchain}} | |||
=== Modes === | |||
{{MOS mode degrees}} | |||
== Scale tree == | |||
{{todo|inline=1|complete table|text=There was previously octachord info in the old scale tree, in the form of the step pattern LsLsLsL. Please add it to the new scale tree.}} | |||
{{MOS tuning spectrum | |||
| Depth = 6 | |||
| 3/2 = Optimal rank range ({{nowrap|L/s {{=}} 3/2}}) porcupine | |||
| 13/8 = Golden porcupine {{nowrap|L/s {{=}} φ}} | |||
}} | |||
{ | {{stub}} | ||
[[Category:Porcupine]] | [[Category:Porcupine]] | ||
[[Category:Abstract MOS patterns]] | [[Category:Abstract MOS patterns]] | ||
Latest revision as of 18:03, 24 May 2026
| ↖ 6L 7s | ↑ 7L 7s | 8L 7s ↗ |
| ← 6L 8s | 7L 8s | 8L 8s → |
| ↙ 6L 9s | ↓ 7L 9s | 8L 9s ↘ |
Scale structure
ssLsLsLsLsLsLsL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
7L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 8 small steps, repeating every octave. 7L 8s is a child scale of 7L 1s, expanding it by 7 tones. Generators that produce this scale range from 160 ¢ to 171.4 ¢, or from 1028.6 ¢ to 1040 ¢.
It is notable for supporting Porcupine, of the porcupine family.
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 | 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 80.0 ¢ |
| Major 1-mosstep | M1ms | L | 80.0 ¢ to 171.4 ¢ | |
| 2-mosstep | Diminished 2-mosstep | d2ms | 2s | 0.0 ¢ to 160.0 ¢ |
| Perfect 2-mosstep | P2ms | L + s | 160.0 ¢ to 171.4 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 171.4 ¢ to 240.0 ¢ |
| Major 3-mosstep | M3ms | 2L + s | 240.0 ¢ to 342.9 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 171.4 ¢ to 320.0 ¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 320.0 ¢ to 342.9 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 342.9 ¢ to 400.0 ¢ |
| Major 5-mosstep | M5ms | 3L + 2s | 400.0 ¢ to 514.3 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 2L + 4s | 342.9 ¢ to 480.0 ¢ |
| Major 6-mosstep | M6ms | 3L + 3s | 480.0 ¢ to 514.3 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 3L + 4s | 514.3 ¢ to 560.0 ¢ |
| Major 7-mosstep | M7ms | 4L + 3s | 560.0 ¢ to 685.7 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 3L + 5s | 514.3 ¢ to 640.0 ¢ |
| Major 8-mosstep | M8ms | 4L + 4s | 640.0 ¢ to 685.7 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 4L + 5s | 685.7 ¢ to 720.0 ¢ |
| Major 9-mosstep | M9ms | 5L + 4s | 720.0 ¢ to 857.1 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 4L + 6s | 685.7 ¢ to 800.0 ¢ |
| Major 10-mosstep | M10ms | 5L + 5s | 800.0 ¢ to 857.1 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 5L + 6s | 857.1 ¢ to 880.0 ¢ |
| Major 11-mosstep | M11ms | 6L + 5s | 880.0 ¢ to 1028.6 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 5L + 7s | 857.1 ¢ to 960.0 ¢ |
| Major 12-mosstep | M12ms | 6L + 6s | 960.0 ¢ to 1028.6 ¢ | |
| 13-mosstep | Perfect 13-mosstep | P13ms | 6L + 7s | 1028.6 ¢ to 1040.0 ¢ |
| Augmented 13-mosstep | A13ms | 7L + 6s | 1040.0 ¢ to 1200.0 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 6L + 8s | 1028.6 ¢ to 1120.0 ¢ |
| Major 14-mosstep | M14ms | 7L + 7s | 1120.0 ¢ to 1200.0 ¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 7L + 8s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 21 | Augmented 12-mosdegree | A12md |
| 20 | Augmented 10-mosdegree | A10md |
| 19 | Augmented 8-mosdegree | A8md |
| 18 | Augmented 6-mosdegree | A6md |
| 17 | Augmented 4-mosdegree | A4md |
| 16 | Augmented 2-mosdegree | A2md |
| 15 | Augmented 0-mosdegree | A0md |
| 14 | Augmented 13-mosdegree | A13md |
| 13 | Major 11-mosdegree | M11md |
| 12 | Major 9-mosdegree | M9md |
| 11 | Major 7-mosdegree | M7md |
| 10 | Major 5-mosdegree | M5md |
| 9 | Major 3-mosdegree | M3md |
| 8 | Major 1-mosdegree | M1md |
| 7 | Major 14-mosdegree | M14md |
| 6 | Major 12-mosdegree | M12md |
| 5 | Major 10-mosdegree | M10md |
| 4 | Major 8-mosdegree | M8md |
| 3 | Major 6-mosdegree | M6md |
| 2 | Major 4-mosdegree | M4md |
| 1 | Perfect 2-mosdegree | P2md |
| 0 | Perfect 0-mosdegree Perfect 15-mosdegree |
P0md P15md |
| −1 | Perfect 13-mosdegree | P13md |
| −2 | Minor 11-mosdegree | m11md |
| −3 | Minor 9-mosdegree | m9md |
| −4 | Minor 7-mosdegree | m7md |
| −5 | Minor 5-mosdegree | m5md |
| −6 | Minor 3-mosdegree | m3md |
| −7 | Minor 1-mosdegree | m1md |
| −8 | Minor 14-mosdegree | m14md |
| −9 | Minor 12-mosdegree | m12md |
| −10 | Minor 10-mosdegree | m10md |
| −11 | Minor 8-mosdegree | m8md |
| −12 | Minor 6-mosdegree | m6md |
| −13 | Minor 4-mosdegree | m4md |
| −14 | Diminished 2-mosdegree | d2md |
| −15 | Diminished 15-mosdegree | d15md |
| −16 | Diminished 13-mosdegree | d13md |
| −17 | Diminished 11-mosdegree | d11md |
| −18 | Diminished 9-mosdegree | d9md |
| −19 | Diminished 7-mosdegree | d7md |
| −20 | Diminished 5-mosdegree | d5md |
| −21 | Diminished 3-mosdegree | d3md |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |||
| 14|0 | 1 | LsLsLsLsLsLsLss | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Perf. |
| 13|1 | 3 | LsLsLsLsLsLssLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 12|2 | 5 | LsLsLsLsLssLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 11|3 | 7 | LsLsLsLssLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 10|4 | 9 | LsLsLssLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 9|5 | 11 | LsLssLsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 8|6 | 13 | LssLsLsLsLsLsLs | Perf. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 7|7 | 15 | sLsLsLsLsLsLsLs | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 6|8 | 2 | sLsLsLsLsLsLssL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Perf. |
| 5|9 | 4 | sLsLsLsLsLssLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Perf. | Min. | Perf. |
| 4|10 | 6 | sLsLsLsLssLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 3|11 | 8 | sLsLsLssLsLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 2|12 | 10 | sLsLssLsLsLsLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 1|13 | 12 | sLssLsLsLsLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 0|14 | 14 | ssLsLsLsLsLsLsL | Perf. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
Scale tree
| Todo: complete table
There was previously octachord info in the old scale tree, in the form of the step pattern LsLsLsL. Please add it to the new scale tree. |
| Generator(edo) | Cents | Step ratio | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | ||||||||
| 2\15 | 160.000 | 1040.000 | 1:1 | 1.000 | Equalized 7L 8s | ||||||
| 13\97 | 160.825 | 1039.175 | 7:6 | 1.167 | |||||||
| 11\82 | 160.976 | 1039.024 | 6:5 | 1.200 | |||||||
| 20\149 | 161.074 | 1038.926 | 11:9 | 1.222 | |||||||
| 9\67 | 161.194 | 1038.806 | 5:4 | 1.250 | |||||||
| 25\186 | 161.290 | 1038.710 | 14:11 | 1.273 | |||||||
| 16\119 | 161.345 | 1038.655 | 9:7 | 1.286 | |||||||
| 23\171 | 161.404 | 1038.596 | 13:10 | 1.300 | |||||||
| 7\52 | 161.538 | 1038.462 | 4:3 | 1.333 | Supersoft 7L 8s | ||||||
| 26\193 | 161.658 | 1038.342 | 15:11 | 1.364 | |||||||
| 19\141 | 161.702 | 1038.298 | 11:8 | 1.375 | |||||||
| 31\230 | 161.739 | 1038.261 | 18:13 | 1.385 | |||||||
| 12\89 | 161.798 | 1038.202 | 7:5 | 1.400 | |||||||
| 29\215 | 161.860 | 1038.140 | 17:12 | 1.417 | |||||||
| 17\126 | 161.905 | 1038.095 | 10:7 | 1.429 | |||||||
| 22\163 | 161.963 | 1038.037 | 13:9 | 1.444 | |||||||
| 5\37 | 162.162 | 1037.838 | 3:2 | 1.500 | Soft 7L 8s Optimal rank range (L/s = 3/2) porcupine | ||||||
| 23\170 | 162.353 | 1037.647 | 14:9 | 1.556 | |||||||
| 18\133 | 162.406 | 1037.594 | 11:7 | 1.571 | |||||||
| 31\229 | 162.445 | 1037.555 | 19:12 | 1.583 | |||||||
| 13\96 | 162.500 | 1037.500 | 8:5 | 1.600 | |||||||
| 34\251 | 162.550 | 1037.450 | 21:13 | 1.615 | |||||||
| 21\155 | 162.581 | 1037.419 | 13:8 | 1.625 | Golden porcupine L/s = φ | ||||||
| 29\214 | 162.617 | 1037.383 | 18:11 | 1.636 | |||||||
| 8\59 | 162.712 | 1037.288 | 5:3 | 1.667 | Semisoft 7L 8s | ||||||
| 27\199 | 162.814 | 1037.186 | 17:10 | 1.700 | |||||||
| 19\140 | 162.857 | 1037.143 | 12:7 | 1.714 | |||||||
| 30\221 | 162.896 | 1037.104 | 19:11 | 1.727 | |||||||
| 11\81 | 162.963 | 1037.037 | 7:4 | 1.750 | |||||||
| 25\184 | 163.043 | 1036.957 | 16:9 | 1.778 | |||||||
| 14\103 | 163.107 | 1036.893 | 9:5 | 1.800 | |||||||
| 17\125 | 163.200 | 1036.800 | 11:6 | 1.833 | |||||||
| 3\22 | 163.636 | 1036.364 | 2:1 | 2.000 | Basic 7L 8s Scales with tunings softer than this are proper | ||||||
| 16\117 | 164.103 | 1035.897 | 11:5 | 2.200 | |||||||
| 13\95 | 164.211 | 1035.789 | 9:4 | 2.250 | |||||||
| 23\168 | 164.286 | 1035.714 | 16:7 | 2.286 | |||||||
| 10\73 | 164.384 | 1035.616 | 7:3 | 2.333 | |||||||
| 27\197 | 164.467 | 1035.533 | 19:8 | 2.375 | |||||||
| 17\124 | 164.516 | 1035.484 | 12:5 | 2.400 | |||||||
| 24\175 | 164.571 | 1035.429 | 17:7 | 2.429 | |||||||
| 7\51 | 164.706 | 1035.294 | 5:2 | 2.500 | Semihard 7L 8s | ||||||
| 25\182 | 164.835 | 1035.165 | 18:7 | 2.571 | |||||||
| 18\131 | 164.885 | 1035.115 | 13:5 | 2.600 | |||||||
| 29\211 | 164.929 | 1035.071 | 21:8 | 2.625 | |||||||
| 11\80 | 165.000 | 1035.000 | 8:3 | 2.667 | |||||||
| 26\189 | 165.079 | 1034.921 | 19:7 | 2.714 | |||||||
| 15\109 | 165.138 | 1034.862 | 11:4 | 2.750 | |||||||
| 19\138 | 165.217 | 1034.783 | 14:5 | 2.800 | |||||||
| 4\29 | 165.517 | 1034.483 | 3:1 | 3.000 | Hard 7L 8s | ||||||
| 17\123 | 165.854 | 1034.146 | 13:4 | 3.250 | |||||||
| 13\94 | 165.957 | 1034.043 | 10:3 | 3.333 | |||||||
| 22\159 | 166.038 | 1033.962 | 17:5 | 3.400 | |||||||
| 9\65 | 166.154 | 1033.846 | 7:2 | 3.500 | |||||||
| 23\166 | 166.265 | 1033.735 | 18:5 | 3.600 | |||||||
| 14\101 | 166.337 | 1033.663 | 11:3 | 3.667 | |||||||
| 19\137 | 166.423 | 1033.577 | 15:4 | 3.750 | |||||||
| 5\36 | 166.667 | 1033.333 | 4:1 | 4.000 | Superhard 7L 8s | ||||||
| 16\115 | 166.957 | 1033.043 | 13:3 | 4.333 | |||||||
| 11\79 | 167.089 | 1032.911 | 9:2 | 4.500 | |||||||
| 17\122 | 167.213 | 1032.787 | 14:3 | 4.667 | |||||||
| 6\43 | 167.442 | 1032.558 | 5:1 | 5.000 | |||||||
| 13\93 | 167.742 | 1032.258 | 11:2 | 5.500 | |||||||
| 7\50 | 168.000 | 1032.000 | 6:1 | 6.000 | |||||||
| 8\57 | 168.421 | 1031.579 | 7:1 | 7.000 | |||||||
| 1\7 | 171.429 | 1028.571 | 1:0 | → ∞ | Collapsed 7L 8s | ||||||
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