7L 8s: Difference between revisions

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{{MOS intro}}
{{MOS intro}}
It is notable for supporting [[Porcupine|porcupine]], of the [[Porcupine_family|porcupine family]].
It is notable for supporting [[Porcupine|porcupine]], of the [[Porcupine_family|porcupine family]].
 
{{Scale tree}}<!-- There was previously octachord info in the old scale tree, in the form of the step pattern LsLsLsL. -->
{| class="wikitable"
|-
! colspan="5" | Generator
! | octachord
! | g
! | 2g
! | 3g
! | 4g
! | 5g
! | 6g
! | 7g
! | Comments
|-
| style="text-align:center;" | 2\15
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 1 1 1 1 1 1 1
| style="text-align:center;" | 160
| style="text-align:center;" | 320
| style="text-align:center;" | 480
| style="text-align:center;" | 640
| style="text-align:center;" | 800
| style="text-align:center;" | 960
| style="text-align:center;" | 1120
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 9\67
| style="text-align:center;" | 4 5 4 5 4 5 4
| style="text-align:center;" | 161.2
| style="text-align:center;" | 322.4
| style="text-align:center;" | 483.6
| style="text-align:center;" | 644.8
| style="text-align:center;" | 806
| style="text-align:center;" | 967.2
| style="text-align:center;" | 1128.4
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7\52
| style="text-align:center;" |
| style="text-align:center;" | 3 4 3 4 3 4 3
| style="text-align:center;" | 161.5
| style="text-align:center;" | 323.1
| style="text-align:center;" | 484.6
| style="text-align:center;" | 646.2
| style="text-align:center;" | 807.7
| style="text-align:center;" | 969.2
| style="text-align:center;" | 1130.8
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5\37
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 2 3 2 3 2 3 2
| style="text-align:center;" | 162.2
| style="text-align:center;" | 324.3
| style="text-align:center;" | 486.5
| style="text-align:center;" | 648.6
| style="text-align:center;" | 810.8
| style="text-align:center;" | 973
| style="text-align:center;" | 1135.1
| style="text-align:center;" | Optimal rank range (L/s=3/2) porcupine
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">2 pi 2 pi 2 pi 2</span>
| style="text-align:center;" | 162.4
| style="text-align:center;" | 324.8
| style="text-align:center;" | 487.2
| style="text-align:center;" | 649.6
| style="text-align:center;" | 812
| style="text-align:center;" | 974.4
| style="text-align:center;" | 1136.8
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13\96
| style="text-align:center;" | 5 8 5 8 5 8 5
| style="text-align:center;" | 162.5
| style="text-align:center;" | 325
| style="text-align:center;" | 487.5
| style="text-align:center;" | 650
| style="text-align:center;" | 812.5
| style="text-align:center;" | 975
| style="text-align:center;" | 1137.5
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 1 phi 1 phi 1 phi 1
| style="text-align:center;" | 162.6
| style="text-align:center;" | 325.1
| style="text-align:center;" | 487.7
| style="text-align:center;" | 650.2
| style="text-align:center;" | 812.8
| style="text-align:center;" | 975.35
| style="text-align:center;" | 1137.9
| style="text-align:center;" | <span style="display: block; text-align: center;">Golden porcupine when L/s=phi</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 8\59
| style="text-align:center;" |
| style="text-align:center;" | 3 5 3 5 3 5 3
| style="text-align:center;" | 162.7
| style="text-align:center;" | 325.4
| style="text-align:center;" | 488.1
| style="text-align:center;" | 650.8
| style="text-align:center;" | 813.6
| style="text-align:center;" | 976.3
| style="text-align:center;" | 1139
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="background-color: #ffffff;">1 √3 1 √3 1 √3 1</span>
| style="text-align:center;" | 162.9
| style="text-align:center;" | 325.9
| style="text-align:center;" | 488.7
| style="text-align:center;" | 651.6
| style="text-align:center;" | 814.55
| style="text-align:center;" | 977.5
| style="text-align:center;" | 1140.4
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" | 3\22
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 1 2 1 2 1 2 1
| style="text-align:center;" | 163.6
| style="text-align:center;" | 327.3
| style="text-align:center;" | 490.9
| style="text-align:center;" | 654.5
| style="text-align:center;" | 818.2
| style="text-align:center;" | 981.8
| style="text-align:center;" | 1145.5
| style="text-align:center;" | Boundary of propriety (generators
 
smaller than this are proper)
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7\51
| style="text-align:center;" |
| style="text-align:center;" | 2 5 2 5 2 5 2
| style="text-align:center;" | 164.7
| style="text-align:center;" | 329.4
| style="text-align:center;" | 494.1
| style="text-align:center;" | 658.8
| style="text-align:center;" | 823.5
| style="text-align:center;" | 988.2
| style="text-align:center;" | 1152.9
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">1 phi+1 1 phi+1 1 phi+1 1</span>
| style="text-align:center;" | 164.9
| style="text-align:center;" | 329.8
| style="text-align:center;" | 494.75
| style="text-align:center;" | 659.7
| style="text-align:center;" | 824.6
| style="text-align:center;" | 989.5
| style="text-align:center;" | 1154.4
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11\80
| style="text-align:center;" | 3 8 3 8 3 8 3
| style="text-align:center;" | 165
| style="text-align:center;" | 330
| style="text-align:center;" | 495
| style="text-align:center;" | 660
| style="text-align:center;" | 825
| style="text-align:center;" | 990
| style="text-align:center;" | 1155
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 1 e 1 e 1 e 1
| style="text-align:center;" | 165.1
| style="text-align:center;" | 330.2
| style="text-align:center;" | 495.3
| style="text-align:center;" | 660.3
| style="text-align:center;" | 825.4
| style="text-align:center;" | 990.5
| style="text-align:center;" | 1155.6
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s=e</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 4\29
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 1 3 1 3 1 3 1
| style="text-align:center;" | 165.5
| style="text-align:center;" | 331
| style="text-align:center;" | 496.6
| style="text-align:center;" | 662.1
| style="text-align:center;" | 827.6
| style="text-align:center;" | 993.1
| style="text-align:center;" | 1158.6
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 1 pi 1 pi 1 pi 1
| style="text-align:center;" | 165.7
| style="text-align:center;" | 331.4
| style="text-align:center;" | 497.1
| style="text-align:center;" | 662.85
| style="text-align:center;" | 828.5
| style="text-align:center;" | 994.3
| style="text-align:center;" | 1160
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s=pi</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5\36
| style="text-align:center;" |
| style="text-align:center;" | 1 4 1 4 1 4 1
| style="text-align:center;" | 166.7
| style="text-align:center;" | 333.3
| style="text-align:center;" | 500
| style="text-align:center;" | 666.7
| style="text-align:center;" | 833.3
| style="text-align:center;" | 1000
| style="text-align:center;" | 1166.7
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 6\43
| style="text-align:center;" | 1 5 1 5 1 5 1
| style="text-align:center;" | 167.4
| style="text-align:center;" | 334.9
| style="text-align:center;" | 502.3
| style="text-align:center;" | 669.8
| style="text-align:center;" | 837.2
| style="text-align:center;" | 1004.65
| style="text-align:center;" | 1172.1
| style="text-align:center;" |
|-
| style="text-align:center;" | 1\7
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 0 1 0 1 0 1 0
| style="text-align:center;" | 171.4
| style="text-align:center;" | 342.9
| style="text-align:center;" | 514.3
| style="text-align:center;" | 685.7
| style="text-align:center;" | 857.1
| style="text-align:center;" | 1028.6
| style="text-align:center;" | 1200
| style="text-align:center;" |
|}
[[Category:Porcupine]]
[[Category:Porcupine]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Revision as of 05:21, 29 February 2024

↖ 6L 7s ↑ 7L 7s 8L 7s ↗
← 6L 8s 7L 8s 8L 8s →
↙ 6L 9s ↓ 7L 9s 8L 9s ↘
Scale structure
Step pattern LsLsLsLsLsLsLss
ssLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\15 to 1\7 (160.0 ¢ to 171.4 ¢)
Dark 6\7 to 13\15 (1028.6 ¢ to 1040.0 ¢)
TAMNAMS information
Related to 7L 1s (pine)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 7L 1s
Sister 8L 7s
Daughters 15L 7s, 7L 15s
Neutralized 14L 1s
2-Flought 22L 8s, 7L 23s
Equal tunings
Equalized (L:s = 1:1) 2\15 (160.0 ¢)
Supersoft (L:s = 4:3) 7\52 (161.5 ¢)
Soft (L:s = 3:2) 5\37 (162.2 ¢)
Semisoft (L:s = 5:3) 8\59 (162.7 ¢)
Basic (L:s = 2:1) 3\22 (163.6 ¢)
Semihard (L:s = 5:2) 7\51 (164.7 ¢)
Hard (L:s = 3:1) 4\29 (165.5 ¢)
Superhard (L:s = 4:1) 5\36 (166.7 ¢)
Collapsed (L:s = 1:0) 1\7 (171.4 ¢)
View • Talk • Edit

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.

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 7L 8s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\15 160.000 1040.000 1:1 1.000 Equalized 7L 8s
11\82 160.976 1039.024 6:5 1.200
9\67 161.194 1038.806 5:4 1.250
16\119 161.345 1038.655 9:7 1.286
7\52 161.538 1038.462 4:3 1.333 Supersoft 7L 8s
19\141 161.702 1038.298 11:8 1.375
12\89 161.798 1038.202 7:5 1.400
17\126 161.905 1038.095 10:7 1.429
5\37 162.162 1037.838 3:2 1.500 Soft 7L 8s
18\133 162.406 1037.594 11:7 1.571
13\96 162.500 1037.500 8:5 1.600
21\155 162.581 1037.419 13:8 1.625
8\59 162.712 1037.288 5:3 1.667 Semisoft 7L 8s
19\140 162.857 1037.143 12:7 1.714
11\81 162.963 1037.037 7:4 1.750
14\103 163.107 1036.893 9:5 1.800
3\22 163.636 1036.364 2:1 2.000 Basic 7L 8s
Scales with tunings softer than this are proper
13\95 164.211 1035.789 9:4 2.250
10\73 164.384 1035.616 7:3 2.333
17\124 164.516 1035.484 12:5 2.400
7\51 164.706 1035.294 5:2 2.500 Semihard 7L 8s
18\131 164.885 1035.115 13:5 2.600
11\80 165.000 1035.000 8:3 2.667
15\109 165.138 1034.862 11:4 2.750
4\29 165.517 1034.483 3:1 3.000 Hard 7L 8s
13\94 165.957 1034.043 10:3 3.333
9\65 166.154 1033.846 7:2 3.500
14\101 166.337 1033.663 11:3 3.667
5\36 166.667 1033.333 4:1 4.000 Superhard 7L 8s
11\79 167.089 1032.911 9:2 4.500
6\43 167.442 1032.558 5:1 5.000
7\50 168.000 1032.000 6:1 6.000
1\7 171.429 1028.571 1:0 → ∞ Collapsed 7L 8s
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