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User:Ganaram inukshuk/Template sandbox

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Revision as of 06:59, 4 October 2025 by Ganaram inukshuk (talk | contribs)
Scale tree and tuning spectrum of 5L 2s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\7 685.714 514.286 1:1 1.000 Equalized 5L 2s
79\138 686.957 513.043 20:19 1.053
75\131 687.023 512.977 19:18 1.056
71\124 687.097 512.903 18:17 1.059
67\117 687.179 512.821 17:16 1.062
63\110 687.273 512.727 16:15 1.067
59\103 687.379 512.621 15:14 1.071
55\96 687.500 512.500 14:13 1.077
51\89 687.640 512.360 13:12 1.083
47\82 687.805 512.195 12:11 1.091
43\75 688.000 512.000 11:10 1.100
39\68 688.235 511.765 10:9 1.111
74\129 688.372 511.628 19:17 1.118
35\61 688.525 511.475 9:8 1.125
66\115 688.696 511.304 17:15 1.133
31\54 688.889 511.111 8:7 1.143
58\101 689.109 510.891 15:13 1.154
27\47 689.362 510.638 7:6 1.167
77\134 689.552 510.448 20:17 1.176
50\87 689.655 510.345 13:11 1.182
73\127 689.764 510.236 19:16 1.188
23\40 690.000 510.000 6:5 1.200
65\113 690.265 509.735 17:14 1.214
42\73 690.411 509.589 11:9 1.222
61\106 690.566 509.434 16:13 1.231
19\33 690.909 509.091 5:4 1.250
72\125 691.200 508.800 19:15 1.267
53\92 691.304 508.696 14:11 1.273
34\59 691.525 508.475 9:7 1.286
49\85 691.765 508.235 13:10 1.300
64\111 691.892 508.108 17:13 1.308
15\26 692.308 507.692 4:3 1.333 Supersoft 5L 2s
71\123 692.683 507.317 19:14 1.357
56\97 692.784 507.216 15:11 1.364
41\71 692.958 507.042 11:8 1.375
67\116 693.103 506.897 18:13 1.385
26\45 693.333 506.667 7:5 1.400
63\109 693.578 506.422 17:12 1.417
37\64 693.750 506.250 10:7 1.429
48\83 693.976 506.024 13:9 1.444
59\102 694.118 505.882 16:11 1.455
70\121 694.215 505.785 19:13 1.462
11\19 694.737 505.263 3:2 1.500 Soft 5L 2s
73\126 695.238 504.762 20:13 1.538
62\107 695.327 504.673 17:11 1.545
51\88 695.455 504.545 14:9 1.556
40\69 695.652 504.348 11:7 1.571
69\119 695.798 504.202 19:12 1.583
29\50 696.000 504.000 8:5 1.600
47\81 696.296 503.704 13:8 1.625
65\112 696.429 503.571 18:11 1.636
18\31 696.774 503.226 5:3 1.667 Semisoft 5L 2s
61\105 697.143 502.857 17:10 1.700
43\74 697.297 502.703 12:7 1.714
68\117 697.436 502.564 19:11 1.727
25\43 697.674 502.326 7:4 1.750
57\98 697.959 502.041 16:9 1.778
32\55 698.182 501.818 9:5 1.800
71\122 698.361 501.639 20:11 1.818
39\67 698.507 501.493 11:6 1.833
46\79 698.734 501.266 13:7 1.857
53\91 698.901 501.099 15:8 1.875
60\103 699.029 500.971 17:9 1.889
67\115 699.130 500.870 19:10 1.900
7\12 700.000 500.000 2:1 2.000 Basic 5L 2s
Scales with tunings softer than this are proper
66\113 700.885 499.115 19:9 2.111
59\101 700.990 499.010 17:8 2.125
52\89 701.124 498.876 15:7 2.143
45\77 701.299 498.701 13:6 2.167
38\65 701.538 498.462 11:5 2.200
69\118 701.695 498.305 20:9 2.222
31\53 701.887 498.113 9:4 2.250
55\94 702.128 497.872 16:7 2.286
24\41 702.439 497.561 7:3 2.333
65\111 702.703 497.297 19:8 2.375
41\70 702.857 497.143 12:5 2.400
58\99 703.030 496.970 17:7 2.429
17\29 703.448 496.552 5:2 2.500 Semihard 5L 2s
61\104 703.846 496.154 18:7 2.571
44\75 704.000 496.000 13:5 2.600
27\46 704.348 495.652 8:3 2.667
64\109 704.587 495.413 19:7 2.714
37\63 704.762 495.238 11:4 2.750
47\80 705.000 495.000 14:5 2.800
57\97 705.155 494.845 17:6 2.833
67\114 705.263 494.737 20:7 2.857
10\17 705.882 494.118 3:1 3.000 Hard 5L 2s
63\107 706.542 493.458 19:6 3.167
53\90 706.667 493.333 16:5 3.200
43\73 706.849 493.151 13:4 3.250
33\56 707.143 492.857 10:3 3.333
56\95 707.368 492.632 17:5 3.400
23\39 707.692 492.308 7:2 3.500
59\100 708.000 492.000 18:5 3.600
36\61 708.197 491.803 11:3 3.667
49\83 708.434 491.566 15:4 3.750
62\105 708.571 491.429 19:5 3.800
13\22 709.091 490.909 4:1 4.000 Superhard 5L 2s
55\93 709.677 490.323 17:4 4.250
42\71 709.859 490.141 13:3 4.333
29\49 710.204 489.796 9:2 4.500
45\76 710.526 489.474 14:3 4.667
61\103 710.680 489.320 19:4 4.750
16\27 711.111 488.889 5:1 5.000
51\86 711.628 488.372 16:3 5.333
35\59 711.864 488.136 11:2 5.500
54\91 712.088 487.912 17:3 5.667
19\32 712.500 487.500 6:1 6.000
60\101 712.871 487.129 19:3 6.333
41\69 713.043 486.957 13:2 6.500
63\106 713.208 486.792 20:3 6.667
22\37 713.514 486.486 7:1 7.000
47\79 713.924 486.076 15:2 7.500
25\42 714.286 485.714 8:1 8.000
53\89 714.607 485.393 17:2 8.500
28\47 714.894 485.106 9:1 9.000
59\99 715.152 484.848 19:2 9.500
31\52 715.385 484.615 10:1 10.000
34\57 715.789 484.211 11:1 11.000
37\62 716.129 483.871 12:1 12.000
40\67 716.418 483.582 13:1 13.000
43\72 716.667 483.333 14:1 14.000
46\77 716.883 483.117 15:1 15.000
49\82 717.073 482.927 16:1 16.000
52\87 717.241 482.759 17:1 17.000
55\92 717.391 482.609 18:1 18.000
58\97 717.526 482.474 19:1 19.000
61\102 717.647 482.353 20:1 20.000
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 2s

[group 1] [group 2]


Scale degrees of the modes of 5L 2s (LsLAsLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m2md A4md
3|3 A4md M6md 		1 LsLAsLs Perf. Maj. Min. Perf. Aug. Maj. Maj. Perf.
3|3 m1md A3md
1|5 A3md M5md 		2 sLAsLsL Perf. Min. Min. Aug. Perf. Maj. Min. Perf.
6|0 A2md A4md 3 LAsLsLs Perf. Maj. Aug. Aug. Aug. Maj. Maj. Perf.
6|0 A1md m6md
4|2 A1md A3md 		4 AsLsLsL Perf. Aug. Maj. Aug. Perf. Maj. Min. Perf.
0|6 d3md d5md d6md 5 sLsLsLA Perf. Min. Min. Dim. Dim. Dim. Dim. Perf.
2|4 d4md M6md
0|6 M1md M6md 		6 LsLsLAs Perf. Maj. Min. Perf. Dim. Min. Maj. Perf.
0|6 d3md M5md 7 sLsLAsL Perf. Min. Min. Dim. Dim. Maj. Min. Perf.
  1. ↑ aaaaa
  2. ↑ bbbbb
Intervals of 5L 2s
Intervals Steps subtended Range in cents
Generic1 Specific Abbrev.
0-diastep Perfect 0-diastep P0ms 0 0.0¢
1-diastep Minor 1-diastep m1ms s 0.0¢ to 171.4¢
Major 1-diastep M1ms L 171.4¢ to 240.0¢
2-diastep Minor 2-diastep m2ms L + s 240.0¢ to 342.9¢
Major 2-diastep M2ms 2L 342.9¢ to 480.0¢
3-diastep Perfect 3-diastep P3ms 2L + s 480.0¢ to 514.3¢
Augmented 3-diastep A3ms 3L 514.3¢ to 720.0¢
4-diastep Diminished 4-diastep d4ms 2L + 2s 480.0¢ to 685.7¢
Perfect 4-diastep P4ms 3L + s 685.7¢ to 720.0¢
5-diastep Minor 5-diastep m5ms 3L + 2s 720.0¢ to 857.1¢
Major 5-diastep M5ms 4L + s 857.1¢ to 960.0¢
6-diastep Minor 6-diastep m6ms 4L + 2s 960.0¢ to 1028.6¢
Major 6-diastep M6ms 5L + s 1028.6¢ to 1200.0¢
7-diastep Perfect 7-diastep P7ms 5L + 2s 1200.0¢

Definition of generic interval.

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