8L 1s: Difference between revisions

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→Scale tree: Middle (basic) 8L 1s scale generator 2\17 was crammed into the same column as endpoints 1\8 and 1\9 -- fixed this by adding another column for it to be consistent with other scale trees.
m →Scale tree: Add {{todo|inline=1|convert table|text=Convert manually-generated table to MOS tuning spectrum template}}
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== Scale tree ==
== Scale tree ==
{{todo|inline=1|convert table|text=Convert manually-generated table to MOS tuning spectrum template}}
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Revision as of 17:20, 28 February 2025

← 7L 1s 8L 1s 9L 1s →
↙ 7L 2s ↓ 8L 2s 9L 2s ↘ 
┌╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLs
sLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\9 to 1\8 (133.3 ¢ to 150.0 ¢)
Dark 7\8 to 8\9 (1050.0 ¢ to 1066.7 ¢)
TAMNAMS information
Name subneutralic
Prefix blu-
Abbrev. blu
Related MOS scales
Parent 1L 7s
Sister 1L 8s
Daughters 9L 8s, 8L 9s
Neutralized 7L 2s
2-Flought 17L 1s, 8L 10s
Equal tunings
Equalized (L:s = 1:1) 1\9 (133.3 ¢)
Supersoft (L:s = 4:3) 4\35 (137.1 ¢)
Soft (L:s = 3:2) 3\26 (138.5 ¢)
Semisoft (L:s = 5:3) 5\43 (139.5 ¢)
Basic (L:s = 2:1) 2\17 (141.2 ¢)
Semihard (L:s = 5:2) 5\42 (142.9 ¢)
Hard (L:s = 3:1) 3\25 (144.0 ¢)
Superhard (L:s = 4:1) 4\33 (145.5 ¢)
Collapsed (L:s = 1:0) 1\8 (150.0 ¢)

8L 1s, named subneutralic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 133.3 ¢ to 150 ¢, or from 1050 ¢ to 1066.7 ¢. Scales of this form are always proper because there is only one small step.

8L 1s generates a scale similar to nonatonic Indonesian gamelan scales (i.e. Pelog and Slendro plus 4 of the 12 microtonal adjustments from the theories of Sundanese composer-muiscologist-teacher Raden Machjar Angga Koesoemadinata or a median between the two) with a generator narrower than 2\17edo, and a largely-unknown scale family with a wider generator.

Intervals

Intervals of 8L 1s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-blustep Perfect 0-blustep P0blus 0 0.0 ¢
1-blustep Diminished 1-blustep d1blus s 0.0 ¢ to 133.3 ¢
Perfect 1-blustep P1blus L 133.3 ¢ to 150.0 ¢
2-blustep Minor 2-blustep m2blus L + s 150.0 ¢ to 266.7 ¢
Major 2-blustep M2blus 2L 266.7 ¢ to 300.0 ¢
3-blustep Minor 3-blustep m3blus 2L + s 300.0 ¢ to 400.0 ¢
Major 3-blustep M3blus 3L 400.0 ¢ to 450.0 ¢
4-blustep Minor 4-blustep m4blus 3L + s 450.0 ¢ to 533.3 ¢
Major 4-blustep M4blus 4L 533.3 ¢ to 600.0 ¢
5-blustep Minor 5-blustep m5blus 4L + s 600.0 ¢ to 666.7 ¢
Major 5-blustep M5blus 5L 666.7 ¢ to 750.0 ¢
6-blustep Minor 6-blustep m6blus 5L + s 750.0 ¢ to 800.0 ¢
Major 6-blustep M6blus 6L 800.0 ¢ to 900.0 ¢
7-blustep Minor 7-blustep m7blus 6L + s 900.0 ¢ to 933.3 ¢
Major 7-blustep M7blus 7L 933.3 ¢ to 1050.0 ¢
8-blustep Perfect 8-blustep P8blus 7L + s 1050.0 ¢ to 1066.7 ¢
Augmented 8-blustep A8blus 8L 1066.7 ¢ to 1200.0 ¢
9-blustep Perfect 9-blustep P9blus 8L + s 1200.0 ¢

Modes

Scale degrees of the modes of 8L 1s
UDP Cyclic
order 		Step
pattern 		Scale degree (bludegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LLLLLLLLs Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf.
7|1 2 LLLLLLLsL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|2 3 LLLLLLsLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf.
5|3 4 LLLLLsLLL Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf.
4|4 5 LLLLsLLLL Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Perf.
3|5 6 LLLsLLLLL Perf. Perf. Maj. Maj. Min. Min. Min. Min. Perf. Perf.
2|6 7 LLsLLLLLL Perf. Perf. Maj. Min. Min. Min. Min. Min. Perf. Perf.
1|7 8 LsLLLLLLL Perf. Perf. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|8 9 sLLLLLLLL Perf. Dim. Min. Min. Min. Min. Min. Min. Perf. Perf.

Scale tree

Todo: convert table

Convert manually-generated table to MOS tuning spectrum template

Generator Cents Remainder Comments
1\9 133.333 133.333 L/s = 1
8\71 135.211 118.310
7\62 135.484 116.129
13\115 135.652 114.783
6\53 135.849 113.208
17\150 136.000 112.000
11\97 136.082 111.340
16\141 136.170 110.638
5\44 136.364 109.091
19\167 136.527 107.784
14\123 136.585 107.317
23\202 136.634 106.931
9\79 136.709 106.329
22\193 136.788 105.699
13\114 136.842 105.263
17\149 136.913 104.698
4\35 137.143 102.857
19\166 137.349 101.205
15\131 137.405 100.763
26\227 137.445 100.441
11\96 137.500 100.000
29\253 137.549 99.605
18\157 137.580 99.363
25\218 134.615 99.083
7\61 137.705 98.361
24\209 137.799 97.608
17\148 137.838 97.297
27\235 137.872 97.021
10\87 137.931 96.552
23\200 138.000 96.000
13\113 138.053 95.575
16\139 138.130 94.964
3\26 138.462 92.308 L/s = 1.5
17\147 138.776 89.796
14\121 138.843 89.256
25\216 138.889 88.889
138.943 88.454
11\95 138.947 88,421
30\259 138.996 88.031
19\164 139.024 87.805
27\233 139.056 87.554
8\69 139.130 86.957
29\250 139.200 86.400
21\181 139.227 86.188
139.242 86.057
34\293 139.249 86.007
13\112 139.286 85.714
31\267 139.326 85.393
18\155 139.355 85.161
23\198 139.394 84.848
5\43 139.535 83.721
22\189 139.683 82.540
17\146 139.726 82.192
29\249 139.759 81.928
12\103 139.803 81.553
31\266 139.850 81.203
19\163 139.877 80.982
139.903 80.773
26\223 139.910 80.717
7\60 140.000 80.000 Bleu is around here
23\197 140.102 79.188
16\137 140.146 78.832
25\214 140.187 78.505
9\77 140.260 77.922 Tsaharuk is between here…
20\171 140.351 77.193
11\94 140.426 76.595 …and here

Quanic is between here…

13\111 140.541 75.676 …and here
2\17 141.176 70.588 L/s = 2
13\110 141.818 65.455
11\93 141.936 64.516
20\169 142.012 63.905
9\76 142.105 63.158
25\211 142.180 62.559
16\135 142.222 62.222
23\194 142.268 61.856
7\59 142.373 61.017
26\219 142.466 60.273
19\160 142.500 60.000
31\261 142.529 59.770
12\101 142.574 59.406
29\244 142.623 59.016
17\143 142.657 58.741
22\185 142.703 58.378
5\42 142.857 57.143
23\193 143.005 55.959
18\151 143.046 55.629
31\260 143.077 55.285
13\109 143.119 55.045
34\285 143.158 54.737
143.1645 54.684
21\176 143.182 54.545
29\243 143.210 54.321
8\67 143.284 53.731
27\226 143.363 53.097
19\159 143.396 52.830
143.406 52.756 L/s = e
30\251 143.426 52.590
11\92 143.478 52.174
25\209 143.541 51.675
14\117 143.590 51.282
17\142 143.662 50.704
3\25 144.000 48.000 L/s = 3
144.260 45.919 L/s = pi
16\133 144.361 45.113
13\108 144.444 44.444
23\191 144.503 43.979
10\83 144.578 43.373
27\224 144.643 42.857
17\141 144.681 42.553
24\199 144.724 42.211
7\58 144.828 41.379
25\207 144.928 40.580
18\149 144.966 40.268
29\240 145.000 40.000
11\91 145.055 39.560
26\215 145.116 39.070
15\124 145.161 38.710
19\157 145.223 38.217
4\33 145.455 36.364 L/s = 4
17\140 145.714 34.286
13\107 145.794 33.645
22\181 145.856 33.149
9\74 145.946 32.432
23\189 146.031 31.746
14\115 146.087 31.304
19\156 146.154 30.769
5\41 146.341 29.268 Bohpier is between here…
16\131 146.565 27.481
11\90 146.667 26.667
17\139 146.763 25.899
6\49 146.939 24.490 …and here
13\106 147.170 22.642
7\57 147.368 21.052
8\65 147.692 18.462
1\8 150.000 0.000
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