8L 1s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
m →Scale tree: Attempt to fix the Todo so that it actually gets flagged on an appropriate Todo page
→Scale tree: Made the proposed table from the Talk page live, to restore the temperaments to the table
 
(3 intermediate revisions by 2 users not shown)
Line 19: Line 19:


== Scale tree ==
== Scale tree ==
{{Todo|complete table|inline=1|text=Convert manually-generated table to MOS tuning spectrum template}}
{{MOS tuning spectrum
{| class="wikitable"
| 7/4 = [[Bleu]] is around here
|-
| 9/5 = [[Tsaharuk]] and [[Quanic]] are around here
! colspan="8" | Generator
| 5/1 = [[Bohpier]] is around here
! | Cents
}}
!Remainder
! | Comments
|-
| | 1\9
|
| |
| |
| |
| |
| |
| |
| | 133.333
|133.333
| style="text-align:center;" | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 17\150
| | 136.000
|112.000
| |
|-
| |
|
| |
| |
| |
| |
| | 11\97
| |
| | 136.082
|111.340
| |
|-
| |
|
| |
| |
| |
| |
| |
| | 16\141
| | 136.170
|110.638
| |
|-
| |
|
| |
| |
| | 5\44
| |
| |
| |
| | 136.364
|109.091
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 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
| style="text-align:center;" | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 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
| style="text-align:center;" | 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
| style="text-align:center;" | …and here
 
Quanic is between here…
|-
| |
|
| |
| |
| |
| |
| |
| | 13\111
| | 140.541
|75.676
| style="text-align:center;" | …and here
|-
| |
|2\17
| |
| |
| |
| |
| |
| |
| | 141.176
|70.588
| style="text-align:center;" | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 27\226
| | 143.363
|53.097
| |
|-
| |
|
| |
| |
| |
| |
| | 19\159
| |
| | 143.396
|52.830
| |
|-
| |
|
| |
| |
| |
| |
| |
| |
| | 143.406
|52.756
| style="text-align:center;" | L/s = e
|-
| |
|
| |
| |
| |
| |
| |
| | 30\251
| | 143.426
|52.590
| |
|-
| |
|
| |
| |
| |
| | 11\92
| |
| |
| | 143.478
|52.174
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 25\209
| | 143.541
|51.675
| |
|-
| |
|
| |
| |
| |
| |
| | 14\117
| |
| | 143.590
|51.282
| |
|-
| |
|
| |
| |
| |
| |
| |
| | 17\142
| | 143.662
|50.704
| |
|-
| |
|
| | 3\25
| |
| |
| |
| |
| |
| | 144.000
|48.000
| style="text-align:center;" | L/s = 3
|-
| |
|
| |
| |
| |
| |
| |
| |
| | 144.260
|45.919
| style="text-align:center;" | 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
| style="text-align:center;" |
|-
| |
|
| |
| |
| |
| |
| |
| | 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
| style="text-align:center;" | 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
| style="text-align:center;" | 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
| style="text-align:center;" | …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
| style="text-align:center;" |
|}


{{todo|expand}}
{{todo|expand}}
[[Category:9-tone scales]]
[[Category:9-tone scales]]
[[Category:Gamelan]]
[[Category:Gamelan]]

Latest revision as of 19:48, 5 May 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

Scale tree and tuning spectrum of 8L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\9 133.333 1066.667 1:1 1.000 Equalized 8L 1s
6\53 135.849 1064.151 6:5 1.200
5\44 136.364 1063.636 5:4 1.250
9\79 136.709 1063.291 9:7 1.286
4\35 137.143 1062.857 4:3 1.333 Supersoft 8L 1s
11\96 137.500 1062.500 11:8 1.375
7\61 137.705 1062.295 7:5 1.400
10\87 137.931 1062.069 10:7 1.429
3\26 138.462 1061.538 3:2 1.500 Soft 8L 1s
11\95 138.947 1061.053 11:7 1.571
8\69 139.130 1060.870 8:5 1.600
13\112 139.286 1060.714 13:8 1.625
5\43 139.535 1060.465 5:3 1.667 Semisoft 8L 1s
12\103 139.806 1060.194 12:7 1.714
7\60 140.000 1060.000 7:4 1.750 Bleu is around here
9\77 140.260 1059.740 9:5 1.800 Tsaharuk and Quanic are around here
2\17 141.176 1058.824 2:1 2.000 Basic 8L 1s
9\76 142.105 1057.895 9:4 2.250
7\59 142.373 1057.627 7:3 2.333
12\101 142.574 1057.426 12:5 2.400
5\42 142.857 1057.143 5:2 2.500 Semihard 8L 1s
13\109 143.119 1056.881 13:5 2.600
8\67 143.284 1056.716 8:3 2.667
11\92 143.478 1056.522 11:4 2.750
3\25 144.000 1056.000 3:1 3.000 Hard 8L 1s
10\83 144.578 1055.422 10:3 3.333
7\58 144.828 1055.172 7:2 3.500
11\91 145.055 1054.945 11:3 3.667
4\33 145.455 1054.545 4:1 4.000 Superhard 8L 1s
9\74 145.946 1054.054 9:2 4.500
5\41 146.341 1053.659 5:1 5.000 Bohpier is around here
6\49 146.939 1053.061 6:1 6.000
1\8 150.000 1050.000 1:0 → ∞ Collapsed 8L 1s
Retrieved from "https://en.xen.wiki/index.php?title=8L_1s&oldid=195448"