8L 1s: Difference between revisions

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→Scale tree: Made the proposed table from the Talk page live, to restore the temperaments to the table
 
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Line 5: Line 5:
| nSmallSteps = 1
| nSmallSteps = 1
| Equalized = 1
| Equalized = 1
| Paucitonic = 1
| Collapsed = 1
| Pattern = LLLLLLs
| Pattern = LLLLLLLLs
}}
}}
{{MOS intro}}


This MOS has a generator between 1\9edo (133 1/3 cents) and 1\8edo (150 cents). It thus generates a scale similar to nonatonic Indonesian gamelan scales (i.e. [http://www.neuroscience-of-music.se/pelog_main.htm Pelog] and Slendro plus 4 of the 12 microtonal adjustments from the theories of Sundanese composer-muiscologist-teacher [http://en.wikipedia.org/wiki/Raden_Machjar_Angga_Koesoemadinata 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.
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 [https://en.wikipedia.org/wiki/Raden_Machjar_Angga_Koesoemadinata 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.


{| class="wikitable"
== Intervals ==
|-
{{MOS intervals}}
! colspan="7" | Generator
! | Cents
! | Comments
|-
| | 1\9
| |
| |
| |
| |
| |
| |
| | 133.333
| style="text-align:center;" | L/s = 1
|-
| |
| |
| |
| |
| |
| |
| | 8\71
| | 135.211
| |
|-
| |
| |
| |
| |
| |
| | 7\62
| |
| | 135.484
| |
|-
| |
| |
| |
| |
| |
| |
| | 13\115
| | 135.652
| |
|-
| |
| |
| |
| |
| | 6\53
| |
| |
| | 135.849
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 17\150
| | 136.000
| |
|-
| |
| |
| |
| |
| |
| | 11\97
| |
| | 136.082
| |
|-
| |
| |
| |
| |
| |
| |
| | 16\141
| | 136.170
| |
|-
| |
| |
| |
| | 5\44
| |
| |
| |
| | 136.364
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 19\167
| | 136.527
| |
|-
| |
| |
| |
| |
| |
| | 14\123
| |
| | 136.585
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\202
| | 136.634
| |
|-
| |
| |
| |
| |
| | 9\79
| |
| |
| | 136.709
| |
|-
| |
| |
| |
| |
| |
| |
| | 22\193
| | 136.788
| |
|-
| |
| |
| |
| |
| |
| | 13\114
| |
| | 136.842
| |
|-
| |
| |
| |
| |
| |
| |
| | 17\149
| | 136.913
| |
|-
| |
| |
| | 4\35
| |
| |
| |
| |
| | 137.143
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 19\166
| | 137.349
| |
|-
| |
| |
| |
| |
| |
| | 15\131
| |
| | 137.405
| |
|-
| |
| |
| |
| |
| |
| |
| | 26\227
| | 137.445
| |
|-
| |
| |
| |
| |
| | 11\96
| |
| |
| | 137.500
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\253
| | 137.549
| |
|-
| |
| |
| |
| |
| |
| | 18\157
| |
| | 137.580
| |
|-
| |
| |
| |
| |
| |
| |
| | 25\218
| | 134.615
| |
|-
| |
| |
| |
| | 7\61
| |
| |
| |
| | 137.705
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 24\209
| | 137.799
| |
|-
| |
| |
| |
| |
| |
| | 17\148
| |
| | 137.838
| |
|-
| |
| |
| |
| |
| |
| |
| | 27\235
| | 137.872
| |
|-
| |
| |
| |
| |
| | 10\87
| |
| |
| | 137.931
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\200
| | 138.000
| |
|-
| |
| |
| |
| |
| |
| | 13\113
| |
| | 138.053
| |
|-
| |
| |
| |
| |
| |
| |
| | 16\139
| | 138.130
| |
|-
| |
| | 3\26
| |
| |
| |
| |
| |
| | 138.462
| style="text-align:center;" | L/s = 1.5
|-
| |
| |
| |
| |
| |
| |
| | 17\147
| | 138.776
| |
|-
| |
| |
| |
| |
| |
| | 14\121
| |
| | 138.843
| |
|-
| |
| |
| |
| |
| |
| |
| | 25\216
| | 138.889
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 138.943
| |
|-
| |
| |
| |
| |
| | 11\95
| |
| |
| | 138.947
| |
|-
| |
| |
| |
| |
| |
| |
| | 30\259
| | 138.996
| |
|-
| |
| |
| |
| |
| |
| | 19\164
| |
| | 139.024
| |
|-
| |
| |
| |
| |
| |
| |
| | 27\233
| | 139.056
| |
|-
| |
| |
| |
| | 8\69
| |
| |
| |
| | 139.130
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 29\250
| | 139.200
| |
|-
| |
| |
| |
| |
| |
| | 21\181
| |
| | 139.227
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 139.242
| |
|-
| |
| |
| |
| |
| |
| |
| | 34\249
| | 139.249
| |
|-
| |
| |
| |
| |
| | 13\112
| |
| |
| | 139.286
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\267
| | 139.326
| |
|-
| |
| |
| |
| |
| |
| | 18\155
| |
| | 139.355
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\198
| | 139.394
| |
|-
| |
| |
| | 5\43
| |
| |
| |
| |
| | 139.535
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 22\189
| | 139.683
| |
|-
| |
| |
| |
| |
| |
| | 17\146
| |
| | 139.726
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\249
| | 139.759
| |
|-
| |
| |
| |
| |
| | 12\103
| |
| |
| | 139.803
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\266
| | 139.850
| |
|-
| |
| |
| |
| |
| |
| | 19\163
| |
| | 139.877
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 139.903
| |
|-
| |
| |
| |
| |
| |
| |
| | 26\223
| | 139.910
| |
|-
| |
| |
| |
| | 7\60
| |
| |
| |
| | 140.000
| style="text-align:center;" | Bleu is around here
|-
| |
| |
| |
| |
| |
| |
| | 23\197
| | 140.102
| |
|-
| |
| |
| |
| |
| |
| | 16\137
| |
| | 140.146
| |
|-
| |
| |
| |
| |
| |
| |
| | 25\214
| | 140.187
| |
|-
| |
| |
| |
| |
| | 9\77
| |
| |
| | 140.260
| | Tsaharuk is between here…
|-
| |
| |
| |
| |
| |
| |
| | 20\171
| | 140.351
| |
|-
| |
| |
| |
| |
| |
| | 11\94
| |
| | 140.426
| style="text-align:center;" | …and here


Quanic is between here…
== Modes ==
|-
{{MOS mode degrees}}
| |
 
| |
== Scale tree ==
| |
{{MOS tuning spectrum
| |
| 7/4 = [[Bleu]] is around here
| |
| 9/5 = [[Tsaharuk]] and [[Quanic]] are around here
| |
| 5/1 = [[Bohpier]] is around here
| | 13\111
}}
| | 140.541
 
| style="text-align:center;" | …and here
{{todo|expand}}
|-
[[Category:9-tone scales]]
| | 2\17
[[Category:Gamelan]]
| |
| |
| |
| |
| |
| |
| | 141.176
| style="text-align:center;" | L/s = 2
|-
| |
| |
| |
| |
| |
| |
| | 13\110
| | 141.818
| |
|-
| |
| |
| |
| |
| |
| | 11\93
| |
| | 141.936
| |
|-
| |
| |
| |
| |
| |
| |
| | 20\169
| | 142.012
| |
|-
| |
| |
| |
| |
| | 9\76
| |
| |
| | 142.105
| |
|-
| |
| |
| |
| |
| |
| |
| | 25\211
| | 142.180
| |
|-
| |
| |
| |
| |
| |
| | 16\135
| |
| | 142.222
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\194
| | 142.268
| |
|-
| |
| |
| |
| | 7\59
| |
| |
| |
| | 142.373
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 26\219
| | 142.466
| |
|-
| |
| |
| |
| |
| |
| | 19\160
| |
| | 142.500
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\261
| | 142.529
| |
|-
| |
| |
| |
| |
| | 12\101
| |
| |
| | 142.574
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\244
| | 142.623
| |
|-
| |
| |
| |
| |
| |
| | 17\143
| |
| | 142.657
| |
|-
| |
| |
| |
| |
| |
| |
| | 22\185
| | 142.703
| |
|-
| |
| |
| | 5\42
| |
| |
| |
| |
| | 142.857
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 23\193
| | 143.005
| |
|-
| |
| |
| |
| |
| |
| | 18\151
| |
| | 143.046
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\260
| | 143.077
| |
|-
| |
| |
| |
| |
| | 13\109
| |
| |
| | 143.119
| |
|-
| |
| |
| |
| |
| |
| |
| | 34\285
| | 143.158
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 143.1645
| |
|-
| |
| |
| |
| |
| |
| | 21\176
| |
| | 143.182
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\243
| | 143.210
| |
|-
| |
| |
| |
| | 8\67
| |
| |
| |
| | 143.284
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 27\226
| | 143.363
| |
|-
| |
| |
| |
| |
| |
| | 19\159
| |
| | 143.396
| |
|-
| |
| |
| |
| |
| |
| |
| |
| | 143.406
| style="text-align:center;" | L/s = e
|-
| |
| |
| |
| |
| |
| |
| | 30\251
| | 143.426
| |
|-
| |
| |
| |
| |
| | 11\92
| |
| |
| | 143.478
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 25\209
| | 143.541
| |
|-
| |
| |
| |
| |
| |
| | 14\117
| |
| | 143.590
| |
|-
| |
| |
| |
| |
| |
| |
| | 17\142
| | 143.662
| |
|-
| |
| | 3\25
| |
| |
| |
| |
| |
| | 144.000
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| |
| | 144.260
| style="text-align:center;" | L/s = pi
|-
| |
| |
| |
| |
| |
| |
| | 16\133
| | 144.361
| |
|-
| |
| |
| |
| |
| |
| | 13\108
| |
| | 144.444
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\191
| | 144.503
| |
|-
| |
| |
| |
| |
| | 10\83
| |
| |
| | 144.578
| |
|-
| |
| |
| |
| |
| |
| |
| | 27\224
| | 144.643
| |
|-
| |
| |
| |
| |
| |
| | 17\141
| |
| | 144.681
| |
|-
| |
| |
| |
| |
| |
| |
| | 24\199
| | 144.724
| |
|-
| |
| |
| |
| | 7\58
| |
| |
| |
| | 144.828
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 25\207
| | 144.928
| |
|-
| |
| |
| |
| |
| |
| | 18\149
| |
| | 144.966
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\240
| | 145.000
| |
|-
| |
| |
| |
| |
| | 11\91
| |
| |
| | 145.055
| |
|-
| |
| |
| |
| |
| |
| |
| | 26\215
| | 145.116
| |
|-
| |
| |
| |
| |
| |
| | 15\124
| |
| | 145.161
| |
|-
| |
| |
| |
| |
| |
| |
| | 19\157
| | 145.223
| |
|-
| |
| |
| | 4\33
| |
| |
| |
| |
| | 145.455
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| |
| |
| | 13\107
| | 145.794
| |
|-
| |
| |
| |
| |
| |
| | 9\74
| |
| | 145.946
| |
|-
| |
| |
| |
| |
| |
| |
| | 14\115
| | 146.087
| |
|-
| |
| |
| |
| | 5\41
| |
| |
| |
| | 146.341
| style="text-align:center;" | Bohpier is between here…
|-
| |
| |
| |
| |
| |
| |
| | 16\131
| | 146.565
| |
|-
| |
| |
| |
| |
| |
| | 11\90
| |
| | 146.667
| |
|-
| |
| |
| |
| |
| |
| |
| | 17\139
| | 146.763
| |
|-
| |
| |
| |
| |
| | 6\49
| |
| |
| | 146.939
| style="text-align:center;" | …and here
|-
| |
| |
| |
| |
| |
| |
| | 13\106
| | 147.170
| |
|-
| |
| |
| |
| |
| |
| | 7\57
| |
| | 147.368
| |
|-
| |
| |
| |
| |
| |
| |
| | 8\65
| | 147.692
| |
|-
| | 1\8
| |
| |
| |
| |
| |
| |
| | 150.000
| style="text-align:center;" |
|}

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
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