9L 2s (3/1-equivalent): Difference between revisions

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{{Infobox MOS
{{Infobox MOS}}
| Equalized = 6
{{MOS intro|Other Names=sub-Arcturus; ultratriatonic}}
| Collapsed = 5
 
| Pattern = LLLLLsLLLLs
This MOS family is the simplest [[tritave]]-equivalent scale using an "ordinary" ~5:3 as a generator. Of course, it is on the extremely flat end of what is "ordinary", being the same size as a neutral sixth.
 
Coincidentally, its categorical name in this scale happens to be "sixth" also, just not in the "ordinary" diatonic sense of the name. Because this "sixth" is so flat, "sixths" in the range of propriety lead, in three steps, when tritave reduced, into the Mavila [[continuum]] and the bottom of the syntonic continuum.
 
== Name ==
The name '''ultratriatonic'''{{idio}} was coined by {{u|ArrowHead294}}, as a back-formation from the name "ultradiatonic" for the octave-equivalent [[9L 2s]] scale with di- being interpreted as 2 (the [[2/1|octave]]) and tri- being interpreted as 3 (the [[3/1|tritave]]). It is not an official name in [[TAMNAMS]].
 
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum
| 21/13 = Golden sub-Arcturus is near here
}}
}}


'''9L 2s<3/1>''' or '''sub-[[Arcturus]]''' is a [[tritave]]-repeating [[MOS scale]] having 9 large steps and 2 small steps. This MOS family is the simplest tritave-equivalent scale using an "ordinary" ~5:3 as a generator. Of course, it is on the extremely flat end of what is "ordinary", being the same size as a neutral sixth. Coincidentally, its categorical name in this scale happens to be "sixth" also, just not in the "ordinary" diatonic sense of the name. Because this "sixth" is so flat, "sixths" in the range of propriety lead, in three steps, when tritave reduced, into the Mavila continuum and the bottom of the syntonic continuum.
{{todo|expand}}


{| class="wikitable"
[[Category:Arcturus]]
|-
! colspan="7" | Generator
! | cents
! | L
! | s
! | 3g
! | Notes
|-
| style="text-align:center;" | 4\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;" | 845.313
577.778
| style="text-align:center;" | 211.328
144.444
| style="text-align:center;" | 0.00
| style="text-align:center;" | 633.985
433.333
| style="text-align:center;" | L=1 s=0
|-
| 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;" | 29\65
| style="text-align:center;" | 848.5645
580
| style="text-align:center;" | 204.826
140
| style="text-align:center;" | 29.261
20
| style="text-align:center;" | 643.739
440
| style="text-align:center;" | L=7 s=1
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 25\56
| style="text-align:center;" |
| style="text-align:center;" | 849.087
580.357
| style="text-align:center;" | 203.78
139.286
| style="text-align:center;" | 33.9635
23.214
| style="text-align:center;" | 645.306
441.071
| style="text-align:center;" | L=6 s=1
|-
| 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;" | 46\103
| style="text-align:center;" | 849.417
580.5825
| style="text-align:center;" | 203.121
138.835
| style="text-align:center;" | 36.931
25.243
| style="text-align:center;" | 646.295
441.748
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 21\47
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 849.81
580.851
| style="text-align:center;" | 202.336
138.298
| style="text-align:center;" | 40.467
27.66
| style="text-align:center;" | 647.474
442.553
| style="text-align:center;" | L=5 s=1
|-
| 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;" | 59\132
| style="text-align:center;" | 850.116
581.061
| style="text-align:center;" | 201.7225
137.879
| style="text-align:center;" | 43.226
29.5455
| style="text-align:center;" | 648.394
443.182
| 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;" | 38\85
| style="text-align:center;" |
| style="text-align:center;" | 850.286
581.1765
| style="text-align:center;" | 201.383
137.647
| style="text-align:center;" | 44.752
28.235
| style="text-align:center;" | 648.902
443.529
| 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;" |
| style="text-align:center;" | 55\123
| style="text-align:center;" | 850.468
581.301
| style="text-align:center;" | 201.02
137.398
| style="text-align:center;" | 46.309
31.707
| style="text-align:center;" | 649.448
443.902
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 17\38
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 850.875
581.579
| style="text-align:center;" | 200.206
136.842
| style="text-align:center;" | 50.051
34.2105
| style="text-align:center;" | 650.669
444.737
| style="text-align:center;" | L=4 s=1
|-
| 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;" | 64\143
| style="text-align:center;" | 851.225
581.818
| style="text-align:center;" | 199.506
136.364
| style="text-align:center;" | 53.2015
36.364
| style="text-align:center;" | 651.719
445.4545
| 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;" | 47\105
| style="text-align:center;" |
| style="text-align:center;" | 851.351
581.905
| style="text-align:center;" | 199.252
136.1905
| style="text-align:center;" | 54.342
37.143
| style="text-align:center;" | 652.099
445.714
| 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;" |
| style="text-align:center;" | 77\172
| style="text-align:center;" | 851.457
581.977
| style="text-align:center;" | 199.042
136.0465
| style="text-align:center;" | 55.289
37.791
| style="text-align:center;" | 652.415
445.93
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 30\67
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 851.622
582.09
| style="text-align:center;" | 198.712
135.821
| style="text-align:center;" | 56.775
38.806
| style="text-align:center;" | 652.91
446.269
| style="text-align:center;" | L=7 s=2
|-
| 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;" | 73\163
| style="text-align:center;" | 851.796
582.209
| style="text-align:center;" | 198.363
135.583
| style="text-align:center;" | 58.342
39.877
| style="text-align:center;" | 653.432
446.626
| 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;" | 43\96
| style="text-align:center;" |
| style="text-align:center;" | 851.917
582.292
| style="text-align:center;" | 198.12
135.417
| style="text-align:center;" | 59.436
40.625
| style="text-align:center;" | 653.797
446.875
| 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;" |
| style="text-align:center;" | 56\125
| style="text-align:center;" | 852.075
582.4
| style="text-align:center;" | 197.803
135.2
| style="text-align:center;" | 60.863
41.6
| style="text-align:center;" | 654.2725
447.2
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13\29
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 852.6005
582.759
| style="text-align:center;" | 196.754
134.483
| style="text-align:center;" | 65.585
44.828
| style="text-align:center;" | 655.847
448.276
| style="text-align:center;" | L=3 s=1
|-
| 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;" | 61\136
| style="text-align:center;" | 853.083
583.088
| style="text-align:center;" | 195.7895
133.8235
| style="text-align:center;" | 69.925
47.764
| style="text-align:center;" | 657.293
449.265
| 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;" | 48\107
| style="text-align:center;" |
| style="text-align:center;" | 853.2135
583.178
| style="text-align:center;" | 195.528
133.645
| style="text-align:center;" | 71.101
48.598
| style="text-align:center;" | 657.685
449.533
| 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;" |
| style="text-align:center;" | 83\185
| style="text-align:center;" | 853.3095
583.243
| style="text-align:center;" | 195.336
133.5135
| style="text-align:center;" | 71.966
49.189
| style="text-align:center;" | 657.974
449.73
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 35\78
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 853.441
583.333
| style="text-align:center;" | 195.072
133.333
| style="text-align:center;" | 73.152
50
| style="text-align:center;" | 658.369
450
| 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;" |
| style="text-align:center;" | 92\205
| style="text-align:center;" | 853.56
583.415
| style="text-align:center;" | 194.834
133.171
| style="text-align:center;" | 74.223
50.732
| style="text-align:center;" | 658.726
450.244
| 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;" | 57\127
| style="text-align:center;" |
| style="text-align:center;" | 853.633
583.465
| style="text-align:center;" | 194.688
133.071
| style="text-align:center;" | 74.88
51.181
| style="text-align:center;" | 658.945
450.294
| 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;" |
| style="text-align:center;" | 79\176
| style="text-align:center;" | 853.718
583.522
| style="text-align:center;" | 194.518
132.9545
| style="text-align:center;" | 75.646
51.7045
| style="text-align:center;" | 659.2
450.568
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 22\49
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 853.939
583.6735
| style="text-align:center;" | 194.077
132.653
| style="text-align:center;" | 77.631
53.061
| style="text-align:center;" | 659.862
451.02
| style="text-align:center;" | L=5 s=2
|-
| 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;" | 75\167
| style="text-align:center;" | 854.171
583.832
| style="text-align:center;" | 193.588
132.335
| style="text-align:center;" | 79.722
54.491
| style="text-align:center;" | 660.559
451.497
| 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;" | 53\118
| style="text-align:center;" |
| style="text-align:center;" | 854.268
583.898
| style="text-align:center;" | 193.419
132.203
| style="text-align:center;" | 80.591
55.085
| style="text-align:center;" | 660.849
451.695
| 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;" |
| style="text-align:center;" | 84\187
| style="text-align:center;" | 854.354
583.957
| style="text-align:center;" | 193.245
132.086
| style="text-align:center;" | 81.367
55.615
| style="text-align:center;" | 661.107
451.872
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 31\69
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 854.5015
584.058
| style="text-align:center;" | 192.952
131.844
| style="text-align:center;" | 82.694
56.522
| style="text-align:center;" | 661.55
452.174
| style="text-align:center;" | L=7 s=3
|-
| 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;" | 71\158
| style="text-align:center;" | 854.676
584.177
| style="text-align:center;" | 192.603
131.646
| style="text-align:center;" | 84.264
57.595
| style="text-align:center;" | 662.073
452.532
| 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;" | 40\89
| style="text-align:center;" |
| style="text-align:center;" | 854.811
584.27
| style="text-align:center;" | 192.3325
131.461
| style="text-align:center;" | 85.481
58.427
| style="text-align:center;" | 662.479
452.809
| 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;" |
| style="text-align:center;" | 49\109
| style="text-align:center;" | 855.007
584.404
| style="text-align:center;" | 191.94
131.193
| style="text-align:center;" | 87.246
59.633
| style="text-align:center;" | 663.067
453.211
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" | 9\20
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 855.88
585
| style="text-align:center;" | 190.1955
130
| style="text-align:center;" | 95.098
65
| style="text-align:center;" | 665.684
455
| style="text-align:center;" | L=2 s=1
|-
| 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;" | 50\111
| style="text-align:center;" | 856.7365
585.586
| style="text-align:center;" | 188.482
128.829
| style="text-align:center;" | 102.808
70.27
| style="text-align:center;" | 668.2545
456.757
| 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;" | 41\91
| style="text-align:center;" |
| style="text-align:center;" | 856.925
585.714
| style="text-align:center;" | 188.105
128.571
| style="text-align:center;" | 104.503
71.429
| style="text-align:center;" | 668.819
457.143
| 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;" |
| style="text-align:center;" | 73\162
| style="text-align:center;" | 857.053
585.8025
| style="text-align:center;" | 187.847
128.395
| style="text-align:center;" | 105.664
72.222
| style="text-align:center;" | 669.206
457.407
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 32\71
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 857.737
585.9155
| style="text-align:center;" | 187.517
128.169
| style="text-align:center;" | 107.152
73.239
| style="text-align:center;" | 669.7025
457.7565
| style="text-align:center;" | L=7 s=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;" |
| style="text-align:center;" | 87\193
| style="text-align:center;" | 857.358
586.01
| style="text-align:center;" | 187.239
127.979
| style="text-align:center;" | 108.402
74.093
| style="text-align:center;" | 670.119
458.031
| 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;" | 55\122
| style="text-align:center;" |
| style="text-align:center;" | 857.85
586.066
| style="text-align:center;" | 187.0775
127.869
| style="text-align:center;" | 109.129
74.59
| style="text-align:center;" | 670.361
458.198
| 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;" |
| style="text-align:center;" | 78\173
| style="text-align:center;" | 857.529
586.127
| style="text-align:center;" | 186.897
127.746
| style="text-align:center;" | 109.94
75.1445
| style="text-align:center;" | 670.6315
458.3815
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 23\51
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 857.744
586.2745
| style="text-align:center;" | 186.466
127.451
| style="text-align:center;" | 111.88
76.471
| style="text-align:center;" | 671.278
458.8235
| style="text-align:center;" | L=5 s=3
|-
| 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;" | 83\184
| style="text-align:center;" | 857.947
586.413
| style="text-align:center;" | 186.061
127.174
| style="text-align:center;" | 113.704
77.717
| style="text-align:center;" | 671.886
459.239
| 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;" | 60\133
| style="text-align:center;" |
| style="text-align:center;" | 858.025
586.466
| style="text-align:center;" | 185.925
127.068
| style="text-align:center;" | 114.403
78.1955
| style="text-align:center;" | 672.119
459.3985
| 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;" |
| style="text-align:center;" | 97\215
| style="text-align:center;" | 858.091
586.512
| style="text-align:center;" | 185.772
126.977
| style="text-align:center;" | 115.002
78.605
| style="text-align:center;" | 672.319
459.535
| style="text-align:center;" | Golden Sub-Arcturus is near here
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 37\82
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 858.199
586.585
| style="text-align:center;" | 185.557
126.829
| style="text-align:center;" | 115.972
79.268
| style="text-align:center;" | 672.643
459.756
| 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;" |
| style="text-align:center;" | 88\195
| style="text-align:center;" | 858.318
586.667
| style="text-align:center;" | 185.318
126.667
| style="text-align:center;" | 117.043
80
| style="text-align:center;" | 672.9995
460
| 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;" | 51\113
| style="text-align:center;" |
| style="text-align:center;" | 858.4045
586.726
| style="text-align:center;" | 185.146
126.548
| style="text-align:center;" | 117.82
80.531
| style="text-align:center;" | 673.258
460.177
| 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;" |
| style="text-align:center;" | 65\144
| style="text-align:center;" | 858.521
586.806
| style="text-align:center;" | 184.912
126.389
| style="text-align:center;" | 118.872
81.25
| style="text-align:center;" | 673.609
460.417
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 14\31
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 858.947
587.097
| style="text-align:center;" | 184.06
125.8065
| style="text-align:center;" | 122.707
83.871
| style="text-align:center;" | 674.882
461.291
| style="text-align:center;" | L=3 s=2
|-
| 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;" | 61\135
| style="text-align:center;" | 859.402
587.407
| style="text-align:center;" | 183.151
125.185
| style="text-align:center;" | 126.797
86.667
| style="text-align:center;" | 676,251
462.222
| 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;" | 47\104
| style="text-align:center;" |
| style="text-align:center;" | 859.537
587.5
| style="text-align:center;" | 182.88
125
| style="text-align:center;" | 128.016
87.5
| style="text-align:center;" | 676.657
462.5
| 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;" |
| style="text-align:center;" | 80\177
| style="text-align:center;" | 859.641
587.571
| style="text-align:center;" | 182.674
124.859
| style="text-align:center;" | 128.946
88.136
| style="text-align:center;" | 676.967
462.712
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 33\73
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 859.788
587.671
| style="text-align:center;" | 182.379
124.6575
| style="text-align:center;" | 130.271
89.041
| style="text-align:center;" | 677.409
463.014
| style="text-align:center;" | L=7 s=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;" | 85\188
| style="text-align:center;" | 859.9265
587.766
| style="text-align:center;" | 182.102
124.468
| style="text-align:center;" | 131.518
89.894
| style="text-align:center;" | 677.824
463.298
| 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;" | 52\115
| style="text-align:center;" |
| style="text-align:center;" | 860.014
587.826
| style="text-align:center;" | 181.926
124.348
| style="text-align:center;" | 132.31
90.435
| style="text-align:center;" | 678.088
463.478
| 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;" |
| style="text-align:center;" | 71\157
| style="text-align:center;" | 860.12
587.898
| style="text-align:center;" | 181.715
124.204
| style="text-align:center;" | 133.258
91.083
| style="text-align:center;" | 678.404
463.694
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 19\42
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 860.408
588.095
| style="text-align:center;" | 181.139
123.8095
| style="text-align:center;" | 135.854
92.857
| style="text-align:center;" | 679.27
464.286
| style="text-align:center;" | L=4 s=3
|-
| 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;" | 62\137
| style="text-align:center;" | 860.739
588.321
| style="text-align:center;" | 180.4775
123.358
| style="text-align:center;" | 138.829
94.8905
| style="text-align:center;" | 680.261
464.9635
| 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;" | 43\95
| style="text-align:center;" |
| style="text-align:center;" | 860.885
588.421
| style="text-align:center;" | 180.185
123.158
| style="text-align:center;" | 140.144
95.7895
| style="text-align:center;" | 680.7
465.263
| 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;" |
| style="text-align:center;" | 67\148
| style="text-align:center;" | 861.02
588.5135
| style="text-align:center;" | 179.915
122.973
| style="text-align:center;" | 141.3615
96.621
| style="text-align:center;" | 681.1055
465.5405
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 24\53
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 861.263
588.679
| style="text-align:center;" | 179.43
122.6415
| style="text-align:center;" | 143.544
98.113
| style="text-align:center;" | 681.833
466.038
| style="text-align:center;" | L=5 s=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;" |
| style="text-align:center;" | 53\117
| style="text-align:center;" | 861.569
588.889
| style="text-align:center;" | 178.816
122.222
| style="text-align:center;" | 146.304
100
| style="text-align:center;" | 682.753
466.667
| 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;" | 29\64
| style="text-align:center;" |
| style="text-align:center;" | 861.823
589.0625
| style="text-align:center;" | 178.308
121.875
| style="text-align:center;" | 148.59
101.5625
| style="text-align:center;" | 683.515
467.1875
| style="text-align:center;" | L=6 s=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;" | 34\75
| style="text-align:center;" | 862.22
589.333
| style="text-align:center;" | 177.516
121.333
| style="text-align:center;" | 152.156
104
| style="text-align:center;" | 684.704
468
| style="text-align:center;" | L=7 s=6
|-
| style="text-align:center;" | 5\11
| 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;" | 864.525
590.909
| colspan="2" style="text-align:center;" | 172.905
118.182
| style="text-align:center;" | 691.62
472.727
| style="text-align:center;" | L=1 s=1
|}

Latest revision as of 14:06, 5 May 2025

↖ 8L 1s⟨3/1⟩ ↑ 9L 1s⟨3/1⟩ 10L 1s⟨3/1⟩ ↗
← 8L 2s⟨3/1⟩ 9L 2s (3/1-equivalent) 10L 2s⟨3/1⟩ →
↙ 8L 3s⟨3/1⟩ ↓ 9L 3s⟨3/1⟩ 10L 3s⟨3/1⟩ ↘ 
┌╥╥╥╥╥┬╥╥╥╥┬┐
│║║║║║│║║║║││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLsLLLLs
sLLLLsLLLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 6\11 to 5\9 (1037.4 ¢ to 1056.6 ¢)
Dark 4\9 to 5\11 (845.3 ¢ to 864.5 ¢)
Related MOS scales
Parent 2L 7s⟨3/1⟩
Sister 2L 9s⟨3/1⟩
Daughters 11L 9s⟨3/1⟩, 9L 11s⟨3/1⟩
Neutralized 7L 4s⟨3/1⟩
2-Flought 20L 2s⟨3/1⟩, 9L 13s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 6\11 (1037.4 ¢)
Supersoft (L:s = 4:3) 23\42 (1041.5 ¢)
Soft (L:s = 3:2) 17\31 (1043.0 ¢)
Semisoft (L:s = 5:3) 28\51 (1044.2 ¢)
Basic (L:s = 2:1) 11\20 (1046.1 ¢)
Semihard (L:s = 5:2) 27\49 (1048.0 ¢)
Hard (L:s = 3:1) 16\29 (1049.4 ¢)
Superhard (L:s = 4:1) 21\38 (1051.1 ¢)
Collapsed (L:s = 1:0) 5\9 (1056.6 ¢)

9L 2s⟨3/1⟩, also called sub-Arcturus or ultratriatonic, is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 9 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1037.4 ¢ to 1056.6 ¢, or from 845.3 ¢ to 864.5 ¢.

This MOS family is the simplest tritave-equivalent scale using an "ordinary" ~5:3 as a generator. Of course, it is on the extremely flat end of what is "ordinary", being the same size as a neutral sixth.

Coincidentally, its categorical name in this scale happens to be "sixth" also, just not in the "ordinary" diatonic sense of the name. Because this "sixth" is so flat, "sixths" in the range of propriety lead, in three steps, when tritave reduced, into the Mavila continuum and the bottom of the syntonic continuum.

Name

The name ultratriatonic[idiosyncratic term] was coined by ArrowHead294, as a back-formation from the name "ultradiatonic" for the octave-equivalent 9L 2s scale with di- being interpreted as 2 (the octave) and tri- being interpreted as 3 (the tritave). It is not an official name in TAMNAMS.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 9L 2s⟨3/1⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 172.9 ¢
Major 1-mosstep M1ms L 172.9 ¢ to 211.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 211.3 ¢ to 345.8 ¢
Major 2-mosstep M2ms 2L 345.8 ¢ to 422.7 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 422.7 ¢ to 518.7 ¢
Major 3-mosstep M3ms 3L 518.7 ¢ to 634.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 634.0 ¢ to 691.6 ¢
Major 4-mosstep M4ms 4L 691.6 ¢ to 845.3 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 845.3 ¢ to 864.5 ¢
Augmented 5-mosstep A5ms 5L 864.5 ¢ to 1056.6 ¢
6-mosstep Diminished 6-mosstep d6ms 4L + 2s 845.3 ¢ to 1037.4 ¢
Perfect 6-mosstep P6ms 5L + s 1037.4 ¢ to 1056.6 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 1056.6 ¢ to 1210.3 ¢
Major 7-mosstep M7ms 6L + s 1210.3 ¢ to 1268.0 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 1268.0 ¢ to 1383.2 ¢
Major 8-mosstep M8ms 7L + s 1383.2 ¢ to 1479.3 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 1479.3 ¢ to 1556.1 ¢
Major 9-mosstep M9ms 8L + s 1556.1 ¢ to 1690.6 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 1690.6 ¢ to 1729.1 ¢
Major 10-mosstep M10ms 9L + s 1729.1 ¢ to 1902.0 ¢
11-mosstep Perfect 11-mosstep P11ms 9L + 2s 1902.0 ¢

Generator chain

Generator chain of 9L 2s⟨3/1⟩
Bright gens Scale degree Abbrev.
19 Augmented 4-mosdegree A4md
18 Augmented 9-mosdegree A9md
17 Augmented 3-mosdegree A3md
16 Augmented 8-mosdegree A8md
15 Augmented 2-mosdegree A2md
14 Augmented 7-mosdegree A7md
13 Augmented 1-mosdegree A1md
12 Augmented 6-mosdegree A6md
11 Augmented 0-mosdegree A0md
10 Augmented 5-mosdegree A5md
9 Major 10-mosdegree M10md
8 Major 4-mosdegree M4md
7 Major 9-mosdegree M9md
6 Major 3-mosdegree M3md
5 Major 8-mosdegree M8md
4 Major 2-mosdegree M2md
3 Major 7-mosdegree M7md
2 Major 1-mosdegree M1md
1 Perfect 6-mosdegree P6md
0 Perfect 0-mosdegree
Perfect 11-mosdegree		 P0md
P11md
−1 Perfect 5-mosdegree P5md
−2 Minor 10-mosdegree m10md
−3 Minor 4-mosdegree m4md
−4 Minor 9-mosdegree m9md
−5 Minor 3-mosdegree m3md
−6 Minor 8-mosdegree m8md
−7 Minor 2-mosdegree m2md
−8 Minor 7-mosdegree m7md
−9 Minor 1-mosdegree m1md
−10 Diminished 6-mosdegree d6md
−11 Diminished 11-mosdegree d11md
−12 Diminished 5-mosdegree d5md
−13 Diminished 10-mosdegree d10md
−14 Diminished 4-mosdegree d4md
−15 Diminished 9-mosdegree d9md
−16 Diminished 3-mosdegree d3md
−17 Diminished 8-mosdegree d8md
−18 Diminished 2-mosdegree d2md
−19 Diminished 7-mosdegree d7md

Modes

Scale degrees of the modes of 9L 2s⟨3/1⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11
10|0 1 LLLLLsLLLLs Perf. Maj. Maj. Maj. Maj. Aug. Perf. Maj. Maj. Maj. Maj. Perf.
9|1 7 LLLLsLLLLLs Perf. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Perf.
8|2 2 LLLLsLLLLsL Perf. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Min. Perf.
7|3 8 LLLsLLLLLsL Perf. Maj. Maj. Maj. Min. Perf. Perf. Maj. Maj. Maj. Min. Perf.
6|4 3 LLLsLLLLsLL Perf. Maj. Maj. Maj. Min. Perf. Perf. Maj. Maj. Min. Min. Perf.
5|5 9 LLsLLLLLsLL Perf. Maj. Maj. Min. Min. Perf. Perf. Maj. Maj. Min. Min. Perf.
4|6 4 LLsLLLLsLLL Perf. Maj. Maj. Min. Min. Perf. Perf. Maj. Min. Min. Min. Perf.
3|7 10 LsLLLLLsLLL Perf. Maj. Min. Min. Min. Perf. Perf. Maj. Min. Min. Min. Perf.
2|8 5 LsLLLLsLLLL Perf. Maj. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Perf.
1|9 11 sLLLLLsLLLL Perf. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Perf.
0|10 6 sLLLLsLLLLL Perf. Min. Min. Min. Min. Perf. Dim. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 9L 2s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
6\11 1037.430 864.525 1:1 1.000 Equalized 9L 2s⟨3/1⟩
35\64 1040.132 861.823 6:5 1.200
29\53 1040.692 861.263 5:4 1.250
52\95 1041.070 860.885 9:7 1.286
23\42 1041.547 860.408 4:3 1.333 Supersoft 9L 2s⟨3/1⟩
63\115 1041.941 860.014 11:8 1.375
40\73 1042.167 859.788 7:5 1.400
57\104 1042.418 859.537 10:7 1.429
17\31 1043.008 858.947 3:2 1.500 Soft 9L 2s⟨3/1⟩
62\113 1043.551 858.404 11:7 1.571
45\82 1043.756 858.199 8:5 1.600
73\133 1043.930 858.025 13:8 1.625
28\51 1044.211 857.744 5:3 1.667 Semisoft 9L 2s⟨3/1⟩
67\122 1044.516 857.439 12:7 1.714
39\71 1044.736 857.219 7:4 1.750
50\91 1045.030 856.925 9:5 1.800
11\20 1046.075 855.880 2:1 2.000 Basic 9L 2s⟨3/1⟩
Scales with tunings softer than this are proper
49\89 1047.144 854.811 9:4 2.250
38\69 1047.453 854.502 7:3 2.333
65\118 1047.687 854.268 12:5 2.400
27\49 1048.016 853.939 5:2 2.500 Semihard 9L 2s⟨3/1⟩
70\127 1048.322 853.633 13:5 2.600
43\78 1048.514 853.441 8:3 2.667
59\107 1048.742 853.213 11:4 2.750
16\29 1049.354 852.601 3:1 3.000 Hard 9L 2s⟨3/1⟩
53\96 1050.038 851.917 10:3 3.333
37\67 1050.333 851.622 7:2 3.500
58\105 1050.604 851.351 11:3 3.667
21\38 1051.080 850.875 4:1 4.000 Superhard 9L 2s⟨3/1⟩
47\85 1051.669 850.286 9:2 4.500
26\47 1052.145 849.810 5:1 5.000
31\56 1052.868 849.087 6:1 6.000
5\9 1056.642 845.313 1:0 → ∞ Collapsed 9L 2s⟨3/1⟩
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