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

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{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro|Other Names=sub-Arcturus}}
{{MOS intro|Other Names=sub-Arcturus; ultratriatonic}}


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.  
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.
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 ==
== Scale properties ==
Line 12: Line 15:
== Scale tree ==
== Scale tree ==
{{MOS tuning spectrum
{{MOS tuning spectrum
| 21/13 = Golden Sub-Arcturus is near here
| 21/13 = Golden sub-Arcturus is near here
}}
}}


Revision as of 17:58, 9 April 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.
MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

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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