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2L 5s (3/1-equivalent)

Revision as of 19:14, 6 March 2025 by ArrowHead294 (talk | contribs)
↖ 1L 4s⟨3/1⟩ ↑ 2L 4s⟨3/1⟩ 3L 4s⟨3/1⟩ ↗
← 1L 5s⟨3/1⟩ 2L 5s (3/1-equivalent) 3L 5s⟨3/1⟩ →
↙ 1L 6s⟨3/1⟩ ↓ 2L 6s⟨3/1⟩ 3L 6s⟨3/1⟩ ↘ 
┌╥┬┬╥┬┬┬┐
│║││║││││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLsss
sssLssL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 3\7 to 1\2 (815.1 ¢ to 951.0 ¢)
Dark 1\2 to 4\7 (951.0 ¢ to 1086.8 ¢)
Related MOS scales
Parent 2L 3s⟨3/1⟩
Sister 5L 2s⟨3/1⟩
Daughters 7L 2s⟨3/1⟩, 2L 7s⟨3/1⟩
Neutralized 4L 3s⟨3/1⟩
2-Flought 9L 5s⟨3/1⟩, 2L 12s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 3\7 (815.1 ¢)
Supersoft (L:s = 4:3) 10\23 (826.9 ¢)
Soft (L:s = 3:2) 7\16 (832.1 ¢)
Semisoft (L:s = 5:3) 11\25 (836.9 ¢)
Basic (L:s = 2:1) 4\9 (845.3 ¢)
Semihard (L:s = 5:2) 9\20 (855.9 ¢)
Hard (L:s = 3:1) 5\11 (864.5 ¢)
Superhard (L:s = 4:1) 6\13 (877.8 ¢)
Collapsed (L:s = 1:0) 1\2 (951.0 ¢)

2L 5s⟨3/1⟩, also called antitriatonic, is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 2 large steps and 5 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 815.1 ¢ to 951 ¢, or from 951 ¢ to 1086.8 ¢.

Name

The name antitriatonic[idiosyncratic term] was coined by ArrowHead294, as a back-formation from "diatonic" with di- being interpreted as 2 (the octave) and tri- being interpreted as 3 (the tritave), while the "anti-" prefix is used in the same way that the octave-equivalent 2L 5s scale is called the "antidiatonic" scale, though it is not an official name in TAMNAMS.

Theory

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 2L 5s⟨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 271.7 ¢
Major 1-mosstep M1ms L 271.7 ¢ to 951.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 543.4 ¢
Major 2-mosstep M2ms L + s 543.4 ¢ to 951.0 ¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0 ¢ to 815.1 ¢
Perfect 3-mosstep P3ms L + 2s 815.1 ¢ to 951.0 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 951.0 ¢ to 1086.8 ¢
Augmented 4-mosstep A4ms 2L + 2s 1086.8 ¢ to 1902.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 951.0 ¢ to 1358.5 ¢
Major 5-mosstep M5ms 2L + 3s 1358.5 ¢ to 1902.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 951.0 ¢ to 1630.2 ¢
Major 6-mosstep M6ms 2L + 4s 1630.2 ¢ to 1902.0 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 1902.0 ¢

Generator chain

Generator chain of 2L 5s⟨3/1⟩
Bright gens Scale degree Abbrev.
8 Augmented 3-mosdegree A3md
7 Augmented 0-mosdegree A0md
6 Augmented 4-mosdegree A4md
5 Major 1-mosdegree M1md
4 Major 5-mosdegree M5md
3 Major 2-mosdegree M2md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 7-mosdegree		 P0md
P7md
−1 Perfect 4-mosdegree P4md
−2 Minor 1-mosdegree m1md
−3 Minor 5-mosdegree m5md
−4 Minor 2-mosdegree m2md
−5 Minor 6-mosdegree m6md
−6 Diminished 3-mosdegree d3md
−7 Diminished 7-mosdegree d7md
−8 Diminished 4-mosdegree d4md

Temperament interpretations

  Todo: expand

Scale tree

Scale tree and tuning spectrum of 2L 5s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
3\7 815.124 1086.831 1:1 1.000 Equalized 2L 5s⟨3/1⟩
16\37 822.467 1079.488 6:5 1.200
13\30 824.181 1077.775 5:4 1.250
23\53 825.377 1076.578 9:7 1.286
10\23 826.937 1075.018 4:3 1.333 Supersoft 2L 5s⟨3/1⟩
27\62 828.271 1073.684 11:8 1.375
17\39 829.057 1072.898 7:5 1.400
24\55 829.944 1072.011 10:7 1.429
7\16 832.105 1069.850 3:2 1.500 Soft 2L 5s⟨3/1⟩
25\57 834.191 1067.764 11:7 1.571
18\41 835.005 1066.950 8:5 1.600
29\66 835.708 1066.248 13:8 1.625
11\25 836.860 1065.095 5:3 1.667 Semisoft 2L 5s⟨3/1⟩
26\59 838.150 1063.805 12:7 1.714
15\34 839.098 1062.857 7:4 1.750
19\43 840.399 1061.556 9:5 1.800
4\9 845.313 1056.642 2:1 2.000 Basic 2L 5s⟨3/1⟩
Scales with tunings softer than this are proper
17\38 850.875 1051.080 9:4 2.250
13\29 852.601 1049.354 7:3 2.333
22\49 853.939 1048.016 12:5 2.400
9\20 855.880 1046.075 5:2 2.500 Semihard 2L 5s⟨3/1⟩
23\51 857.744 1044.211 13:5 2.600
14\31 858.947 1043.008 8:3 2.667
19\42 860.408 1041.547 11:4 2.750
5\11 864.525 1037.430 3:1 3.000 Hard 2L 5s⟨3/1⟩
16\35 869.465 1032.490 10:3 3.333
11\24 871.729 1030.226 7:2 3.500
17\37 873.871 1028.084 11:3 3.667
6\13 877.825 1024.130 4:1 4.000 Superhard 2L 5s⟨3/1⟩
13\28 883.051 1018.904 9:2 4.500
7\15 887.579 1014.376 5:1 5.000
8\17 895.038 1006.917 6:1 6.000
1\2 950.978 950.978 1:0 → ∞ Collapsed 2L 5s⟨3/1⟩
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