2L 5s (3/1-equivalent)

↖ 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 ¢)
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2L 5s⟨3/1⟩ 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 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.

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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