8L 3s

↖ 7L 2s	↑ 8L 2s	9L 2s ↗
← 7L 3s	8L 3s	9L 3s →
↙ 7L 4s	↓ 8L 4s	9L 4s ↘

Scale structure
Step pattern	LLLsLLLsLLs sLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	4\11 to 3\8 (436.4 ¢ to 450.0 ¢)
Dark	5\8 to 7\11 (750.0 ¢ to 763.6 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	3L 5s
Sister	3L 8s
Daughters	11L 8s, 8L 11s
Neutralized	5L 6s
2-Flought	19L 3s, 8L 14s
Equal tunings
Equalized (L:s = 1:1)	4\11 (436.4 ¢)
Supersoft (L:s = 4:3)	15\41 (439.0 ¢)
Soft (L:s = 3:2)	11\30 (440.0 ¢)
Semisoft (L:s = 5:3)	18\49 (440.8 ¢)
Basic (L:s = 2:1)	7\19 (442.1 ¢)
Semihard (L:s = 5:2)	17\46 (443.5 ¢)
Hard (L:s = 3:1)	10\27 (444.4 ¢)
Superhard (L:s = 4:1)	13\35 (445.7 ¢)
Collapsed (L:s = 1:0)	3\8 (450.0 ¢)
View • Talk • Edit

8L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 3 small steps, repeating every octave. 8L 3s is a child scale of 3L 5s, expanding it by 3 tones. Generators that produce this scale range from 436.4 ¢ to 450 ¢, or from 750 ¢ to 763.6 ¢.

The only significant harmonic entropy minimum with this MOS pattern is sensi, in which the generator is 9/7 and two of them make a 5/3.

Modes

Modes of 8L 3s

UDP	Cyclic order	Step pattern
10|0	1	LLLsLLLsLLs
9|1	5	LLLsLLsLLLs
8|2	9	LLsLLLsLLLs
7|3	2	LLsLLLsLLsL
6|4	6	LLsLLsLLLsL
5|5	10	LsLLLsLLLsL
4|6	3	LsLLLsLLsLL
3|7	7	LsLLsLLLsLL
2|8	11	sLLLsLLLsLL
1|9	4	sLLLsLLsLLL
0|10	8	sLLsLLLsLLL

Proposed Names

R-4981 has proposed names based on shogi pieces.

Modes of 8L 3s

UDP	Cyclic order	Step pattern
10|0	1	LLLsLLLsLLs
9|1	5	LLLsLLsLLLs
8|2	9	LLsLLLsLLLs
7|3	2	LLsLLLsLLsL
6|4	6	LLsLLsLLLsL
5|5	10	LsLLLsLLLsL
4|6	3	LsLLLsLLsLL
3|7	7	LsLLsLLLsLL
2|8	11	sLLLsLLLsLL
1|9	4	sLLLsLLsLLL
0|10	8	sLLsLLLsLLL

Intervals

Intervals of 8L 3s

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 109.1 ¢
	Major 1-mosstep	M1ms	L	109.1 ¢ to 150.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	150.0 ¢ to 218.2 ¢
	Major 2-mosstep	M2ms	2L	218.2 ¢ to 300.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	300.0 ¢ to 327.3 ¢
	Major 3-mosstep	M3ms	3L	327.3 ¢ to 450.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	300.0 ¢ to 436.4 ¢
	Perfect 4-mosstep	P4ms	3L + s	436.4 ¢ to 450.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	450.0 ¢ to 545.5 ¢
	Major 5-mosstep	M5ms	4L + s	545.5 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	600.0 ¢ to 654.5 ¢
	Major 6-mosstep	M6ms	5L + s	654.5 ¢ to 750.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	750.0 ¢ to 763.6 ¢
	Augmented 7-mosstep	A7ms	6L + s	763.6 ¢ to 900.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	750.0 ¢ to 872.7 ¢
	Major 8-mosstep	M8ms	6L + 2s	872.7 ¢ to 900.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	900.0 ¢ to 981.8 ¢
	Major 9-mosstep	M9ms	7L + 2s	981.8 ¢ to 1050.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	1050.0 ¢ to 1090.9 ¢
	Major 10-mosstep	M10ms	8L + 2s	1090.9 ¢ to 1200.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	8L + 3s	1200.0 ¢

Scale tree

Todo: review Review entries from past page revision and enter them into the scale tree.

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 8L 3s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\11						436.364	763.636	1:1	1.000	Equalized 8L 3s
					23\63	438.095	761.905	6:5	1.200
				19\52		438.462	761.538	5:4	1.250
					34\93	438.710	761.290	9:7	1.286
			15\41			439.024	760.976	4:3	1.333	Supersoft 8L 3s
					41\112	439.286	760.714	11:8	1.375
				26\71		439.437	760.563	7:5	1.400
					37\101	439.604	760.396	10:7	1.429
		11\30				440.000	760.000	3:2	1.500	Soft 8L 3s
					40\109	440.367	759.633	11:7	1.571
				29\79		440.506	759.494	8:5	1.600
					47\128	440.625	759.375	13:8	1.625
			18\49			440.816	759.184	5:3	1.667	Semisoft 8L 3s
					43\117	441.026	758.974	12:7	1.714
				25\68		441.176	758.824	7:4	1.750
					32\87	441.379	758.621	9:5	1.800
	7\19					442.105	757.895	2:1	2.000	Basic 8L 3s Scales with tunings softer than this are proper
					31\84	442.857	757.143	9:4	2.250
				24\65		443.077	756.923	7:3	2.333
					41\111	443.243	756.757	12:5	2.400
			17\46			443.478	756.522	5:2	2.500	Semihard 8L 3s Sensi is in this region;
					44\119	443.697	756.303	13:5	2.600
				27\73		443.836	756.164	8:3	2.667
					37\100	444.000	756.000	11:4	2.750
		10\27				444.444	755.556	3:1	3.000	Hard 8L 3s
					33\89	444.944	755.056	10:3	3.333
				23\62		445.161	754.839	7:2	3.500
					36\97	445.361	754.639	11:3	3.667
			13\35			445.714	754.286	4:1	4.000	Superhard 8L 3s
					29\78	446.154	753.846	9:2	4.500
				16\43		446.512	753.488	5:1	5.000
					19\51	447.059	752.941	6:1	6.000
3\8						450.000	750.000	1:0	→ ∞	Collapsed 8L 3s

Todo: review make pentachordal analysis its own section?