8L 13s

↖ 7L 12s	↑ 8L 12s	9L 12s ↗
← 7L 13s	8L 13s	9L 13s →
↙ 7L 14s	↓ 8L 14s	9L 14s ↘

┌╥┬╥┬┬╥┬╥┬┬╥┬┬╥┬╥┬┬╥┬┬┐ │║│║││║│║││║││║│║││║│││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLssLsLssLssLsLssLss ssLssLsLssLssLsLssLsL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	13\21 to 5\8 (742.9¢ to 750.0¢)
Dark	3\8 to 8\21 (450.0¢ to 457.1¢)
TAMNAMS information
Descends from	5L 3s (oneirotonic)
Ancestor's step ratio range	1:1 to 3:2 (soft)
Related MOS scales
Parent	8L 5s
Sister	13L 8s
Daughters	21L 8s, 8L 21s
Neutralized	16L 5s
2-Flought	29L 13s, 8L 34s
Equal tunings
Equalized (L:s = 1:1)	13\21 (742.9¢)
Supersoft (L:s = 4:3)	44\71 (743.7¢)
Soft (L:s = 3:2)	31\50 (744.0¢)
Semisoft (L:s = 5:3)	49\79 (744.3¢)
Basic (L:s = 2:1)	18\29 (744.8¢)
Semihard (L:s = 5:2)	41\66 (745.5¢)
Hard (L:s = 3:1)	23\37 (745.9¢)
Superhard (L:s = 4:1)	28\45 (746.7¢)
Collapsed (L:s = 1:0)	5\8 (750.0¢)

8L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 13 small steps, repeating every octave. 8L 13s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 742.9¢ to 750¢, or from 450¢ to 457.1¢.

Modes

Modes of 8L 13s

UDP	Cyclic order	Step pattern
20|0	1	LsLssLsLssLssLsLssLss
19|1	14	LsLssLssLsLssLsLssLss
18|2	6	LsLssLssLsLssLssLsLss
17|3	19	LssLsLssLsLssLssLsLss
16|4	11	LssLsLssLssLsLssLsLss
15|5	3	LssLsLssLssLsLssLssLs
14|6	16	LssLssLsLssLsLssLssLs
13|7	8	LssLssLsLssLssLsLssLs
12|8	21	sLsLssLsLssLssLsLssLs
11|9	13	sLsLssLssLsLssLsLssLs
10|10	5	sLsLssLssLsLssLssLsLs
9|11	18	sLssLsLssLsLssLssLsLs
8|12	10	sLssLsLssLssLsLssLsLs
7|13	2	sLssLsLssLssLsLssLssL
6|14	15	sLssLssLsLssLsLssLssL
5|15	7	sLssLssLsLssLssLsLssL
4|16	20	ssLsLssLsLssLssLsLssL
3|17	12	ssLsLssLssLsLssLsLssL
2|18	4	ssLsLssLssLsLssLssLsL
1|19	17	ssLssLsLssLsLssLssLsL
0|20	9	ssLssLsLssLssLsLssLsL

Intervals

Intervals of 8L 13s

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 57.1¢
	Major 1-mosstep	M1ms	L	57.1¢ to 150.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 114.3¢
	Major 2-mosstep	M2ms	L + s	114.3¢ to 150.0¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	150.0¢ to 171.4¢
	Major 3-mosstep	M3ms	2L + s	171.4¢ to 300.0¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	150.0¢ to 228.6¢
	Major 4-mosstep	M4ms	2L + 2s	228.6¢ to 300.0¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	150.0¢ to 285.7¢
	Major 5-mosstep	M5ms	2L + 3s	285.7¢ to 300.0¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	300.0¢ to 342.9¢
	Major 6-mosstep	M6ms	3L + 3s	342.9¢ to 450.0¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	300.0¢ to 400.0¢
	Major 7-mosstep	M7ms	3L + 4s	400.0¢ to 450.0¢
8-mosstep	Perfect 8-mosstep	P8ms	3L + 5s	450.0¢ to 457.1¢
	Augmented 8-mosstep	A8ms	4L + 4s	457.1¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	450.0¢ to 514.3¢
	Major 9-mosstep	M9ms	4L + 5s	514.3¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	450.0¢ to 571.4¢
	Major 10-mosstep	M10ms	4L + 6s	571.4¢ to 600.0¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	600.0¢ to 628.6¢
	Major 11-mosstep	M11ms	5L + 6s	628.6¢ to 750.0¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	600.0¢ to 685.7¢
	Major 12-mosstep	M12ms	5L + 7s	685.7¢ to 750.0¢
13-mosstep	Diminished 13-mosstep	d13ms	4L + 9s	600.0¢ to 742.9¢
	Perfect 13-mosstep	P13ms	5L + 8s	742.9¢ to 750.0¢
14-mosstep	Minor 14-mosstep	m14ms	5L + 9s	750.0¢ to 800.0¢
	Major 14-mosstep	M14ms	6L + 8s	800.0¢ to 900.0¢
15-mosstep	Minor 15-mosstep	m15ms	5L + 10s	750.0¢ to 857.1¢
	Major 15-mosstep	M15ms	6L + 9s	857.1¢ to 900.0¢
16-mosstep	Minor 16-mosstep	m16ms	6L + 10s	900.0¢ to 914.3¢
	Major 16-mosstep	M16ms	7L + 9s	914.3¢ to 1050.0¢
17-mosstep	Minor 17-mosstep	m17ms	6L + 11s	900.0¢ to 971.4¢
	Major 17-mosstep	M17ms	7L + 10s	971.4¢ to 1050.0¢
18-mosstep	Minor 18-mosstep	m18ms	6L + 12s	900.0¢ to 1028.6¢
	Major 18-mosstep	M18ms	7L + 11s	1028.6¢ to 1050.0¢
19-mosstep	Minor 19-mosstep	m19ms	7L + 12s	1050.0¢ to 1085.7¢
	Major 19-mosstep	M19ms	8L + 11s	1085.7¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	7L + 13s	1050.0¢ to 1142.9¢
	Major 20-mosstep	M20ms	8L + 12s	1142.9¢ to 1200.0¢
21-mosstep	Perfect 21-mosstep	P21ms	8L + 13s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 8L 13s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\21						742.857	457.143	1:1	1.000	Equalized 8L 13s
					70\113	743.363	456.637	6:5	1.200
				57\92		743.478	456.522	5:4	1.250
					101\163	743.558	456.442	9:7	1.286
			44\71			743.662	456.338	4:3	1.333	Supersoft 8L 13s
					119\192	743.750	456.250	11:8	1.375
				75\121		743.802	456.198	7:5	1.400
					106\171	743.860	456.140	10:7	1.429
		31\50				744.000	456.000	3:2	1.500	Soft 8L 13s
					111\179	744.134	455.866	11:7	1.571
				80\129		744.186	455.814	8:5	1.600
					129\208	744.231	455.769	13:8	1.625
			49\79			744.304	455.696	5:3	1.667	Semisoft 8L 13s
					116\187	744.385	455.615	12:7	1.714
				67\108		744.444	455.556	7:4	1.750
					85\137	744.526	455.474	9:5	1.800
	18\29					744.828	455.172	2:1	2.000	Basic 8L 13s Scales with tunings softer than this are proper
					77\124	745.161	454.839	9:4	2.250
				59\95		745.263	454.737	7:3	2.333
					100\161	745.342	454.658	12:5	2.400
			41\66			745.455	454.545	5:2	2.500	Semihard 8L 13s
					105\169	745.562	454.438	13:5	2.600
				64\103		745.631	454.369	8:3	2.667
					87\140	745.714	454.286	11:4	2.750
		23\37				745.946	454.054	3:1	3.000	Hard 8L 13s
					74\119	746.218	453.782	10:3	3.333
				51\82		746.341	453.659	7:2	3.500
					79\127	746.457	453.543	11:3	3.667
			28\45			746.667	453.333	4:1	4.000	Superhard 8L 13s
					61\98	746.939	453.061	9:2	4.500
				33\53		747.170	452.830	5:1	5.000
					38\61	747.541	452.459	6:1	6.000
5\8						750.000	450.000	1:0	→ ∞	Collapsed 8L 13s

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