5L 10s

↖ 4L 9s	↑ 5L 9s	6L 9s ↗
← 4L 10s	5L 10s	6L 10s →
↙ 4L 11s	↓ 5L 11s	6L 11s ↘

┌╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┐ │║││║││║││║││║│││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLssLssLssLss ssLssLssLssLssL
Equave	2/1 (1200.0¢)
Period	1\5 (240.0¢)
Generator size
Bright	2\15 to 1\5 (160.0¢ to 240.0¢)
Dark	0\5 to 1\15 (0.0¢ to 80.0¢)
TAMNAMS information
Descends from	5L 5s (pentawood)
Ancestor's step ratio range	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	5L 5s
Sister	10L 5s
Daughters	15L 5s, 5L 15s
Neutralized	10L 5s
2-Flought	20L 10s, 5L 25s
Equal tunings
Equalized (L:s = 1:1)	2\15 (160.0¢)
Supersoft (L:s = 4:3)	7\50 (168.0¢)
Soft (L:s = 3:2)	5\35 (171.4¢)
Semisoft (L:s = 5:3)	8\55 (174.5¢)
Basic (L:s = 2:1)	3\20 (180.0¢)
Semihard (L:s = 5:2)	7\45 (186.7¢)
Hard (L:s = 3:1)	4\25 (192.0¢)
Superhard (L:s = 4:1)	5\30 (200.0¢)
Collapsed (L:s = 1:0)	1\5 (240.0¢)

5L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 10 small steps, with a period of 1 large step and 2 small steps that repeats every 240.0¢, or 5 times every octave. 5L 10s is a child scale of 5L 5s, expanding it by 5 tones. Generators that produce this scale range from 160¢ to 240¢, or from 0¢ to 80¢.

Modes

Modes of 5L 10s

UDP	Cyclic order	Step pattern
10|0(5)	1	LssLssLssLssLss
5|5(5)	3	sLssLssLssLssLs
0|10(5)	2	ssLssLssLssLssL

Intervals

Intervals of 5L 10s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0¢ to 80.0¢
	Augmented 1-mosstep	A1ms	L	80.0¢ to 240.0¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0¢ to 160.0¢
	Perfect 2-mosstep	P2ms	L + s	160.0¢ to 240.0¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	240.0¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	240.0¢ to 320.0¢
	Augmented 4-mosstep	A4ms	2L + 2s	320.0¢ to 480.0¢
5-mosstep	Diminished 5-mosstep	d5ms	L + 4s	240.0¢ to 400.0¢
	Perfect 5-mosstep	P5ms	2L + 3s	400.0¢ to 480.0¢
6-mosstep	Perfect 6-mosstep	P6ms	2L + 4s	480.0¢
7-mosstep	Perfect 7-mosstep	P7ms	2L + 5s	480.0¢ to 560.0¢
	Augmented 7-mosstep	A7ms	3L + 4s	560.0¢ to 720.0¢
8-mosstep	Diminished 8-mosstep	d8ms	2L + 6s	480.0¢ to 640.0¢
	Perfect 8-mosstep	P8ms	3L + 5s	640.0¢ to 720.0¢
9-mosstep	Perfect 9-mosstep	P9ms	3L + 6s	720.0¢
10-mosstep	Perfect 10-mosstep	P10ms	3L + 7s	720.0¢ to 800.0¢
	Augmented 10-mosstep	A10ms	4L + 6s	800.0¢ to 960.0¢
11-mosstep	Diminished 11-mosstep	d11ms	3L + 8s	720.0¢ to 880.0¢
	Perfect 11-mosstep	P11ms	4L + 7s	880.0¢ to 960.0¢
12-mosstep	Perfect 12-mosstep	P12ms	4L + 8s	960.0¢
13-mosstep	Perfect 13-mosstep	P13ms	4L + 9s	960.0¢ to 1040.0¢
	Augmented 13-mosstep	A13ms	5L + 8s	1040.0¢ to 1200.0¢
14-mosstep	Diminished 14-mosstep	d14ms	4L + 10s	960.0¢ to 1120.0¢
	Perfect 14-mosstep	P14ms	5L + 9s	1120.0¢ to 1200.0¢
15-mosstep	Perfect 15-mosstep	P15ms	5L + 10s	1200.0¢

Tuning spectrum

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

Blackwood / blacksmith / ferrier range (although these temperaments are better tuned with a generator above 80 cents; see 10L 5s )

Scale Tree and Tuning Spectrum of 5L 10s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\15						160.000	80.000	1:1	1.000	Equalized 5L 10s
					11\80	165.000	75.000	6:5	1.200
				9\65		166.154	73.846	5:4	1.250
					16\115	166.957	73.043	9:7	1.286
			7\50			168.000	72.000	4:3	1.333	Supersoft 5L 10s
					19\135	168.889	71.111	11:8	1.375
				12\85		169.412	70.588	7:5	1.400
					17\120	170.000	70.000	10:7	1.429
		5\35				171.429	68.571	3:2	1.500	Soft 5L 10s
					18\125	172.800	67.200	11:7	1.571
				13\90		173.333	66.667	8:5	1.600
					21\145	173.793	66.207	13:8	1.625
			8\55			174.545	65.455	5:3	1.667	Semisoft 5L 10s
					19\130	175.385	64.615	12:7	1.714
				11\75		176.000	64.000	7:4	1.750
					14\95	176.842	63.158	9:5	1.800
	3\20					180.000	60.000	2:1	2.000	Basic 5L 10s Scales with tunings softer than this are proper
					13\85	183.529	56.471	9:4	2.250
				10\65		184.615	55.385	7:3	2.333
					17\110	185.455	54.545	12:5	2.400
			7\45			186.667	53.333	5:2	2.500	Semihard 5L 10s
					18\115	187.826	52.174	13:5	2.600
				11\70		188.571	51.429	8:3	2.667
					15\95	189.474	50.526	11:4	2.750
		4\25				192.000	48.000	3:1	3.000	Hard 5L 10s
					13\80	195.000	45.000	10:3	3.333
				9\55		196.364	43.636	7:2	3.500
					14\85	197.647	42.353	11:3	3.667
			5\30			200.000	40.000	4:1	4.000	Superhard 5L 10s
					11\65	203.077	36.923	9:2	4.500
				6\35		205.714	34.286	5:1	5.000
					7\40	210.000	30.000	6:1	6.000
1\5						240.000	0.000	1:0	→ ∞	Collapsed 5L 10s

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