8L 5s

8L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 5 small steps, repeating every octave. 8L 5s is a child scale of 5L 3s, expanding it by 5 tones. Generators that produce this scale range from 738.5 ¢ to 750 ¢, or from 450 ¢ to 461.5 ¢.

↖ 7L 4s	↑ 8L 4s	9L 4s ↗
← 7L 5s	8L 5s	9L 5s →
↙ 7L 6s	↓ 8L 6s	9L 6s ↘

Scale structure
Step pattern	LLsLLsLsLLsLs sLsLLsLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	8\13 to 5\8 (738.5 ¢ to 750.0 ¢)
Dark	3\8 to 5\13 (450.0 ¢ to 461.5 ¢)
TAMNAMS information
Related to	5L 3s (oneirotonic)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	5L 3s
Sister	5L 8s
Daughters	13L 8s, 8L 13s
Neutralized	3L 10s
2-Flought	21L 5s, 8L 18s
Equal tunings
Equalized (L:s = 1:1)	8\13 (738.5 ¢)
Supersoft (L:s = 4:3)	29\47 (740.4 ¢)
Soft (L:s = 3:2)	21\34 (741.2 ¢)
Semisoft (L:s = 5:3)	34\55 (741.8 ¢)
Basic (L:s = 2:1)	13\21 (742.9 ¢)
Semihard (L:s = 5:2)	31\50 (744.0 ¢)
Hard (L:s = 3:1)	18\29 (744.8 ¢)
Superhard (L:s = 4:1)	23\37 (745.9 ¢)
Collapsed (L:s = 1:0)	5\8 (750.0 ¢)
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8L 5s represents the chromatic scale of Semidim, Tridec, Ammonite, and Petrtri temperaments. It represents tempered chains of the 13:10 or 17:13 semisixth, thus rendering 10:13:17 as an equidistant triad and tempering out 170:169. Also, the ratio between the generator of this MOS and its inverse is close to logarithmic phi, or even logarithmic phi itself; based on this relation to the golden sequence, Lériendil has proposed the name aureate for this scale.

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 8L 5s

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 92.3 ¢
	Major 1-mosstep	M1ms	L	92.3 ¢ to 150.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	150.0 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	2L	184.6 ¢ to 300.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	150.0 ¢ to 276.9 ¢
	Major 3-mosstep	M3ms	2L + s	276.9 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	300.0 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	3L + s	369.2 ¢ to 450.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	450.0 ¢ to 461.5 ¢
	Augmented 5-mosstep	A5ms	4L + s	461.5 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	450.0 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	4L + 2s	553.8 ¢ to 600.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	600.0 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	5L + 2s	646.2 ¢ to 750.0 ¢
8-mosstep	Diminished 8-mosstep	d8ms	4L + 4s	600.0 ¢ to 738.5 ¢
	Perfect 8-mosstep	P8ms	5L + 3s	738.5 ¢ to 750.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	750.0 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	6L + 3s	830.8 ¢ to 900.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	900.0 ¢ to 923.1 ¢
	Major 10-mosstep	M10ms	7L + 3s	923.1 ¢ to 1050.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	900.0 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	7L + 4s	1015.4 ¢ to 1050.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	1050.0 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	8L + 4s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	8L + 5s	1200.0 ¢

Generator chain

Generator chain of 8L 5s

Bright gens	Scale degree	Abbrev.
20	Augmented 4-mosdegree	A4md
19	Augmented 9-mosdegree	A9md
18	Augmented 1-mosdegree	A1md
17	Augmented 6-mosdegree	A6md
16	Augmented 11-mosdegree	A11md
15	Augmented 3-mosdegree	A3md
14	Augmented 8-mosdegree	A8md
13	Augmented 0-mosdegree	A0md
12	Augmented 5-mosdegree	A5md
11	Major 10-mosdegree	M10md
10	Major 2-mosdegree	M2md
9	Major 7-mosdegree	M7md
8	Major 12-mosdegree	M12md
7	Major 4-mosdegree	M4md
6	Major 9-mosdegree	M9md
5	Major 1-mosdegree	M1md
4	Major 6-mosdegree	M6md
3	Major 11-mosdegree	M11md
2	Major 3-mosdegree	M3md
1	Perfect 8-mosdegree	P8md
0	Perfect 0-mosdegree Perfect 13-mosdegree	P0md P13md
−1	Perfect 5-mosdegree	P5md
−2	Minor 10-mosdegree	m10md
−3	Minor 2-mosdegree	m2md
−4	Minor 7-mosdegree	m7md
−5	Minor 12-mosdegree	m12md
−6	Minor 4-mosdegree	m4md
−7	Minor 9-mosdegree	m9md
−8	Minor 1-mosdegree	m1md
−9	Minor 6-mosdegree	m6md
−10	Minor 11-mosdegree	m11md
−11	Minor 3-mosdegree	m3md
−12	Diminished 8-mosdegree	d8md
−13	Diminished 13-mosdegree	d13md
−14	Diminished 5-mosdegree	d5md
−15	Diminished 10-mosdegree	d10md
−16	Diminished 2-mosdegree	d2md
−17	Diminished 7-mosdegree	d7md
−18	Diminished 12-mosdegree	d12md
−19	Diminished 4-mosdegree	d4md
−20	Diminished 9-mosdegree	d9md

Modes

Scale degrees of the modes of 8L 5s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13
12|0	1	LLsLLsLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
11|1	9	LLsLsLLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
10|2	4	LLsLsLLsLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
9|3	12	LsLLsLLsLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
8|4	7	LsLLsLsLLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
7|5	2	LsLLsLsLLsLsL	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
6|6	10	LsLsLLsLLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
5|7	5	LsLsLLsLsLLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
4|8	13	sLLsLLsLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
3|9	8	sLLsLsLLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
2|10	3	sLLsLsLLsLsLL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
1|11	11	sLsLLsLLsLsLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
0|12	6	sLsLLsLsLLsLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 8L 5s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\13						738.462	461.538	1:1	1.000	Equalized 8L 5s
					45\73	739.726	460.274	6:5	1.200
				37\60		740.000	460.000	5:4	1.250
					66\107	740.187	459.813	9:7	1.286
			29\47			740.426	459.574	4:3	1.333	Supersoft 8L 5s
					79\128	740.625	459.375	11:8	1.375
				50\81		740.741	459.259	7:5	1.400
					71\115	740.870	459.130	10:7	1.429
		21\34				741.176	458.824	3:2	1.500	Soft 8L 5s
					76\123	741.463	458.537	11:7	1.571
				55\89		741.573	458.427	8:5	1.600
					89\144	741.667	458.333	13:8	1.625
			34\55			741.818	458.182	5:3	1.667	Semisoft 8L 5s
					81\131	741.985	458.015	12:7	1.714
				47\76		742.105	457.895	7:4	1.750
					60\97	742.268	457.732	9:5	1.800
	13\21					742.857	457.143	2:1	2.000	Basic 8L 5s Scales with tunings softer than this are proper
					57\92	743.478	456.522	9:4	2.250
				44\71		743.662	456.338	7:3	2.333
					75\121	743.802	456.198	12:5	2.400
			31\50			744.000	456.000	5:2	2.500	Semihard 8L 5s
					80\129	744.186	455.814	13:5	2.600
				49\79		744.304	455.696	8:3	2.667
					67\108	744.444	455.556	11:4	2.750
		18\29				744.828	455.172	3:1	3.000	Hard 8L 5s
					59\95	745.263	454.737	10:3	3.333
				41\66		745.455	454.545	7:2	3.500
					64\103	745.631	454.369	11:3	3.667
			23\37			745.946	454.054	4:1	4.000	Superhard 8L 5s
					51\82	746.341	453.659	9:2	4.500
				28\45		746.667	453.333	5:1	5.000
					33\53	747.170	452.830	6:1	6.000
5\8						750.000	450.000	1:0	→ ∞	Collapsed 8L 5s