6L 1s

← 5L 1s 6L 1s 7L 1s →

↙ 5L 2s ↓ 6L 2s 7L 2s ↘
	Scale structure
Step pattern	LLLLLLs; sLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
	Generator size
Bright	1\7 to 1\6 (171.4 ¢ to 200.0 ¢)
Dark	5\6 to 6\7 (1000.0 ¢ to 1028.6 ¢)
	TAMNAMS information
Name	archaeotonic
Prefix	arch-
Abbrev.	arc
	Related MOS scales
Parent	1L 5s
Sister	1L 6s
Daughters	7L 6s, 6L 7s
Neutralized	5L 2s
2-Flought	13L 1s, 6L 8s
	Equal tunings
Equalized (L:s = 1:1)	1\7 (171.4 ¢)
Supersoft (L:s = 4:3)	4\27 (177.8 ¢)
Soft (L:s = 3:2)	3\20 (180.0 ¢)
Semisoft (L:s = 5:3)	5\33 (181.8 ¢)
Basic (L:s = 2:1)	2\13 (184.6 ¢)
Semihard (L:s = 5:2)	5\32 (187.5 ¢)
Hard (L:s = 3:1)	3\19 (189.5 ¢)
Superhard (L:s = 4:1)	4\25 (192.0 ¢)
Collapsed (L:s = 1:0)	1\6 (200.0 ¢)
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6L 1s, named archaeotonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 171.4 ¢ to 200 ¢, or from 1000 ¢ to 1028.6 ¢. Scales of this form are always proper because there is only one small step.

Names

The TAMNAMS system uses the name archeotonic.

Notation

JKLMNOPJ = LLLsLLL (Horthathian mode), &/@ = chroma up/down

Modes

Scale degrees of the modes of 6L 1s
UDP	Cyclic order	Step pattern	Scale degree (archdegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7
6\|0	1	LLLLLLs	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.
5\|1	2	LLLLLsL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
4\|2	3	LLLLsLL	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.
3\|3	4	LLLsLLL	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Perf.
2\|4	5	LLsLLLL	Perf.	Perf.	Maj.	Min.	Min.	Min.	Perf.	Perf.
1\|5	6	LsLLLLL	Perf.	Perf.	Min.	Min.	Min.	Min.	Perf.	Perf.
0\|6	7	sLLLLLL	Perf.	Dim.	Min.	Min.	Min.	Min.	Perf.	Perf.

Proposed Names

Temperaments

There are two notable harmonic entropy minima with this MOS pattern. The first is tetracot, in which four generators make a 3/2, and the second is known as roulette7, the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament roulette. (Other temperaments like didacus, luna, hemithirds, and hemiwürschmidt have very similar 7-note MOSes.)

The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.

Scales

Tetracot7 – 34edo, 41edo, and POTE tuning
Bluebirds7 – 329edo tuning
Glacial7 – 84edo tuning
Deutone7 – 44edo tuning
Leantone7 – 81edo tuning
Roulette7 – 37edo tuning

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 6L 1s
Generator^(edo)						Cents		Step ratio		Comments^{(always proper)}
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments^{(always proper)}
1\7						171.429	1028.571	1:1	1.000	Equalized 6L 1s
					6\41	175.610	1024.390	6:5	1.200
				5\34		176.471	1023.529	5:4	1.250
					9\61	177.049	1022.951	9:7	1.286
			4\27			177.778	1022.222	4:3	1.333	Supersoft 6L 1s
					11\74	178.378	1021.622	11:8	1.375
				7\47		178.723	1021.277	7:5	1.400
					10\67	179.104	1020.896	10:7	1.429
		3\20				180.000	1020.000	3:2	1.500	Soft 6L 1s
					11\73	180.822	1019.178	11:7	1.571
				8\53		181.132	1018.868	8:5	1.600
					13\86	181.395	1018.605	13:8	1.625
			5\33			181.818	1018.182	5:3	1.667	Semisoft 6L 1s
					12\79	182.278	1017.722	12:7	1.714
				7\46		182.609	1017.391	7:4	1.750
					9\59	183.051	1016.949	9:5	1.800
	2\13					184.615	1015.385	2:1	2.000	Basic 6L 1s
					9\58	186.207	1013.793	9:4	2.250
				7\45		186.667	1013.333	7:3	2.333
					12\77	187.013	1012.987	12:5	2.400
			5\32			187.500	1012.500	5:2	2.500	Semihard 6L 1s
					13\83	187.952	1012.048	13:5	2.600
				8\51		188.235	1011.765	8:3	2.667
					11\70	188.571	1011.429	11:4	2.750
		3\19				189.474	1010.526	3:1	3.000	Hard 6L 1s
					10\63	190.476	1009.524	10:3	3.333
				7\44		190.909	1009.091	7:2	3.500
					11\69	191.304	1008.696	11:3	3.667
			4\25			192.000	1008.000	4:1	4.000	Superhard 6L 1s
					9\56	192.857	1007.143	9:2	4.500
				5\31		193.548	1006.452	5:1	5.000
					6\37	194.595	1005.405	6:1	6.000
1\6						200.000	1000.000	1:0	→ ∞	Collapsed 6L 1s