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 ¢)

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. 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

MOS modes

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

• Roulette7
• Bluebirds7

Scale tree

Generator ranges:

• Chroma-positive generator: 171.4286 cents (1\7) to 200 cents (1\6)
• Chroma-negative generator: 1000 cents (5\6) to 1028.5714 cents (6\7)

Generator						Cents	Remainder	L	s	L/s	Comments
1\7						171.429	171.429	1	1	1.000
					6\41	175.610	146.341	6	5	1.200
				5\34		176.471	141.765	5	4	1.250	Tetracot is in this region
					9\61	177.049	137.704	9	7	1.286	Tetracot/modus/wollemia
			4\27			177.778	133.333	4	3	1.333
					11\74	178.378	129.730	11	8	1.375
				7\47		178.723	127.660	7	5	1.400
					10\67	179.104	125.373	10	7	1.429
		3\20				180.000	120.000	3	2	1.500
					11\73	180.822	115.068	11	7	1.571
				8\53		181.132	113.208	8	5	1.600
					13\86	181.395	111.628	13	8	1.625	Wilson Golden 2 (181.3227¢)
			5\33			181.818	109.091	5	3	1.667
					12\79	182.278	106.329	12	7	1.714	Bluebirds
				7\46		182.609	104.348	7	4	1.750
					9\59	183.051	101.695	9	5	1.800
	2\13					184.615	92.308	2	1	2.000	Basic archeotonic
					9\58	186.207	82.759	9	4	2.250
				7\45		186.667	80.000	7	3	2.333
					12\77	187.013	77.922	12	5	2.400
			5\32			187.500	75.000	5	2	2.500
					13\83	187.952	72.289	13	5	2.600	Golden glacial (188.0298¢)
				8\51		188.235	70.588	8	3	2.667
					11\70	188.571	68.571	11	4	2.750
		3\19				189.474	63.159	3	1	3.000	Spell
					10\63	190.476	57.143	10	3	3.333
				7\44		190.909	54.545	7	2	3.500	Isra/deutone
					11\69	191.304	52.174	11	3	3.667
			4\25			192.000	48.000	4	1	4.000	Isra/leantone
					9\56	192.857	42.857	9	2	4.500
				5\31		193.548	38.709	5	1	5.000	Didacus/hemithirds/hemiwürschmidt
					6\37	194.595	32.432	6	1	6.000	Didacus/roulette
1\6						200.000	0.000	1	0	→ inf