6L 1s

←5L 1s	6L 1s	7L 1s→
↙5L 2s	↓6L 2s	7L 2s↘

Scale structure
Step pattern	LLLLLLs
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Step size ranges
Large	1\7 to 1\6 (171.4¢ to 200.0¢)
Small	0\6 to 1\7 (0.0¢ to 171.4¢)
Generator ranges
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	arch(a)eotonic
Prefix	arch-
Abbrev.	arch
Related scales
Parent	1L 5s
Sister	1L 6s
Daughters	7L 6s 6L 7s
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 arch(a)eotonic 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

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