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.

arch

Related MOS scales

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.

Names

The TAMNAMS system uses the name archeotonic.

Notation

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

Modes

MOS modes

MODMOSes

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

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	Tetracot is in this region
					9\61	177.049	1022.951	9:7	1.286	Tetracot/modus/wollemia
			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	Wilson Golden 2 (181.3227¢)
			5\33			181.818	1018.182	5:3	1.667	Semisoft 6L 1s
					12\79	182.278	1017.722	12:7	1.714	Bluebirds
				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	Golden glacial (188.0298¢)
				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 Spell
					10\63	190.476	1009.524	10:3	3.333
				7\44		190.909	1009.091	7:2	3.500	Isra/deutone
					11\69	191.304	1008.696	11:3	3.667
			4\25			192.000	1008.000	4:1	4.000	Superhard 6L 1s Isra/leantone
					9\56	192.857	1007.143	9:2	4.500
				5\31		193.548	1006.452	5:1	5.000	Didacus/hemithirds/hemiwürschmidt
					6\37	194.595	1005.405	6:1	6.000	Didacus/roulette
1\6						200.000	1000.000	1:0	→ ∞	Collapsed 6L 1s