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

1\7 (171.4¢)

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¢)

3\20 (180.0¢)

5\33 (181.8¢)

2\13 (184.6¢)

5\32 (187.5¢)

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

Scale degree qualities of 6L 1s modes
UDP	Rotational Order	Step pattern	Scale degree (archdegree)
UDP	Rotational 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

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