6L 1s

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← 5L 1s6L 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
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.

Names

The TAMNAMS system uses the name archeotonic.

Notation

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

Modes

MOS modes

Archeotonic.png

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

Scale tree

Scale Tree and Tuning Spectrum of 6L 1s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
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