6L 1s

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6L 1s
Brightest mode LLLsLLL
Period 2/1
Range for bright generator 1\7 (171.4¢) to 1\6 (200.0¢)
Range for dark generator 5\6 (1,000.0¢) to 6\7 (1,028.6¢)
Parent MOS 1L 5s
Daughter MOSes 7L 6s, 6L 7s
Sister MOS 1L 6s
TAMNAMS name archeotonic
Equal tunings
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¢)

6L 1s is the MOS scale built from a generator between 1\7 (171¢) and 1\6 (200¢). 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

Generator ranges:

  • Chroma-positive generator: [[1]] 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