6L 1s
| ← 5L 1s | 6L 1s | 7L 1s → |
| ↙ 5L 2s | ↓ 6L 2s | 7L 2s ↘ |
┌╥╥╥╥╥╥┬┐ │║║║║║║││ │││││││││ └┴┴┴┴┴┴┴┘
sLLLLLL
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
TAMNAMS suggests the temperament-agnostic name archaeotonic as the name of 6L 1s. The name was originally used as a name for the 6L 1s scale in 13edo.
Scale properties
{{subst:MOS data temporary}}
Proposed names
Temperaments
There are two notable harmonic entropy minima with this MOS pattern. The first is tetracot, in which the generator is identified with 10/9 and four generators make a 3/2. These produce very soft tunings of archaeotonic, ranging from 4:3 in 27edo to 7:6 in 48edo. The second is known as didacus, which is at a basic level the temperament in the 2.5.7 subgroup defined by 3136/3125, where two generators make 5/4 and five make 7/4, and produces very hard tunings, ranging from 4:1 in 25edo to 7:1 in 43edo; it has various extensions that span portions of this range, including roulette and mediantone to the no-twos 19-limit, and hemithirds (along with its 5-limit microtemperament restriction luna) and hemiwürschmidt to the full 7-limit.
The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, i.e. Bluebirds, where the generator is identified with 143/128; 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
| 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 | |||||