1L 6s
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Scale structure
Step pattern
Lssssss
ssssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
6\7 to 1\1 (1028.6¢ to 1200.0¢)
Dark
0\1 to 1\7 (0.0¢ to 171.4¢)
TAMNAMS information
Name
onyx
Prefix
on-
Abbrev.
on
Related MOS scales
Parent
1L 5s
Sister
6L 1s
Daughters
7L 1s, 1L 7s
Neutralized
2L 5s
2-Flought
8L 6s, 1L 13s
Equal tunings
Equalized (L:s = 1:1)
6\7 (1028.6¢)
Supersoft (L:s = 4:3)
19\22 (1036.4¢)
Soft (L:s = 3:2)
13\15 (1040.0¢)
Semisoft (L:s = 5:3)
20\23 (1043.5¢)
Basic (L:s = 2:1)
7\8 (1050.0¢)
Semihard (L:s = 5:2)
15\17 (1058.8¢)
Hard (L:s = 3:1)
8\9 (1066.7¢)
Superhard (L:s = 4:1)
9\10 (1080.0¢)
Collapsed (L:s = 1:0)
1\1 (1200.0¢)
| ↑ 1L 5s | 2L 5s ↗ | |
| 1L 6s | 2L 6s → | |
| ↓ 1L 7s | 2L 7s ↘ |
┌╥┬┬┬┬┬┬┐ │║│││││││ │││││││││ └┴┴┴┴┴┴┴┘
ssssssL
1L 6s, named onyx in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 6 small steps, repeating every octave. Generators that produce this scale range from 1028.6¢ to 1200¢, or from 0¢ to 171.4¢.
Name
TAMNAMS suggests the temperament-agnostic name onyx as the name of 1L 6s. The name derives from several naming puns/reasonings:
- The name sounds like its step counts of one large step and six small steps.
- Onyxes come in different colors and types, which is a metaphor for this scale's generator range being quite large and containing the generator ranges of other MOS scales, such as 7L 1s, 8L 1s, and 9L 1s.
- Building on the observation that it is the 7-note (heptatonic) MOS that is the ancestor of all xL 1s scales with x>6, the name "onyx" also sounds similar to "one x", as in 1 large step and x small steps.
- The name "onyx" is also supposed to be vaguely reminiscent of "anti-archaeotonic" as "chi" (the greek letter) is written like an "x" (this is related to why "christmas" is abbreviated sometimes as "X-mas") and the letters "o" and "n" and their sounds are also present in "archaeotonic", and "x" is vaguely reminiscent of negation and multiplication. There is also something like a "y" sound in "archaeotonic" in the "aeo" part.
Scale properties
Intervals
The intervals of 1L 6s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-onstep and perfect 7-onstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-onstep | Perfect 0-onstep | P0ons | 0 | 0.0¢ |
| 1-onstep | Perfect 1-onstep | P1ons | s | 0.0¢ to 171.4¢ |
| Augmented 1-onstep | A1ons | L | 171.4¢ to 1200.0¢ | |
| 2-onstep | Minor 2-onstep | m2ons | 2s | 0.0¢ to 342.9¢ |
| Major 2-onstep | M2ons | L + s | 342.9¢ to 1200.0¢ | |
| 3-onstep | Minor 3-onstep | m3ons | 3s | 0.0¢ to 514.3¢ |
| Major 3-onstep | M3ons | L + 2s | 514.3¢ to 1200.0¢ | |
| 4-onstep | Minor 4-onstep | m4ons | 4s | 0.0¢ to 685.7¢ |
| Major 4-onstep | M4ons | L + 3s | 685.7¢ to 1200.0¢ | |
| 5-onstep | Minor 5-onstep | m5ons | 5s | 0.0¢ to 857.1¢ |
| Major 5-onstep | M5ons | L + 4s | 857.1¢ to 1200.0¢ | |
| 6-onstep | Diminished 6-onstep | d6ons | 6s | 0.0¢ to 1028.6¢ |
| Perfect 6-onstep | P6ons | L + 5s | 1028.6¢ to 1200.0¢ | |
| 7-onstep | Perfect 7-onstep | P7ons | L + 6s | 1200.0¢ |
Generator chain
A chain of bright generators, each a perfect 6-onstep, produces the following scale degrees. A chain of 7 bright generators contains the scale degrees of one of the modes of 1L 6s. Expanding the chain to 8 scale degrees produces the modes of either 7L 1s (for soft-of-basic tunings) or 1L 7s (for hard-of-basic tunings).
| Bright gens | Scale Degree | Abbrev. |
|---|---|---|
| 7 | Augmented 0-ondegree | A0ond |
| 6 | Augmented 1-ondegree | A1ond |
| 5 | Major 2-ondegree | M2ond |
| 4 | Major 3-ondegree | M3ond |
| 3 | Major 4-ondegree | M4ond |
| 2 | Major 5-ondegree | M5ond |
| 1 | Perfect 6-ondegree | P6ond |
| 0 | Perfect 0-ondegree Perfect 7-ondegree |
P0ond P7ond |
| -1 | Perfect 1-ondegree | P1ond |
| -2 | Minor 2-ondegree | m2ond |
| -3 | Minor 3-ondegree | m3ond |
| -4 | Minor 4-ondegree | m4ond |
| -5 | Minor 5-ondegree | m5ond |
| -6 | Diminished 6-ondegree | d6ond |
| -7 | Diminished 7-ondegree | d7ond |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (ondegree) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||
| 6|0 | 1 | Lssssss | Perf. | Aug. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 5|1 | 7 | sLsssss | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 4|2 | 6 | ssLssss | Perf. | Perf. | Min. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 3|3 | 5 | sssLsss | Perf. | Perf. | Min. | Min. | Maj. | Maj. | Perf. | Perf. |
| 2|4 | 4 | ssssLss | Perf. | Perf. | Min. | Min. | Min. | Maj. | Perf. | Perf. |
| 1|5 | 3 | sssssLs | Perf. | Perf. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 0|6 | 2 | ssssssL | Perf. | Perf. | Min. | Min. | Min. | Min. | Dim. | Perf. |
Theory
Low harmonic entropy scales
There is one notable harmonic entropy minimum: porcupine, in which the generator is around 150¢ to 170¢, two generators make a 6/5 (315.6¢), and three make a 4/3 (498¢).
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 6\7 | 1028.571 | 171.429 | 1:1 | 1.000 | Equalized 1L 6s | |||||
| 31\36 | 1033.333 | 166.667 | 6:5 | 1.200 | ||||||
| 25\29 | 1034.483 | 165.517 | 5:4 | 1.250 | ||||||
| 44\51 | 1035.294 | 164.706 | 9:7 | 1.286 | ||||||
| 19\22 | 1036.364 | 163.636 | 4:3 | 1.333 | Supersoft 1L 6s | |||||
| 51\59 | 1037.288 | 162.712 | 11:8 | 1.375 | Porcupine/Porcupinefish | |||||
| 32\37 | 1037.838 | 162.162 | 7:5 | 1.400 | ||||||
| 45\52 | 1038.462 | 161.538 | 10:7 | 1.429 | ||||||
| 13\15 | 1040.000 | 160.000 | 3:2 | 1.500 | Soft 1L 6s | |||||
| 46\53 | 1041.509 | 158.491 | 11:7 | 1.571 | Hemikleismic | |||||
| 33\38 | 1042.105 | 157.895 | 8:5 | 1.600 | ||||||
| 53\61 | 1042.623 | 157.377 | 13:8 | 1.625 | Wilson Golden 1 (1042.4790¢) | |||||
| 20\23 | 1043.478 | 156.522 | 5:3 | 1.667 | Semisoft 1L 6s | |||||
| 47\54 | 1044.444 | 155.556 | 12:7 | 1.714 | ||||||
| 27\31 | 1045.161 | 154.839 | 7:4 | 1.750 | Nusecond | |||||
| 34\39 | 1046.154 | 153.846 | 9:5 | 1.800 | ||||||
| 7\8 | 1050.000 | 150.000 | 2:1 | 2.000 | Basic 1L 6s Scales with tunings softer than this are proper | |||||
| 29\33 | 1054.545 | 145.455 | 9:4 | 2.250 | ||||||
| 22\25 | 1056.000 | 144.000 | 7:3 | 2.333 | ||||||
| 37\42 | 1057.143 | 142.857 | 12:5 | 2.400 | ||||||
| 15\17 | 1058.824 | 141.176 | 5:2 | 2.500 | Semihard 1L 6s Progression (incomplete) | |||||
| 38\43 | 1060.465 | 139.535 | 13:5 | 2.600 | Golden jerome (1060.7571¢) | |||||
| 23\26 | 1061.538 | 138.462 | 8:3 | 2.667 | ||||||
| 31\35 | 1062.857 | 137.143 | 11:4 | 2.750 | ||||||
| 8\9 | 1066.667 | 133.333 | 3:1 | 3.000 | Hard 1L 6s | |||||
| 25\28 | 1071.429 | 128.571 | 10:3 | 3.333 | ||||||
| 17\19 | 1073.684 | 126.316 | 7:2 | 3.500 | Negri (incomplete) | |||||
| 26\29 | 1075.862 | 124.138 | 11:3 | 3.667 | ||||||
| 9\10 | 1080.000 | 120.000 | 4:1 | 4.000 | Superhard 1L 6s | |||||
| 19\21 | 1085.714 | 114.286 | 9:2 | 4.500 | Miracle (incomplete) | |||||
| 10\11 | 1090.909 | 109.091 | 5:1 | 5.000 | ||||||
| 11\12 | 1100.000 | 100.000 | 6:1 | 6.000 | Passion, ripple (incomplete) | |||||
| 1\1 | 1200.000 | 0.000 | 1:0 | → ∞ | Collapsed 1L 6s | |||||