1L 6s

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1L 6s 2L 6s →
↓ 1L 7s 2L 7s ↘ 
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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 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

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

Intervals

Intervals of 1L 6s
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

Generator chain of 1L 6s
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

Scale degrees of the modes of 1L 6s
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 between 150 and 170 ¢, two generators make a 6/5 (315.6 ¢), and three make a 4/3 (498 ¢).

Scale tree

Scale tree and tuning spectrum of 1L 6s
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
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