6L 6s: Difference between revisions

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{{Infobox MOS}}
{{Infobox MOS}}
This is the bi-equal chromatic scale of [[Hexe]] temperament. It has a generator of up to the familiar semitone of 12edo (100¢) and two closed circles of minor sevenths representing the 2.9 subgroup separated thereby.
{{MOS intro}}
== Modes ==
6L 6s represents the bi-equal chromatic scale of [[Hexe]] temperament.<!-- Text removed for later rewording: "has two closed circles of minor sevenths representing the 2.9 subgroup separated thereby" -->
==Modes ==
{{MOS modes}}
{{MOS modes}}
== Scale tree ==
==Scale tree==
{| class="wikitable center-all"
{{Scale tree|
! colspan="6" rowspan="2" | Generator
Comments=
! colspan="2" | Cents
6/5:  [[Semimist]] ↑;
! rowspan="2" | L
5/4: Optimal [[hexe]];
! rowspan="2" | s
13/8: Unnamed golden tuning;
! rowspan="2" | L/s
13/5: Unnamed golden tuning;
! rowspan="2" | Comments
|-
! Chroma-positive
! Chroma-negative
|-
| 1\12 || || || || || || 100.000 || 100.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 6\66 || 109.091 || 90.909 || 6 || 5 || 1.200 || Semimist↑
|-
| || || || || 5\54 || || 111.111 || 88.889 || 5 || 4 || 1.250 || Hexe is optimal around here
|-
| || || || || || 9\96 || 112.500 || 87.500 || 9 || 7 || 1.286 ||
|-
| || || || 4\42 || || || 114.286 || 85.714 || 4 || 3 || 1.333 ||
|-
| || || || || || 11\114 || 115.789 || 84.211 || 11 || 8 || 1.375 ||
|-
| || || || || 7\72 || || 116.667 || 83.333 || 7 || 5 || 1.400 ||
|-
| || || || || || 10\102 || 117.647 || 98.824 || 10 || 7 || 1.428 ||
|-
| || || 3\30 || || || || 120.000 || 80.000 || 3 || 2 || 1.500 || L/s = 3/2
|-
| || || || || || 11\108 || 122.222 || 77.778 || 11 || 7 || 1.571 ||
|-
| || || || || 8\78 || || 123.077 || 76.923 || 8 || 5 || 1.600 ||
|-
| || || || || || 13\126 || 123.810 || 76.190 || 13 || 8 || 1.625 || Unnamed golden tuning
|-
| || || || 5\48 || || || 125.000 || 75.000 || 5 || 3 || 1.667 ||
|-
| || || || || || 12\114 || 126.316 || 73.684 || 12 || 7 || 1.714 ||
|-
| || || || || 7\66 || || 127.273 || 72.727 || 7 || 4 || 1.750 ||
|-
| || || || || || 9\84 || 128.571 || 71.429 || 9 || 5 || 1.800 ||
|-
| || 2\18 || || || || || 133.333 || 66.667 || 2 || 1 || 2.000 || Basic 6L 6s
|-
| || || || || || 9\78 || 138.462 || 61.538 || 9 || 4 || 2.250 ||
|-
| || || || || 7\60 || || 140.000 || 60.000 || 7 || 3 || 2.333 ||
|-
| || || || || || 12\102 || 141.176 || 58.824 || 12 || 5 || 2.400 ||
|-
| || || || 5\42 || || || 142.857 || 57.143 || 5 || 2 || 2.500 ||
|-
| || || || || || 13\108 || 144.444 || 55.556 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
| || || || || 8\66 || || 145.455 || 54.545 || 8 || 3 || 2.667 ||
|-
| || || || || || 11\90 || 146.667 || 53.333 || 11 || 4 || 2.750 ||
|-
| || || 3\24 || || || || 150.000 || 50.000 || 3 || 1 || 3.000 || L/s = 3/1
|-
| || || || || || 10\78 || 153.846 || 46.154 || 10 || 3 || 3.333 ||
|-
| || || || || 7\54 || || 155.556 || 44.444 || 7 || 2 || 3.500 ||
|-
| || || || || || 11\84 || 157.143 || 42.857 || 11 || 3 || 3.667 ||
|-
| || || || 4\30 || || || 160.000 || 40.000 || 4 || 1 || 4.000 ||
|-
| || || || || || 9\66 || 163.636 || 36.364 || 9 || 2 || 4.500 ||
|-
| || || || || 5\36 || || 166.667 || 33.333 || 5 || 1 || 5.000 ||
|-
| || || || || || 6\42 || 171.429 || 28.571 || 6 || 1 || 6.000 ||
|-
| 1\6 || || || || || || 200.000 || 0.000 || 1 || 0 || → inf ||
|}


}}
[[Category:12-tone scales]]
[[Category:12-tone scales]]

Revision as of 23:39, 18 February 2024

↖ 5L 5s ↑ 6L 5s 7L 5s ↗
← 5L 6s 6L 6s 7L 6s →
↙ 5L 7s ↓ 6L 7s 7L 7s ↘
Scale structure
Step pattern LsLsLsLsLsLs
sLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 1\6 (200.0 ¢)
Generator size
Bright 1\12 to 1\6 (100.0 ¢ to 200.0 ¢)
Dark 0\6 to 1\12 (0.0 ¢ to 100.0 ¢)
Related MOS scales
Parent none
Sister 6L 6s (self)
Daughters 12L 6s, 6L 12s
Neutralized 12edo
2-Flought 18L 6s, 6L 18s
Equal tunings
Equalized (L:s = 1:1) 1\12 (100.0 ¢)
Supersoft (L:s = 4:3) 4\42 (114.3 ¢)
Soft (L:s = 3:2) 3\30 (120.0 ¢)
Semisoft (L:s = 5:3) 5\48 (125.0 ¢)
Basic (L:s = 2:1) 2\18 (133.3 ¢)
Semihard (L:s = 5:2) 5\42 (142.9 ¢)
Hard (L:s = 3:1) 3\24 (150.0 ¢)
Superhard (L:s = 4:1) 4\30 (160.0 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
View • Talk • Edit

6L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 6 small steps, with a period of 1 large step and 1 small step that repeats every 200.0 ¢, or 6 times every octave. Generators that produce this scale range from 100 ¢ to 200 ¢, or from 0 ¢ to 100 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. 6L 6s represents the bi-equal chromatic scale of Hexe temperament.

Modes

Modes of 6L 6s
UDP Cyclic
order		 Step
pattern
6|0(6) 1 LsLsLsLsLsLs
0|6(6) 2 sLsLsLsLsLsL

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 6L 6s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\12 100.000 100.000 1:1 1.000 Equalized 6L 6s
6\66 109.091 90.909 6:5 1.200
5\54 111.111 88.889 5:4 1.250
9\96 112.500 87.500 9:7 1.286
4\42 114.286 85.714 4:3 1.333 Supersoft 6L 6s
11\114 115.789 84.211 11:8 1.375
7\72 116.667 83.333 7:5 1.400
10\102 117.647 82.353 10:7 1.429
3\30 120.000 80.000 3:2 1.500 Soft 6L 6s
11\108 122.222 77.778 11:7 1.571
8\78 123.077 76.923 8:5 1.600
13\126 123.810 76.190 13:8 1.625
5\48 125.000 75.000 5:3 1.667 Semisoft 6L 6s
12\114 126.316 73.684 12:7 1.714
7\66 127.273 72.727 7:4 1.750
9\84 128.571 71.429 9:5 1.800
2\18 133.333 66.667 2:1 2.000 Basic 6L 6s
9\78 138.462 61.538 9:4 2.250
7\60 140.000 60.000 7:3 2.333
12\102 141.176 58.824 12:5 2.400
5\42 142.857 57.143 5:2 2.500 Semihard 6L 6s
13\108 144.444 55.556 13:5 2.600
8\66 145.455 54.545 8:3 2.667
11\90 146.667 53.333 11:4 2.750
3\24 150.000 50.000 3:1 3.000 Hard 6L 6s
10\78 153.846 46.154 10:3 3.333
7\54 155.556 44.444 7:2 3.500
11\84 157.143 42.857 11:3 3.667
4\30 160.000 40.000 4:1 4.000 Superhard 6L 6s
9\66 163.636 36.364 9:2 4.500
5\36 166.667 33.333 5:1 5.000
6\42 171.429 28.571 6:1 6.000
1\6 200.000 0.000 1:0 → ∞ Collapsed 6L 6s
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