6L 6s: Difference between revisions

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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.
{{Infobox MOS}}
{{MOS intro}}


{| class="wikitable"
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" -->
|-
 
| | 0/6
== Scale properties ==
| |
{{TAMNAMS use}}
| |
 
| |
=== Intervals ===
| | <span style="font-size: 12.8000001907349px;">0</span>
{{MOS intervals}}
|-
 
| | 1/36
=== Generator chain ===
| |
{{MOS genchain}}
| |
 
| |
=== Modes ===
| | <span style="font-size: 12.8000001907349px;">33.333</span>
{{MOS mode degrees}}
|-
 
| |
== Scale tree ==
| | <span style="font-size: 12.8000001907349px;">4/138</span>
{{MOS tuning spectrum
| |
| 6/5 = ↑&nbsp;[[Semimist]]
| |
| 5/4 = Optimal [[hexe]]
| | 34.783
| 13/8 = Unnamed golden tuning
|-
| 13/5 = Unnamed golden tuning
| |
}}
| | <span style="font-size: 12.8000001907349px;">3/102</span>
 
| |
{{todo|expand}}
| |
[[Category:12-tone scales]]
| | 35.294
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">5/168</span>
| |
| | 35.714
|-
| |
| | 2/66
| |
| |
| | <span style="font-size: 12.8000001907349px;">36.364</span>
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">5/162</span>
| |
| | 37.037
|-
| |
| | <span style="font-size: 12.8000001907349px;">3/96</span>
| |
| |
| | 37.5
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/126</span>
| |
| |
| | 38.095
|-
| |
| | 5/156
| |
| |
| | 38.4615
|-
| |
| | 6/186
| |
| |
| | 38.71
|-
| | 1/30
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">40</span>
|-
| |
| | 5/144
| |
| |
| | 41.667
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/114</span>
| |
| |
| | 42.105
|-
| |
| |
| | 7/198
| |
| | 42.424
|-
| |
| | <span style="font-size: 12.8000001907349px;">3/84</span>
| |
| |
| | 42.857
|-
| |
| |
| |
| | 8/222
| | 43.243
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">5/138</span>
| |
| | 43.478
|-
| |
| |
| |
| | 7/192
| | 43.75
|-
| |
| | 2/54
| |
| |
| | <span style="font-size: 12.8000001907349px;">44.444</span>
|-
| |
| |
| |
| | 7/186
| | 45.384
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">5/132</span>
| |
| | 45.4545
|-
| |
| |
| |
| | 8/210
| | 45.714
|-
| |
| | <span style="font-size: 12.8000001907349px;">3/78</span>
| |
| |
| | 46.154
|-
| |
| |
| | 7/180
| |
| | 46.333
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/102</span>
| |
| |
| | 47.118
|-
| |
| | <span style="font-size: 12.8000001907349px;">5/126</span>
| |
| |
| | 47.619
|-
| |
| | 6/150
| |
| |
| | 48
|-
| |
| | 7/174
| |
| |
| | 48.276
|-
| |
| | 8/198
| |
| |
| | 48.485
|-
| |
| | 9/222
| |
| |
| | 48.649
|-
| |
| | 10/246
| |
| |
| | 48.7805
|-
| |
| | 11/270
| |
| |
| | 48.889
|-
| |
| | 12/294
| |
| |
| | 49.082
|-
| |
| |
| |
| |
| | 200/(1+pi)
|-
| | 1/24
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">50</span>
|-
| |
| |
| |
| |
| | 200/(1+e)
|-
| |
| | 7/162
| |
| |
| | 51.852
|-
| |
| | 6/138
| |
| |
| | 52.174
|-
| |
| | 5/114
| |
| |
| | 52.632
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/90</span>
| |
| |
| | 53.333
|-
| |
| |
| | 7/156
| |
| | 53.846
|-
| |
| | <span style="font-size: 12.8000001907349px;">3/66</span>
| |
| |
| | 54.5455
|-
| |
| |
| |
| | 8/174
| | 55.1724
|-
| |
| |
| |
| |
| | 200/(2+phi)
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">5/108</span>
| |
| | 55.556
|-
| |
| |
| |
| | 7/150
| | 56
|-
| |
| | 2/42
| |
| |
| | <span style="font-size: 12.8000001907349px;">57.143</span>
|-
| |
| |
| |
| | 7/144
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">58.333</span>
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">5/102</span>
| |
| | 58.225
|-
| |
| |
| |
| | 8/162
| | 59.189
|-
| |
| | <span style="font-size: 12.8000001907349px;">3/60</span>
| |
| |
| | 60
|-
| |
| |
| | 7/138
| |
| | 60.87
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/78</span>
| |
| |
| | 61.5385
|-
| |
| | 5/96
| |
| |
| | 62.5
|-
| |
| | 6/114
| |
| |
| | 63,158
|-
| |
| | 7/132
| |
| |
| | 63.727
|-
| |
| | 8/150
| |
| |
| | 64
|-
| |
| | 9/168
| |
| |
| | 64.286
|-
| |
| | 10/186
| |
| |
| | 64,516
|-
| |
| | 11/204
| |
| |
| | 64.706
|-
| |
| | 12/222
| |
| |
| | 64.865
|-
| |
| | 13/240
| |
| |
| | 65
|-
| | 1/18
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">66,667</span>
|-
| |
| | 18/318
| |
| |
| | 67.9245
|-
| |
| | 17/300
| |
| |
| | 68
|-
| |
| | 16/282
| |
| |
| | 68.085
|-
| |
| | 15/264
| |
| |
| | 68.182
|-
| |
| | 14/246
| |
| |
| | 68.293
|-
| |
| | 13/228
| |
| |
| | 68.421
|-
| |
| | 12/210
| |
| |
| | 68.571
|-
| |
| | 11/192
| |
| |
| | 68.75
|-
| |
| | 10/174
| |
| |
| | 68.9655
|-
| |
| | 9/156
| |
| |
| | 69.231
|-
| |
| | 8/138
| |
| |
| | 69.565
|-
| |
| | 7/120
| |
| |
| | 70
|-
| |
| | 6/102
| |
| |
| | 70.588
|-
| |
| | <span style="font-size: 12.8000001907349px;">5/84</span>
| |
| |
| | 71.286
|-
| |
| |
| | 9/150
| |
| | 72
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/66</span>
| |
| |
| | 72.364
|-
| |
| |
| |
| |
| | 200/(1+sqrt(3))
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">7/114</span>
| |
| | 73.368
|-
| |
| | 3/48
| |
| |
| | <span style="font-size: 12.8000001907349px;">75</span>
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">8/126</span>
| |
| | 76.1905
|-
| |
| |
| |
| |
| | 200/(1+phi)
|-
| |
| | <span style="font-size: 12.8000001907349px;">5/78</span>
| |
| |
| | 76.923
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">12/186</span>
| |
| | 77.419
|-
| |
| | <span style="font-size: 12.8000001907349px;">7/108</span>
| |
| |
| | 77.778
|-
| |
| |
| |
| |
| | 200/(1+pi/2)
|-
| |
| | <span style="font-size: 12.8000001907349px;">9/138</span>
| |
| |
| | 78.261
|-
| |
| | 11/168
| |
| |
| | 78.571
|-
| |
| | 13/198
| |
| |
| | 78.788
|-
| | 2/30
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">80</span>
|-
| |
| | <span style="font-size: 12.8000001907349px;">9/132</span>
| |
| |
| | 81.818
|-
| |
| | <span style="font-size: 12.8000001907349px;">7/102</span>
| |
| |
| | 81.765
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">12/174</span>
| |
| | 82.759
|-
| |
| | 5/72
| |
| |
| | <span style="font-size: 12.8000001907349px;">83.333</span>
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">13/186</span>
| |
| | 83.871
|-
| |
| | <span style="font-size: 12.8000001907349px;">8/114</span>
| |
| |
| | 84.2105
|-
| |
| | <span style="font-size: 12.8000001907349px;">11/156</span>
| |
| |
| | 84.5385
|-
| | 3/42
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">85.714</span>
|-
| | 1/12
| |
| |
| |
| | 100
|}

Latest revision as of 14:01, 5 May 2025

↖ 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.

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 interval regions.

Intervals

Intervals of 6L 6s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 100.0 ¢
Major 1-mosstep M1ms L 100.0 ¢ to 200.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 200.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 200.0 ¢ to 300.0 ¢
Major 3-mosstep M3ms 2L + s 300.0 ¢ to 400.0 ¢
4-mosstep Perfect 4-mosstep P4ms 2L + 2s 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 400.0 ¢ to 500.0 ¢
Major 5-mosstep M5ms 3L + 2s 500.0 ¢ to 600.0 ¢
6-mosstep Perfect 6-mosstep P6ms 3L + 3s 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 600.0 ¢ to 700.0 ¢
Major 7-mosstep M7ms 4L + 3s 700.0 ¢ to 800.0 ¢
8-mosstep Perfect 8-mosstep P8ms 4L + 4s 800.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 800.0 ¢ to 900.0 ¢
Major 9-mosstep M9ms 5L + 4s 900.0 ¢ to 1000.0 ¢
10-mosstep Perfect 10-mosstep P10ms 5L + 5s 1000.0 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 1000.0 ¢ to 1100.0 ¢
Major 11-mosstep M11ms 6L + 5s 1100.0 ¢ to 1200.0 ¢
12-mosstep Perfect 12-mosstep P12ms 6L + 6s 1200.0 ¢

Generator chain

Generator chain of 6L 6s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
2 Augmented 0-mosdegree A0md Augmented 2-mosdegree A2md Augmented 4-mosdegree A4md Augmented 6-mosdegree A6md Augmented 8-mosdegree A8md Augmented 10-mosdegree A10md
1 Major 1-mosdegree M1md Major 3-mosdegree M3md Major 5-mosdegree M5md Major 7-mosdegree M7md Major 9-mosdegree M9md Major 11-mosdegree M11md
0 Perfect 0-mosdegree
Perfect 2-mosdegree		 P0md
P2md		 Perfect 2-mosdegree
Perfect 4-mosdegree		 P2md
P4md		 Perfect 4-mosdegree
Perfect 6-mosdegree		 P4md
P6md		 Perfect 6-mosdegree
Perfect 8-mosdegree		 P6md
P8md		 Perfect 8-mosdegree
Perfect 10-mosdegree		 P8md
P10md		 Perfect 10-mosdegree
Perfect 12-mosdegree		 P10md
P12md
−1 Minor 1-mosdegree m1md Minor 3-mosdegree m3md Minor 5-mosdegree m5md Minor 7-mosdegree m7md Minor 9-mosdegree m9md Minor 11-mosdegree m11md
−2 Diminished 2-mosdegree d2md Diminished 4-mosdegree d4md Diminished 6-mosdegree d6md Diminished 8-mosdegree d8md Diminished 10-mosdegree d10md Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 6L 6s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
6|0(6) 1 LsLsLsLsLsLs Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf.
0|6(6) 2 sLsLsLsLsLsL Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf.

Scale tree

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 ↑ Semimist
5\54 111.111 88.889 5:4 1.250 Optimal hexe
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 Unnamed golden tuning
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 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 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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