3L 6s: Difference between revisions

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This MOS has generators which range between 0 and 133.333 cents and three periods per octave and runs Lss Lss Lss.
This MOS has generators which range between 0 and 133.333 cents and three periods per octave and runs Lss Lss Lss.  


{| class="wikitable"
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator
! colspan="2" | Cents
! rowspan="2" | L
! rowspan="2" | s
! rowspan="2" | L/s
! rowspan="2" | Comments
|-
|-
! colspan="5" | Generator
! Chroma-positive
! | Cents
! Chroma-negative
! | Comments
|-
|-
| | 0\3
| 2\9 || || || || || || 266.667 || 133.333 || 1 || 1 || 1.000 ||  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 11\48 || 275.000 || 125.000 || 6 || 5 || 1.200 ||  
| |  
| |  
| |  
| | 1\21
| | 57.143
| |  
|-
|-
| |  
| || || || || 9\39 || || 276.923 || 123.077 || 5 || 4 || 1.250 ||
| |  
| |  
| | 1\18
| |  
| | 66.667
| style="text-align:center;" | L/s=4
|-
|-
| |  
| || || || || || 16\69 || 278.261 || 121.739 || 9 || 7 || 1.286 ||  
| |  
| |  
| |  
| |  
| | 400/(2+pi)
| |  
|-
|-
| |  
| || || || 7\30 || || || 280.000 || 120.000 || 4 || 3 || 1.333 ||
| |  
| | 1\15
| |  
| |  
| | 80
| style="text-align:center;" | L/s=3
|-
|-
| |  
| || || || || || 19\81 || 281.481 || 118.519 || 11 || 8 || 1.375 ||  
| |  
| |  
| |  
| |  
| | 400/(2+e)
| |  
|-
|-
| |  
| || || || || 12\51 || || 282.353 || 117.647 || 7 || 5 || 1.400 ||  
| |  
| |  
| |  
| | 3\42
| | 85.714
| |  
|-
|-
| |  
| || || || || || 17\72 || 283.333 || 116.667 || 10 || 7 || 1.428 ||  
| |  
| |  
| |  
| |  
| | 400/(3+phi)
| |  
|-
|-
| |  
| || || 5\21 || || || || 285.714 || 114.286 || 3 || 2 || 1.500 ||  
| |  
| |  
| | 2\27
| |  
| | 88.889
| style="text-align:center;" | Augene is around here
|-
|-
| |  
| || || || || || 18\75 || 288.000 || 112.000 || 11 || 7 || 1.571 ||
| | 1\12
|-
| |  
| || || || || 13\54 || || 288.889 || 111.111 || 8 || 5 || 1.600 ||
| |  
|-
| |  
| || || || || || 21\87 || 289.655 || 110.345 || 13 || 8 || 1.625 || Unnamed golden tuning
| | 100
|-
| style="text-align:center;" | Boundary of propriety (generators
| || || || 8\33 || || || 290.909 || 109.091 || 5 || 3 || 1.667 ||
 
|-
larger than this are proper)
| || || || || || 19\78 || 292.308 || 107.692 || 12 || 7 || 1.714 ||
|-
| || || || || 11\45 || || 293.333 || 106.667 || 7 || 4 || 1.750 ||
|-
| || || || || || 14\57 || 294.737 || 105.263 || 9 || 5 || 1.800 || August
|-
| || 3\12 || || || || || 300.000 || 100.000 || 2 || 1 || 2.000 || Basic tcherepnin<br>(Generators smaller than this are proper)
|-
| || || || || || 13\51 || 305.882 || 94.118 || 9 || 4 || 2.250 ||
|-
| || || || || 10\39 || || 307.692 || 92.308 || 7 || 3 || 2.333 ||
|-
| || || || || || 17\66 || 309.091 || 90.909 || 12 || 5 || 2.400 || Augene (optimal around here)
|-
| || || || 7\27 || || || 311.111 || 88.889 || 5 || 2 || 2.500 ||
|-
| || || || || || 18\69 || 313.043 || 86.957 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
| || || || || 11\42 || || 314.286 || 85.714 || 8 || 3 || 2.667 ||
|-
| || || || || || 15\57 || 315.789 || 84.211 || 11 || 4 || 2.750 || August
|-
|-
| |  
| || || 4\15 || || || || 320.000 || 80.000 || 3 || 1 || 3.000 ||  
| |  
| |  
| |  
| |  
| | 400/(2+sqrt(3))
| |  
|-
|-
| |  
| || || || || || 13\48 || 325.000 || 75.000 || 10 || 3 || 3.333 || Inflated
| |  
| |  
| | 3\33
| |  
| | 109.091
| style="text-align:center;" | August is around here
|-
|-
| |  
| || || || || 9\33 || || 327.273 || 72.727 || 7 || 2 || 3.500 ||  
| |  
| |  
| |  
| |  
| | 400/(2+phi)
| |  
|-
|-
| |  
| || || || || || 14\51 || 329.412 || 70.588 || 11 || 3 || 3.667 ||  
| |  
| |  
| |  
| | 5\54
| | 111.111
| |  
|-
|-
| |  
| || || || 5\18 || || || 333.333 || 66.667 || 4 || 1 || 4.000 ||  
| |  
| |  
| |  
| |  
| | 400/(2+pi/2)
| |  
|-
|-
| |  
| || || || || || 11\39 || 338.462 || 61.538 || 9 || 2 || 4.500 ||  
| |  
| | 2\21
| |  
| |  
| | 114.286
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 6\21 || || 342.857 || 57.143 || 5 || 1 || 5.000 ||  
| |  
| |  
| | 3\30
| |  
| | 120
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 7\24 || 350.000 || 50.000 || 6 || 1 || 6.000 || Hemiug, hemiaug↓
| |  
| |  
| |  
| | 4\39
| | 123.077
| |  
|-
|-
| | 1\9
| 1\3 || || || || || || 400.000 || 0.000 || 1 || 0 || → inf ||
| |  
| |  
| |  
| |  
| | 133.333
| style="text-align:center;" |  
|}
|}
.


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:Tcherepnin| ]] <!--main article-->

Revision as of 13:19, 3 March 2022

↖ 2L 5s ↑ 3L 5s 4L 5s ↗
← 2L 6s 3L 6s 4L 6s →
↙ 2L 7s ↓ 3L 7s 4L 7s ↘ 
┌╥┬┬╥┬┬╥┬┬┐
│║││║││║│││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLss
ssLssLssL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 2\9 to 1\3 (266.7 ¢ to 400.0 ¢)
Dark 0\3 to 1\9 (0.0 ¢ to 133.3 ¢)
TAMNAMS information
Name tcherepnin
Prefix cher-
Abbrev. ch
Related MOS scales
Parent 3L 3s
Sister 6L 3s
Daughters 9L 3s, 3L 9s
Neutralized 6L 3s
2-Flought 12L 6s, 3L 15s
Equal tunings
Equalized (L:s = 1:1) 2\9 (266.7 ¢)
Supersoft (L:s = 4:3) 7\30 (280.0 ¢)
Soft (L:s = 3:2) 5\21 (285.7 ¢)
Semisoft (L:s = 5:3) 8\33 (290.9 ¢)
Basic (L:s = 2:1) 3\12 (300.0 ¢)
Semihard (L:s = 5:2) 7\27 (311.1 ¢)
Hard (L:s = 3:1) 4\15 (320.0 ¢)
Superhard (L:s = 4:1) 5\18 (333.3 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

This MOS has generators which range between 0 and 133.333 cents and three periods per octave and runs Lss Lss Lss.

Scale tree

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
2\9 266.667 133.333 1 1 1.000
11\48 275.000 125.000 6 5 1.200
9\39 276.923 123.077 5 4 1.250
16\69 278.261 121.739 9 7 1.286
7\30 280.000 120.000 4 3 1.333
19\81 281.481 118.519 11 8 1.375
12\51 282.353 117.647 7 5 1.400
17\72 283.333 116.667 10 7 1.428
5\21 285.714 114.286 3 2 1.500
18\75 288.000 112.000 11 7 1.571
13\54 288.889 111.111 8 5 1.600
21\87 289.655 110.345 13 8 1.625 Unnamed golden tuning
8\33 290.909 109.091 5 3 1.667
19\78 292.308 107.692 12 7 1.714
11\45 293.333 106.667 7 4 1.750
14\57 294.737 105.263 9 5 1.800 August
3\12 300.000 100.000 2 1 2.000 Basic tcherepnin
(Generators smaller than this are proper)
13\51 305.882 94.118 9 4 2.250
10\39 307.692 92.308 7 3 2.333
17\66 309.091 90.909 12 5 2.400 Augene (optimal around here)
7\27 311.111 88.889 5 2 2.500
18\69 313.043 86.957 13 5 2.600 Unnamed golden tuning
11\42 314.286 85.714 8 3 2.667
15\57 315.789 84.211 11 4 2.750 August
4\15 320.000 80.000 3 1 3.000
13\48 325.000 75.000 10 3 3.333 Inflated
9\33 327.273 72.727 7 2 3.500
14\51 329.412 70.588 11 3 3.667
5\18 333.333 66.667 4 1 4.000
11\39 338.462 61.538 9 2 4.500
6\21 342.857 57.143 5 1 5.000
7\24 350.000 50.000 6 1 6.000 Hemiug, hemiaug↓
1\3 400.000 0.000 1 0 → inf
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