1L 6s: Difference between revisions

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Other scales include very improper (incomplete) versions of [[negri]], 12edo, etc.
Other scales include very improper (incomplete) versions of [[negri]], 12edo, etc.


== Scale tree ==
{| class="wikitable center-all"
{| class="wikitable"
! 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\1
| 6\7 || || || || || || 1028.571 || 171.429 || 1 || 1 || 1.000 ||  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
|
| || || || || || 31\36 || 1033.333 || 166.667 || 6 || 5 || 1.200 ||
|
|
|
|1\11
|109.09
|
|-
|-
| |  
| || || || || 25\29 || || 1034.483 || 165.517 || 5 || 4 || 1.250 ||
| |  
| |  
| | 1\10
| |  
| | 120
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || || 44\51 || 1035.294 || 164.706 || 9 || 7 || 1.286 ||  
| |  
| |  
| |  
| | 2\19
| | 126.32
| style="text-align:center;" | Negri is around here
|-
|-
| |  
| || || || 19\22 || || || 1036.364 || 163.636 || 4 || 3 || 1.333 ||  
| |  
| |  
| |  
| |  
| | 1200/(6+pi)
| |  
|-
|-
| |  
| || || || || || 51\59 || 1037.288 || 162.712 || 11 || 8 || 1.375 ||  
| |  
| | 1\9
| |  
| |  
| | 133.33
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || 32\37 || || 1037.838 || 162.162 || 7 || 5 || 1.400 || Porcupine is in this region
| |  
| |  
| |  
| |  
| | 1200/(6+e)
| |  
|-
|-
| |  
| || || || || || 45\52 || 1038.462 || 161.538 || 10 || 7 || 1.428 ||  
| |  
| |  
| |  
| | 3\26
| | 138.46
| |  
|-
|-
| |  
| || || 13\15 || || || || 1040.000 || 160.000 || 3 || 2 || 1.500 || L/s = 3/2
| |  
| |  
| |  
| |  
| | 1200/(7+phi)
| |  
|-
|-
| |  
| || || || || || 46\53 || 1041.509 || 158.491 || 11 || 7 || 1.571 || Hemikleismic
| |  
| |  
| | 2\17
| |  
| | 141,18
| |  
|-
|-
| |  
| || || || || 33\38 || || 1042.105 || 157.895 || 8 || 5 || 1.600 ||  
| | 1\8
| |  
| |  
| |  
| | 150
| style="text-align:center;" | Boundary of propriety (generators
 
larger than this are proper)
|-
|-
| |  
| || || || || || 53\61 || 1042.623 || 157.377 || 13 || 8 || 1.625 || Golden porcupine/hemikleismic (?)
| |  
| |  
| |  
| |  
| | 1200/(6+sqrt(3))
| |
|-
|-
| |  
| || || || 20\23 || || || 1043.478 || 156.522 || 5 || 3 || 1.667 ||  
| |  
| |  
| | 3\23
| |  
| | 156.52
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 47\54 || 1044.444 || 155.556 || 12 || 7 || 1.714 ||  
| |  
| |  
| |  
| |  
| | 1200/(6+phi)
| style="text-align:center;" | Golden porcupine / golden hemikleismic
|-
|-
| |  
| || || || || 27\31 || || 1045.161 || 154.839 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| | 5\38
| | 157.89
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 34\39 || 1046.154 || 153.846 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| |  
| | 1200/(6+pi/2)
| |  
|-
|-
| |  
| || 7\8 || || || || || 1050.000 || 150.000 || 2 || 1 || 2.000 || Basic antiarcheotonic<br>(Generators smaller than this are proper)
| |  
| | 2\15
| |  
| |  
| | 160
| style="text-align:center;" | Optimum rank range (L/s=3/2) porcupine
|-
|-
| |  
| || || || || || 29\33 || 1054.545 || 145.455 || 9 || 4 || 2.250 ||
| |  
| |  
| | 3\22
| |  
| | 163.64
| style="text-align:center;" | Porcupine is around here
|-
|-
|
| || || || || 22\25 || || 1056.000 || 144.000 || 7 || 3 || 2.333 ||  
|
|
|
|4\29
|165.52
|
|-
|-
| | 1\7
| || || || || || 37\42 || 1057.143 || 142.857 || 12 || 5 || 2.400 ||
| |  
|-
| |  
| || || || 15\17 || || || 1058.824 || 141.176 || 5 || 2 || 2.500 || Progression (incomplete)
| |  
|-
| |  
| || || || || || 38\43 || 1060.465 || 139.535 || 13 || 5 || 2.600 || Unnamed golden tuning
| | 171.43
|-
| style="text-align:center;" |  
| || || || || 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 || L/s = 3/1
|-
| || || || || || 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 ||
|-
| || || || || || 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 || → inf ||
|}
|}
[[Category:Scales]]
[[Category:MOS scales]]
[[Category:7-tone scales]]
[[Category:Abstract MOS patterns]]
[[Category:Antiarcheotonic| ]] <!-- main article -->

Revision as of 12:41, 11 April 2021

User:IlL/Template:RTT restriction

↑ 1L 5s 2L 5s ↗
1L 6s 2L 6s →
↓ 1L 7s 2L 7s ↘
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 ¢)
View • Talk • Edit

There is one notable low-harmonic-entropy scale with this 1L 6s or antiarcheotonic MOS pattern: porcupine, in which two generators make a 6/5 and three make a 4/3.

Other scales include very improper (incomplete) versions of negri, 12edo, etc.

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
6\7 1028.571 171.429 1 1 1.000
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
51\59 1037.288 162.712 11 8 1.375
32\37 1037.838 162.162 7 5 1.400 Porcupine is in this region
45\52 1038.462 161.538 10 7 1.428
13\15 1040.000 160.000 3 2 1.500 L/s = 3/2
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 Golden porcupine/hemikleismic (?)
20\23 1043.478 156.522 5 3 1.667
47\54 1044.444 155.556 12 7 1.714
27\31 1045.161 154.839 7 4 1.750
34\39 1046.154 153.846 9 5 1.800
7\8 1050.000 150.000 2 1 2.000 Basic antiarcheotonic
(Generators smaller 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 Progression (incomplete)
38\43 1060.465 139.535 13 5 2.600 Unnamed golden tuning
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 L/s = 3/1
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
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 → inf
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