2L 6s: Difference between revisions

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Two notable harmonic entropy minima for this [[MOSScales|MOS]] pattern are [[Diaschismic_family|srutal/pajara]] and shrutar. They are both improper.  
Two notable harmonic entropy minima for this [[MOS scale|MOS]] pattern are [[srutal]]/[[pajara]] and [[shrutar]]. They are both improper.  


In addition to the true MOS form, LsssLsss, these scales also have an interesting near-MOS form, LssLssss, in which the period is the only generic interval represented by more than two specific intervals.
In addition to the true MOS form, LsssLsss, these scales also have an interesting near-MOS form, LssLssss, in which the period is the only generic interval represented by more than two specific intervals.


{| 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="10" | Generator
! Chroma-positive
! | Cents
! Chroma-negative
! | Comments
|-
|-
| | 0\2
| 3\8 || || || || || || 450.000 || 150.000 || 1 || 1 || 1.000 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 16\42 || 457.143 || 142.857 || 6 || 5 || 1.200 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1\26
| | 46.15
| |  
|-
|-
| |  
| || || || || 13\34 || || 458.824 || 141.176 || 5 || 4 || 1.250 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1\24
| |  
| | 50
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 23\60 || 460.000 || 140.000 || 9 || 7 || 1.286 || Fifive/crepuscular/fifives
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 2\46
| | 52.17
| style="text-align:center;" | Shrutar is around here
|-
|-
| |  
| || || || 10\26 || || || 461.538 || 138.462 || 4 || 3 || 1.333 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1\22
| |  
| |  
| | 54.55
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 27\70 || 462.857 || 137.143 || 11 || 8 || 1.375 ||  
| |  
| |  
| |  
| |  
| |  
| | 1\20
| |  
| |  
| |  
| | 60
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 17\44 || || 463.636 || 136.364 || 7 || 5 || 1.400 ||  
| |  
| |  
| |  
| |  
| | 1\18
| |  
| |  
| |  
| |  
| | 66.67
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 24\62 || 464.516 || 135.484 || 10 || 7 || 1.428 ||  
| |  
| |  
| |  
| | 1\16
| |  
| |  
| |  
| |  
| |  
| | 75
| style="text-align:center;" |  
|-
|-
| |  
| || || 7\18 || || || || 466.667 || 133.333 || 3 || 2 || 1.500 || L/s = 3/2
| |  
| |  
| | 1\14
| |  
| |  
| |  
| |  
| |  
| |  
| | 85.71
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || || 25\64 || 468.750 || 131.250 || 11 || 7 || 1.571 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 600/(3+pi)
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
|-
| |  
| || || || || 18\46 || || 469.565 || 130.435 || 8 || 5 || 1.600 ||  
| |  
| | 1\12
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 100
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || || 29\74 || 470.270 || 129.730 || 13 || 8 || 1.625 || Unnamed golden tuning
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 600/(3+e)
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
|-
| |  
| || || || 11\28 || || || 471.429 || 128.571 || 5 || 3 || 1.667 || Supersharp/octokaidecal is around here
| |  
| |  
| |  
| | 3\34
| |  
| |  
| |  
| |  
| |
| | 105.88
| style="text-align:center;" | Srutal/Pajara is around here
|-
|-
| |  
| || || || || || 26\66 || 472.727 || 127.273 || 12 || 7 || 1.714 ||  
| |  
| |  
| |  
| |  
| |  
| | 8\90
| |
| |  
| |  
| | 106.67
| |  
|-
|-
| |  
| || || || || 15\38 || || 473.864 || 126.316 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 21\236
| |  
| | 106.78
| |  
|-
|-
| |  
| || || || || || 19\48 || 475.000 || 125.000 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 34\382
| | 106.81
| |  
|-
|-
| |  
| || 4\10 || || || || || 480.000 || 120.000 || 2 || 1 || 2.000 || Basic 2L 6s<br>(Generators smaller than this are proper)
| |  
| |  
| |  
| |  
| |  
| |  
| | 13\146
| |  
| |  
| | 106.85
| |  
|-
|-
| |  
| || || || || || 17\42 || 485.714 || 114.286 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| |  
| | 5\56
| |  
| |  
| |  
| |  
| | 107.14
| |  
|-
|-
| |  
| || || || || 13\32 || || 487.500 || 112.500 || 7 || 3 || 2.333 ||  
| |  
| |  
| | 2\22
| |  
| |  
| |  
| |  
| |  
| |  
| | 109.09
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 22\54 || 488.889 || 111.111 || 12 || 5 || 2.400 ||
| | 1\10
| |
| |
| |
| |
| |
| |
| |
| |
| | 120
| style="text-align:center;" | Boundary of propriety
 
(generators larger than this are proper)
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(3+sqrt(3))
| |
|-
| |
| |
| |
| | 3\28
| |
| |
| |
| |
| |
| |
| | 128.57
| style="text-align:center;" | Supersharp
|-
| |
| |
| |  
| |  
| |  
| | 8\74
| |
| |
| |
| |  
| | 129.73
| style="text-align:center;" | Supersharp
|-
| |
| |
| |
| |
| |
| |
| |
| | 21\194
| |
| |  
| | 129.9
| |
|-
| |  
| |
| |
| |
| |
| |
| |
| |
| |
| | 55\508
| | 129.92
| style="text-align:center;" | Unnamed golden temperament
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 34\314
| |  
| | 129.94
| |  
|-
|-
| |  
| || || || 9\22 || || || 490.909 || 109.091 || 5 || 2 || 2.500 || Srutal/pajara
| |  
| |  
| |  
| |  
| |  
| | 13\120
| |  
| |  
| |  
| | 130
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 23\56 || 492.857 || 107.143 || 13 || 5 || 2.600 || Srutal/keen
| |  
| |  
| |  
| | 5\46
| |  
| |  
| |  
| |  
| |
| | 130.43
| style="text-align:center;" | Twothirdtonic
|-
|-
| |  
| || || || || 14\34 || || 494.118 || 105.882 || 8 || 3 || 2.667 || Srutal
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 600/(3+pi/2)
| |  
|-
|-
| |  
| || || || || || 19\46 || 495.652 || 104.348 || 11 || 4 || 2.750 || Srutal/diaschismic
| |  
| | 2\18
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 133.33
| style="text-align:center;" | Optimum rank range (L/s=3/2)
|-
|-
|
| || || 5\12 || || || || 500.000 || 100.000 || 3 || 1 || 3.000 || L/s = 3/1
|
|
|3\26
|
|
|
|
|
|
|138.46
|`
|-
|-
|
| || || || || || 16\38 || 505.263 || 94.737 || 10 || 3 || 3.333 || Bimeantone (incomplete)
|
|
|
|4\34
|
|
|
|
|
|141.18
|
|-
|-
|
| || || || || 11\26 || || 507.692 || 92.308 || 7 || 2 || 3.500 || Teff/pombe (incomplete)
|
|
|
|
|5\42
|
|
|
|
|142.86
|
|-
|-
|
| || || || || || 17\40 || 510.000 || 90.000 || 11 || 3 || 3.667 ||  
|
|
|
|
|
|
|11\92
|
|
|143.48
|
|-
|-
|
| || || || 6\14 || || || 514.286 || 85.714 || 4 || 1 || 4.000 ||
|
|
|
|
|
|6\50
|
|
|
|144
|
|-
|-
|
| || || || || || 13\30 || 520.000 || 80.000 || 9 || 2 || 4.500 ||  
|
|
|
|
|
|
|7\58
|
|
|144.83
|
|-
|-
|
| || || || || 7\16 || || 525.000 || 75.000 || 5 || 1 || 5.000 ||  
|
|
|
|
|
|
|
|8\66
|
|145.455
|
|-
|-
|
| || || || || || 8\18 || 533.333 || 66.667 || 6 || 1 || 6.000 || Shrutar (incomplete)↓
|
|
|
|
|
|
|
|
|9\47
|145.95
|
|-
|-
| | 1\8
| 1\2 || || || || || || 600.000 || 0.000 || 1 || 0 || → inf ||
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 150
| style="text-align:center;" |  
|}
|}


[[Category:Scales]]
[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Revision as of 16:18, 31 August 2021

↖ 1L 5s ↑ 2L 5s 3L 5s ↗
← 1L 6s 2L 6s 3L 6s →
↙ 1L 7s ↓ 2L 7s 3L 7s ↘
Scale structure
Step pattern LsssLsss
sssLsssL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 3\8 to 1\2 (450.0 ¢ to 600.0 ¢)
Dark 0\2 to 1\8 (0.0 ¢ to 150.0 ¢)
TAMNAMS information
Name subaric
Prefix subar-
Abbrev. sb
Related MOS scales
Parent 2L 4s
Sister 6L 2s
Daughters 8L 2s, 2L 8s
Neutralized 4L 4s
2-Flought 10L 6s, 2L 14s
Equal tunings
Equalized (L:s = 1:1) 3\8 (450.0 ¢)
Supersoft (L:s = 4:3) 10\26 (461.5 ¢)
Soft (L:s = 3:2) 7\18 (466.7 ¢)
Semisoft (L:s = 5:3) 11\28 (471.4 ¢)
Basic (L:s = 2:1) 4\10 (480.0 ¢)
Semihard (L:s = 5:2) 9\22 (490.9 ¢)
Hard (L:s = 3:1) 5\12 (500.0 ¢)
Superhard (L:s = 4:1) 6\14 (514.3 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)
View • Talk • Edit

Two notable harmonic entropy minima for this MOS pattern are srutal/pajara and shrutar. They are both improper.

In addition to the true MOS form, LsssLsss, these scales also have an interesting near-MOS form, LssLssss, in which the period is the only generic interval represented by more than two specific intervals.

Scale tree

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
3\8 450.000 150.000 1 1 1.000
16\42 457.143 142.857 6 5 1.200
13\34 458.824 141.176 5 4 1.250
23\60 460.000 140.000 9 7 1.286 Fifive/crepuscular/fifives
10\26 461.538 138.462 4 3 1.333
27\70 462.857 137.143 11 8 1.375
17\44 463.636 136.364 7 5 1.400
24\62 464.516 135.484 10 7 1.428
7\18 466.667 133.333 3 2 1.500 L/s = 3/2
25\64 468.750 131.250 11 7 1.571
18\46 469.565 130.435 8 5 1.600
29\74 470.270 129.730 13 8 1.625 Unnamed golden tuning
11\28 471.429 128.571 5 3 1.667 Supersharp/octokaidecal is around here
26\66 472.727 127.273 12 7 1.714
15\38 473.864 126.316 7 4 1.750
19\48 475.000 125.000 9 5 1.800
4\10 480.000 120.000 2 1 2.000 Basic 2L 6s
(Generators smaller than this are proper)
17\42 485.714 114.286 9 4 2.250
13\32 487.500 112.500 7 3 2.333
22\54 488.889 111.111 12 5 2.400
9\22 490.909 109.091 5 2 2.500 Srutal/pajara
23\56 492.857 107.143 13 5 2.600 Srutal/keen
14\34 494.118 105.882 8 3 2.667 Srutal
19\46 495.652 104.348 11 4 2.750 Srutal/diaschismic
5\12 500.000 100.000 3 1 3.000 L/s = 3/1
16\38 505.263 94.737 10 3 3.333 Bimeantone (incomplete)
11\26 507.692 92.308 7 2 3.500 Teff/pombe (incomplete)
17\40 510.000 90.000 11 3 3.667
6\14 514.286 85.714 4 1 4.000
13\30 520.000 80.000 9 2 4.500
7\16 525.000 75.000 5 1 5.000
8\18 533.333 66.667 6 1 6.000 Shrutar (incomplete)↓
1\2 600.000 0.000 1 0 → inf
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