6L 2s: Difference between revisions

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== Scale tree ==
== Scale tree ==
{| class="wikitable"
 
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 1\8 || || || || || || 150.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 6\46 || 156.522 || 6 || 5 || 1.200 || Bison
|-
| || || || || 5\38 || || 157.895 || 5 || 4 || 1.250 ||
|-
| || || || || || 9\68 || 158.824 || 9 || 7 || 1.286 ||
|-
| || || || 4\30 || || || 160.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 11\82 || 160.976 || 11 || 8 || 1.375 ||
|-
| || || || || 7\52 || || 161.538 || 7 || 5 || 1.400 ||
|-
| || || || || || 10\74 || 162.162 || 10 || 7 || 1.428 ||
|-
| || || 3\22 || || || || 163.636 || 3 || 2 || 1.500 || L/s = 3/2, hedgehog is around here
|-
| || || || || || 11\80 || 165.000 || 11 || 7 || 1.571 || Echidna
|-
| || || || || 8\58 || || 165.517 || 8 || 5 || 1.600 ||
|-
|-
! colspan="6" | Generator
| || || || || || 13\94 || 165.957 || 13 || 8 || 1.625 || Supers, pogo
! | Cents
! | Comments
|-
|-
| | 1\8
| || || || 5\36 || || || 166.667 || 5 || 3 || 1.667 ||  
| |  
| |  
| |  
| |  
| |  
| | 150
| style="text-align:center;" |  
|-
|-
|
| || || || || || 12\86 || 167.442 || 12 || 7 || 1.714 ||  
|
|
|
|
|6\46
|156.52
|
|-
|-
|
| || || || || 7\50 || || 168.000 || 7 || 4 || 1.750 ||
|
|
|
|5\38
|
|157.895
|
|-
|-
|
| || || || || || 9\64 || 168.750 || 9 || 5 || 1.800 ||
|
|
|4\30
|
|
|160
|
|-
|-
| |  
| || 2\14 || || || || || 171.429 || 2 || 1 || 2.000 || Basic echinoid<br>(Generators smaller than this are proper)
| |  
| | 3\22
| |  
| |  
| |  
| | 163.64
| style="text-align:center;" | Hedgehog is around here
|-
|-
| |  
| || || || || || 9\62 || 174.194 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| |  
| |  
| | 164.99
| |  
|-
|-
| |  
| || || || || 7\48 || || 175.000 || 7 || 3 || 2.333 ||  
| |  
| |  
| |  
| | 8\58
| |  
| | 165.52
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 12\82 || 175.610 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| |  
| | 13\94
| | 165.96
| style="text-align:center;" | Golden hedgehog/echidna
|-
|-
| |  
| || || || 5\34 || || || 176.471 || 5 || 2 || 2.500 ||  
| |  
| |
| | 5\36
| |  
| |  
| | 166.67
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 13\88 || 177.273 || 13 || 5 || 2.600 || Unnamed golden tuning
| |  
| |  
| |  
| |  
| |  
| | 167.72
| |  
|-
|-
| |  
| || || || || 8\54 || || 177.778 || 8 || 3 || 2.667 ||
| | 2\14
| |  
| |  
| |  
| |  
| | 171.43
| style="text-align:center;" | Boundary of propriety for near-MOS
 
Optimum rank range (L/s=2/1) for MOS
|-
|-
| |  
| || || || || || 11\74 || 178.378 || 11 || 4 || 2.750 ||
| |  
| |  
| | 5\34
| |  
| |  
| | 176.47
| |  
|-
|-
| |  
| || || 3\20 || || || || 180.000 || 3 || 1 || 3.000 || L/s = 3/1
| |  
| |  
| |  
| |  
| | 13\88
| | 177.27
| |  
|-
|-
| |  
| || || || || || 10\66 || 181.818 || 10 || 3 || 3.333 ||
| |  
| |  
| |  
| | 8\54
| |  
| | 177.78
| |  
|-
|-
| |  
| || || || || 7\46 || || 182.609 || 7 || 2 || 3.500 ||  
| |  
| |  
| |  
| |  
| |  
| | 178.15
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
|-
| |  
| || || || || || 11\72 || 183.333 || 11 || 3 || 3.667 || Unidec
| |  
| | 3\20
| |  
| |  
| |  
| | 180
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || 4\26 || || || 184.615 || 4 || 1 || 4.000 ||
| |  
| |  
| |  
| |  
| |  
| | 180.815
| | <span style="display: block; text-align: center;">L/s = pi</span>
|-
|-
| |  
| || || || || || 9\58 || 186.207 || 9 || 2 || 4.500 || Secant
| |  
| |  
| | 4\26
| |  
| |  
| | 184.615
| style="text-align:center;" | L/s = 4
|-
|-
|
| || || || || 5\32 || || 187.500 || 5 || 1 || 5.000 ||  
|
|
|
|5\32
|
|187.5
|
|-
|-
|
| || || || || || 6\38 || 189.474 || 6 || 1 || 6.000 ||
|
|
|
|
|6\38
|189.47
|
|-
|-
| | 1\6
| 1\6 || || || || || || 200.000 || 1 || 0 || → inf ||
| |  
| |  
| |  
| |  
| |  
| | 200
| style="text-align:center;" |  
|}
|}
[[Category:Scale theory]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:Echidnoid| ]] <!-- main article -->

Revision as of 20:47, 1 January 2022

↖ 5L 1s ↑ 6L 1s 7L 1s ↗
← 5L 2s 6L 2s 7L 2s →
↙ 5L 3s ↓ 6L 3s 7L 3s ↘
Scale structure
Step pattern LLLsLLLs
sLLLsLLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 1\8 to 1\6 (150.0 ¢ to 200.0 ¢)
Dark 2\6 to 3\8 (400.0 ¢ to 450.0 ¢)
TAMNAMS information
Name ekic
Prefix ek-
Abbrev. ek
Related MOS scales
Parent 2L 4s
Sister 2L 6s
Daughters 8L 6s, 6L 8s
Neutralized 4L 4s
2-Flought 14L 2s, 6L 10s
Equal tunings
Equalized (L:s = 1:1) 1\8 (150.0 ¢)
Supersoft (L:s = 4:3) 4\30 (160.0 ¢)
Soft (L:s = 3:2) 3\22 (163.6 ¢)
Semisoft (L:s = 5:3) 5\36 (166.7 ¢)
Basic (L:s = 2:1) 2\14 (171.4 ¢)
Semihard (L:s = 5:2) 5\34 (176.5 ¢)
Hard (L:s = 3:1) 3\20 (180.0 ¢)
Superhard (L:s = 4:1) 4\26 (184.6 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
View • Talk • Edit

6L 2s is a MOS scale with a half-octave period and a generator larger than 1\8 and smaller than 1\6. There is only one significant (though small) harmonic entropy minimum with this MOS pattern: hedgehog, in which two generators are 6/5 and three are 4/3, same as porcupine.

In addition to the true MOS, LLLsLLLs, there is also a near-MOS, LLLLsLLs, in which the period is the only interval with more than two flavors. The true MOS is always proper, because there is only one small step per period, but the near-MOS is only proper if the generator is smaller than 2\14 (which includes hedgehog).

Scale tree

Generator Cents L s L/s Comments
1\8 150.000 1 1 1.000
6\46 156.522 6 5 1.200 Bison
5\38 157.895 5 4 1.250
9\68 158.824 9 7 1.286
4\30 160.000 4 3 1.333
11\82 160.976 11 8 1.375
7\52 161.538 7 5 1.400
10\74 162.162 10 7 1.428
3\22 163.636 3 2 1.500 L/s = 3/2, hedgehog is around here
11\80 165.000 11 7 1.571 Echidna
8\58 165.517 8 5 1.600
13\94 165.957 13 8 1.625 Supers, pogo
5\36 166.667 5 3 1.667
12\86 167.442 12 7 1.714
7\50 168.000 7 4 1.750
9\64 168.750 9 5 1.800
2\14 171.429 2 1 2.000 Basic echinoid
(Generators smaller than this are proper)
9\62 174.194 9 4 2.250
7\48 175.000 7 3 2.333
12\82 175.610 12 5 2.400
5\34 176.471 5 2 2.500
13\88 177.273 13 5 2.600 Unnamed golden tuning
8\54 177.778 8 3 2.667
11\74 178.378 11 4 2.750
3\20 180.000 3 1 3.000 L/s = 3/1
10\66 181.818 10 3 3.333
7\46 182.609 7 2 3.500
11\72 183.333 11 3 3.667 Unidec
4\26 184.615 4 1 4.000
9\58 186.207 9 2 4.500 Secant
5\32 187.500 5 1 5.000
6\38 189.474 6 1 6.000
1\6 200.000 1 0 → inf
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