6L 2s: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="7" | Generator
! colspan="6" | Generator
! | Cents
! | Cents
!1400edo
! | Comments
! | Comments
|-
|-
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| |  
| |  
| |  
| |  
|
| | 150
| | 150
|175
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
|6\46
|
|
|
|
Line 38: Line 34:
|
|
|
|
|
|6\46
|156.52…
|156.52
|182.60…
|
|
|-
|-
|
|11\84
|
|
|
|
|
|
|
|
|157.14…
|183.3̄
|
|
|-
|5\38
|5\38
|
|
|
|157.895
|
|
|
|
|157.89…
|184.21…
|
|-
|
|9\68
|
|
|
|
|
|158.82…
|185.29…
|
|
|-
|-
|
|
|
|13\98
|
|
|
|
|
|
|159.18…
|185.71…
|
|-
|4\30
|4\30
|
|
|
|
|
|
|
|
|160
|160
|186.6̄
|
|
|-
|-
|
|
|11\82
|
|
|
|
|160.97…
|187.80…
|
|-
|
|7\52
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|
|
|
|
|161.53…
|188.46…
|
|-
|
|
|10\74
|
|
|
|
|162.16…
|189.18…
|
|-
| | 3\22
| |  
| |  
| |  
| |  
| | 3\22
| |  
| |  
| |  
| |  
| |  
| |  
|
| | 163.64
| | 163.6̄3̄
|190.9̄0̄
| style="text-align:center;" | Hedgehog is around here
| style="text-align:center;" | Hedgehog is around here
|-
|
|
|
|
|17\124
|
|
|164.51…
|191.93…
|
|-
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|
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|14\102
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|
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|164.70…
|192.15…
|
|-
|-
| |  
| |  
Line 170: Line 71:
| |  
| |  
| |  
| |  
|
| | 164.99
| | 164.98…
|192.48…
| |  
| |  
|-
|
|
|11\80
|
|
|
|
|165
|192.5
|
|-
|-
| |  
| |  
| | 8\58
| |  
| |  
| |  
| |  
| |  
| |  
| | 8\58
| |  
| |  
|
| | 165.52
| | 165.51…
|193.10…
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| |  
| |  
| |  
| | 13\94
| |  
| |  
| |  
| |  
| |  
| |  
|
| | 13\94
| | 165.95…
| | 165.96
|193.61…
| style="text-align:center;" | Golden hedgehog/echidna
| style="text-align:center;" | Golden hedgehog/echidna
|-
|-
| |  
| |  
| | 5\36
| |  
| |  
| |  
| |  
| | 5\36
| |  
| |  
| |  
| |  
|
| | 166.67
| | 166.
|194.4̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 225: Line 107:
| |  
| |  
| |  
| |  
|
| | 167.72
| | 167.72…
|195.67…
| |  
| |  
|-
|-
|
| |  
|7\50
|
|
|
|
|
|168
|196
|
|-
|
|9\64
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|
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|
|168.75
|196.875
|
|-
|
|11\78
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|
|
|
|
|169.23…
|197.43…
|
|-
|
|13\92
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|
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|169.59…
|197.82…
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|-
|
|15\106
|
|
|
|
|
|169.81…
|198.11…
|
|-
|
|17\120
|
|
|
|
|
|170
|198.3̄
|
|-
|
|19\134
|
|
|
|
|
|170.14…
|198.50…
|
|-
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|
|21\148
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|170.27…
|198.64…
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|-
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|23\162
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|
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|170.37…
|198.76…
|
|-
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|25\176
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|
|170.4̄5̄
|198.86…
|
|-
|
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|
|27\190
|
|170.52…
|198.94…
|
|-
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|29\204
|170.58…
|199.01…
|
|-
| | 2\14
| | 2\14
| |  
| |  
Line 367: Line 116:
| |  
| |  
| |  
| |  
| |
| | 171.43
|
| | 171.42…
|200
| style="text-align:center;" | Boundary of propriety for near-MOS
| style="text-align:center;" | Boundary of propriety for near-MOS


Optimum rank range (L/s=2/1) for MOS
Optimum rank range (L/s=2/1) for MOS
|-
|
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|17\118
|172.88…
|201.69…
|
|-
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|15\104
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|173.07…
|201.92…
|
|-
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|13\90
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|173.3̄
|202.2̄
|
|-
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|11\76
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|173.68…
|202.63…
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|-
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|9\62
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|174.19…
|203.22…
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|-
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|7\48
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|175
|204.16̄
|
|-
|-
| |  
| |  
| | 5\34
| |  
| |  
| |  
| |  
| | 5\34
| |  
| |  
| |  
| |  
|
| | 176.47
| | 176.47…
|205.88…
| |  
| |  
|-
|-
| |  
| |  
| |  
| |  
| | 13\88
| |  
| |  
| |  
| |  
| |  
| |  
|
| | 13\88
| | 177.2̄7̄
| | 177.27
|206.8̄1̄
| |  
| |  
|-
|-
| |  
| |  
| | 8\54
| |  
| |  
| |  
| |  
| |  
| |  
| | 8\54
| |  
| |  
|
| | 177.78
| | 177.
|207.40…
| |  
| |  
|-
|-
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| | 178.15
| | 178.15…
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|207.84…
| style="text-align:center;" |<span style="display: block; text-align: center;">L/s = e</span>
|-
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|11\74
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|178.37…
|208.10…
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|-
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|14\94
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|178.72…
|208.51…
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|-
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|17\114
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|178.94…
|208.77…
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|-
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|20\134
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|179.10…
|208.95…
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|-
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|23\154
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|179.22…
|209.0̄9̄…
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|-
|-
| |
| |  
| |  
| | 3\20
| | 3\20
Line 545: Line 163:
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| |  
| |  
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| | 180
| | 180
|210
| style="text-align:center;" | L/s = 3
| style="text-align:center;" | L/s = 3
|-
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Line 557: Line 172:
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| | 180.815
| | 180.81…
| | <span style="display: block; text-align: center;">L/s = pi</span>
|210.95…
| |<span style="display: block; text-align: center;">L/s = pi</span>
|-
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|13\86
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|181.39…
|211.62…
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|-
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|10\66
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|181.8̄1̄
|212.1̄2̄
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|-
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|7\46
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|182.60…
|213.04…
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|-
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|11\72
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|183.3̄
|213.8̄
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|-
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|15\98
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|183.67…
|214.28…
|
|-
|-
| |  
| |  
| | 4\26
| |  
| |  
| |  
| |  
| | 4\26
| |  
| |  
| |  
| |  
|
| | 184.615
| | 184.61…
|215.38…
| style="text-align:center;" | L/s = 4
| style="text-align:center;" | L/s = 4
|-
|-
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|13\84
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|185.71…
|216.6̄
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|-
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|9\58
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|186.20…
|217.24…
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|-
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|5\32
|5\32
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|187.5
|187.5
|218.75
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|-
|-
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|16\102
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|188.23…
|219.60…
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|-
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|11\70
|
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|188.57…
|220
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|-
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|6\38
|6\38
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|189.47
|189.47
|221.05…
|
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|-
|-
Line 700: Line 208:
| |  
| |  
| |  
| |  
|
| | 200
| | 200
|233.3̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|}
|}
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Revision as of 18:15, 23 August 2021

↖ 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 ¢)

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 Comments
1\8 150
6\46 156.52
5\38 157.895
4\30 160
3\22 163.64 Hedgehog is around here
164.99
8\58 165.52
13\94 165.96 Golden hedgehog/echidna
5\36 166.67
167.72
2\14 171.43 Boundary of propriety for near-MOS

Optimum rank range (L/s=2/1) for MOS

5\34 176.47
13\88 177.27
8\54 177.78
178.15 L/s = e
3\20 180 L/s = 3
180.815 L/s = pi
4\26 184.615 L/s = 4
5\32 187.5
6\38 189.47
1\6 200