6L 2s: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="6" | Generator
! colspan="7" | Generator
! | Cents
! | Cents
!1400edo
! | Comments
! | Comments
|-
|-
Line 26: Line 27:
| |  
| |  
| |  
| |  
|
| | 150
| | 150
|175
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
|6\46
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|
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Line 34: Line 39:
|
|
|
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|6\46
|156.52…
|156.52
|182.60…
|
|
|-
|-
|
|11\84
|
|
|
|
|
|
|
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|157.14…
|183.3̄
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|
|-
|5\38
|5\38
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|
|157.895
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|
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|157.89…
|184.21…
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|-
|
|9\68
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|
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|158.82…
|185.29…
|
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|-
|-
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|13\98
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|
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|
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|
|159.18…
|185.71…
|
|-
|4\30
|4\30
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|
|
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|160
|160
|186.6̄
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|
|-
|-
|
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|11\82
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|
|
|
|160.97…
|187.80…
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|-
|
|7\52
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|
|
|
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|161.53…
|188.46…
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|-
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|10\74
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|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
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|164.51…
|191.93…
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|-
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|14\102
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|164.70…
|192.15…
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|-
|-
| |  
| |  
Line 71: Line 170:
| |  
| |  
| |  
| |  
| | 164.99
|
| | 164.98…
|192.48…
| |  
| |  
|-
|
|
|11\80
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|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
|
| | 165.96
| | 165.95…
|193.61…
| style="text-align:center;" | Golden hedgehog/echidna
| style="text-align:center;" | Golden hedgehog/echidna
|-
|-
| |  
| |  
| | 5\36
| |  
| |  
| |  
| |  
| | 5\36
| |  
| |  
| |  
| |  
| | 166.67
|
| | 166.6̄
|194.4̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 107: Line 225:
| |  
| |  
| |  
| |  
| | 167.72
|
| | 167.72…
|195.67…
| |  
| |  
|-
|-
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|7\50
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|
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|168
|196
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|-
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|9\64
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|168.75
|196.875
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|-
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|11\78
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|169.23…
|197.43…
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|-
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|13\92
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|169.59…
|197.82…
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|-
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|15\106
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|169.81…
|198.11…
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|-
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|17\120
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|170
|198.3̄
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|-
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|19\134
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|170.14…
|198.50…
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|-
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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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|170.37…
|198.76…
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|-
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|25\176
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|170.4̄5̄
|198.86…
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|-
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|27\190
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|170.52…
|198.94…
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|-
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|29\204
|170.58…
|199.01…
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|-
| | 2\14
| |  
| |  
| | 2\14
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| | 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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|-
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|15\104
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|173.07…
|201.92…
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|-
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|13\90
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|173.3̄
|202.2̄
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|-
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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
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|-
|-
| |  
| |  
| | 5\34
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| |  
| |  
| |  
| | 5\34
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| |  
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| | 176.47
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| | 176.47…
|205.88…
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| |  
|-
|-
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| |  
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| |  
| | 13\88
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| |  
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| |  
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| | 13\88
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| | 177.27
| | 177.2̄7̄
|206.8̄1̄
| |  
| |  
|-
|-
| |  
| |  
| | 8\54
| |  
| |  
| |  
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| |  
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| | 8\54
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| | 177.78
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| | 177.7̄
|207.40…
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|-
|-
Line 154: Line 480:
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| | 178.15
|
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
| | 178.15…
|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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|23\154
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|179.22…
|209.0̄9̄…
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|-
|-
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| | 3\20
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| |  
| | 3\20
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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 172: Line 557:
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| | 180.815
|
| | <span style="display: block; text-align: center;">L/s = pi</span>
| | 180.81…
|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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|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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|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…
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|-
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| | 4\26
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| | 4\26
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| | 184.615
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| | 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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|16\102
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|188.23…
|219.60…
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|11\70
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|188.57…
|220
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|6\38
|6\38
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|189.47
|189.47
|221.05…
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Line 208: Line 700:
| |  
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| | 200
| | 200
|233.3̄
| style="text-align:center;" |  
| style="text-align:center;" |  
|}
|}
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Revision as of 17:03, 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 ¢)
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 1400edo Comments
1\8 150 175
6\46 156.52… 182.60…
11\84 157.14… 183.3̄
5\38 157.89… 184.21…
9\68 158.82… 185.29…
13\98 159.18… 185.71…
4\30 160 186.6̄
11\82 160.97… 187.80…
7\52 161.53… 188.46…
10\74 162.16… 189.18…
3\22 163.6̄3̄ 190.9̄0̄ Hedgehog is around here
17\124 164.51… 191.93…
14\102 164.70… 192.15…
164.98… 192.48…
11\80 165 192.5
8\58 165.51… 193.10…
13\94 165.95… 193.61… Golden hedgehog/echidna
5\36 166.6̄ 194.4̄
167.72… 195.67…
7\50 168 196
9\64 168.75 196.875
11\78 169.23… 197.43…
13\92 169.59… 197.82…
15\106 169.81… 198.11…
17\120 170 198.3̄
19\134 170.14… 198.50…
21\148 170.27… 198.64…
23\162 170.37… 198.76…
25\176 170.4̄5̄ 198.86…
27\190 170.52… 198.94…
29\204 170.58… 199.01…
2\14 171.42… 200 Boundary of propriety for near-MOS

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

17\118 172.88… 201.69…
15\104 173.07… 201.92…
13\90 173.3̄ 202.2̄
11\76 173.68… 202.63…
9\62 174.19… 203.22…
7\48 175 204.16̄
5\34 176.47… 205.88…
13\88 177.2̄7̄ 206.8̄1̄
8\54 177.7̄ 207.40…
178.15… 207.84… L/s = e
11\74 178.37… 208.10…
14\94 178.72… 208.51…
17\114 178.94… 208.77…
20\134 179.10… 208.95…
23\154 179.22… 209.0̄9̄…
3\20 180 210 L/s = 3
180.81… 210.95… L/s = pi
13\86 181.39… 211.62…
10\66 181.8̄1̄ 212.1̄2̄
7\46 182.60… 213.04…
11\72 183.3̄ 213.8̄
15\98 183.67… 214.28…
4\26 184.61… 215.38… L/s = 4
13\84 185.71… 216.6̄
9\58 186.20… 217.24…
5\32 187.5 218.75
16\102 188.23… 219.60…
11\70 188.57… 220
6\38 189.47 221.05…
1\6 200 233.3̄
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