1L 4s: Difference between revisions

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The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Gamelismic_clan|slendric or gamelismic]], in which the generator is 8/7 and three of them make a 3/2. Other scales include very [[Rothenberg_propriety|improper]] (incomplete) versions of [[Porcupine_family|porcupine]], [[Marvel_temperaments|negri]], etc.
The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Gamelismic clan|slendric or gamelismic]], in which the generator is 8/7 and three of them make a 3/2. Other scales include very [[improper]] (incomplete) versions of [[Porcupine family|porcupine]], [[Marvel temperaments#Negri|negri]], etc.


{| class="wikitable"
{| class="wikitable center-9 center-12"
|-
|-
! colspan="8" | Generator
! colspan="8" | Generator
! | Generator (s)
! Generator (s)
! | L-s
! L-s
! |<nowiki> |L-2s|</nowiki>
! <nowiki> |L-2s|</nowiki>
! | Comments
! Comments
|-
|-
| | 0\1
| 0\1
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| style="text-align:center;" |  
|
| |  
|
| |  
|
| style="text-align:center;" |  
|
|-
|-
|
|
Line 29: Line 29:
|
|
|
|
|1\12
| 1\12
|100
| 100
|700
| 700
|600
| 600
|
|
|-
|-
Line 41: Line 41:
|
|
|
|
|1\11
| 1\11
|
|
|109.09
| 109.09
|654.545
| 654.545
|545.455
| 545.455
|
|
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| | 1\10
| 1\10
| |  
|
| |  
|
| style="text-align:center;" | 120
| 120
| | 600
| 600
| | 480
| 480
| style="text-align:center;" |  
|
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| |  
|
| | 2\19
| 2\19
| |  
|
| style="text-align:center;" | 126.32
| 126.32
| | 568.42
| 568.42
| | 442.11
| 442.11
| style="text-align:center;" | Negri is around here
| Negri is around here
|-
|-
| |  
|
| |  
|
| |  
|
| |  
|
| | 1\9
| 1\9
| |  
|
| |  
|
| |  
|
| style="text-align:center;" | 133.33
| 133.33
| | 533.33
| 533.33
| | 400
| 400
| style="text-align:center;" |  
|
|-
|-
| |  
|
| |  
|
| |  
|
| | 1\8
| 1\8
| |  
|
| |  
|
| |  
|
| |  
|
| style="text-align:center;" | 150
| 150
| | 450
| 450
| | 300
| 300
| style="text-align:center;" | L/s = 4
| L/s = 4
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 2\15
| 2\15
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 160
| 160
| | 400
| 400
| | 240
| 240
| style="text-align:center;" |  
|
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 3\22
| 3\22
| |  
|  
| |  
|  
| style="text-align:center;" | 163.64
| 163.64
| | 381.82
| 381.82
| | 218.18
| 218.18
| style="text-align:center;" | Porcupine is around here
| Porcupine is around here
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 1200/(4+pi)
| 1200/(4+pi)
| | 359.85
| 359.85
| | 191.82
| 191.82
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 1\7
| 1\7
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 171.43
| 171.43
| | 342.86
| 342.86
| | 171.43
| 171.43
| style="text-align:center;" | L/s = 3
| L/s = 3
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(4+e)</span>
| 1200/(4+e)
| | 306.915
| 306.915
| | 128.3
| 128.3
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 3\20
| 3\20
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 180
| 180
| | 300
| 300
| | 120
| 120
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(5+phi)</span>
| 1200/(5+phi)
| | 293.386
| 293.386
| | 112.064
| 112.064
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 2\13
| 2\13
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 184.615
| 184.615
| | 276.92
| 276.92
| | 92.31
| 92.31
| |  
|  
|-
|-
| |  
|  
| | 1\6
| 1\6
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 200
| 200
| | 200
| 200
| | 0
| 0
| style="text-align:center;" | Boundary of propriety (generators
| Boundary of propriety (generators <br> larger than this are [[strictly proper]])
 
larger than this are strictly proper)
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 1200/(4+sqrt(3))
| 1200/(4+sqrt(3))
| | 153.25
| 153.25
| | 56.095
| 56.095
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 3\17
| 3\17
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 211.76
| 211.76
| | 141.18
| 141.18
| | 70.59
| 70.59
| style="text-align:center;" |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 8\45
| 8\45
| |  
|  
| |  
|  
| style="text-align:center;" | 213.33
| 213.33
| | 133.33
| 133.33
| | 80
| 80
| style="text-align:center;" |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 1200/(4+phi)
| 1200/(4+phi)
| | 132.01
| 132.01
| | 81.59
| 81.59
| style="text-align:center;" | Golden machine
| Golden machine
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 13\73
| 13\73
| |  
|  
| style="text-align:center;" | 213.70
| 213.70
| | 131.51
| 131.51
| | 82.19
| 82.19
| style="text-align:center;" |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 5\28
| 5\28
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 214.29
| 214.29
| | 128.57
| 128.57
| | 85.71
| 85.71
| style="text-align:center;" |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(8+pi)</span>
| 1200/(8+pi)
| | 122.955
| 122.955
| | 92.45
| 92.45
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 2\11
| 2\11
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 218.18
| 218.18
| | 109.09
| 109.09
| | 109.09
| 109.09
| style="text-align:center;" | Optimum rank range (L/s=3/2) machine
| Optimum rank range (L/s=3/2) machine
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 3\16
| 3\16
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 225
| 225
| | 75
| 75
| | 150
| 150
| style="text-align:center;" | Gorgo is around here
| Gorgo is around here
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 4\21
| 4\21
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 228.57
| 228.57
| | 57.14
| 57.14
| | 171.43
| 171.43
| style="text-align:center;" |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 5\26
| 5\26
| |  
|  
| |  
|  
| style="text-align:center;" | 230.77
| 230.77
| | 46.15
| 46.15
| | 184.62
| 184.62
| style="text-align:center;" |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 6\31
| 6\31
| |  
|  
| style="text-align:center;" | 232.26
| 232.26
| | 38.71
| 38.71
| | 193.55
| 193.55
| style="text-align:center;" |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 7\36
| 7\36
| style="text-align:center;" | 233.33
| 233.33
| | 33.33
| 33.33
| | 200
| 200
| style="text-align:center;" | Slendric is around here
| Slendric is around here
|-
|-
| | 1\5
| 1\5
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| style="text-align:center;" | 240
| 240
| | 0
| 0
| | 240
| 240
| style="text-align:center;" |  
|
|}
|}

Revision as of 00:59, 2 January 2021

The only notable low-harmonic-entropy scale for this MOS pattern is slendric or gamelismic, in which the generator is 8/7 and three of them make a 3/2. Other scales include very improper (incomplete) versions of porcupine, negri, etc.

Generator Generator (s) L-s |L-2s| Comments
0\1
1\12 100 700 600
1\11 109.09 654.545 545.455
1\10 120 600 480
2\19 126.32 568.42 442.11 Negri is around here
1\9 133.33 533.33 400
1\8 150 450 300 L/s = 4
2\15 160 400 240
3\22 163.64 381.82 218.18 Porcupine is around here
1200/(4+pi) 359.85 191.82
1\7 171.43 342.86 171.43 L/s = 3
1200/(4+e) 306.915 128.3
3\20 180 300 120
1200/(5+phi) 293.386 112.064
2\13 184.615 276.92 92.31
1\6 200 200 0 Boundary of propriety (generators
larger than this are strictly proper)
1200/(4+sqrt(3)) 153.25 56.095
3\17 211.76 141.18 70.59
8\45 213.33 133.33 80
1200/(4+phi) 132.01 81.59 Golden machine
13\73 213.70 131.51 82.19
5\28 214.29 128.57 85.71
1200/(8+pi) 122.955 92.45
2\11 218.18 109.09 109.09 Optimum rank range (L/s=3/2) machine
3\16 225 75 150 Gorgo is around here
4\21 228.57 57.14 171.43
5\26 230.77 46.15 184.62
6\31 232.26 38.71 193.55
7\36 233.33 33.33 200 Slendric is around here
1\5 240 0 240
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