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2L 5s: 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
|-
|-
! colspan="7" | generator in degrees of an [[EDO|edo]]
| 3\7 || || || || || || 514.286 || 1 || 1 || 1.000 ||
! | generator in cents
! | tetrachord
! | L in cents
! | s in cents
! | L to s ratio
! | comments
|-
|-
| style="text-align:center;" | 3\7
| || || || || || 16\37 || 518.919 || 6 || 5 || 1.200 ||  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| |
| |  
| style="text-align:center;" | 514.3
| style="text-align:center;" | 1 1 1
| style="text-align:center;" | 171.4
| style="text-align:center;" | 171.4
| style="text-align:center;" | 1.00
| style="text-align:center;" |  
|-
|-
|
| || || || || 13\30 || || 520.000 || 5 || 4 || 1.250 ||  
|
|
|
|
|
|19\44
|518.2
|6 6 7
|190.9
|163.6
|1.17
|
|-
|-
|
| || || || || || 23\53 || 520.755 || 9 || 7 || 1.286 ||  
|
|
|
|
|16\37
|
|518.9
|5 5 6
|194.6
|162.2
|1.20
|
|-
|-
| style="text-align:center;" |  
| || || || 10\23 || || || 521.739 || 4 || 3 || 1.333 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" | 13\30
| |  
| |  
| style="text-align:center;" | 520.0
| style="text-align:center;" | 4 4 5
| style="text-align:center;" | 200.0
| style="text-align:center;" | 160.0
| style="text-align:center;" | 1.25
| style="text-align:center;" | Mavila extends from here...
|-
|-
| style="text-align:center;" |  
| || || || || || 27\62 || 522.581 || 11 || 8 || 1.375 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 10\23
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" | 521.7
| style="text-align:center;" | 3 3 4
| style="text-align:center;" | 208.7
| style="text-align:center;" | 156.5
| style="text-align:center;" | 1.33
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || 17\39 || || 523.077 || 7 || 5 || 1.400 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 17\39
| |
| |  
| style="text-align:center;" | 523.1
| style="text-align:center;" | 5 5 7
| style="text-align:center;" | 215.4
| style="text-align:center;" | 153.8
| style="text-align:center;" | 1.40
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 24\55 || 523.636 || 10 || 7 || 1.428 ||
| style="text-align:center;" |  
| style="text-align:center;" | 7\16
| style="text-align:center;" |  
| style="text-align:center;" |  
| |
| |  
| style="text-align:center;" | 525.0
| style="text-align:center;" | 2 2 3
| style="text-align:center;" | 225.0
| style="text-align:center;" | 150.0
| style="text-align:center;" | 1.50
| style="text-align:center;" | Mavila in Armodue
 
Optimum rank range (L/s=3/2)
|-
|-
| |  
| || || 7\16 || || || || 525.000 || 3 || 2 || 1.500 || L/s = 3/2, mavila is in this region
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 526.3
| style="text-align:center;" | <span style="display: block; text-align: center;">2 2 pi</span>
| style="text-align:center;" | 231.5
| style="text-align:center;" | 147.4
| style="text-align:center;" | <span style="display: block; text-align: center;">pi/2</span>
| |
|-
|-
| style="text-align:center;" |  
| || || || || || 25\57 || 526.316 || 11 || 7 || 1.571 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 18\41
| |
| |
| style="text-align:center;" | 526.8
| style="text-align:center;" | 5 5 8
| style="text-align:center;" | 234.1
| style="text-align:center;" | 146.3
| style="text-align:center;" | 1.60
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 18\41 || || 526.829 || 8 || 5 || 1.600 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 1200*5/(13-phi)
| style="text-align:center;" | 1 1 phi
| style="text-align:center;" | 235.7
| style="text-align:center;" | 145.7
| style="text-align:center;" | phi
| style="text-align:center;" | Golden mavila
|-
|-
| |  
| || || || || || 29\66 || 527.273 || 13 || 8 || 1.625 || Golden mavila
| |  
| |  
| |  
| |
| | 29\66
| |
| style="text-align:center;" | 527.3
| style="text-align:center;" | 8 8 13
| style="text-align:center;" | 236.4
| style="text-align:center;" | 145.5
| style="text-align:center;" | 1.625
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || 11\25 || || || 528.000 || 5 || 3 || 1.667 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 11\25
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" | 528.0
| style="text-align:center;" | 3 3 5
| style="text-align:center;" | 240.0
| style="text-align:center;" | 144.0
| style="text-align:center;" | 1.67
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 26\59 || 528.814 || 12 || 7 || 1.714 ||  
| |  
| |  
| |  
| |  
| |  
| |
| style="text-align:center;" | 529.1
| style="text-align:center;" | <span style="background-color: #ffffff;"><span style="line-height: 1.5;">1 1 </span>√3 </span>
| style="text-align:center;" | 245.6
| style="text-align:center;" | 141.8
| style="text-align:center;" | <span style="background-color: #ffffff; display: block; text-align: center;">√3</span>
| |  
|-
|-
| style="text-align:center;" |  
| || || || || 15\34 || || 529.412 || 7 || 4 || 1.750 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 15\34
| |
| |  
| style="text-align:center;" | 529.4
| style="text-align:center;" | 4 4 7
| style="text-align:center;" | 247.1
| style="text-align:center;" | 141.2
| style="text-align:center;" | 1.75
| style="text-align:center;" | ...to somewhere around here
|-
|-
| style="text-align:center;" |  
| || || || || || 19\43 || 530.233 || 9 || 5 || 1.800 ||
| style="text-align:center;" | 4\9
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" | 533.3
| style="text-align:center;" | 1 1 2
| style="text-align:center;" | 266.7
| style="text-align:center;" | 133.3
| style="text-align:center;" | 2.00
| style="text-align:center;" | Boundary of propriety (generators
 
smaller than this are proper)
|-
|-
| style="text-align:center;" |  
| || 4\9 || || || || || 533.333 || 2 || 1 || 2.000 || Basic antidiatonic<br>(Generators smaller than this are proper)
| style="text-align:center;" |
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 13\29
| |  
| |  
| style="text-align:center;" | 537.9
| style="text-align:center;" | 3 3 7
| style="text-align:center;" | 289.7
| style="text-align:center;" | 124.1
| style="text-align:center;" | 2.33
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 17\38 || 536.842 || 9 || 4 || 2.250 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 9\20
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" | 540.0
| style="text-align:center;" | 2 2 5
| style="text-align:center;" | 300.0
| style="text-align:center;" | 120.0
| style="text-align:center;" | 2.50
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 13\29 || || 537.931 || 7 || 3 || 2.333 ||  
| |  
| |  
| |  
| |  
| |  
| |
| style="text-align:center;" | 541.4
| style="text-align:center;" | <span style="display: block; text-align: center;">1 1 phi+1</span>
| style="text-align:center;" | 306.9
| style="text-align:center;" | 117.2
| style="text-align:center;" | <span style="display: block; text-align: center;">1 1 phi+1</span>
| |  
|-
|-
| style="text-align:center;" |  
| || || || || || 22\49 || 538.776 || 12 || 5 || 2.400 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 14\31
| |  
| |
| style="text-align:center;" | 541.9
| style="text-align:center;" | 3 3 8
| style="text-align:center;" | 309.7
| style="text-align:center;" | 116.1
| style="text-align:center;" | 2.66
| style="text-align:center;" |  
|-
|-
| |  
| || || || 9\20 || || || 540.000 || 5 || 2 || 2.500 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 542<span style="line-height: 1.5;">.5</span>
| style="text-align:center;" | 1 1 e
| style="text-align:center;" | 321.55
| style="text-align:center;" | 115.0
| style="text-align:center;" | e
| style="text-align:center;" | L/s = e
|-
|-
| style="text-align:center;" |  
| || || || || || 23\51 || 541.176 || 13 || 5 || 2.600 || Unnamed golden tuning
| style="text-align:center;" |  
| style="text-align:center;" | 5\11
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" | 545.5
| style="text-align:center;" | 1 1 3
| style="text-align:center;" | 327.3
| style="text-align:center;" | 109.1
| style="text-align:center;" | 3.00
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || 14\31 || || 541.935 || 8 || 3 || 2.667 ||
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 546.8
| style="text-align:center;" | 1 1 pi
| style="text-align:center;" | 334.1
| style="text-align:center;" | 106.35
| style="text-align:center;" | pi
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
|-
| style="text-align:center;" |  
| || || || || || 19\42 || 542.857 || 11 || 4 || 2.750 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 11\24
| |  
| |  
| style="text-align:center;" | 550.0
| style="text-align:center;" | 2 2 7
| style="text-align:center;" | 350.0
| style="text-align:center;" | 100.0
| style="text-align:center;" | 3.50
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |
| || || 5\11 || || || || 545.455 || 3 || 1 || 3.000 || L/s = 3/1
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 6\13
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 553.8
| style="text-align:center;" | 1 1 4
| style="text-align:center;" | 369.2
| style="text-align:center;" | 92.3
| style="text-align:center;" | 4.00
| style="text-align:center;" | Thuja is optimal around here
 
L/s = 4
|-
|-
| style="text-align:center;" |  
| || || || || || 16\35 || 548.571 || 10 || 3 || 3.333 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 7\15
| |
| |
| style="text-align:center;" | 560.0
| style="text-align:center;" | 1 1 5
| style="text-align:center;" | 400.0
| style="text-align:center;" | 80.0
| style="text-align:center;" | 5.00
| style="text-align:center;" | ie. (11/8)^5 = 5/1
|-
|-
| style="text-align:center;" |  
| || || || || 11\24 || || 550.000 || 7 || 2 || 3.500 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" | 8\17
| style="text-align:center;" |  
| style="text-align:center;" | 564.7
| style="text-align:center;" | 1 1 6
| style="text-align:center;" | 423.5
| style="text-align:center;" | 70.6
| style="text-align:center;" | 6.00
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 17\37 || 551.351 || 11 || 3 || 3.667 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" | 9\19
| style="text-align:center;" | 568.4
| style="text-align:center;" | 1 1 7
| style="text-align:center;" | 442.1
| style="text-align:center;" | 63.2
| style="text-align:center;" | 7.00
| style="text-align:center;" | Liese/Triton is around here
|-
|-
| style="text-align:center;" | 1\2
| || || || 6\13 || || || 553.846 || 4 || 1 || 4.000 ||
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| || || || || || 13\28 || 557.143 || 9 || 2 || 4.500 ||
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| || || || || 7\15 || || 560.000 || 5 || 1 || 5.000 ||  
| |  
|-
| |  
| || || || || || 8\17 || 564.706 || 6 || 1 || 6.000 || Liese↓, triton↓
| style="text-align:center;" | 600.0
|-
| style="text-align:center;" | 0 0 1
| 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
| style="text-align:center;" | 600.0
| style="text-align:center;" | 0
| style="text-align:center;" | —
| style="text-align:center;" |  
|}
|}


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