7L 1s: Difference between revisions

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! colspan="6" | [[generator|Generator]]
! colspan="6" | [[generator|Generator]]
! |[[Cent]]s
! |[[Cent]]s
!Remainder
! |Scale in [[EDO|EDO]] steps
! |Scale in [[EDO|EDO]] steps
! |Comments
! |Comments
Line 27: Line 28:
| |  
| |  
| | 171.43
| | 171.43
|0.00
| style="text-align:center;" |1 1 1 1 1 1 1 0
| style="text-align:center;" |1 1 1 1 1 1 1 0
| style="text-align:center;" |
| style="text-align:center;" |
Line 37: Line 39:
|6\43
|6\43
|167.44
|167.44
|27.91
| style="text-align:center;" |6 6 6 6 6 6 6 1
| style="text-align:center;" |6 6 6 6 6 6 6 1
|
|
Line 47: Line 50:
|
|
|166.67
|166.67
|33.32
| style="text-align:center;" |5 5 5 5 5 5 5 1
| style="text-align:center;" |5 5 5 5 5 5 5 1
|
|
Line 57: Line 61:
| |  
| |  
| |165.52
| |165.52
|41.38
| style="text-align:center;" |4 4 4 4 4 4 4 1
| style="text-align:center;" |4 4 4 4 4 4 4 1
| style="text-align:center;" |L/s = 4
| style="text-align:center;" |L/s = 4
Line 67: Line 72:
| |  
| |  
| |163.97
| |163.97
|52.19
| style="text-align:center;" |π π π π π π π 1
| style="text-align:center;" |π π π π π π π 1
| style="text-align:center;" |<span style="display: block; text-align: center;">L/s = π</span>
| style="text-align:center;" |<span style="display: block; text-align: center;">L/s = π</span>
Line 77: Line 83:
| |  
| |  
| |163.64
| |163.64
|54.55
| style="text-align:center;" |3 3 3 3 3 3 3 1
| style="text-align:center;" |3 3 3 3 3 3 3 1
| style="text-align:center;" |L/s = 3
| style="text-align:center;" |L/s = 3
Line 87: Line 94:
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |162.87
| style="text-align:center;" |162.87
|59.92
| style="text-align:center;" | e e e e e e e e 1
| style="text-align:center;" | e e e e e e e e 1
| style="text-align:center;" |<span style="display: block; text-align: center;">L/s = e</span>
| style="text-align:center;" |<span style="display: block; text-align: center;">L/s = e</span>
Line 96: Line 104:
| |8\59
| |8\59
| |
| |
| |162,71
| |162.71
|61.02
| style="text-align:center;" |<span style="display: block; text-align: center;">8 8 8 8 8 8 8 3</span>
| style="text-align:center;" |<span style="display: block; text-align: center;">8 8 8 8 8 8 8 3</span>
| |
| |
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| |13\96
| |13\96
| |162.5
| |162.5
| style="text-align:center;" |<span style="display: block; text-align: center;">13 13 13 13 13 13 13 5</span>
|62.5
| style="text-align:center;" |<span style="display: block; text-align: center;">[[Tel:13 13 13 13 13 13 13|13 13 13 13 13 13 13]] 5</span>
| |  
| |  
|-
|-
Line 117: Line 127:
| |
| |
| |162.16
| |162.16
|64.86
| style="text-align:center;" |5 5 5 5 5 5 5 2
| style="text-align:center;" |5 5 5 5 5 5 5 2
| style="text-align:center;" |Porcupine is in this general region
| style="text-align:center;" |Porcupine is in this general region
Line 127: Line 138:
| |
| |
| |161.54
| |161.54
|69.23
| style="text-align:center;" | 7 7 7 7 7 7 7 3
| style="text-align:center;" | 7 7 7 7 7 7 7 3
| style="text-align:center;" |
| style="text-align:center;" |
Line 137: Line 149:
| |
| |
| |160
| |160
|80
| style="text-align:center;" |2 2 2 2 2 2 2 1
| style="text-align:center;" |2 2 2 2 2 2 2 1
| style="text-align:center;" |Optimum rank range (L/s=2/1) porcupine
| style="text-align:center;" |Optimum rank range (L/s=2/1) porcupine
Line 147: Line 160:
| |
| |
| | 158.37
| | 158.37
|91.43
| style="text-align:center;" |<span style="background-color: #ffffff;">√3 √3 √3 √3 √3 √3 √3 1</span>
| style="text-align:center;" |<span style="background-color: #ffffff;">√3 √3 √3 √3 √3 √3 √3 1</span>
| |  
| |  
Line 157: Line 171:
| |
| |
| |157.89
| |157.89
|94.73
| style="text-align:center;" |5 5 5 5 5 5 5 3
| style="text-align:center;" |5 5 5 5 5 5 5 3
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 167: Line 182:
| |13\99
| |13\99
| |157.58
| |157.58
| style="text-align:center;" |13 13 13 13 13 13 13 8
|96.97
| style="text-align:center;" |[[Tel:13 13 13 13 13 13 13|13 13 13 13 13 13 13]] 8
| style="text-align:center;" |Golden porcupine / golden hemikleismic
| style="text-align:center;" |Golden porcupine / golden hemikleismic
|-
|-
Line 177: Line 193:
| |  
| |  
| | 157.38
| | 157.38
|98.36
| style="text-align:center;" |8 8 8 8 8 8 8 5
| style="text-align:center;" |8 8 8 8 8 8 8 5
| style="text-align:center;" |
| style="text-align:center;" |
Line 186: Line 203:
| |
| |
| |(11\84)
| |(11\84)
| |157.14)
| |(157.14)
| style="text-align:center;" |<span style="display: block; text-align: center;">11 11 11 11 11 11 11 7 </span><span style="display: block; text-align: center;">π π π π π π π 2</span>
|(100)
| style="text-align:center;" |<span style="display: block; text-align: center;">[[Tel:11 11 11 11 11 11 11|11 11 11 11 11 11 11]] 7 </span><span style="display: block; text-align: center;">π π π π π π π 2</span>
| |
| |
|-
|-
Line 197: Line 215:
| |  
| |  
| |156.52
| |156.52
|104.348
| style="text-align:center;" |3 3 3 3 3 3 3 2
| style="text-align:center;" |3 3 3 3 3 3 3 2
| style="text-align:center;" |
| style="text-align:center;" |
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| | 10\77
| | 10\77
| | 155.84
| | 155.84
| style="text-align:center;" |10 10 10 10 10 10 10 7
|109.09
| style="text-align:center;" |[[Tel:10 10 10 10 10 10 10|10 10 10 10 10 10 10]] 7
| style="text-align:center;" |Greeley is around here
| style="text-align:center;" |Greeley is around here
|-
|-
Line 217: Line 237:
| |
| |
| | 155.56
| | 155.56
|111.11
| style="text-align:center;" |7 7 7 7 7 7 7 5
| style="text-align:center;" |7 7 7 7 7 7 7 5
| style="text-align:center;" |
| style="text-align:center;" |
Line 227: Line 248:
| |  
| |  
| |154.84
| |154.84
|116.13
| style="text-align:center;" |4 4 4 4 4 4 4 3
| style="text-align:center;" |4 4 4 4 4 4 4 3
| style="text-align:center;" |
| style="text-align:center;" |
Line 237: Line 259:
|
|
|153.85
|153.85
|123.08
| style="text-align:center;" |5 5 5 5 5 5 5 4
| style="text-align:center;" |5 5 5 5 5 5 5 4
|
|
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|6\47
|6\47
|153.19
|153.19
|127.66
| style="text-align:center;" |6 6 6 6 6 6 6 5
| style="text-align:center;" |6 6 6 6 6 6 6 5
|
|
Line 257: Line 281:
| |
| |
| |150
| |150
|150
| style="text-align:center;" |1 1 1 1 1 1 1 1
| style="text-align:center;" |1 1 1 1 1 1 1 1
| style="text-align:center;" |
| style="text-align:center;" |
|}
|}

Revision as of 15:29, 23 August 2022

← 6L 1s 7L 1s 8L 1s →
↙ 6L 2s ↓ 7L 2s 8L 2s ↘
Scale structure
Step pattern LLLLLLLs
sLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\8 to 1\7 (150.0 ¢ to 171.4 ¢)
Dark 6\7 to 7\8 (1028.6 ¢ to 1050.0 ¢)
TAMNAMS information
Name pine
Prefix pine-
Abbrev. p
Related MOS scales
Parent 1L 6s
Sister 1L 7s
Daughters 8L 7s, 7L 8s
Neutralized 6L 2s
2-Flought 15L 1s, 7L 9s
Equal tunings
Equalized (L:s = 1:1) 1\8 (150.0 ¢)
Supersoft (L:s = 4:3) 4\31 (154.8 ¢)
Soft (L:s = 3:2) 3\23 (156.5 ¢)
Semisoft (L:s = 5:3) 5\38 (157.9 ¢)
Basic (L:s = 2:1) 2\15 (160.0 ¢)
Semihard (L:s = 5:2) 5\37 (162.2 ¢)
Hard (L:s = 3:1) 3\22 (163.6 ¢)
Superhard (L:s = 4:1) 4\29 (165.5 ¢)
Collapsed (L:s = 1:0) 1\7 (171.4 ¢)
View • Talk • Edit

There are two notable harmonic entropy minima with this MOS pattern. The first is porcupine, in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is greeley, in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.

Scales of this form are always proper, because there is only one small step.

Generator Cents Remainder Scale in EDO steps Comments
1\7 171.43 0.00 1 1 1 1 1 1 1 0
6\43 167.44 27.91 6 6 6 6 6 6 6 1
5\36 166.67 33.32 5 5 5 5 5 5 5 1
4\29 165.52 41.38 4 4 4 4 4 4 4 1 L/s = 4
163.97 52.19 π π π π π π π 1 L/s = π
3\22 163.64 54.55 3 3 3 3 3 3 3 1 L/s = 3
162.87 59.92 e e e e e e e e 1 L/s = e
8\59 162.71 61.02 8 8 8 8 8 8 8 3
13\96 162.5 62.5 [13 13 13 13 13 13|13 13 13 13 13 13 13] 5
5\37 162.16 64.86 5 5 5 5 5 5 5 2 Porcupine is in this general region
7\52 161.54 69.23 7 7 7 7 7 7 7 3
2\15 160 80 2 2 2 2 2 2 2 1 Optimum rank range (L/s=2/1) porcupine
158.37 91.43 √3 √3 √3 √3 √3 √3 √3 1
5\38 157.89 94.73 5 5 5 5 5 5 5 3
13\99 157.58 96.97 [13 13 13 13 13 13|13 13 13 13 13 13 13] 8 Golden porcupine / golden hemikleismic
8\61 157.38 98.36 8 8 8 8 8 8 8 5
(11\84) (157.14) (100) [11 11 11 11 11 11|11 11 11 11 11 11 11] 7 π π π π π π π 2
3\23 156.52 104.348 3 3 3 3 3 3 3 2
10\77 155.84 109.09 [10 10 10 10 10 10|10 10 10 10 10 10 10] 7 Greeley is around here
7\54 155.56 111.11 7 7 7 7 7 7 7 5
4\31 154.84 116.13 4 4 4 4 4 4 4 3
5\39 153.85 123.08 5 5 5 5 5 5 5 4
6\47 153.19 127.66 6 6 6 6 6 6 6 5
1\8 150 150 1 1 1 1 1 1 1 1
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