4L 3s: Difference between revisions

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4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of [[4edo|4edo]], 300¢) to 2\7edo (two degrees of [[7edo|7edo]], or approx. 342.857¢). The spectrum looks like this:
4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of [[4edo]], 300¢) to 2\7edo (two degrees of [[7edo]], or approx. 342.857¢). The spectrum looks like this:


{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="7" | Generator
! colspan="8" | Generator
! | Tetrachord
! | Tetrachord
! | g in cents
! | g in cents
Line 12: Line 12:
|-
|-
| | 1\4
| | 1\4
| |
| |  
| |  
| |  
| |  
Line 32: Line 33:
| |  
| |  
| | 8\31
| | 8\31
| |
| | 7 1 7
| | 7 1 7
| | 309.677
| | 309.677
Line 37: Line 39:
| | 929.023
| | 929.023
| | 38.71
| | 38.71
| style="text-align:center;" | Myna is around here
| style="text-align:center;" | [[Myna]] is around here
|-
|-
| |  
| |  
Line 45: Line 47:
| |  
| |  
| | 7\27
| | 7\27
| |
| |  
| |  
| | 6 1 6
| | 6 1 6
Line 58: Line 61:
| |  
| |  
| | 6\23
| | 6\23
| |
| |  
| |  
| |  
| |  
Line 71: Line 75:
| |  
| |  
| | 5\19
| | 5\19
| |
| |  
| |  
| |  
| |  
Line 86: Line 91:
| |  
| |  
| | 9\34
| | 9\34
| |
| |  
| |  
| |  
| |  
Line 93: Line 99:
| | 951.941
| | 951.941
| | 70.588
| | 70.588
| style="text-align:center;" | Hanson/Keemun is around here
| style="text-align:center;" | [[Hanson]]/Keemun is around here
|-
|-
| |
| |  
| |  
| |  
| |  
Line 112: Line 119:
| |  
| |  
| | 4\15
| | 4\15
| |
| |  
| |  
| |  
| |  
Line 123: Line 131:
| style="text-align:center;" | L/s = 3
| style="text-align:center;" | L/s = 3
|-
|-
| |
| |  
| |  
| |  
| |  
Line 142: Line 151:
| |  
| |  
| | 11\41
| | 11\41
| |
| |  
| |  
| |  
| |  
Line 158: Line 168:
| |  
| |  
| | 29\108
| | 29\108
| |
| | 21 8 21
| | 21 8 21
| | 322.222
| | 322.222
Line 171: Line 182:
| |  
| |  
| | 18\67
| | 18\67
| |
| |  
| |  
| | 13 5 13
| | 13 5 13
Line 183: Line 195:
| |  
| |  
| | 7\26
| | 7\26
| |
| |  
| |  
| |  
| |  
Line 195: Line 208:
| |  
| |  
| | 3\11
| | 3\11
| |
| |  
| |  
| |  
| |  
Line 205: Line 219:
| | 981.818
| | 981.818
| | 109.091
| | 109.091
| style="text-align:center;" | Boundary of propriety (generators
| style="text-align:center;" | Boundary of propriety (generators <br>larger than this are proper)
 
larger than this are proper)
|-
|-
| |  
| |  
Line 216: Line 228:
| |  
| |  
| |  
| |  
| | <span style="background-color: #ffffff;">√3 1 √3</span>
| |
| | <span style="background-color: #f5f5f5;">√3 1 √3</span>
| | 330.217
| | 330.217
| | 660.434
| | 660.434
Line 227: Line 240:
| |  
| |  
| | 8\29
| | 8\29
| |
| |  
| |  
| |  
| |  
Line 243: Line 257:
| |  
| |  
| | 21\76
| | 21\76
| |
| |  
| |  
| | 13 8 13
| | 13 8 13
Line 251: Line 266:
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |  
| |  
| |  
| |  
Line 270: Line 286:
| |  
| |  
| | 13\47
| | 13\47
| |
| |  
| |  
| |  
| |  
Line 279: Line 296:
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |
| |  
| |  
| |  
| |  
Line 296: Line 314:
| |  
| |  
| | 5\18
| | 5\18
| |
| |  
| |  
| |  
| |  
Line 311: Line 330:
| |  
| |  
| | 7\25
| | 7\25
| |
| |  
| |  
| |  
| |  
Line 326: Line 346:
| |  
| |  
| | 9\32
| | 9\32
| |
| |  
| |  
| |  
| |  
Line 341: Line 362:
| |  
| |  
| | 11\39
| | 11\39
| |
| |  
| |  
| | 6 5 6
| | 6 5 6
Line 356: Line 378:
| |  
| |  
| | 13\46
| | 13\46
| |
| | 7 6 7
| | 7 6 7
| | 339.130
| | 339.130
Line 362: Line 385:
| | 156.522
| | 156.522
| style="text-align:center;" | (17/14)^3=9/5
| style="text-align:center;" | (17/14)^3=9/5
|-
| |
| |
| |
| |
| |
| |
| |
| | 15\53
| | 8 7 8
| | 339.623
| | 679.245
| | 1018.868
| | 158.491
| style="text-align:center;" | [[Amity]] is around here
|-
|-
| | 2\7
| | 2\7
| |
| |  
| |  
| |  
| |  

Revision as of 09:30, 31 May 2019

4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 2\7edo (two degrees of 7edo, or approx. 342.857¢). The spectrum looks like this:

Generator Tetrachord g in cents 2g 3g 4g Comments
1\4 1 0 1 300.000 600.000 900.000 0.000
8\31 7 1 7 309.677 619.355 929.023 38.71 Myna is around here
7\27 6 1 6 311.111 622.222 933.333 44.444
6\23 5 1 5 313.043 626.087 939.13 52.174
5\19 4 1 4 315.789 631.579 947.368 63.158 L/s = 4
9\34 7 2 7 317.647 634.294 951.941 70.588 Hanson/Keemun is around here
pi 1 pi 319.272 638.545 957.817 77.089 L/s = pi
4\15 3 1 3 320.000 640.000 960.000 80.000 L/s = 3
e 1 e 321.6245 641.249 964.874 86.498 L/s = e
11\41 8 3 8 321.951 643.902 965.854 87.805
29\108 21 8 21 322.222 644.444 966.667 88.889
18\67 13 5 13 322.388 644.776 967.364 89.522
7\26 5 2 5 323.077 646.154 969.231 92.308 Orgone is around here
3\11 2 1 2 327.273 654.545 981.818 109.091 Boundary of propriety (generators
larger than this are proper)
√3 1 √3 330.217 660.434 990.651 120.868
8\29 5 3 5 331.034 662.069 993.013 124.138
21\76 13 8 13 331.579 663.158 994.739 126.316
34\123 21 13 21 331.707 663.415 995.122 126.829 Unnamed golden temperament
13\47 8 5 8 331.915 663.83 995.745 127.66
pi 2 pi 332.3165 664.633 996.9495 129.266
5\18 3 2 3 333.333 666.667 1000.000 133.333 Optimum rank range (L/s=3/2)
7\25 4 3 4 336.000 672.000 1008.000 144.000
9\32 5 4 5 337.5 675 1012.5 150 Sixix
11\39 6 5 6 338.462 676.923 1015.385 153.846 Sixix
13\46 7 6 7 339.130 678.261 1017.391 156.522 (17/14)^3=9/5
15\53 8 7 8 339.623 679.245 1018.868 158.491 Amity is around here
2\7 1 1 1 342.857 685.714 1028.571 171.429

There are two notable harmonic entropy minima: hanson/keemun, in which the generator is 6/5 and 6 of them make a 3/1, and myna, in which the generator is also 6/5 but now 10 of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).

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