7L 4s: Difference between revisions

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'''7L 4s''' or '''sixixoid''' has a generator of an augmented minor or diminished neutral third of 327.273 (3/11edo) to 342.857 (2/7edo) cents. Its harmonic entropy minimum, insofar as it may be said to have one, is improper (Amity/Hitchcock/Sixix) and also tonally awkward because its large and steps are extremely unequal (L>=4 s=1). However, it is still notable for representing 17:14 with tolerable accuracy for as much as that's worth.
'''7L 4s''' or '''sixixoid''' has a generator of an augmented minor or diminished neutral third of 327.273 (3/11edo) to 342.857 (2/7edo) cents. Its harmonic entropy minimum, insofar as it may be said to have one, is improper (Amity/Hitchcock/Sixix) and also tonally awkward because its large and steps are extremely unequal (L>=4 s=1). However, it is still notable for representing 17:14 with tolerable accuracy for as much as that's worth.


{| class="wikitable"
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
|-
| | 3/11
| 3\11 || || || || || || 327.273 || 1 || 1 || 1.000 ||
| |  
| |  
| |  
| |  
| | 327.273
|-
|-
| |  
| || || || || || 17\62 || 329.032 || 6 || 5 || 1.200 ||
| |  
| |  
| |  
| | 14/51
| | 329.412
|-
|-
| |  
| || || || || 14\51 || || 329.412 || 5 || 4 || 1.250 ||
| |  
| |  
| | 11/40
| |  
| | 330
|-
|-
| |  
| || || || || || 25\91 || 329.670 || 9 || 7 || 1.286 ||
| |  
| |  
| |  
| | 19/69
| | 330.435
|-
|-
| |  
| || || || 11\40 || || || 330.000 || 4 || 3 || 1.333 ||
| |  
| | 8/29
| |  
| |  
| | 331.0335
|-
|-
| |  
| || || || || || 30\109 || 330.275 || 11 || 8 || 1.375 ||
| |  
| |  
| |  
| |  
| | 331.425
|-
|-
| |  
| || || || || 19\69 || || 330.435 || 7 || 5 || 1.400 ||
| |  
| |  
| |  
| | 21/76
| | 331.579
|-
|-
| |  
| || || || || || 27\98 || 330.612 || 10 || 7 || 1.428 ||
| |  
| |  
| |  
| |  
| | 331.672
|-
|-
| |  
| || || 8\29 || || || || 331.034 || 3 || 2 || 1.500 || L/s = 3/2
| |  
| |  
| | 13/47
| |  
| | 331.915
|-
|-
| |  
| || || || || || 29\105 || 331.429 || 11 || 7 || 1.571 ||
| |  
| |  
| |  
| |  
| | 332.2255
|-
|-
| |  
| || || || || 21\76 || || 331.579 || 8 || 5 || 1.600 ||
| |  
| |  
| |  
| | 18/65
| | 332.308
|-
|-
| |  
| || || || || || 34\123 || 331.707 || 13 || 8 || 1.625 || Unnamed golden tuning
| | 5/18
| |  
| |  
| |  
| | 333.33
|-
|-
| |  
| || || || 13\47 || || || 331.915 || 5 || 3 || 1.667 ||
| |  
| |  
| |  
| | 17/61
| | 334.426
|-
|-
| |  
| || || || || || 31\112 || 332.143 || 12 || 7 || 1.714 ||
| |  
| |  
| | 12/43
| |  
| | 334.884
|-
|-
| |  
| || || || || 18\65 || || 332.308 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| |  
| | 335.179
|-
|-
| |  
| || || || || || 23\83 || 332.530 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| | 19/68
| | 335.294
|-
|-
| |  
| || 5\18 || || || || || 333.333 || 2 || 1 || 2.000 || Basic sixixoid<br>(Generators smaller than this are proper)
| |  
| |  
| |  
| |  
| | 335.413
|-
|-
| |  
| || || || || || 22\79 || 334.177 || 9 || 4 || 2.250 ||
| |  
| | 7/25
| |  
| |  
| | 336
|-
|-
| |  
| || || || || 17\61 || || 334.426 || 7 || 3 || 2.333 ||
| |  
| |  
| |  
| |  
| | 336.2615
|-
|-
| |  
| || || || || || 29\104 || 334.615 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| | 16/57
| | 336.842
|-
|-
| |  
| || || || 12\43 || || || 334.884 || 5 || 2 || 2.500 ||
| |  
| |  
| | 9/32
| |  
| | 337.5
|-
|-
| |  
| || || || || || 31\111 || 335.135 || 13 || 5 || 2.600 || Unnamed golden tuning
| |  
| |  
| |  
| | 11/39
| | 338.4615
|-
|-
| | 2/7
| || || || || 19\68 || || 335.294 || 8 || 3 || 2.667 ||
| |  
|-
| |  
| || || || || || 26\93 || 335.484 || 11 || 4 || 2.750 ||
| |  
|-
| |  
| || || 7\25 || || || || 336.000 || 3 || 1 || 3.000 || L/s = 3/1
| | 342.857
|-
| || || || || || 23\82 || 336.585 || 10 || 3 || 3.333 ||
|-
| || || || || 16\57 || || 336.842 || 7 || 2 || 3.500 ||
|-
| || || || || || 25\89 || 337.079 || 11 || 3 || 3.667 ||
|-
| || || || 9\32 || || || 337.500 || 4 || 1 || 4.000 || Sixix
|-
| || || || || || 20\71 || 338.028 || 9 || 2 || 4.500 ||
|-
| || || || || 11\39 || || 338.462 || 5 || 1 || 5.000 ||
|-
| || || || || || 13\46 || 339.130 || 6 || 1 || 6.000 || Amity/hitchcock↓
|-
| 2\7 || || || || || || 342.857 || 1 || 0 || → inf ||
|}
|}


[[Category:Scales]]
[[Category:Scales]]
[[Category:MOS scales]]
[[Category:MOS scales]]
[[Category:11-tone scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Revision as of 09:32, 12 April 2021

↖ 6L 3s ↑ 7L 3s 8L 3s ↗
← 6L 4s 7L 4s 8L 4s →
↙ 6L 5s ↓ 7L 5s 8L 5s ↘ 
┌╥╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLs
sLsLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\11 to 2\7 (327.3 ¢ to 342.9 ¢)
Dark 5\7 to 8\11 (857.1 ¢ to 872.7 ¢)
TAMNAMS information
Related to 4L 3s (smitonic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 4L 3s
Sister 4L 7s
Daughters 11L 7s, 7L 11s
Neutralized 3L 8s
2-Flought 18L 4s, 7L 15s
Equal tunings
Equalized (L:s = 1:1) 3\11 (327.3 ¢)
Supersoft (L:s = 4:3) 11\40 (330.0 ¢)
Soft (L:s = 3:2) 8\29 (331.0 ¢)
Semisoft (L:s = 5:3) 13\47 (331.9 ¢)
Basic (L:s = 2:1) 5\18 (333.3 ¢)
Semihard (L:s = 5:2) 12\43 (334.9 ¢)
Hard (L:s = 3:1) 7\25 (336.0 ¢)
Superhard (L:s = 4:1) 9\32 (337.5 ¢)
Collapsed (L:s = 1:0) 2\7 (342.9 ¢)

7L 4s or sixixoid has a generator of an augmented minor or diminished neutral third of 327.273 (3/11edo) to 342.857 (2/7edo) cents. Its harmonic entropy minimum, insofar as it may be said to have one, is improper (Amity/Hitchcock/Sixix) and also tonally awkward because its large and steps are extremely unequal (L>=4 s=1). However, it is still notable for representing 17:14 with tolerable accuracy for as much as that's worth.

Scale tree

Generator Cents L s L/s Comments
3\11 327.273 1 1 1.000
17\62 329.032 6 5 1.200
14\51 329.412 5 4 1.250
25\91 329.670 9 7 1.286
11\40 330.000 4 3 1.333
30\109 330.275 11 8 1.375
19\69 330.435 7 5 1.400
27\98 330.612 10 7 1.428
8\29 331.034 3 2 1.500 L/s = 3/2
29\105 331.429 11 7 1.571
21\76 331.579 8 5 1.600
34\123 331.707 13 8 1.625 Unnamed golden tuning
13\47 331.915 5 3 1.667
31\112 332.143 12 7 1.714
18\65 332.308 7 4 1.750
23\83 332.530 9 5 1.800
5\18 333.333 2 1 2.000 Basic sixixoid
(Generators smaller than this are proper)
22\79 334.177 9 4 2.250
17\61 334.426 7 3 2.333
29\104 334.615 12 5 2.400
12\43 334.884 5 2 2.500
31\111 335.135 13 5 2.600 Unnamed golden tuning
19\68 335.294 8 3 2.667
26\93 335.484 11 4 2.750
7\25 336.000 3 1 3.000 L/s = 3/1
23\82 336.585 10 3 3.333
16\57 336.842 7 2 3.500
25\89 337.079 11 3 3.667
9\32 337.500 4 1 4.000 Sixix
20\71 338.028 9 2 4.500
11\39 338.462 5 1 5.000
13\46 339.130 6 1 6.000 Amity/hitchcock↓
2\7 342.857 1 0 → inf
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