6L 4s: Difference between revisions

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Line 5: Line 5:
| Equalized = 2
| Equalized = 2
| Paucitonic = 1
| Paucitonic = 1
| Pattern = sLsLLsLsLL
| Pattern = LsLsLLsLsL
| Name = dipentic
| Name = dipentic
}}
}}


'''6L 4s''' is a [[MOSScales|MOS]] pattern with 6 large steps and 4 small steps. Good temperaments include [[antikythera|antikythera]], [[Lemba|lemba]], and [[Echidnic|echidnic]].
'''6L 4s''' is a [[MOS]] pattern with 6 large steps and 4 small steps. Good temperaments include [[antikythera]], [[lemba]], and [[echidnic]].


== Scale tree ==
== Scale tree ==
 
{| class="wikitable center-all"
{| class="wikitable"
! colspan="6" rowspan="2" | Generator
! colspan="2" | Cents
! rowspan="2" | L
! rowspan="2" | s
! rowspan="2" | L/s
! rowspan="2" | Comments
|-
! Chroma-positive
! Chroma-negative
|-
| 3\10 || || || || || || 360.000 || 240.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 17\56 || 364.286 || 235.714 || 6 || 5 || 1.200 ||
|-
| || || || || 14\46 || || 365.217 || 234.783 || 5 || 4 || 1.250 || Echidnic
|-
| || || || || || 25\82 || 365.854 || 234.146 || 9 || 7 || 1.286 ||
|-
| || || || 11\36 || || || 366.667 || 233.333 || 4 || 3 || 1.333 || Baladic
|-
| || || || || || 30\98 || 367.347 || 232.653 || 11 || 8 || 1.375 ||
|-
| || || || || 19\62 || || 367.742 || 232.258 || 7 || 5 || 1.400 ||
|-
| || || || || || 27\88 || 368.182 || 231.818 || 10 || 7 || 1.428 ||
|-
| || || 8\26 || || || || 369.231 || 230.769 || 3 || 2 || 1.500 || L/s = 3/2, lemba
|-
| || || || || || 29\94 || 370.213 || 229.787 || 11 || 7 || 1.571 ||
|-
| || || || || 21\68 || || 370.588 || 229.412 || 8 || 5 || 1.600 ||
|-
| || || || || || 34\110 || 370.909 || 229.091 || 13 || 8 || 1.625 || Unnamed golden tuning
|-
| || || || 13\42 || || || 371.429 || 228.571 || 5 || 3 || 1.667 ||
|-
|-
! colspan="5" | Generator
| || || || || || 31\100 || 372.000 || 228.000 || 12 || 7 || 1.714 ||
! | Cents
! | Comments
|-
|-
| | 1\6
| || || || || 18\58 || || 372.414 || 227.586 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| |  
| | 200
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 23\74 || 372.973 || 227.027 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| | 6\34
| | 211.765
| style="text-align:center;" |  
|-
|-
| |  
| || 5\16 || || || || || 375.000 || 225.000 || 2 || 1 || 2.000 || Basic dipentic<br>(Generators smaller than this are proper)
| |  
| |  
| | 5\28
| |  
| | 214.29
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 22\70 || 377.143 || 222.857 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| |  
| | 217.51
| style="text-align:center;" | L/s = pi
|-
|-
| |  
| || || || || 17\54 || || 377.778 || 222.222 || 7 || 3 || 2.333 ||  
| |  
| | 4\22
| |  
| |  
| | 218.18
| style="text-align:center;" | Antikythera is around here
|-
|-
| |  
| || || || || || 29\92 || 378.261 || 221.739 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| |  
| | 219.695
| style="text-align:center;" | L/s = e
|-
|-
| |  
| || || || 12\38 || || || 378.947 || 221.053 || 5 || 2 || 2.500 ||  
| |  
| |  
| |  
| | 11\60
| | 220
| |  
|-
|-
| |  
| || || || || || 31\98 || 379.592 || 220.408 || 13 || 5 || 2.600 || Unnamed golden tuning
| |  
| |  
| |  
| |  
| | 220.3
| |  
|-
|-
| |  
| || || || || 19\60 || || 380.000 || 220.000 || 8 || 3 || 2.667 || Divination
| |  
| |  
| | 7\38
| |  
| | 221.05
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 26\82 || 380.488 || 219.512 || 11 || 4 || 2.750 || Soothsaying
| | 3\16
| |  
| |  
| |  
| | 225
| style="text-align:center;" | Boundary of propriety (generators larger than this are proper)
|-
|-
| |  
| || || 7\22 || || || || 381.818 || 218.182 || 3 || 1 || 3.000 || L/s = 3/1, antikythera/astrology
| |  
| |  
| |  
| |  
| | 227.79
| |  
|-
|-
| |  
| || || || || || 23\72 || 383.333 || 216.667 || 10 || 3 || 3.333 || Wizard
| |  
| |  
| | 8\42
| |  
| | 228.57
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 16\50 || || 384.000 || 216.000 || 7 || 2 || 3.500 ||  
| |  
| |  
| |  
| |  
| | 229.18
| style="text-align:center;" | L/s = Φ
|-
|-
| |  
| || || || || || 25\78 || 384.615 || 215.385 || 11 || 3 || 3.667 ||  
| |  
| |  
| |  
| | 13\68
| | 229.48
| |  
|-
|-
| |  
| || || || 9\28 || || || 385.714 || 214.286 || 4 || 1 || 4.000 ||
| |  
| |  
| |  
| |  
| | 229.6
| |  
|-
|-
| |  
| || || || || || 20\62 || 387.097 || 212.903 || 9 || 2 || 4.500 ||  
| |  
| | 5\26
| |  
| |  
| | 230.77
| style="text-align:center;" | Lemba is around here
|-
|-
| |  
| || || || || 11\34 || || 388.235 || 211.765 || 5 || 1 || 5.000 ||  
| |  
| |  
| | 7\36
| |  
| | 233.33
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 13\40 || 390.000 || 210.000 || 6 || 1 || 6.000 ||  
| |  
| |  
| |  
| | 9\46
| | 234.78
| style="text-align:center;" | Echidnic is around here
|-
|-
| | 2\10
| 2\6 || || || || || || 400.000 || 200.000 || 1 || 0 || → inf ||
| |  
| |  
| |  
| |  
| | 240
| style="text-align:center;" |  
|}
|}


{{todo|cleanup <!-- table styling -->}}
[[Category:Scales]]
 
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:Dipentic]]

Revision as of 18:55, 14 October 2021

↖ 5L 3s ↑ 6L 3s 7L 3s ↗
← 5L 4s 6L 4s 7L 4s →
↙ 5L 5s ↓ 6L 5s 7L 5s ↘
Scale structure
Step pattern LLsLsLLsLs
sLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 3\10 to 2\6 (360.0 ¢ to 400.0 ¢)
Dark 1\6 to 2\10 (200.0 ¢ to 240.0 ¢)
TAMNAMS information
Name lemon
Prefix lem-
Abbrev. le
Related MOS scales
Parent 4L 2s
Sister 4L 6s
Daughters 10L 6s, 6L 10s
Neutralized 2L 8s
2-Flought 16L 4s, 6L 14s
Equal tunings
Equalized (L:s = 1:1) 3\10 (360.0 ¢)
Supersoft (L:s = 4:3) 11\36 (366.7 ¢)
Soft (L:s = 3:2) 8\26 (369.2 ¢)
Semisoft (L:s = 5:3) 13\42 (371.4 ¢)
Basic (L:s = 2:1) 5\16 (375.0 ¢)
Semihard (L:s = 5:2) 12\38 (378.9 ¢)
Hard (L:s = 3:1) 7\22 (381.8 ¢)
Superhard (L:s = 4:1) 9\28 (385.7 ¢)
Collapsed (L:s = 1:0) 2\6 (400.0 ¢)
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6L 4s is a MOS pattern with 6 large steps and 4 small steps. Good temperaments include antikythera, lemba, and echidnic.

Scale tree

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
3\10 360.000 240.000 1 1 1.000
17\56 364.286 235.714 6 5 1.200
14\46 365.217 234.783 5 4 1.250 Echidnic
25\82 365.854 234.146 9 7 1.286
11\36 366.667 233.333 4 3 1.333 Baladic
30\98 367.347 232.653 11 8 1.375
19\62 367.742 232.258 7 5 1.400
27\88 368.182 231.818 10 7 1.428
8\26 369.231 230.769 3 2 1.500 L/s = 3/2, lemba
29\94 370.213 229.787 11 7 1.571
21\68 370.588 229.412 8 5 1.600
34\110 370.909 229.091 13 8 1.625 Unnamed golden tuning
13\42 371.429 228.571 5 3 1.667
31\100 372.000 228.000 12 7 1.714
18\58 372.414 227.586 7 4 1.750
23\74 372.973 227.027 9 5 1.800
5\16 375.000 225.000 2 1 2.000 Basic dipentic
(Generators smaller than this are proper)
22\70 377.143 222.857 9 4 2.250
17\54 377.778 222.222 7 3 2.333
29\92 378.261 221.739 12 5 2.400
12\38 378.947 221.053 5 2 2.500
31\98 379.592 220.408 13 5 2.600 Unnamed golden tuning
19\60 380.000 220.000 8 3 2.667 Divination
26\82 380.488 219.512 11 4 2.750 Soothsaying
7\22 381.818 218.182 3 1 3.000 L/s = 3/1, antikythera/astrology
23\72 383.333 216.667 10 3 3.333 Wizard
16\50 384.000 216.000 7 2 3.500
25\78 384.615 215.385 11 3 3.667
9\28 385.714 214.286 4 1 4.000
20\62 387.097 212.903 9 2 4.500
11\34 388.235 211.765 5 1 5.000
13\40 390.000 210.000 6 1 6.000
2\6 400.000 200.000 1 0 → inf
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