1L 7s: Difference between revisions

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This MOS pattern is somewhat of a wasteland as far as low-harmonic-entropy scales are concerned. However, there is one interesting no-5's scale, [[Chromatic_pairs#Bleu|bleu]]. In this scale, 5 steps make a 3/2, and the chord 11:12:13:14 is represented as three equal steps.
{{Infobox MOS
| Periods = 1
| nLargeSteps = 1
| nSmallSteps = 7
| Equalized = 7
| Paucitonic = 1
| Pattern = Lsssssss
}}


{| class="wikitable"
'''1L 7s''' is the MOS pattern Lsssssss with small steps ranging from 0\1 (0¢) to 1\8 (one step of [[8edo]] = 150¢).
 
This MOS pattern is somewhat of a wasteland as far as low-harmonic-entropy scales are concerned. However, there is one interesting no-5's scale, [[Chromatic_pairs #Bleu|bleu]]. In this scale, 5 steps make a 3/2, and the chord 11:12:13:14 is represented as three equal steps.
 
== Modes ==
* 7|0 Lsssssss
* 6|1 sLssssss
* 5|2 ssLsssss
* 4|3 sssLssss
* 3|4 ssssLsss
* 2|5 sssssLss
* 1|6 ssssssLs
* 0|7 sssssssL
 
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 1050 cents (7\8) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 150 cents (1\8)
 
{| class="wikitable center-all"
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
! Cents
! L
! s
! L/s
! Comments
|-
| 1\8 || || || || || || 150.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\41 || 146.341 || 6 || 5 || 1.200 || [[Bohpier]]
|-
| || || || || 4\33 || || 145.455 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\58 || 144.828 || 9 || 7 || 1.286 ||
|-
| || || || 3\25 || || || 144.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\67 || 143.284 || 11 || 8 || 1.375 ||
|-
|-
! colspan="7" | Generator
| || || || || 5\42 || || 142.857 || 7 || 5 || 1.400 ||  
! | Cents
! | Comments
|-
|-
| | 0\1
| || || || || || 7\59 || 142.373 || 10 || 7 || 1.429 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
|
| || || 2\17 || || || || 141.176 || 3 || 2 || 1.500 ||  
|
|
|
|
|
|1\14
|85.71
|
|-
|-
|
| || || || || || 7\60 || 140.000 || 11 || 7 || 1.571 || [[Bleu]]
|
|
|
|
|1\13
|
|92.31
|
|-
|-
|
| || || || || 5\43 || || 139.535 || 8 || 5 || 1.600 || [[Jerome]]/bleu
|
|
|
|1\12
|
|
|100
|
|-
|-
| |  
| || || || || || 8\69 || 139.130 || 13 || 8 || 1.625 || Golden jerome (139.2429¢)
| |  
| |  
| | 1\11
| |  
| |  
| |  
| | 109.09
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || 3\26 || || || 138.462 || 5 || 3 || 1.667 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(7+pi)
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
|-
| |  
| || || || || || 7\61 || 137.705 || 12 || 7 || 1.714 ||  
| |  
| | 1\10
| |  
| |  
| |  
| |  
| | 120
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || 4\35 || || 137.143 || 7 || 4 || 1.750 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(7+e)
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
|-
| |  
| || || || || || 5\44 || 136.364 || 9 || 5 || 1.800 || [[Twothirdtonic]]
| |  
| |  
| |  
| | 3\29
| |  
| |  
| | 124.14
| |  
|-
|-
| |  
| || 1\9 || || || || || 133.333 || 2 || 1 || 2.000 || Basic 1L 7s <br>(small steps larger than this are proper)
| |  
| |  
| |  
| |  
| |  
| | 8\77
| | 124.675
| |  
|-
|-
| |  
| || || || || || 4\37 || 129.730 || 9 || 4 || 2.250 ||  
| |  
| |  
| |  
| |  
| | 5\48
| |  
| | 125
| |  
|-
|-
| |  
| || || || || 3\28 || || 128.571 || 7 || 3 || 2.333 ||  
| |  
| |  
| | 2\19
| |  
| |  
| |  
| | 126.32
| |  
|-
|-
| |  
| || || || || || 5\47 || 127.660 || 12 || 5 || 2.400 ||  
| | 1\9
|-
| |  
| || || || 2\19 || || || 126.316 || 5 || 2 || 2.500 ||  
| |  
| |  
| |  
| |  
| | 133.33
| style="text-align:center;" | Boundary of propriety:
 
generators larger than this are proper
|-
|-
| |  
| || || || || || 5\48 || 125.000 || 13 || 5 || 2.600 || Golden [[negri]] (124.7656¢)
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(7+sqrt(3))
| |
|-
|-
| |  
| || || || || 3\29 || || 124.138 || 8 || 3 || 2.667 || Negri
| |  
| |  
| | 3\26
| |  
| |  
| |  
| | 138.46
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 4\39 || 123.077 || 11 || 4 || 2.750 ||  
| |  
| |  
| |  
| |  
| | 8\69
| |  
| | 139.13
| style="text-align:center;" |  
|-
|-
| |  
| || || 1\10 || || || || 120.000 || 3 || 1 || 3.000 ||  
| |  
| |  
| |  
| |  
| |  
| | 13\112
| | 139.29
| style="text-align:center;" | Golden bleu
|-
|-
| |  
| || || || || || 3\31 || 116.129 || 10 || 3 || 3.333 || [[Miracle]]
| |  
| |  
| |  
| | 5\43
| |  
| |  
| | 139.53
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 2\21 || || 114.286 || 7 || 2 || 3.500 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 1200/(7+pi/2)
| |  
|-
|-
| |  
| || || || || || 3\32 || 112.500 || 11 || 3 || 3.667 ||  
| |  
| | 2\17
| |  
| |  
| |  
| |  
| | 141.18
| style="text-align:center;" | Bleu is around here
 
Optimum rank range (L/s=3/2)
|-
|-
|
| || || || 1\11 || || || 109.091 || 4 || 1 || 4.000 ||  
|
|
|3\25
|
|
|
|144
|
|-
|-
|
| || || || || || 2\23 || 104.348 || 9 || 2 || 4.500 ||  
|
|
|
|4\33
|
|
|145.455
|
|-
|-
|
| || || || || 1\12 || || 100.000 || 5 || 1 || 5.000 || [[Ripple]]/[[passion]]
|
|
|
|
|5\41
|
|146.34
|
|-
|-
|
| || || || || || 1\13 || 92.308 || 6 || 1 || 6.000 ||  
|
|
|
|
|
|6\49
|146.94
|
|-
|-
| | 1\8
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||  
| |  
| |  
| |  
| |  
| |  
| |  
| | 150
| style="text-align:center;" |  
|}
|}
[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:scales]]
[[Category:8-tone scales]]

Revision as of 09:55, 20 February 2022

↑ 1L 6s 2L 6s ↗
1L 7s 2L 7s →
↓ 1L 8s 2L 8s ↘
Scale structure
Step pattern Lsssssss
sssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\8 to 1\1 (1050.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\8 (0.0 ¢ to 150.0 ¢)
TAMNAMS information
Name antipine
Prefix apine-
Abbrev. ap
Related MOS scales
Parent 1L 6s
Sister 7L 1s
Daughters 8L 1s, 1L 8s
Neutralized 2L 6s
2-Flought 9L 7s, 1L 15s
Equal tunings
Equalized (L:s = 1:1) 7\8 (1050.0 ¢)
Supersoft (L:s = 4:3) 22\25 (1056.0 ¢)
Soft (L:s = 3:2) 15\17 (1058.8 ¢)
Semisoft (L:s = 5:3) 23\26 (1061.5 ¢)
Basic (L:s = 2:1) 8\9 (1066.7 ¢)
Semihard (L:s = 5:2) 17\19 (1073.7 ¢)
Hard (L:s = 3:1) 9\10 (1080.0 ¢)
Superhard (L:s = 4:1) 10\11 (1090.9 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
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1L 7s is the MOS pattern Lsssssss with small steps ranging from 0\1 (0¢) to 1\8 (one step of 8edo = 150¢).

This MOS pattern is somewhat of a wasteland as far as low-harmonic-entropy scales are concerned. However, there is one interesting no-5's scale, bleu. In this scale, 5 steps make a 3/2, and the chord 11:12:13:14 is represented as three equal steps.

Modes

  • 7|0 Lsssssss
  • 6|1 sLssssss
  • 5|2 ssLsssss
  • 4|3 sssLssss
  • 3|4 ssssLsss
  • 2|5 sssssLss
  • 1|6 ssssssLs
  • 0|7 sssssssL

Scale tree

Generator ranges:

  • Chroma-positive generator: 1050 cents (7\8) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 150 cents (1\8)
Small step
(chroma-negative generator) 		Cents L s L/s Comments
1\8 150.000 1 1 1.000
5\41 146.341 6 5 1.200 Bohpier
4\33 145.455 5 4 1.250
7\58 144.828 9 7 1.286
3\25 144.000 4 3 1.333
8\67 143.284 11 8 1.375
5\42 142.857 7 5 1.400
7\59 142.373 10 7 1.429
2\17 141.176 3 2 1.500
7\60 140.000 11 7 1.571 Bleu
5\43 139.535 8 5 1.600 Jerome/bleu
8\69 139.130 13 8 1.625 Golden jerome (139.2429¢)
3\26 138.462 5 3 1.667
7\61 137.705 12 7 1.714
4\35 137.143 7 4 1.750
5\44 136.364 9 5 1.800 Twothirdtonic
1\9 133.333 2 1 2.000 Basic 1L 7s
(small steps larger than this are proper)
4\37 129.730 9 4 2.250
3\28 128.571 7 3 2.333
5\47 127.660 12 5 2.400
2\19 126.316 5 2 2.500
5\48 125.000 13 5 2.600 Golden negri (124.7656¢)
3\29 124.138 8 3 2.667 Negri
4\39 123.077 11 4 2.750
1\10 120.000 3 1 3.000
3\31 116.129 10 3 3.333 Miracle
2\21 114.286 7 2 3.500
3\32 112.500 11 3 3.667
1\11 109.091 4 1 4.000
2\23 104.348 9 2 4.500
1\12 100.000 5 1 5.000 Ripple/passion
1\13 92.308 6 1 6.000
0\1 0.000 1 0 → inf
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