1L 8s: Difference between revisions

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This MOS, with a generator of up to 1/9edo (133.333 cents), represents temperaments like Miracle (2<L<3 s=1) and Negri (3<L<4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3/28edo (L near 4 s=3).
{{Infobox MOS
| Periods = 1
| nLargeSteps = 1
| nSmallSteps = 8
| Equalized = 8
| Paucitonic = 1
| Pattern = Lssssssss
}}


{| class="wikitable"
'''1L 8s''' is the MOS pattern Lssssssss with small steps ranging from 0\1 (0¢) to 1\9 (one step of [[9edo]] = 133.3¢).
 
This MOS represents temperaments like Miracle and Negri. Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3\28 (around [[14/13]]).
 
== Modes ==
* 8|0 Lssssssss
* 7|1 sLsssssss
* 6|2 ssLssssss
* 5|3 sssLsssss
* 4|4 ssssLssss
* 3|5 sssssLsss
* 2|6 ssssssLss
* 1|7 sssssssLs
* 0|8 ssssssssL
 
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 1066.6667 cents (8\9) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 133.3333 cents (1\9)
 
{| 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\9 || || || || || || 133.333 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\46 || 130.435 || 6 || 5 || 1.200 ||
|-
| || || || || 4\37 || || 129.730 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\65 || 129.231 || 9 || 7 || 1.286 ||
|-
| || || || 3\28 || || || 128.571 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\75 || 128.000 || 11 || 8 || 1.375 ||
|-
| || || || || 5\47 || || 127.660 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\66 || 127.273 || 10 || 7 || 1.429 ||
|-
| || || 2\19 || || || || 126.316 || 3 || 2 || 1.500 || [[Negri]]
|-
| || || || || || 7\67 || 125.373 || 11 || 7 || 1.571 ||
|-
|-
| | 0/1
| || || || || 5\48 || || 125.000 || 8 || 5 || 1.600 ||  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 8\77 || 124.675 || 13 || 8 || 1.625 || Golden negri (124.7656¢)
| |  
| |  
| |  
| | 1/13
| | 92.308
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || 3\29 || || || 124.138 || 5 || 3 || 1.667 ||  
| |  
| |  
| | 1/12
| |  
| | 100
| style="text-align:center;" |  
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || || 7\68 || 123.529 || 12 || 7 || 1.714 ||  
| |  
| |  
| |  
| | 2/23
| | 104.348
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 4\39 || || 123.077 || 7 || 4 || 1.750 ||  
| |  
| |  
| |  
| |  
| | 1200/(8+pi)
| |  
| |  
|-
|-
| |  
| || || || || || 5\49 || 122.449 || 9 || 5 || 1.800 ||  
| |  
| | 1/11
| |  
| |  
| | 109.091
| |
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || 1\10 || || || || || 120.000 || 2 || 1 || 2.000 || Basic 1L 8s <br>(small steps larger than this are proper)
| |  
| |  
| |  
| |  
| | 1200/(8+e)
| |  
| |  
|-
|-
| |  
| || || || || || 4\41 || 117.073 || 9 || 4 || 2.250 || [[Miracle]]
| |  
| |  
| |  
| | 3/32
| | 112.5
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 3\31 || || 116.129 || 7 || 3 || 2.333 || Miracle/[[revelation]]
| |  
| |  
| |  
| |  
| | 1200/(9+phi)
| |  
| |  
|-
|-
| |  
| || || || || || 5\52 || 115.385 || 12 || 5 || 2.400 ||  
| |  
| |  
| | 2/21
| |  
| | 114.286
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || 2\21 || || || 114.286 || 5 || 2 || 2.500 ||  
| |  
| |  
| |  
| | 3/31
| | 116.129
| style="text-align:center;" | Miracle is around here
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 5\53 || 113.208 || 13 || 5 || 2.600 || Golden [[misneb]] (113.0153¢)
| | 1/10
| |  
| |  
| |  
| | 120
| |
 
Negri generators from here...
| style="text-align:center;" | Boundary of propriety:
 
generators larger than this are proper
|-
|-
| |  
| || || || || 3\32 || || 112.500 || 8 || 3 || 2.667 ||  
| |  
| |  
| |  
| |  
| | 1200/(8+<span style="line-height: 1.5;">sqrt(3))</span>
| |  
| |  
|-
|-
| |  
| || || || || || 4\43 || 111.628 || 11 || 4 || 2.750 ||  
| |  
| |  
| |  
| | 4/39
| | 123.077
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || 1\11 || || || || 109.091 || 3 || 1 || 3.000 ||  
| |  
| |  
| | 3/29
| |  
| | 124.138
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 3\34 || 105.882 || 10 || 3 || 3.333 ||  
| |  
| |  
| |  
| |  
| | 1200/(8+phi)
| |  
| |  
|-
|-
| |  
| || || || || 2\23 || || 104.348 || 7 || 2 || 3.500 ||  
| |  
| |  
| |  
| | 5/48
| | 125
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 3\35 || 102.857 || 11 || 3 || 3.667 ||  
| |  
| |  
| |  
| |  
| | 1200/(8+pih)
| |  
| |  
|-
|-
| |  
| || || || 1\12 || || || 100.000 || 4 || 1 || 4.000 || [[Ripple]]
| |  
| | 2/19
| |  
| |  
| | 126.316
| style="text-align:center;" | ...to here
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 2\25 || 96.000 || 9 || 2 || 4.500 || [[Passion]]
| |  
| |  
| |  
| | 5/47
| | 127.66
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 1\13 || || 92.308 || 5 || 1 || 5.000 ||  
| |  
| |  
| | 3/28
| |  
| | 128.571
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 1\14 || 85.714 || 6 || 1 || 6.000 ||  
| |  
| |  
| |  
| | 4/37
| | 129.73
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| | 1/9
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||  
| |  
| |  
| |  
| |  
| | 133.333
| style="text-align:center;" |  
| style="text-align:center;" |  
|}
|}


[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:9-tone scales]]

Revision as of 10:39, 20 February 2022

↑ 1L 7s 2L 7s ↗
1L 8s 2L 8s →
↓ 1L 9s 2L 9s ↘ 
┌╥┬┬┬┬┬┬┬┬┐
│║│││││││││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lssssssss
ssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 8\9 to 1\1 (1066.7 ¢ to 1200.0 ¢)
Dark 0\1 to 1\9 (0.0 ¢ to 133.3 ¢)
TAMNAMS information
Name antisubneutralic
Prefix ablu-
Abbrev. ablu
Related MOS scales
Parent 1L 7s
Sister 8L 1s
Daughters 9L 1s, 1L 9s
Neutralized 2L 7s
2-Flought 10L 8s, 1L 17s
Equal tunings
Equalized (L:s = 1:1) 8\9 (1066.7 ¢)
Supersoft (L:s = 4:3) 25\28 (1071.4 ¢)
Soft (L:s = 3:2) 17\19 (1073.7 ¢)
Semisoft (L:s = 5:3) 26\29 (1075.9 ¢)
Basic (L:s = 2:1) 9\10 (1080.0 ¢)
Semihard (L:s = 5:2) 19\21 (1085.7 ¢)
Hard (L:s = 3:1) 10\11 (1090.9 ¢)
Superhard (L:s = 4:1) 11\12 (1100.0 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 8s is the MOS pattern Lssssssss with small steps ranging from 0\1 (0¢) to 1\9 (one step of 9edo = 133.3¢).

This MOS represents temperaments like Miracle and Negri. Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3\28 (around 14/13).

Modes

  • 8|0 Lssssssss
  • 7|1 sLsssssss
  • 6|2 ssLssssss
  • 5|3 sssLsssss
  • 4|4 ssssLssss
  • 3|5 sssssLsss
  • 2|6 ssssssLss
  • 1|7 sssssssLs
  • 0|8 ssssssssL

Scale tree

Generator ranges:

  • Chroma-positive generator: 1066.6667 cents (8\9) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 133.3333 cents (1\9)
Small step
(chroma-negative generator) 		Cents L s L/s Comments
1\9 133.333 1 1 1.000
5\46 130.435 6 5 1.200
4\37 129.730 5 4 1.250
7\65 129.231 9 7 1.286
3\28 128.571 4 3 1.333
8\75 128.000 11 8 1.375
5\47 127.660 7 5 1.400
7\66 127.273 10 7 1.429
2\19 126.316 3 2 1.500 Negri
7\67 125.373 11 7 1.571
5\48 125.000 8 5 1.600
8\77 124.675 13 8 1.625 Golden negri (124.7656¢)
3\29 124.138 5 3 1.667
7\68 123.529 12 7 1.714
4\39 123.077 7 4 1.750
5\49 122.449 9 5 1.800
1\10 120.000 2 1 2.000 Basic 1L 8s
(small steps larger than this are proper)
4\41 117.073 9 4 2.250 Miracle
3\31 116.129 7 3 2.333 Miracle/revelation
5\52 115.385 12 5 2.400
2\21 114.286 5 2 2.500
5\53 113.208 13 5 2.600 Golden misneb (113.0153¢)
3\32 112.500 8 3 2.667
4\43 111.628 11 4 2.750
1\11 109.091 3 1 3.000
3\34 105.882 10 3 3.333
2\23 104.348 7 2 3.500
3\35 102.857 11 3 3.667
1\12 100.000 4 1 4.000 Ripple
2\25 96.000 9 2 4.500 Passion
1\13 92.308 5 1 5.000
1\14 85.714 6 1 6.000
0\1 0.000 1 0 → inf
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