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1L 10s: Difference between revisions

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This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).
{{Infobox MOS
| Name =
| Periods = 1
| nLargeSteps = 1
| nSmallSteps = 10
| Equalized = 10
| Paucitonic = 1
| Pattern = Lssssssssss
}}


{| class="wikitable"
This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).
 
== Modes ==
* 10|0 Lssssssssss
* 9|1 sLsssssssss
* 8|2 ssLssssssss
* 7|3 sssLsssssss
* 6|4 ssssLssssss
* 5|5 sssssLsssss
* 4|6 ssssssLssss
* 3|7 sssssssLsss
* 2|8 ssssssssLss
* 1|9 sssssssssLs
* 0|10 ssssssssssL
 
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 1090.9091 cents (10\11) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 109.0909 cents (1\11)
 
{| 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\11 || || || || || || 109.091 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\56 || 107.143 || 6 || 5 || 1.200 ||
|-
| || || || || 4\45 || || 106.667 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\79 || 106.329 || 9 || 7 || 1.286 ||
|-
| || || || 3\34 || || || 105.882 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\91 || 105.495 || 11 || 8 || 1.375 ||
|-
| || || || || 5\57 || || 105.263 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\80 || 105.000 || 10 || 7 || 1.429 || [[Septendesemi]]
|-
| || || 2\23 || || || || 104.348 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\81 || 103.704 || 11 || 7 || 1.571 ||
|-
|-
| | 0/1
| || || || || 5\58 || || 103.448 || 8 || 5 || 1.600 ||  
| |  
| |  
| |  
| |  
| | 0
|-
|-
| |  
| || || || || || 8\93 || 103.226 || 13 || 8 || 1.625 || Golden [[ripple]] (103.2877¢)
| |  
| |  
| |  
| | 1/15
| | 80
|-
|-
| |  
| || || || 3\35 || || || 102.857 || 5 || 3 || 1.667 ||
| |  
| |  
| | 1/14
| |  
| | 85.714
|-
|-
| |  
| || || || || || 7\82 || 102.439 || 12 || 7 || 1.714 ||
| |  
| |  
| |  
| | 2/27
| | 88.889
|-
|-
| |  
| || || || || 4\47 || || 102.128 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| |  
| | 1200/(10+pi)
|-
|-
| |  
| || || || || || 5\59 || 101.695 || 9 || 5 || 1.800 ||
| |  
| | 1/13
| |  
| |  
| | 92.308
|-
|-
| |  
| || 1\12 || || || || || 100.000 || 2 || 1 || 2.000 || Basic 1L 10s <br>(small steps larger than this are proper)
| |  
| |  
| |  
| |  
| | 1200/(10+e)
|-
|-
| |  
| || || || || || 4\49 || 97.959 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| | 3/38
| | 94.737
|-
|-
| |  
| || || || || 3\37 || || 97.297 || 7 || 3 || 2.333 || [[Passion]]
| |  
| |  
| |  
| |  
| | 1200/(11+phi)
|-
|-
| |  
| || || || || || 5\62 || 96.774 || 12 || 5 || 2.400 ||
| |  
| |  
| | 2/25
| |  
| | 96
|-
|-
| |  
| || || || 2\25 || || || 96.000 || 5 || 2 || 2.500 ||
| |  
| |  
| |  
| | 3/37
| | 97.297
|-
|-
| |  
| || || || || || 5\63 || 95.238 || 13 || 5 || 2.600 || Unnamed golden tuning (95.102¢)
| | 1/12
| |  
| |  
| |  
| | 100
|-
|-
| |  
| || || || || 3\38 || || 94.737 || 8 || 3 || 2.667 ||
| |  
| |  
| |  
| |  
| | 1200/(10+sqrt(3))
|-
|-
| |  
| || || || || || 4\51 || 94.118 || 11 || 4 || 2.750 ||
| |  
| |  
| |  
| | 4/47
| | 102.128
|-
|-
| |  
| || || 1\13 || || || || 92.308 || 3 || 1 || 3.000 ||
| |  
| |  
| | 3/35
| |  
| | 102.857
|-
|-
| |  
| || || || || || 3\40 || 90.000 || 10 || 3 || 3.333 ||
| |  
| |  
| |  
| |  
| | 1200/(10+phi)
|-
|-
| |  
| || || || || 2\27 || || 88.889 || 7 || 2 || 3.500 ||
| |  
| |  
| |  
| | 5/58
| | 103.448
|-
|-
| |  
| || || || || || 3\41 || 87.805 || 11 || 3 || 3.667 || [[Octacot]]
| |  
| |  
| |  
| |  
| | 1200/(10+pi/2)
|-
|-
| |  
| || || || 1\14 || || || 85.714 || 4 || 1 || 4.000 ||
| |  
| | 2/23
| |  
| |  
| | 104.348
|-
|-
| |  
| || || || || || 2\29 || 82.759 || 9 || 2 || 4.500 ||
| |  
| |  
| |  
| | 5/57
| | 105.263
|-
|-
| |  
| || || || || 1\15 || || 80.000 || 5 || 1 || 5.000 || [[Valentine]]
| |  
| |  
| | 3/34
| |  
| | 105.882
|-
|-
| |  
| || || || || || 1\16 || 75.000 || 6 || 1 || 6.000 ||
| |  
| |  
| |  
| | 4/45
| | 106.667
|-
|-
| | 1/11
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
| |  
| |  
| |  
| |  
| | 109.091
|}
|}


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