1L 10s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Keenan Pepper (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
968 edits
Xenllium (talk | contribs)
autopatrolled
4,516 edits
No edit summary
Line 1: Line 1:
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]]

Revision as of 05:55, 22 February 2022

↑ 1L 9s 2L 9s ↗
1L 10s 2L 10s →
↓ 1L 11s 2L 11s ↘ 
┌╥┬┬┬┬┬┬┬┬┬┬┐
│║│││││││││││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lssssssssss
ssssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\11 to 1\1 (1090.9 ¢ to 1200.0 ¢)
Dark 0\1 to 1\11 (0.0 ¢ to 109.1 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 1L 9s
Sister 10L 1s
Daughters 11L 1s, 1L 11s
Neutralized 2L 9s
2-Flought 12L 10s, 1L 21s
Equal tunings
Equalized (L:s = 1:1) 10\11 (1090.9 ¢)
Supersoft (L:s = 4:3) 31\34 (1094.1 ¢)
Soft (L:s = 3:2) 21\23 (1095.7 ¢)
Semisoft (L:s = 5:3) 32\35 (1097.1 ¢)
Basic (L:s = 2:1) 11\12 (1100.0 ¢)
Semihard (L:s = 5:2) 23\25 (1104.0 ¢)
Hard (L:s = 3:1) 12\13 (1107.7 ¢)
Superhard (L:s = 4:1) 13\14 (1114.3 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

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)
Small step
(chroma-negative generator) 		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
5\58 103.448 8 5 1.600
8\93 103.226 13 8 1.625 Golden ripple (103.2877¢)
3\35 102.857 5 3 1.667
7\82 102.439 12 7 1.714
4\47 102.128 7 4 1.750
5\59 101.695 9 5 1.800
1\12 100.000 2 1 2.000 Basic 1L 10s
(small steps larger than this are proper)
4\49 97.959 9 4 2.250
3\37 97.297 7 3 2.333 Passion
5\62 96.774 12 5 2.400
2\25 96.000 5 2 2.500
5\63 95.238 13 5 2.600 Unnamed golden tuning (95.102¢)
3\38 94.737 8 3 2.667
4\51 94.118 11 4 2.750
1\13 92.308 3 1 3.000
3\40 90.000 10 3 3.333
2\27 88.889 7 2 3.500
3\41 87.805 11 3 3.667 Octacot
1\14 85.714 4 1 4.000
2\29 82.759 9 2 4.500
1\15 80.000 5 1 5.000 Valentine
1\16 75.000 6 1 6.000
0\1 0.000 1 0 → inf
Retrieved from "https://en.xen.wiki/index.php?title=1L_10s&oldid=86227"