Xenharmonic Wiki

1L 11s: Difference between revisions

← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,025 edits
No edit summary
ArrowHead294 (talk | contribs)
15,215 edits
mNo edit summary
 
(16 intermediate revisions by 9 users not shown)
Line 1: Line 1:
{{Infobox MOS
{{Infobox MOS}}
| Periods = 1
{{MOS intro}}
| nLargeSteps = 1
 
| nSmallSteps = 11
The simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, or [[passion]] (5;4 = +3 generators), and even there it implies a val with warts for 3 and (for the most part) 5.
| Equalized = 11
 
| Paucitonic = 1
== Scale properties ==
| Pattern = Lsssssssssss
{{TAMNAMS use}}
}}


'''1L 11s''' is the MOS pattern Lsssssssssss with small steps ranging from 0\1 (0¢) to 1\12 (one step of [[12edo]] = 100¢).
=== Intervals ===
{{MOS intervals}}


This MOS, also called the "happy dodecatonic", is not a complete scale for any "interesting" temperament ― the simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, and even there it implies a val with warts for 3 and (for the most part) 5. Perhaps the only use for it is to extend it to 13 tones, i.e. to make it into a different MOS.
=== Generator chain ===
{{MOS genchain}}


== Modes ==
=== Modes ===
* 11|0 Lsssssssssss
{{MOS mode degrees}}
* 10|1 sLssssssssss
* 9|2 ssLsssssssss
* 8|3 sssLssssssss
* 7|4 ssssLsssssss
* 6|5 sssssLssssss
* 5|6 ssssssLsssss
* 4|7 sssssssLssss
* 3|8 ssssssssLsss
* 2|9 sssssssssLss
* 1|10 ssssssssssLs
* 0|11 sssssssssssL


== Scale tree ==
== Scale tree ==
Generator ranges:
{{MOS tuning spectrum
* Chroma-positive generator: 1100 cents (11\12) to 1200 cents (1\1)
| 6/5 = ↑ [[Passionate]]  
* Chroma-negative generator: 0 cents (0\1) to 100 cents (1\12)
| 5/4 = [[Passion]]  
 
| 13/8 = Unnamed golden tuning  
{| class="wikitable center-all"
| 12/5 = [[Slithy]]
! colspan="8" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
| 13/5 = Golden [[octacot]] (88.118¢)  
! Cents
| 10/3 = [[Marvolo]]
! L
| 7/2 = [[Nautilus]]
! s
| 4/1 = [[Nuke]]  
! L/s
| 9/2 = [[Valentine]]
! Comments
| 6/1 = [[Slurpee]], ↓ [[unicorn]]  
|-
}}
| 1\12 || || || || || || || || 100.000 || 1 || 1 || 1.000 ||
|-
| || || || || || || || 7\85 || 98.824 || 8 || 7 || 1.143 || [[Passionate]]/[[pash]]
|-
| || || || || || || 6\73 || || 98.630 || 7 || 6 || 1.167 || Passionate
|-
| || || || || || 5\61 || || || 98.361 || 6 || 5 || 1.200 ||
|-
| || || || || 4\49 || || || || 97.959 || 5 || 4 || 1.250 || [[Passion]]
|-
| || || || || || 7\86 || || || 97.674 || 9 || 7 || 1.286 ||
|-
| || || || 3\37 || || || || || 97.297 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\99 || || || 96.970 || 11 || 8 || 1.375 ||
|-
| || || || || 5\62 || || || || 96.774 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\87 || || || 96.552 || 10 || 7 || 1.429 ||
|-
| || || 2\25 || || || || || || 96.000 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\88 || || || 95.455 || 11 || 7 || 1.571 ||
|-
| || || || || 5\63 || || || || 95.238 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\101 || || || 95.050 || 13 || 8 || 1.625 || Unnamed golden tuning (95.1020¢)
|-
| || || || 3\38 || || || || || 94.737 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\89 || || || 94.382 || 12 || 7 || 1.714 ||
|-
| || || || || 4\51 || || || || 94.118 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\64 || || || 93.750 || 9 || 5 || 1.800 ||
|-
| || 1\13 || || || || || || || 92.308 || 2 || 1 || 2.000 || Basic 1L 11s <br>(small steps larger than this are proper)
|-
| || || || || || || 5\66 || || 90.909 || 11 || 5 || 2.200 ||
|-
| || || || || || 4\53 || || || 90.566 || 9 || 4 || 2.250 ||
|-
| || || || || || || 7\93 || || 90.323 || 16 || 7 || 2.286 ||
|-
| || || || || 3\40 || || || || 90.000 || 7 || 3 || 2.333 ||
|-
| || || || || || || 8\107 || || 89.720 || 19 || 8 || 2.375 ||
|-
| || || || || || 5\67 || || || 89.552 || 12 || 5 || 2.400 ||
|-
| || || || || || || 7\94 || || 89.362 || 17 || 7 || 2.429 ||
|-
| || || || 2\27 || || || || || 88.889 || 5 || 2 || 2.500 ||
|-
| || || || || || || 7\95 || || 88.421 || 18 || 7 || 2.571 ||
|-
| || || || || || 5\68 || || || 88.235 || 13 || 5 || 2.600 || [[Octacot]]
|-
| || || || || || || 8\109 || || 88.073 || 21 || 8 || 2.625 || Golden octacot (88.1184¢)
|-
| || || || || 3\41 || || || || 87.805 || 8 || 3 || 2.667 || Octacot
|-
| || || || || || || 7\96 || || 87.500 || 19 || 7 || 2.714 ||
|-
| || || || || || 4\55 || || || 87.273 || 11 || 4 || 2.750 ||
|-
| || || || || || || 5\69 || || 86.957 || 14 || 5 || 2.800 ||
|-
| || || 1\14 || || || || || || 85.714 || 3 || 1 || 3.000 ||
|-
| || || || || || || || 5\71 || 84.507 || 16 || 5 || 3.200 ||
|-
| || || || || || || 4\57 || || 84.211 || 13 || 4 || 3.250 ||
|-
| || || || || || || || 7\100 || 84.000 || 23 || 7 || 3.286 ||
|-
| || || || || || 3\43 || || || 83.721 || 10 || 3 || 3.333 ||
|-
| || || || || || || || 8\115 || 83.478 || 27 || 8 || 3.375 ||
|-
| || || || || || || 5\72 || || 83.333 || 17 || 5 || 3.400 ||
|-
| || || || || || || || 7\101 || 83.168 || 24 || 7 || 3.429 ||
|-
| || || || || 2\29 || || || || 82.759 || 7 || 2 || 3.500 ||
|-
| || || || || || || || 7\102 || 82.353 || 25 || 7 || 3.571 ||
|-
| || || || || || || 5\73 || || 82.192 || 18 || 5 || 3.600 ||
|-
| || || || || || || || 8\117 || 82.051 || 29 || 8 || 3.625 ||
|-
| || || || || || 3\44 || || || 81.818 || 11 || 3 || 3.667 ||
|-
| || || || || || || || 7\103 || 81.553 || 26 || 7 || 3.714 ||
|-
| || || || || || || 4\59 || || 81.356 || 15 || 4 || 3.750 ||
|-
| || || || || || || || 5\74 || 81.081 || 19 || 5 || 3.800 ||
|-
| || || || 1\15 || || || || || 80.000 || 4 || 1 || 4.000 ||
|-
| || || || || || || || 4\61 || 78.689 || 17 || 4 || 4.250 ||
|-
| || || || || || || 3\46 || || 78.261 || 13 || 3 || 4.333 ||
|-
| || || || || || || || 5\77 || 77.922 || 22 || 5 || 4.400 || [[Valentine]]
|-
| || || || || || 2\31 || || || 77.419 || 9 || 2 || 4.500 ||
|-
| || || || || || || || 5\78 || 76.923 || 23 || 5 || 4.600 ||
|-
| || || || || || || 3\47 || || 76.596 || 14 || 3 || 4.667 ||
|-
| || || || || || || || 4\63 || 76.190 || 19 || 4 || 4.750 ||
|-
| || || || || 1\16 || || || || 75.000 || 5 || 1 || 5.000 ||
|-
| || || || || || || || 3\49 || 73.469 || 16 || 3 || 5.333 ||
|-
| || || || || || || 2\33 || || 72.727 || 11 || 2 || 5.500 ||
|-
| || || || || || || || 3\50 || 72.000 || 17 || 3 || 5.667 ||
|-
| || || || || || 1\17 || || || 70.588 || 6 || 1 || 6.000 ||
|-
| || || || || || || || 2\35 || 68.571 || 13 || 2 || 6.500 ||
|-
| || || || || || || 1\18 || || 66.667 || 7 || 1 || 7.000 ||
|-
| || || || || || || || 1\19 || 63.158 || 8 || 1 || 8.000 || [[Unicorn]]
|-
| 0\1 || || || || || || || || 0.000 || 1 || 0 || → inf ||
|}


[[Category:Abstract MOS patterns]]
{{Todo| expand }}
[[Category:12-tone scales]]
Retrieved from "https://en.xen.wiki/w/1L_11s"