11L 2s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Moremajorthanmajor (talk | contribs)
autopatrolled
3,126 edits
No edit summary
Fredg999 (talk | contribs)
autopatrolled, Interface administrators, Sysops
6,125 edits
+Infobox, name still missing, misc. edits
Line 1: Line 1:
This is the mega chromatic scale of Heinz temperament. Its generator of 5\11edo to 6\13edo hits so close to 11/8 as to be able to be called nothing but that interval, making it an 11+-limit scale.
{{Infobox MOS
| Other names =
| Periods = 1
| nLargeSteps = 11
| nSmallSteps = 2
| Equalized = 6
| Paucitonic = 5
| Pattern = LLLLLLsLLLLLs
}}
The '''11L 2s''' [[MOS scale]] is notable for correponding to the mega chromatic scale of [[Heinz]] temperament. Its generator of 5\11 to 6\13 hits so close to 11/8 as to be able to be called nothing but that interval, making it an 11+-limit scale.


== Scale tree ==
{| class="wikitable"
{| class="wikitable"
! colspan="8" | generator
! colspan="8" | generator
! | L
! L
! | s
! s
! | L/s
! L/s
! | gen (cents)
! gen (cents)
! | comment
! comment
|-
|-
| | 5\11
| 5\11
| |
| |
| |
| |
| |
|
|
|
|
| | 1
|
| | 0
|
| |
|
| | 545.455
|
| |
|
| 1
| 0
|
| 545.455
|
|-
|-
| |
| |
| |
| |
| |
| |
|
|
|41\90
|
| | 8
|
| | 1
|
| | 8.000
|
| | 546.667
|
| |
|
| 41\90
| 8
| 1
| 8.000
| 546.667
|
|-
|-
| |
| |
| |
| |
| |
| |
|36\79
|
|
| | 7
|
| | 1
|
| | 7.000
|
| | 546.835
|
| |
|
| 36\79
|
| 7
| 1
| 7.000
| 546.835
|
|-
|-
| |
| |
| |
| |
| |
| |31\68
|
|
|
|
| | 6
|
| | 1
|
| | 6.000
|
| | 547.059
| 31\68
| |
|
|
| 6
| 1
| 6.000
| 547.059
|
|-
|-
| |
| |
| |
| |
| | 26\57
| |
|
|
|
|
| | 5
|
| | 1
|
| | 5.000
| 26\57
| | 547.368
|
| |
|
|
| 5
| 1
| 5.000
| 547.368
|
|-
|-
| |
| |
| |
| | 21\46
| |
| |
|
|
|
|
| | 4
|
| | 1
| 21\46
| | 4.000
|
| | 547.826
|
| |
|
|
| 4
| 1
| 4.000
| 547.826
| Heinz is around here
|-
|-
| |
| |
| |
| |
| | 37\81
| |
|
|
|
|
| | 7
|
| | 2
|
| | 3.500
| 37\81
| | 548.148
|
| |
|
|
| 7
| 2
| 3.500
| 548.148
|
|-
|-
| |
| |
| | 16\35
| |
| |
| |
|
|
|
|
| | 3
| 16\35
| | 1
|
| | 3.000
|
| | 548.571
|
| |
|
|
| 3
| 1
| 3.000
| 548.571
|
|-
|-
| |
| |
| |
| |
| | 43\94
| |
|
|
|
|
| | 8
|
| | 3
|
| | 2.667
| 43\94
| | 548.936
|
| |
|
|
| 8
| 3
| 2.667
| 548.936
|
|-
|-
| |
| |
| |
| | 27\59
| |
| |
|
|
|
|
| | 5
|
| | 2
| 27\59
| | 2.500
|
| | 549.153
|
| |
|
|
| 5
| 2
| 2.500
| 549.153
|
|-
|-
| |
| |
| |
| |
| | 38\83
| |
|
|
|
|
| | 7
|
| | 3
|
| | 2.333
| 38\83
| | 549.398
|
| |
|
|
| 7
| 3
| 2.333
| 549.398
|
|-
|-
| |
|
| | 11\24
| 11\24
| |
|
| |
| |
| |
|
|
|
|
| | 2
|
| | 1
|
| | 2.000
|
| | 550.000
| 2
| |
| 1
| 2.000
| 550.000
|
|-
|-
| |
| |
| |
| |
| | 39\85
| |
|
|
|
|
| | 7
|
| | 4
|
| | 1.750
| 39\85
| | 550.588
|
| |
|
|
| 7
| 4
| 1.750
| 550.588
|
|-
|-
| |
| |
| |
| | 28\61
| |
| |
|
|
|
|
| | 5
|
| | 3
| 28\61
| | 1.667
|
| | 550.820
|
| |
|
|
| 5
| 3
| 1.667
| 550.820
|
|-
|-
| |
| |
| |
| |
| |
| | (5φ+1)/(11φ+2)
|
|
|
|
| | φ
|
| | 1
|
| | 1.618
|
| | 550.965
| (5φ+1)/(11φ+2)
| |
|
|
| φ
| 1
| 1.618
| 550.965
|
|-
|-
| |
| |
| |
| |
| | 45\98
| |
|
|
|
|
| | 8
|
| | 5
|
| | 1.600
| 45\98
| | 551.020
|
| |
|
|
| 8
| 5
| 1.600
| 551.020
|
|-
|-
| |
| |
| | 17\37
| |
| |
| |
|
|
|
|
| | 3
| 17\37
| | 2
|
| | 1.500
|
| | 551.351
|
| |
|
|
| 3
| 2
| 1.500
| 551.351
|
|-
|-
| |
| |
| |
| |
| | 40\87
| |
|
|
|
|
| | 7
|
| | 5
|
| | 1.400
| 40\87
| | 551.724
|
| |
|
|
| 7
| 5
| 1.400
| 551.724
|
|-
|-
| |
| |
| |
| | 23\50
| |
| |
|
|
|
|
| | 4
|
| | 3
| 23\50
| | 1.333
|
| | 552.000
|
| |
|
|
| 4
| 3
| 1.333
| 552.000
|
|-
|-
| |
| |
| |
| |
| | 29\63
| |
|
|
|
|
| | 5
|
| | 4
|
| | 1.250
| 29\63
| | 552.381
|
| |
|
|
| 5
| 4
| 1.250
| 552.381
|
|-
|-
| |
| |
| |
| |
| |
| |35\76
|
|
|
|
| | 6
|
| | 5
|
| | 1.200
|
| | 552.632
| 35\76
| |
|
|
| 6
| 5
| 1.200
| 552.632
|
|-
|-
| |
| |
| |
| |
| |
| |
|41\89
|
|
| | 7
|
| | 6
|
| | 1.167
|
| | 552.809
|
| |
|
| 41\89
|
| 7
| 6
| 1.167
| 552.809
|
|-
|-
|
|
Line 324: Line 334:
|
|
|
|
|47\102
| 47\102
|8
| 8
|7
| 7
|1.125
| 1.125
|552.941
| 552.941
|
|
|-
|-
| | 6\13
| 6\13
| |
|
| |
|
| |
|
| |
|
| |
|
|
|
|
| 1
| 1
| 1.000
| 553.846
|
|
| | 1
| | 1
| | 1.000
| | 553.846
| |
|}
|}

Revision as of 20:21, 15 August 2022

↖ 10L 1s ↑ 11L 1s 12L 1s ↗
← 10L 2s 11L 2s 12L 2s →
↙ 10L 3s ↓ 11L 3s 12L 3s ↘ 
┌╥╥╥╥╥╥┬╥╥╥╥╥┬┐
│║║║║║║│║║║║║││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLsLLLLLs
sLLLLLsLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\13 to 6\11 (646.2 ¢ to 654.5 ¢)
Dark 5\11 to 6\13 (545.5 ¢ to 553.8 ¢)
TAMNAMS information
Related to 2L 7s (balzano)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 2L 9s
Sister 2L 11s
Daughters 13L 11s, 11L 13s
Neutralized 9L 4s
2-Flought 24L 2s, 11L 15s
Equal tunings
Equalized (L:s = 1:1) 7\13 (646.2 ¢)
Supersoft (L:s = 4:3) 27\50 (648.0 ¢)
Soft (L:s = 3:2) 20\37 (648.6 ¢)
Semisoft (L:s = 5:3) 33\61 (649.2 ¢)
Basic (L:s = 2:1) 13\24 (650.0 ¢)
Semihard (L:s = 5:2) 32\59 (650.8 ¢)
Hard (L:s = 3:1) 19\35 (651.4 ¢)
Superhard (L:s = 4:1) 25\46 (652.2 ¢)
Collapsed (L:s = 1:0) 6\11 (654.5 ¢)

The 11L 2s MOS scale is notable for correponding to the mega chromatic scale of Heinz temperament. Its generator of 5\11 to 6\13 hits so close to 11/8 as to be able to be called nothing but that interval, making it an 11+-limit scale.

Scale tree

generator L s L/s gen (cents) comment
5\11 1 0 545.455
41\90 8 1 8.000 546.667
36\79 7 1 7.000 546.835
31\68 6 1 6.000 547.059
26\57 5 1 5.000 547.368
21\46 4 1 4.000 547.826 Heinz is around here
37\81 7 2 3.500 548.148
16\35 3 1 3.000 548.571
43\94 8 3 2.667 548.936
27\59 5 2 2.500 549.153
38\83 7 3 2.333 549.398
11\24 2 1 2.000 550.000
39\85 7 4 1.750 550.588
28\61 5 3 1.667 550.820
(5φ+1)/(11φ+2) φ 1 1.618 550.965
45\98 8 5 1.600 551.020
17\37 3 2 1.500 551.351
40\87 7 5 1.400 551.724
23\50 4 3 1.333 552.000
29\63 5 4 1.250 552.381
35\76 6 5 1.200 552.632
41\89 7 6 1.167 552.809
47\102 8 7 1.125 552.941
6\13 1 1 1.000 553.846
Retrieved from "https://en.xen.wiki/index.php?title=11L_2s&oldid=94372"