5L 12s: Difference between revisions

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{{Infobox MOS
| Periods = 1
| nLargeSteps = 5
| nSmallSteps = 12
| Equalized = 7
| Paucitonic = 2
| Pattern = sssLssLsssLssLssL
| Name = Superpyth mega-chromatic
}}
'''5L 12s''' is the MOS pattern of the [[superpyth]] mega-chromatic scale. In contrast to the [[12L 5s|schismic mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are smaller than chromatic semitones, here the reverse is true: mega-chromatic semitones are larger than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|improper]].
The supra/quasisuper version is proper, but the superpyth/ultrapyth version is improper (it doesn't become proper until you add 5 more notes to form the schismic 22-note scale).
== Modes ==
* 16|0 LssLssLsssLssLsss
* 15|1 LssLsssLssLssLsss
* 14|2 LssLsssLssLsssLss
* 13|3 LsssLssLssLsssLss
* 12|4 LsssLssLsssLssLss
* 11|5 sLssLssLsssLssLss
* 10|6 sLssLsssLssLssLss
* 9|7 sLssLsssLssLsssLs
* 8|8 sLsssLssLssLsssLs
* 7|9 sLsssLssLsssLssLs
* 6|10 ssLssLssLsssLssLs
* 5|11 ssLssLsssLssLssLs
* 4|12 ssLssLsssLssLsssL
* 3|13 ssLsssLssLssLsssL
* 2|14 ssLsssLssLsssLssL
* 1|15 sssLssLssLsssLssL
* 0|16 sssLssLsssLssLssL
== Scale tree ==
== Scale tree ==
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" | Generator
! colspan="6" | Generator
! Cents
! Fifth <br>(cents)
! L
! L
! s
! s
Line 16: Line 49:
| || || || || || 76\129 || 706.977 || 9 || 7 || 1.286 ||  
| || || || || || 76\129 || 706.977 || 9 || 7 || 1.286 ||  
|-
|-
| || || || 33\56 || || || 707.143 || 4 || 3 || 1.333 || Supra
| || || || 33\56 || || || 707.143 || 4 || 3 || 1.333 || [[Supra]]
|-
|-
| || || || || || 89\151 || 707.285 || 11 || 8 || 1.375 ||
| || || || || || 89\151 || 707.285 || 11 || 8 || 1.375 ||
Line 24: Line 57:
| || || || || || 79\134 || 707.463 || 10 || 7 || 1.428 ||
| || || || || || 79\134 || 707.463 || 10 || 7 || 1.428 ||
|-
|-
| || || 23\39 || || || || 707.692 || 3 || 2 || 1.500 || L/s = 3/2
| || || 23\39 || || || || 707.692 || 3 || 2 || 1.500 ||  
|-
|-
| || || || || || 82\139 || 707.914 || 11 || 7 || 1.571 ||
| || || || || || 82\139 || 707.914 || 11 || 7 || 1.571 ||
Line 30: Line 63:
| || || || || 59\100 || || 708.000 || 8 || 5 || 1.600 ||  
| || || || || 59\100 || || 708.000 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 95\161 || 708.075 || 13 || 8 || 1.625 || Golden supra
| || || || || || 95\161 || 708.075 || 13 || 8 || 1.625 || Golden supra (Fifth = 708.0539 cents)
|-
|-
| || || || 36\61 || || || 708.197 || 5 || 3 || 1.667 || Quasisuper, quasisupra
| || || || 36\61 || || || 708.197 || 5 || 3 || 1.667 || [[Quasisuper]] / [[quasisupra]]
|-
|-
| || || || || || 85\144 || 708.333 || 12 || 7 || 1.714 ||  
| || || || || || 85\144 || 708.333 || 12 || 7 || 1.714 ||  
Line 40: Line 73:
| || || || || || 62\105 || 708.571 || 9 || 5 || 1.800 ||
| || || || || || 62\105 || 708.571 || 9 || 5 || 1.800 ||
|-
|-
| || 13\22 || || || || || 709.091 || 2 || 1 || 2.000 || Basic 5L 12s<br>(Generators smaller than this are proper)
| || 13\22 || || || || || 709.091 || 2 || 1 || 2.000 || Basic 5L 12s <br>(Fifths smaller than this are proper)
|-
|-
| || || || || || 55\93 || 709.677 || 9 || 4 || 2.250 ||
| || || || || || 55\93 || 709.677 || 9 || 4 || 2.250 ||
Line 48: Line 81:
| || || || || || 71\120 || 710.000 || 12 || 5 || 2.400 ||
| || || || || || 71\120 || 710.000 || 12 || 5 || 2.400 ||
|-
|-
| || || || 29\49 || || || 710.204 || 5 || 2 || 2.500 || Superpyth
| || || || 29\49 || || || 710.204 || 5 || 2 || 2.500 || [[Superpyth]]
|-
|-
| || || || || || 74\125 || 710.400 || 13 || 5 || 2.600 || Unnamed golden tuning
| || || || || || 74\125 || 710.400 || 13 || 5 || 2.600 || Golden superpyth (Fifth = 710.4345 cents)
|-
|-
| || || || || 45\76 || || 710.526 || 8 || 3 || 2.667 ||
| || || || || 45\76 || || 710.526 || 8 || 3 || 2.667 ||
Line 56: Line 89:
| || || || || || 61\103 || 710.680 || 11 || 4 || 2.750 ||
| || || || || || 61\103 || 710.680 || 11 || 4 || 2.750 ||
|-
|-
| || || 16\27 || || || || 711.111 || 3 || 1 || 3.000 || L/s = 3/1
| || || 16\27 || || || || 711.111 || 3 || 1 || 3.000 ||  
|-
|-
| || || || || || 51\86 || 711.628 || 10 || 3 || 3.333 ||
| || || || || || 51\86 || 711.628 || 10 || 3 || 3.333 ||
Line 68: Line 101:
| || || || || || 41\69 || 713.043 || 9 || 2 || 4.500 ||
| || || || || || 41\69 || 713.043 || 9 || 2 || 4.500 ||
|-
|-
| || || || || 22\37 || || 713.514 || 5 || 1 || 5.000 ||
| || || || || 22\37 || || 713.514 || 5 || 1 || 5.000 || [[Oceanfront]] / [[Ultrapyth]]
|-
|-
| || || || || || 25\42 || 714.286 || 6 || 1 || 6.000 || Hemiseven↓
| || || || || || 25\42 || 714.286 || 6 || 1 || 6.000 || [[Hemiseven]]↓
|-
|-
| 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
| 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
Line 78: Line 111:
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:17-tone scales]]
[[Category:17-tone scales]]
 
[[Category:Mega chromatic scale]]
{{todo| intro }}

Revision as of 08:19, 12 February 2022

↖ 4L 11s ↑ 5L 11s 6L 11s ↗
← 4L 12s 5L 12s 6L 12s →
↙ 4L 13s ↓ 5L 13s 6L 13s ↘ 
┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐
│║││║││║│││║││║││││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLsssLssLsss
sssLssLsssLssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\17 to 3\5 (705.9 ¢ to 720.0 ¢)
Dark 2\5 to 7\17 (480.0 ¢ to 494.1 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 5L 7s
Sister 12L 5s
Daughters 17L 5s, 5L 17s
Neutralized 10L 7s
2-Flought 22L 12s, 5L 29s
Equal tunings
Equalized (L:s = 1:1) 10\17 (705.9 ¢)
Supersoft (L:s = 4:3) 33\56 (707.1 ¢)
Soft (L:s = 3:2) 23\39 (707.7 ¢)
Semisoft (L:s = 5:3) 36\61 (708.2 ¢)
Basic (L:s = 2:1) 13\22 (709.1 ¢)
Semihard (L:s = 5:2) 29\49 (710.2 ¢)
Hard (L:s = 3:1) 16\27 (711.1 ¢)
Superhard (L:s = 4:1) 19\32 (712.5 ¢)
Collapsed (L:s = 1:0) 3\5 (720.0 ¢)

5L 12s is the MOS pattern of the superpyth mega-chromatic scale. In contrast to the schismic mega-chromatic scale, in which mega-chromatic semitones (negative diminished seconds) are smaller than chromatic semitones, here the reverse is true: mega-chromatic semitones are larger than chromatic semitones, so the diatonic scale subset is actually improper.

The supra/quasisuper version is proper, but the superpyth/ultrapyth version is improper (it doesn't become proper until you add 5 more notes to form the schismic 22-note scale).

Modes

  • 16|0 LssLssLsssLssLsss
  • 15|1 LssLsssLssLssLsss
  • 14|2 LssLsssLssLsssLss
  • 13|3 LsssLssLssLsssLss
  • 12|4 LsssLssLsssLssLss
  • 11|5 sLssLssLsssLssLss
  • 10|6 sLssLsssLssLssLss
  • 9|7 sLssLsssLssLsssLs
  • 8|8 sLsssLssLssLsssLs
  • 7|9 sLsssLssLsssLssLs
  • 6|10 ssLssLssLsssLssLs
  • 5|11 ssLssLsssLssLssLs
  • 4|12 ssLssLsssLssLsssL
  • 3|13 ssLsssLssLssLsssL
  • 2|14 ssLsssLssLsssLssL
  • 1|15 sssLssLssLsssLssL
  • 0|16 sssLssLsssLssLssL

Scale tree

Generator Fifth
(cents) 		L s L/s Comments
10\17 705.882 1 1 1.000
53\90 706.667 6 5 1.200
43\73 706.849 5 4 1.250
76\129 706.977 9 7 1.286
33\56 707.143 4 3 1.333 Supra
89\151 707.285 11 8 1.375
56\95 707.368 7 5 1.400
79\134 707.463 10 7 1.428
23\39 707.692 3 2 1.500
82\139 707.914 11 7 1.571
59\100 708.000 8 5 1.600
95\161 708.075 13 8 1.625 Golden supra (Fifth = 708.0539 cents)
36\61 708.197 5 3 1.667 Quasisuper / quasisupra
85\144 708.333 12 7 1.714
49\83 708.434 7 4 1.750
62\105 708.571 9 5 1.800
13\22 709.091 2 1 2.000 Basic 5L 12s
(Fifths smaller than this are proper)
55\93 709.677 9 4 2.250
42\71 709.859 7 3 2.333
71\120 710.000 12 5 2.400
29\49 710.204 5 2 2.500 Superpyth
74\125 710.400 13 5 2.600 Golden superpyth (Fifth = 710.4345 cents)
45\76 710.526 8 3 2.667
61\103 710.680 11 4 2.750
16\27 711.111 3 1 3.000
51\86 711.628 10 3 3.333
35\59 711.864 7 2 3.500
54\91 712.088 11 3 3.667
19\32 712.500 4 1 4.000
41\69 713.043 9 2 4.500
22\37 713.514 5 1 5.000 Oceanfront / Ultrapyth
25\42 714.286 6 1 6.000 Hemiseven↓
3\5 720.000 1 0 → inf
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