12L 5s: Difference between revisions

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== Modes ==
== Modes ==
* 16|0 LLLsLLsLLLsLLsLLs
Mode names are borrowed from the [[Subaru scale]], proposed by Declan Paul Boushy.
* 15|1 LLLsLLsLLsLLLsLLs
* 14|2 LLsLLLsLLsLLLsLLs
* 13|3 LLsLLLsLLsLLsLLLs
* 12|4 LLsLLsLLLsLLsLLLs
* 11|5 LLsLLsLLLsLLsLLsL
* 10|6 LLsLLsLLsLLLsLLsL
* 9|7 LsLLLsLLsLLLsLLsL
* 8|8 LsLLLsLLsLLsLLLsL
* 7|9 LsLLsLLLsLLsLLLsL
* 6|10 LsLLsLLLsLLsLLsLL
* 5|11 LsLLsLLsLLLsLLsLL
* 4|12 sLLLsLLsLLLsLLsLL
* 3|13 sLLLsLLsLLsLLLsLL
* 2|14 sLLsLLLsLLsLLLsLL
* 1|15 sLLsLLLsLLsLLsLLL
* 0|16 sLLsLLsLLLsLLsLLL


{| class="wikitable"
! Mode
! UDP
! Mode name
|-
| LLLsLLsLLLsLLsLLs
| 16<nowiki>|</nowiki>0
| Harumi
|-
| LLLsLLsLLsLLLsLLs
| 15<nowiki>|</nowiki>1
| Yuzuha
|-
| LLsLLLsLLsLLLsLLs
| 14<nowiki>|</nowiki>2
| Maho
|-
| LLsLLLsLLsLLsLLLs
| 13<nowiki>|</nowiki>3
| Sakura
|-
| LLsLLsLLLsLLsLLLs
| 12<nowiki>|</nowiki>4
| Hanako
|-
| LLsLLsLLLsLLsLLsL
| 11<nowiki>|</nowiki>5
| Saori
|-
| LLsLLsLLsLLLsLLsL
| 10<nowiki>|</nowiki>6
| Machiko
|-
| LsLLLsLLsLLLsLLsL
| 9<nowiki>|</nowiki>7
| Sae
|-
| LsLLLsLLsLLsLLLsL
| 8<nowiki>|</nowiki>8
| Kaguya
|-
| LsLLsLLLsLLsLLLsL
| 7<nowiki>|</nowiki>9
| Nae
|-
| LsLLsLLLsLLsLLsLL
| 6<nowiki>|</nowiki>10
| Sachiko
|-
| LsLLsLLsLLLsLLsLL
| 5<nowiki>|</nowiki>11
| Kaori
|-
| sLLLsLLsLLLsLLsLL
| 4<nowiki>|</nowiki>12
| Kanako
|-
| sLLLsLLsLLsLLLsLL
| 3<nowiki>|</nowiki>13
| Sakurajima
|-
| sLLsLLLsLLsLLLsLL
| 2<nowiki>|</nowiki>14
| Kaho
|-
| sLLsLLLsLLsLLsLLL
| 1<nowiki>|</nowiki>15
| Suzuha
|-
| sLLsLLsLLLsLLsLLL
| 0<nowiki>|</nowiki>16
| Narumi
|}
== Scales ==
== Scales ==
* [[Pythagorean17]] – Pythagorean tuning
* [[Pythagorean17]] – Pythagorean tuning
Line 38: Line 95:
* [[Cotoneum17]] – 217edo tuning
* [[Cotoneum17]] – 217edo tuning
* [[Garibaldi17]] – 94edo tuning
* [[Garibaldi17]] – 94edo tuning
* [[Subaru scale]] – 41edo tuning


== Scale tree ==
== Scale tree ==
Generator ranges:  
Generator ranges:  
* Chroma-positive generator: 494.1176 cents (7\17) to 500 cents (5\12)
* Bright generator: 494.1176 cents (7\17) to 500 cents (5\12)
* Chroma-negative generator: 700 cents (7\12) to 705.8824 cents (10\17)
* Dark generator: 700 cents (7\12) to 705.8824 cents (10\17)


{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" | Generator
! colspan="6" | Bright generator
! Cents
! Cents
! L
! L

Revision as of 11:18, 10 June 2023

↖ 11L 4s ↑ 12L 4s 13L 4s ↗
← 11L 5s 12L 5s 13L 5s →
↙ 11L 6s ↓ 12L 6s 13L 6s ↘ 
┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬╥╥┬┐
│║║║│║║│║║║│║║│║║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLLsLLsLLs
sLLsLLsLLLsLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\17 to 5\12 (494.1 ¢ to 500.0 ¢)
Dark 7\12 to 10\17 (700.0 ¢ to 705.9 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 5L 7s
Sister 5L 12s
Daughters 17L 12s, 12L 17s
Neutralized 7L 10s
2-Flought 29L 5s, 12L 22s
Equal tunings
Equalized (L:s = 1:1) 7\17 (494.1 ¢)
Supersoft (L:s = 4:3) 26\63 (495.2 ¢)
Soft (L:s = 3:2) 19\46 (495.7 ¢)
Semisoft (L:s = 5:3) 31\75 (496.0 ¢)
Basic (L:s = 2:1) 12\29 (496.6 ¢)
Semihard (L:s = 5:2) 29\70 (497.1 ¢)
Hard (L:s = 3:1) 17\41 (497.6 ¢)
Superhard (L:s = 4:1) 22\53 (498.1 ¢)
Collapsed (L:s = 1:0) 5\12 (500.0 ¢)

12L 5s is the MOS pattern of the Pythagorean/schismic enharmonic or mega-chromatic scale. In contrast to the superpyth enharmonic scale, in which the enharmonic diesis (negative diminished second) is larger than the chromatic semitone, here the reverse is true: the enharmonic diesis is smaller than the chromatic semitone, so the diatonic scale subset is actually proper.

This MOS separates its small steps by intervals of 3L-2L-3L-2L-2L. Its major third of -4 generators approximates an interval between 24/19 and 32/25, thus its generator is a perfect fourth between 7\17 (494.118 cents) and 5\12 (500 cents).

The leapday/leapweek version is proper, but the Pythagorean/schismic version is improper (it does not become proper until you add 12 more notes to form the schismic 29-note scale).

Modes

Mode names are borrowed from the Subaru scale, proposed by Declan Paul Boushy.

Mode UDP Mode name
LLLsLLsLLLsLLsLLs 16|0 Harumi
LLLsLLsLLsLLLsLLs 15|1 Yuzuha
LLsLLLsLLsLLLsLLs 14|2 Maho
LLsLLLsLLsLLsLLLs 13|3 Sakura
LLsLLsLLLsLLsLLLs 12|4 Hanako
LLsLLsLLLsLLsLLsL 11|5 Saori
LLsLLsLLsLLLsLLsL 10|6 Machiko
LsLLLsLLsLLLsLLsL 9|7 Sae
LsLLLsLLsLLsLLLsL 8|8 Kaguya
LsLLsLLLsLLsLLLsL 7|9 Nae
LsLLsLLLsLLsLLsLL 6|10 Sachiko
LsLLsLLsLLLsLLsLL 5|11 Kaori
sLLLsLLsLLLsLLsLL 4|12 Kanako
sLLLsLLsLLsLLLsLL 3|13 Sakurajima
sLLsLLLsLLsLLLsLL 2|14 Kaho
sLLsLLLsLLsLLsLLL 1|15 Suzuha
sLLsLLsLLLsLLsLLL 0|16 Narumi

Scales

Scale tree

Generator ranges:

  • Bright generator: 494.1176 cents (7\17) to 500 cents (5\12)
  • Dark generator: 700 cents (7\12) to 705.8824 cents (10\17)
Bright generator Cents L s L/s Comments
7\17 494.118 1 1 1.000
40\97 494.845 6 5 1.200
33\80 495.000 5 4 1.250
59\143 495.105 9 7 1.286
26\63 495.238 4 3 1.333 Leapfrog
71\172 495.349 11 8 1.375
45\109 495.413 7 5 1.400 Leapweek
64\155 495.484 10 7 1.428
19\46 495.652 3 2 1.500
69\167 495.808 11 7 1.571 Leapday / polypyth
50\121 495.868 8 5 1.600
81\196 495.918 13 8 1.625 Golden neogothic (495.9044¢)
31\75 496.000 5 3 1.667
74\179 496.089 12 7 1.714
43\104 496.154 7 4 1.750
55\133 496.241 9 5 1.800
12\29 496.552 2 1 2.000 Basic 12L 5s
(Generators smaller than this are proper)
53\128 496.875 9 4 2.250
41\99 496.970 7 3 2.333 Undecental
70\169 497.041 12 5 2.400 Argent tuning (497.0563¢)
29\70 497.143 5 2 2.500
75\181 497.238 13 5 2.600 Unnamed golden tuning (497.2540¢)
46\111 497.297 8 3 2.667
63\152 497.368 11 4 2.750 Kwai
17\41 497.561 3 1 3.000 Garibaldi / andromeda
56\135 497.778 10 3 3.333
39\94 497.872 7 2 3.500 Garibaldi / cassandra
61\147 497.959 11 3 3.667
22\53 498.113 4 1 4.000 Garibaldi / helenus, Pythagorean tuning (498.0450¢)
49\118 498.305 9 2 4.500 Pontiac
27\65 498.462 5 1 5.000 Photia
32\77 498.701 6 1 6.000 Grackle↓
5\12 500.000 1 0 → inf
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