12L 5s: Difference between revisions

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'''12L 5s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Garibaldi temperament|Helmholtz/Garibaldi]] mega-chromatic scale. In contrast to the [[5L 12s|superpyth mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are larger than chromatic semitones, here the reverse is true: mega-chromatic semitones are smaller than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|proper]].
'''12L 5s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] mega-chromatic scale. In contrast to the [[5L 12s|superpyth mega-chromatic scale]], in which mega-chromatic semitones (negative diminished seconds) are larger than chromatic semitones, here the reverse is true: mega-chromatic semitones are smaller than chromatic semitones, so the [[5L 7s|diatonic scale]] subset is actually [[Rothenberg propriety|proper]].


This MOS separates its small steps by intervals of 3L-2L-2L-3L-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 (494.412 cents) and 5\12 (500 cents).
This MOS separates its small steps by intervals of 3L-2L-2L-3L-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 doesn't become proper until you add 12 more notes to form the schismic 29-note scale).
The leapday/leapweek version is proper, but the Pythagorean/schismic version is improper (it doesn't become proper until you add 12 more notes to form the schismic 29-note scale).
Line 49: Line 49:
! Comments
! Comments
|-
|-
| 7\17 || || || || || || 494.412 || 1 || 1 || 1.000 ||  
| 7\17 || || || || || || 494.118 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || || 40\97 || 494.845 || 6 || 5 || 1.200 ||  
| || || || || || 40\97 || 494.845 || 6 || 5 || 1.200 ||  
Line 105: Line 105:
| || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||
| || || || || || 61\147 || 497.959 || 11 || 3 || 3.667 ||
|-
|-
| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[Helenus]] / [[Pythagorean]]
| || || || 22\53 || || || 498.113 || 4 || 1 || 4.000 || Garibaldi / [[Helenus]] / [[Pythagorean tuning|Pythagorean]]
|-
|-
| || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || [[Pontiac]]
| || || || || || 49\118 || 498.305 || 9 || 2 || 4.500 || [[Pontiac]]

Revision as of 07:29, 12 February 2022

↖ 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 ¢)
View • Talk • Edit

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

This MOS separates its small steps by intervals of 3L-2L-2L-3L-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 doesn't become proper until you add 12 more notes to form the schismic 29-note scale).

Modes

  • 16|0 LLLsLLsLLLsLLsLLs
  • 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

Scales

Scale tree

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 (Generator = 495.9044 cents)
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 (Generator: 497.0563 cents)
29\70 497.143 5 2 2.500
75\181 497.238 13 5 2.600 Unnamed golden tuning (Generator: 497.2540 cents)
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
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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