12L 5s: Difference between revisions

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→Scale tree: adopt the template
Line 88: Line 88:
* [[Pythagorean17]] – Pythagorean tuning
* [[Pythagorean17]] – Pythagorean tuning
* [[Nestoria17]] – 171edo tuning
* [[Nestoria17]] – 171edo tuning


== Scale tree ==
== Scale tree ==
Generator ranges:
{{Scale tree|Comments=
* Bright generator: 494.1176 cents (7\17) to 500 cents (5\12)
4/3: [[Leapfrog]];
* Dark generator: 700 cents (7\12) to 705.8824 cents (10\17)
7/5: [[Leapweek]];
 
11/7: [[Leapday]] / [[polypyth]];
{| class="wikitable center-all"
13/8: Golden neogothic (495.9044¢);
! colspan="6" | Bright generator
7/3: [[Undecental]];
! Cents
12/5: Argent tuning (497.0563¢);
! L
13/5: Unnamed golden tuning (497.2540¢)
! s
11/4: [[Kwai]];
! L/s
3/1: [[Garibaldi]] / [[andromeda]];
! Comments
7/2: Garibaldi / [[cassandra]];
|-
4/1: Garibaldi / [[helenus]], Pythagorean tuning (498.0450¢);
| 7\17 || || || || || || 494.118 || 1 || 1 || 1.000 ||
9/2: [[Pontiac]];
|-
5/1: [[Photia]];
| || || || || || 40\97 || 494.845 || 6 || 5 || 1.200 ||
6/1: ↓ [[Grackle]]
|-
}}
| || || || || 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 <br>(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 ||
|}


[[Category:17-tone scales]]
[[Category:17-tone scales]]
[[Category:Mega chromatic scales]]
[[Category:Mega chromatic scales]]

Revision as of 09:56, 7 August 2024

Todo: review

Adopt scale tree template, add note that mode names are tuning-specific (they only apply to specific tunings)

↖ 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 a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 5 small steps, repeating every octave. 12L 5s is a grandchild scale of 5L 2s, expanding it by 10 tones. Generators that produce this scale range from 494.1 ¢ to 500 ¢, or from 700 ¢ to 705.9 ¢. Temperaments supported by this scale include those under the Pythagorean and schismic families, characterized by a diesis (the difference between a large step and two small steps) that is smaller than the chroma.

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

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 12L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\17 494.118 705.882 1:1 1.000 Equalized 12L 5s
40\97 494.845 705.155 6:5 1.200
33\80 495.000 705.000 5:4 1.250
59\143 495.105 704.895 9:7 1.286
26\63 495.238 704.762 4:3 1.333 Supersoft 12L 5s
71\172 495.349 704.651 11:8 1.375
45\109 495.413 704.587 7:5 1.400
64\155 495.484 704.516 10:7 1.429
19\46 495.652 704.348 3:2 1.500 Soft 12L 5s
69\167 495.808 704.192 11:7 1.571
50\121 495.868 704.132 8:5 1.600
81\196 495.918 704.082 13:8 1.625
31\75 496.000 704.000 5:3 1.667 Semisoft 12L 5s
74\179 496.089 703.911 12:7 1.714
43\104 496.154 703.846 7:4 1.750
55\133 496.241 703.759 9:5 1.800
12\29 496.552 703.448 2:1 2.000 Basic 12L 5s
Scales with tunings softer than this are proper
53\128 496.875 703.125 9:4 2.250
41\99 496.970 703.030 7:3 2.333
70\169 497.041 702.959 12:5 2.400
29\70 497.143 702.857 5:2 2.500 Semihard 12L 5s
75\181 497.238 702.762 13:5 2.600
46\111 497.297 702.703 8:3 2.667
63\152 497.368 702.632 11:4 2.750
17\41 497.561 702.439 3:1 3.000 Hard 12L 5s
56\135 497.778 702.222 10:3 3.333
39\94 497.872 702.128 7:2 3.500
61\147 497.959 702.041 11:3 3.667
22\53 498.113 701.887 4:1 4.000 Superhard 12L 5s
49\118 498.305 701.695 9:2 4.500
27\65 498.462 701.538 5:1 5.000
32\77 498.701 701.299 6:1 6.000
5\12 500.000 700.000 1:0 → ∞ Collapsed 12L 5s
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