12L 5s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,543 edits
m Todo
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
Line 4: Line 4:


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).
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).
==Intervals==
 
{{MOS intervals}}
== Scale properties ==
== Modes ==
{{TAMNAMS use}}
{{MOS mode degrees}}
{{MOS data}}
 
=== Proposed tuning-specific names ===
=== Proposed tuning-specific names ===
[[Declan Paul Boushy]] has proposed names for these modes corresponding to step ratios [[Subaru scale|3:1]] and [[Tanegashima scale|4:1]].
[[Declan Paul Boushy]] has proposed names for these modes corresponding to step ratios [[Subaru scale|3:1]] and [[Tanegashima scale|4:1]].
Line 22: Line 23:


== Scale tree ==
== Scale tree ==
{{Scale tree|Comments=
{{MOS tuning spectrum
4/3: [[Leapfrog]];
| 4/3 = [[Leapfrog]]  
7/5: [[Leapweek]];
| 7/5 = [[Leapweek]]  
3/2: [[Leapday]];
| 3/2 = [[Leapday]]  
11/7: [[Polypyth]];
| 11/7 = [[Polypyth]]  
13/8: Golden neogothic (495.904¢);
| 13/8 = Golden neogothic (495.904{{c}})  
7/3: [[Undecental]];
| 7/3 = [[Undecental]]  
12/5: Argent tuning (497.056¢);
| 12/5 = Argent tuning (497.056{{c}})  
13/5: Unnamed golden tuning (497.254¢);
| 13/5 = Unnamed golden tuning (497.254{{c}})  
11/4: [[Kwai]];
| 11/4 = [[Kwai]]  
3/1: [[Garibaldi]] / [[andromeda]];
| 3/1 = [[Garibaldi]] / [[andromeda]]  
7/2: Garibaldi / [[cassandra]];
| 7/2 = Garibaldi / [[cassandra]]  
4/1: Garibaldi / [[helenus]], Pythagorean tuning (498.045¢);
| 4/1 = Garibaldi / [[helenus]], Pythagorean tuning (498.045{{c}})  
9/2: [[Pontiac]];
| 9/2 = [[Pontiac]]  
5/1: [[Photia]];
| 5/1 = [[Photia]]  
6/1: ↓ [[Grackle]], ↓↓ [[gracecordial]];
| 6/1 = ↓ [[Grackle]], ↓↓ [[gracecordial]]  
}}
}}


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

Revision as of 16:47, 28 February 2025

↖ 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, also called p-enharmonic, 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).

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.
MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Proposed tuning-specific names

Declan Paul Boushy has proposed names for these modes corresponding to step ratios 3:1 and 4:1.

Scales

Scale tree

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
Leapfrog
71\172 495.349 704.651 11:8 1.375
45\109 495.413 704.587 7:5 1.400 Leapweek
64\155 495.484 704.516 10:7 1.429
19\46 495.652 704.348 3:2 1.500 Soft 12L 5s
Leapday
69\167 495.808 704.192 11:7 1.571 Polypyth
50\121 495.868 704.132 8:5 1.600
81\196 495.918 704.082 13:8 1.625 Golden neogothic (495.904 ¢)
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 Undecental
70\169 497.041 702.959 12:5 2.400 Argent tuning (497.056 ¢)
29\70 497.143 702.857 5:2 2.500 Semihard 12L 5s
75\181 497.238 702.762 13:5 2.600 Unnamed golden tuning (497.254 ¢)
46\111 497.297 702.703 8:3 2.667
63\152 497.368 702.632 11:4 2.750 Kwai
17\41 497.561 702.439 3:1 3.000 Hard 12L 5s
Garibaldi / andromeda
56\135 497.778 702.222 10:3 3.333
39\94 497.872 702.128 7:2 3.500 Garibaldi / cassandra
61\147 497.959 702.041 11:3 3.667
22\53 498.113 701.887 4:1 4.000 Superhard 12L 5s
Garibaldi / helenus, Pythagorean tuning (498.045 ¢)
49\118 498.305 701.695 9:2 4.500 Pontiac
27\65 498.462 701.538 5:1 5.000 Photia
32\77 498.701 701.299 6:1 6.000 ↓ Grackle, ↓↓ gracecordial
5\12 500.000 700.000 1:0 → ∞ Collapsed 12L 5s
Retrieved from "https://en.xen.wiki/index.php?title=12L_5s&oldid=183738"