7L 12s: Difference between revisions

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== Scale tree ==
== Scale tree ==
Generator ranges:
{{Scale tree|Comments=
* Chroma-positive generator: 505.2632 cents (8\19) to 514.2857 cents (3\7)
3/2: [[Flattone]];
* Chroma-negative generator: 685.7143 cents (4\7) to 694.7368 cents (11\19)
13/8: Golden flattone (506.9365¢);
 
13/5: Unnamed golden tuning (508.6329¢);
{| class="wikitable center-all"
}}
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 8\19 || || || || || || 505.263 || 1 || 1 || 1.000 ||
|-
| || || || || || 43\102 || 505.882 || 6 || 5 || 1.200 ||
|-
| || || || || 35\83 || || 506.024 || 5 || 4 || 1.250 ||
|-
| || || || || || 62\147 || 506.122 || 9 || 7 || 1.286 ||
|-
| || || || 27\64 || || || 506.250 || 4 || 3 || 1.333 ||
|-
| || || || || || 73\173 || 506.358 || 11 || 8 || 1.375 ||
|-
| || || || || 46\109 || || 506.422 || 7 || 5 || 1.400 ||
|-
| || || || || || 65\154 || 506.494 || 10 || 7 || 1.428 ||
|-
| || || 19\45 || || || || 506.667 || 3 || 2 || 1.500 || [[Flattone]]
|-
| || || || || || 68\161 || 506.832 || 11 || 7 || 1.571 ||
|-
| || || || || 49\116 || || 506.897 || 8 || 5 || 1.600 ||
|-
| || || || || || 79\187 || 506.952 || 13 || 8 || 1.625 || Golden flattone (506.9365¢)
|-
| || || || 30\71 || || || 507.042 || 5 || 3 || 1.667 ||
|-
| || || || || || 71\168 || 507.143 || 12 || 7 || 1.714 ||
|-
| || || || || 41\97 || || 507.216 || 7 || 4 || 1.750 ||
|-
| || || || || || 52\123 || 507.317 || 9 || 5 || 1.800 ||
|-
| || 11\26 || || || || || 507.692 || 2 || 1 || 2.000 || Basic 7L 12s <br>(Generators smaller than this are proper)
|-
| || || || || || 47\111 || 508.108 || 9 || 4 || 2.250 ||
|-
| || || || || 36\85 || || 508.235 || 7 || 3 || 2.333 ||
|-
| || || || || || 61\144 || 508.333 || 12 || 5 || 2.400 ||
|-
| || || || 25\59 || || || 508.475 || 5 || 2 || 2.500 ||
|-
| || || || || || 64\151 || 508.609 || 13 || 5 || 2.600 || Unnamed golden tuning (508.6329¢)
|-
| || || || || 39\92 || || 508.696 || 8 || 3 || 2.667 ||
|-
| || || || || || 53\125 || 508.800 || 11 || 4 || 2.750 ||
|-
| || || 14\33 || || || || 509.091 || 3 || 1 || 3.000 ||
|-
| || || || || || 45\106 || 509.434 || 10 || 3 || 3.333 ||
|-
| || || || || 31\73 || || 509.589 || 7 || 2 || 3.500 ||
|-
| || || || || || 48\113 || 509.735 || 11 || 3 || 3.667 ||
|-
| || || || 17\40 || || || 510.000 || 4 || 1 || 4.000 ||
|-
| || || || || || 37\87 || 510.345 || 9 || 2 || 4.500 ||
|-
| || || || || 20\47 || || 510.638 || 5 || 1 || 5.000 ||
|-
| || || || || || 23\54 || 511.111 || 6 || 1 || 6.000 ||
|-
| 3\7 || || || || || || 514.286 || 1 || 0 || → inf ||
|}


[[Category:19-tone scales]]
[[Category:19-tone scales]]
[[Category:Mega chromatic scales]]
[[Category:Mega chromatic scales]]

Revision as of 10:24, 7 August 2024

Todo: review

Adopt scale tree template, review entries

↖ 6L 11s ↑ 7L 11s 8L 11s ↗
← 6L 12s 7L 12s 8L 12s →
↙ 6L 13s ↓ 7L 13s 8L 13s ↘
Scale structure
Step pattern LsLssLssLsLssLssLss
ssLssLssLsLssLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 8\19 to 3\7 (505.3 ¢ to 514.3 ¢)
Dark 4\7 to 11\19 (685.7 ¢ to 694.7 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 1:1 to 3:2 (soft)
Related MOS scales
Parent 7L 5s
Sister 12L 7s
Daughters 19L 7s, 7L 19s
Neutralized 14L 5s
2-Flought 26L 12s, 7L 31s
Equal tunings
Equalized (L:s = 1:1) 8\19 (505.3 ¢)
Supersoft (L:s = 4:3) 27\64 (506.2 ¢)
Soft (L:s = 3:2) 19\45 (506.7 ¢)
Semisoft (L:s = 5:3) 30\71 (507.0 ¢)
Basic (L:s = 2:1) 11\26 (507.7 ¢)
Semihard (L:s = 5:2) 25\59 (508.5 ¢)
Hard (L:s = 3:1) 14\33 (509.1 ¢)
Superhard (L:s = 4:1) 17\40 (510.0 ¢)
Collapsed (L:s = 1:0) 3\7 (514.3 ¢)
View • Talk • Edit

7L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 12 small steps, repeating every octave. 7L 12s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 505.3 ¢ to 514.3 ¢, or from 685.7 ¢ to 694.7 ¢. Temperaments associated with this scale include flattone, as the flattone enharmonic scale.

Modes

Modes of 7L 12s
UDP Cyclic
order		 Step
pattern
18|0 1 LsLssLssLsLssLssLss
17|1 9 LsLssLssLssLsLssLss
16|2 17 LssLsLssLssLsLssLss
15|3 6 LssLsLssLssLssLsLss
14|4 14 LssLssLsLssLssLsLss
13|5 3 LssLssLsLssLssLssLs
12|6 11 LssLssLssLsLssLssLs
11|7 19 sLsLssLssLsLssLssLs
10|8 8 sLsLssLssLssLsLssLs
9|9 16 sLssLsLssLssLsLssLs
8|10 5 sLssLsLssLssLssLsLs
7|11 13 sLssLssLsLssLssLsLs
6|12 2 sLssLssLsLssLssLssL
5|13 10 sLssLssLssLsLssLssL
4|14 18 ssLsLssLssLsLssLssL
3|15 7 ssLsLssLssLssLsLssL
2|16 15 ssLssLsLssLssLsLssL
1|17 4 ssLssLsLssLssLssLsL
0|18 12 ssLssLssLsLssLssLsL

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 7L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
8\19 505.263 694.737 1:1 1.000 Equalized 7L 12s
43\102 505.882 694.118 6:5 1.200
35\83 506.024 693.976 5:4 1.250
62\147 506.122 693.878 9:7 1.286
27\64 506.250 693.750 4:3 1.333 Supersoft 7L 12s
73\173 506.358 693.642 11:8 1.375
46\109 506.422 693.578 7:5 1.400
65\154 506.494 693.506 10:7 1.429
19\45 506.667 693.333 3:2 1.500 Soft 7L 12s
68\161 506.832 693.168 11:7 1.571
49\116 506.897 693.103 8:5 1.600
79\187 506.952 693.048 13:8 1.625
30\71 507.042 692.958 5:3 1.667 Semisoft 7L 12s
71\168 507.143 692.857 12:7 1.714
41\97 507.216 692.784 7:4 1.750
52\123 507.317 692.683 9:5 1.800
11\26 507.692 692.308 2:1 2.000 Basic 7L 12s
Scales with tunings softer than this are proper
47\111 508.108 691.892 9:4 2.250
36\85 508.235 691.765 7:3 2.333
61\144 508.333 691.667 12:5 2.400
25\59 508.475 691.525 5:2 2.500 Semihard 7L 12s
64\151 508.609 691.391 13:5 2.600
39\92 508.696 691.304 8:3 2.667
53\125 508.800 691.200 11:4 2.750
14\33 509.091 690.909 3:1 3.000 Hard 7L 12s
45\106 509.434 690.566 10:3 3.333
31\73 509.589 690.411 7:2 3.500
48\113 509.735 690.265 11:3 3.667
17\40 510.000 690.000 4:1 4.000 Superhard 7L 12s
37\87 510.345 689.655 9:2 4.500
20\47 510.638 689.362 5:1 5.000
23\54 511.111 688.889 6:1 6.000
3\7 514.286 685.714 1:0 → ∞ Collapsed 7L 12s
Retrieved from "https://en.xen.wiki/index.php?title=7L_12s&oldid=149718"