12L 7s: Difference between revisions

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== Scale tree ==
== Scale tree ==
Generator ranges:
{{Scale tree|Comments=
* Chroma-positive generator: 694.7368 cents (11\19) to 700 cents (7\12)
13/8: [[Golden meantone]] (696.2145¢);
* Chroma-negative generator: 500 cents (5\12) to 505.2632 cents (8\19)
5/3: [[Meantone]] / [[meanpop]];
 
7/3: Meantone / [[huygens]];
{| class="wikitable center-all"
5/2: Meantone / huygens / [[grosstone]];
! colspan="6" | Generator
13/5: Golden grosstone (697.3969¢);
! Cents
3/1: Meantone / [[meridetone]]
! L
}}
! s
! L/s
! Comments
|-
| 11\19 || || || || || || 694.737 || 1 || 1 || 1.000 ||
|-
| || || || || || 62\107 || 695.327 || 6 || 5 || 1.200 ||
|-
| || || || || 51\88 || || 695.455 || 5 || 4 || 1.250 ||
|-
| || || || || || 91\157 || 695.541 || 9 || 7 || 1.286 ||
|-
| || || || 40\69 || || || 695.652 || 4 || 3 || 1.333 ||
|-
| || || || || || 109\188 || 695.745 || 11 || 8 || 1.375 ||
|-
| || || || || 69\119 || || 695.798 || 7 || 5 || 1.400 ||
|-
| || || || || || 98\169 || 695.858 || 10 || 7 || 1.428 ||
|-
| || || 29\50 || || || || 696.000 || 3 || 2 || 1.500 || [[Meantone]] / [[Meanpop]]
|-
| || || || || || 105\181 || 696.133 || 11 || 7 || 1.571 ||
|-
| || || || || 76\131 || || 696.183 || 8 || 5 || 1.600 ||
|-
| || || || || || 123\212 || 696.226 || 13 || 8 || 1.625 || [[Golden meantone]] (696.2145¢)
|-
| || || || 47\81 || || || 696.296 || 5 || 3 || 1.667 || Meantone / Meanpop
|-
| || || || || || 112\193 || 696.373 || 12 || 7 || 1.714 ||
|-
| || || || || 65\112 || || 696.429 || 7 || 4 || 1.750 ||
|-
| || || || || || 83\143 || 696.503 || 9 || 5 || 1.800 ||
|-
| || 18\31 || || || || || 696.774 || 2 || 1 || 2.000 || Basic 12L 7s <br>(Generators smaller than this are proper)
|-
| || || || || || 79\136 || 697.059 || 9 || 4 || 2.250 ||
|-
| || || || || 61\105 || || 697.143 || 7 || 3 || 2.333 || Meantone / [[Huygens]]
|-
| || || || || || 104\179 || 697.207 || 12 || 5 || 2.400 ||
|-
| || || || 43\74 || || || 697.297 || 5 || 2 || 2.500 || Meantone / Huygens / [[Grosstone]]
|-
| || || || || || 111\191 || 697.382 || 13 || 5 || 2.600 || Golden grosstone (697.3969¢)
|-
| || || || || 68\117 || || 697.436 || 8 || 3 || 2.667 ||
|-
| || || || || || 93\160 || 697.500 || 11 || 4 || 2.750 ||
|-
| || || 25\43 || || || || 697.674 || 3 || 1 || 3.000 || Meantone / [[Meridetone]]
|-
| || || || || || 82\141 || 697.872 || 10 || 3 || 3.333 ||
|-
| || || || || 57\98 || || 697.959 || 7 || 2 || 3.500 ||
|-
| || || || || || 89\153 || 698.039 || 11 || 3 || 3.667 ||
|-
| || || || 32\55 || || || 698.182 || 4 || 1 || 4.000 ||
|-
| || || || || || 71\122 || 698.361 || 9 || 2 || 4.500 ||
|-
| || || || || 39\67 || || 698.507 || 5 || 1 || 5.000 ||
|-
| || || || || || 46\79 || 698.734 || 6 || 1 || 6.000 ||
|-
| 7\12 || || || || || || 700.000 || 1 || 0 || → inf ||
|}


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

Revision as of 10:15, 7 August 2024

Todo: review

Adopt scale tree, review entries

↖ 11L 6s ↑ 12L 6s 13L 6s ↗
← 11L 7s 12L 7s 13L 7s →
↙ 11L 8s ↓ 12L 8s 13L 8s ↘
Scale structure
Step pattern LLsLLsLLsLsLLsLLsLs
sLsLLsLLsLsLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\19 to 7\12 (694.7 ¢ to 700.0 ¢)
Dark 5\12 to 8\19 (500.0 ¢ to 505.3 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 7L 5s
Sister 7L 12s
Daughters 19L 12s, 12L 19s
Neutralized 5L 14s
2-Flought 31L 7s, 12L 26s
Equal tunings
Equalized (L:s = 1:1) 11\19 (694.7 ¢)
Supersoft (L:s = 4:3) 40\69 (695.7 ¢)
Soft (L:s = 3:2) 29\50 (696.0 ¢)
Semisoft (L:s = 5:3) 47\81 (696.3 ¢)
Basic (L:s = 2:1) 18\31 (696.8 ¢)
Semihard (L:s = 5:2) 43\74 (697.3 ¢)
Hard (L:s = 3:1) 25\43 (697.7 ¢)
Superhard (L:s = 4:1) 32\55 (698.2 ¢)
Collapsed (L:s = 1:0) 7\12 (700.0 ¢)
View • Talk • Edit

12L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 7 small steps, repeating every octave. 12L 7s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 694.7 ¢ to 700 ¢, or from 500 ¢ to 505.3 ¢. Temperaments associated with this scale include meantone, as the meantone enharmonic scale.

Modes

Modes of 12L 7s
UDP Cyclic
order		 Step
pattern
18|0 1 LLsLLsLLsLsLLsLLsLs
17|1 12 LLsLLsLsLLsLLsLLsLs
16|2 4 LLsLLsLsLLsLLsLsLLs
15|3 15 LLsLsLLsLLsLLsLsLLs
14|4 7 LLsLsLLsLLsLsLLsLLs
13|5 18 LsLLsLLsLLsLsLLsLLs
12|6 10 LsLLsLLsLsLLsLLsLLs
11|7 2 LsLLsLLsLsLLsLLsLsL
10|8 13 LsLLsLsLLsLLsLLsLsL
9|9 5 LsLLsLsLLsLLsLsLLsL
8|10 16 LsLsLLsLLsLLsLsLLsL
7|11 8 LsLsLLsLLsLsLLsLLsL
6|12 19 sLLsLLsLLsLsLLsLLsL
5|13 11 sLLsLLsLsLLsLLsLLsL
4|14 3 sLLsLLsLsLLsLLsLsLL
3|15 14 sLLsLsLLsLLsLLsLsLL
2|16 6 sLLsLsLLsLLsLsLLsLL
1|17 17 sLsLLsLLsLLsLsLLsLL
0|18 9 sLsLLsLLsLsLLsLLsLL

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 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\19 694.737 505.263 1:1 1.000 Equalized 12L 7s
62\107 695.327 504.673 6:5 1.200
51\88 695.455 504.545 5:4 1.250
91\157 695.541 504.459 9:7 1.286
40\69 695.652 504.348 4:3 1.333 Supersoft 12L 7s
109\188 695.745 504.255 11:8 1.375
69\119 695.798 504.202 7:5 1.400
98\169 695.858 504.142 10:7 1.429
29\50 696.000 504.000 3:2 1.500 Soft 12L 7s
105\181 696.133 503.867 11:7 1.571
76\131 696.183 503.817 8:5 1.600
123\212 696.226 503.774 13:8 1.625
47\81 696.296 503.704 5:3 1.667 Semisoft 12L 7s
112\193 696.373 503.627 12:7 1.714
65\112 696.429 503.571 7:4 1.750
83\143 696.503 503.497 9:5 1.800
18\31 696.774 503.226 2:1 2.000 Basic 12L 7s
Scales with tunings softer than this are proper
79\136 697.059 502.941 9:4 2.250
61\105 697.143 502.857 7:3 2.333
104\179 697.207 502.793 12:5 2.400
43\74 697.297 502.703 5:2 2.500 Semihard 12L 7s
111\191 697.382 502.618 13:5 2.600
68\117 697.436 502.564 8:3 2.667
93\160 697.500 502.500 11:4 2.750
25\43 697.674 502.326 3:1 3.000 Hard 12L 7s
82\141 697.872 502.128 10:3 3.333
57\98 697.959 502.041 7:2 3.500
89\153 698.039 501.961 11:3 3.667
32\55 698.182 501.818 4:1 4.000 Superhard 12L 7s
71\122 698.361 501.639 9:2 4.500
39\67 698.507 501.493 5:1 5.000
46\79 698.734 501.266 6:1 6.000
7\12 700.000 500.000 1:0 → ∞ Collapsed 12L 7s
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