7L 5s

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↖ 6L 4s ↑7L 4s 8L 4s ↗
← 6L 5s7L 5s 8L 5s →
↙ 6L 6s ↓7L 6s 8L 6s ↘
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Scale structure
Step pattern LLsLsLLsLsLs
sLsLsLLsLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\12 to 3\7 (500.0¢ to 514.3¢)
Dark 4\7 to 7\12 (685.7¢ to 700.0¢)
TAMNAMS information
Descends from 5L 2s (diatonic)
Required step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 5L 2s
Sister 5L 7s
Daughters 12L 7s, 7L 12s
Neutralized 2L 10s
Equal tunings
Equalized (L:s = 1:1) 5\12 (500.0¢)
Supersoft (L:s = 4:3) 18\43 (502.3¢)
Soft (L:s = 3:2) 13\31 (503.2¢)
Semisoft (L:s = 5:3) 21\50 (504.0¢)
Basic (L:s = 2:1) 8\19 (505.3¢)
Semihard (L:s = 5:2) 19\45 (506.7¢)
Hard (L:s = 3:1) 11\26 (507.7¢)
Superhard (L:s = 4:1) 14\33 (509.1¢)
Collapsed (L:s = 1:0) 3\7 (514.3¢)

7L 5s, also called m-chromatic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 5 small steps, repeating every octave. 7L 5s is a child scale of 5L 2s, expanding it by 5 tones. Generators that produce this scale range from 500¢ to 514.3¢, or from 685.7¢ to 700¢. 7L 5s represents the chromatic scale of meantone, or meantone chromatic scale. Such scales are characterized by having a small step (diatonic semitone) that is larger than the chroma (chromatic semitone), the reverse of 5L 7s.

Meantone is the only notable harmonic entropy minimum.

Modes

Both Eliora and Ganaram have independently proposed mode names based on names of the months. The latter scheme uses mode names from the Gregorian calendar, starting with January assigned to the step pattern LsLsLsLLsLsL, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.

Modes of 7L 5s
UDP Rotational order Step pattern Mode names
11|0 1 LLsLsLLsLsLs July
10|1 6 LLsLsLsLLsLs December
9|2 11 LsLLsLsLLsLs May
8|3 4 LsLLsLsLsLLs October
7|4 9 LsLsLLsLsLLs March
6|5 2 LsLsLLsLsLsL August
5|6 7 LsLsLsLLsLsL January
4|7 12 sLLsLsLLsLsL June
3|8 5 sLLsLsLsLLsL November
2|9 10 sLsLLsLsLLsL April
1|10 3 sLsLLsLsLsLL September
0|11 8 sLsLsLLsLsLL February
Modes of 7L 5s
UDP Rotational order Step pattern Mode names
11|0 1 LLsLsLLsLsLs Martian
10|1 6 LLsLsLsLLsLs Aprilian
9|2 11 LsLLsLsLLsLs Maian
8|3 4 LsLLsLsLsLLs Junian
7|4 9 LsLsLLsLsLLs Quintillian or Julian
6|5 2 LsLsLLsLsLsL Sextilian or Augustan
5|6 7 LsLsLsLLsLsL Septembian
4|7 12 sLLsLsLLsLsL Octobian
3|8 5 sLLsLsLsLLsL Novembian
2|9 10 sLsLLsLsLLsL Decembian
1|10 3 sLsLLsLsLsLL Janian
0|11 8 sLsLsLLsLsLL Februan

Scales

  • Meaneb471a – an equal beating tuning of meantone
  • Meantone12 – 31edo tuning
  • Ratwolf – 20/13 wolf fifth tuning of meantone
  • Meaneb471 – the other equal beating tuning of meantone
  • Flattone12 – 13-limit POTE tuning of flattone

Scale tree

Scale Tree and Tuning Spectrum of 7L 5s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
5\12 500.000 700.000 1:1 1.000 Equalized 7L 5s
28\67 501.493 698.507 6:5 1.200
23\55 501.818 698.182 5:4 1.250
41\98 502.041 697.959 9:7 1.286
18\43 502.326 697.674 4:3 1.333 Supersoft 7L 5s
Meantone / meridetone
49\117 502.564 697.436 11:8 1.375
31\74 502.703 697.297 7:5 1.400 Meantone / huygens / grosstone
44\105 502.857 697.143 10:7 1.429
13\31 503.226 696.774 3:2 1.500 Soft 7L 5s
47\112 503.571 696.429 11:7 1.571
34\81 503.704 696.296 8:5 1.600 Meantone
55\131 503.817 696.183 13:8 1.625 Golden meantone (503.7855¢)
21\50 504.000 696.000 5:3 1.667 Semisoft 7L 5s
Meantone / meanpop
50\119 504.202 695.798 12:7 1.714
29\69 504.348 695.652 7:4 1.750
37\88 504.545 695.455 9:5 1.800
8\19 505.263 694.737 2:1 2.000 Basic 7L 5s
Scales with tunings softer than this are proper
35\83 506.024 693.976 9:4 2.250
27\64 506.250 693.750 7:3 2.333
46\109 506.422 693.578 12:5 2.400
19\45 506.667 693.333 5:2 2.500 Semihard 7L 5s
Flattone
49\116 506.897 693.103 13:5 2.600 Golden flattone (506.9365¢)
30\71 507.042 692.958 8:3 2.667
41\97 507.216 692.784 11:4 2.750
11\26 507.692 692.308 3:1 3.000 Hard 7L 5s
36\85 508.235 691.765 10:3 3.333
25\59 508.475 691.525 7:2 3.500
39\92 508.696 691.304 11:3 3.667
14\33 509.091 690.909 4:1 4.000 Superhard 7L 5s
31\73 509.589 690.411 9:2 4.500
17\40 510.000 690.000 5:1 5.000
20\47 510.638 689.362 6:1 6.000
3\7 514.286 685.714 1:0 → ∞ Collapsed 7L 5s