6L 7s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 5L 6s ↑ 6L 6s 7L 6s ↗
← 5L 7s 6L 7s 7L 7s →
↙ 5L 8s ↓ 6L 8s 7L 8s ↘ 
┌╥┬╥┬╥┬╥┬╥┬╥┬┬┐
│║│║│║│║│║│║│││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLsLss
ssLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\13 to 1\6 (184.6 ¢ to 200.0 ¢)
Dark 5\6 to 11\13 (1000.0 ¢ to 1015.4 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 6L 1s
Sister 7L 6s
Daughters 13L 6s, 6L 13s
Neutralized 12L 1s
2-Flought 19L 7s, 6L 20s
Equal tunings
Equalized (L:s = 1:1) 2\13 (184.6 ¢)
Supersoft (L:s = 4:3) 7\45 (186.7 ¢)
Soft (L:s = 3:2) 5\32 (187.5 ¢)
Semisoft (L:s = 5:3) 8\51 (188.2 ¢)
Basic (L:s = 2:1) 3\19 (189.5 ¢)
Semihard (L:s = 5:2) 7\44 (190.9 ¢)
Hard (L:s = 3:1) 4\25 (192.0 ¢)
Superhard (L:s = 4:1) 5\31 (193.5 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)

6L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 7 small steps, repeating every octave. 6L 7s is a child scale of 6L 1s, expanding it by 6 tones. Generators that produce this scale range from 184.6 ¢ to 200 ¢, or from 1000 ¢ to 1015.4 ¢.

This MOS is the chromatic scale of a family of temperaments which are index-2 subtemperaments (that is, taking every other step of the generator chain) of various meantone temperaments: that is, those that are generated by a mean tone, that being specifically a whole tone of tunings with a fifth in between that of 26edo and 12edo, and roughly speaking between 10/9 and 9/8.

The most notable temperaments generating this scale are didacus in the 2.5.7 subgroup and its extensions, with its generator identified with ~28/25, whose optimum makes a superhard tuning, similarly to the situation with 5L 6s and slendric.

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.

Intervals

Intervals of 6L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 92.3 ¢
Major 1-mosstep M1ms L 92.3 ¢ to 200.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 184.6 ¢
Perfect 2-mosstep P2ms L + s 184.6 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 200.0 ¢ to 276.9 ¢
Major 3-mosstep M3ms 2L + s 276.9 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 200.0 ¢ to 369.2 ¢
Major 4-mosstep M4ms 2L + 2s 369.2 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 400.0 ¢ to 461.5 ¢
Major 5-mosstep M5ms 3L + 2s 461.5 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 400.0 ¢ to 553.8 ¢
Major 6-mosstep M6ms 3L + 3s 553.8 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 600.0 ¢ to 646.2 ¢
Major 7-mosstep M7ms 4L + 3s 646.2 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 600.0 ¢ to 738.5 ¢
Major 8-mosstep M8ms 4L + 4s 738.5 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 800.0 ¢ to 830.8 ¢
Major 9-mosstep M9ms 5L + 4s 830.8 ¢ to 1000.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 800.0 ¢ to 923.1 ¢
Major 10-mosstep M10ms 5L + 5s 923.1 ¢ to 1000.0 ¢
11-mosstep Perfect 11-mosstep P11ms 5L + 6s 1000.0 ¢ to 1015.4 ¢
Augmented 11-mosstep A11ms 6L + 5s 1015.4 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 1000.0 ¢ to 1107.7 ¢
Major 12-mosstep M12ms 6L + 6s 1107.7 ¢ to 1200.0 ¢
13-mosstep Perfect 13-mosstep P13ms 6L + 7s 1200.0 ¢

Generator chain

Generator chain of 6L 7s
Bright gens Scale degree Abbrev.
18 Augmented 10-mosdegree A10md
17 Augmented 8-mosdegree A8md
16 Augmented 6-mosdegree A6md
15 Augmented 4-mosdegree A4md
14 Augmented 2-mosdegree A2md
13 Augmented 0-mosdegree A0md
12 Augmented 11-mosdegree A11md
11 Major 9-mosdegree M9md
10 Major 7-mosdegree M7md
9 Major 5-mosdegree M5md
8 Major 3-mosdegree M3md
7 Major 1-mosdegree M1md
6 Major 12-mosdegree M12md
5 Major 10-mosdegree M10md
4 Major 8-mosdegree M8md
3 Major 6-mosdegree M6md
2 Major 4-mosdegree M4md
1 Perfect 2-mosdegree P2md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 11-mosdegree P11md
−2 Minor 9-mosdegree m9md
−3 Minor 7-mosdegree m7md
−4 Minor 5-mosdegree m5md
−5 Minor 3-mosdegree m3md
−6 Minor 1-mosdegree m1md
−7 Minor 12-mosdegree m12md
−8 Minor 10-mosdegree m10md
−9 Minor 8-mosdegree m8md
−10 Minor 6-mosdegree m6md
−11 Minor 4-mosdegree m4md
−12 Diminished 2-mosdegree d2md
−13 Diminished 13-mosdegree d13md
−14 Diminished 11-mosdegree d11md
−15 Diminished 9-mosdegree d9md
−16 Diminished 7-mosdegree d7md
−17 Diminished 5-mosdegree d5md
−18 Diminished 3-mosdegree d3md

Modes

Scale degrees of the modes of 6L 7s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
12|0 1 LsLsLsLsLsLss Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf.
11|1 3 LsLsLsLsLssLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
10|2 5 LsLsLsLssLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf.
9|3 7 LsLsLssLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
8|4 9 LsLssLsLsLsLs Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
7|5 11 LssLsLsLsLsLs Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
6|6 13 sLsLsLsLsLsLs Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
5|7 2 sLsLsLsLsLssL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf.
4|8 4 sLsLsLsLssLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf.
3|9 6 sLsLsLssLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf.
2|10 8 sLsLssLsLsLsL Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
1|11 10 sLssLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|12 12 ssLsLsLsLsLsL Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\13 184.615 1015.385 1:1 1.000 Equalized 6L 7s
11\71 185.915 1014.085 6:5 1.200
9\58 186.207 1013.793 5:4 1.250
16\103 186.408 1013.592 9:7 1.286
7\45 186.667 1013.333 4:3 1.333 Supersoft 6L 7s
19\122 186.885 1013.115 11:8 1.375
12\77 187.013 1012.987 7:5 1.400
17\109 187.156 1012.844 10:7 1.429
5\32 187.500 1012.500 3:2 1.500 Soft 6L 7s
18\115 187.826 1012.174 11:7 1.571
13\83 187.952 1012.048 8:5 1.600
21\134 188.060 1011.940 13:8 1.625
8\51 188.235 1011.765 5:3 1.667 Semisoft 6L 7s
19\121 188.430 1011.570 12:7 1.714
11\70 188.571 1011.429 7:4 1.750
14\89 188.764 1011.236 9:5 1.800
3\19 189.474 1010.526 2:1 2.000 Basic 6L 7s
Scales with tunings softer than this are proper
13\82 190.244 1009.756 9:4 2.250
10\63 190.476 1009.524 7:3 2.333
17\107 190.654 1009.346 12:5 2.400
7\44 190.909 1009.091 5:2 2.500 Semihard 6L 7s
18\113 191.150 1008.850 13:5 2.600
11\69 191.304 1008.696 8:3 2.667
15\94 191.489 1008.511 11:4 2.750
4\25 192.000 1008.000 3:1 3.000 Hard 6L 7s
13\81 192.593 1007.407 10:3 3.333
9\56 192.857 1007.143 7:2 3.500
14\87 193.103 1006.897 11:3 3.667 Hemithirds/luna
5\31 193.548 1006.452 4:1 4.000 Superhard 6L 7s
Didacus/hemiwürschmidt
11\68 194.118 1005.882 9:2 4.500
6\37 194.595 1005.405 5:1 5.000 Roulette/mediantone
7\43 195.349 1004.651 6:1 6.000
1\6 200.000 1000.000 1:0 → ∞ Collapsed 6L 7s
Retrieved from "https://en.xen.wiki/index.php?title=6L_7s&oldid=195298"