7L 19s

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Scale structure
Step pattern LssLsssLsssLssLsssLsssLsss
sssLsssLsssLssLsssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\26 to 3\7 (507.7 ¢ to 514.3 ¢)
Dark 4\7 to 15\26 (685.7 ¢ to 692.3 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent 7L 12s
Sister 19L 7s
Daughters 26L 7s, 7L 26s
Neutralized 14L 12s
2-Flought 33L 19s, 7L 45s
Equal tunings
Equalized (L:s = 1:1) 11\26 (507.7 ¢)
Supersoft (L:s = 4:3) 36\85 (508.2 ¢)
Soft (L:s = 3:2) 25\59 (508.5 ¢)
Semisoft (L:s = 5:3) 39\92 (508.7 ¢)
Basic (L:s = 2:1) 14\33 (509.1 ¢)
Semihard (L:s = 5:2) 31\73 (509.6 ¢)
Hard (L:s = 3:1) 17\40 (510.0 ¢)
Superhard (L:s = 4:1) 20\47 (510.6 ¢)
Collapsed (L:s = 1:0) 3\7 (514.3 ¢)

7L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 19 small steps, repeating every octave. 7L 19s is a great-grandchild scale of 5L 2s, expanding it by 19 tones. Generators that produce this scale range from 507.7 ¢ to 514.3 ¢, or from 685.7 ¢ to 692.3 ¢.

Even this far towards 7edo in the 5L 2s descendants, there are still multiple available temperaments. If the (bright) generator is taken as 4/3, we are rather beyond the range of standard meantone or even flattone. Instead, we have flattertone in the soft range (with a 33-tone scale of 26L 7s) and deeptone in the hard one (where the 33-tone scale is 7L 26s).

In flattertone, the minor 8-mosstep is a large neutral or submajor third that can still be considered to approximate 5/4, while in deeptone, this approximation fails and 5/4 is instead equated to the minor 9-mosstep. While the major 8-mosstep, minor 10-mosstep and even diminished 11-mosstep can also be close, no major temperament seems to equate 5/4 to these intervals, although the 26 & 33 temperament (equating 5/4 to the major 8-mosstep) seems promising, if rather complex.

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 7L 19s
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 46.2 ¢
Major 1-mosstep M1ms L 46.2 ¢ to 171.4 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 92.3 ¢
Major 2-mosstep M2ms L + s 92.3 ¢ to 171.4 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 138.5 ¢
Major 3-mosstep M3ms L + 2s 138.5 ¢ to 171.4 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4 ¢ to 184.6 ¢
Major 4-mosstep M4ms 2L + 2s 184.6 ¢ to 342.9 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 171.4 ¢ to 230.8 ¢
Major 5-mosstep M5ms 2L + 3s 230.8 ¢ to 342.9 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 171.4 ¢ to 276.9 ¢
Major 6-mosstep M6ms 2L + 4s 276.9 ¢ to 342.9 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 171.4 ¢ to 323.1 ¢
Major 7-mosstep M7ms 2L + 5s 323.1 ¢ to 342.9 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 342.9 ¢ to 369.2 ¢
Major 8-mosstep M8ms 3L + 5s 369.2 ¢ to 514.3 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 342.9 ¢ to 415.4 ¢
Major 9-mosstep M9ms 3L + 6s 415.4 ¢ to 514.3 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 342.9 ¢ to 461.5 ¢
Major 10-mosstep M10ms 3L + 7s 461.5 ¢ to 514.3 ¢
11-mosstep Diminished 11-mosstep d11ms 2L + 9s 342.9 ¢ to 507.7 ¢
Perfect 11-mosstep P11ms 3L + 8s 507.7 ¢ to 514.3 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 514.3 ¢ to 553.8 ¢
Major 12-mosstep M12ms 4L + 8s 553.8 ¢ to 685.7 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 514.3 ¢ to 600.0 ¢
Major 13-mosstep M13ms 4L + 9s 600.0 ¢ to 685.7 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 514.3 ¢ to 646.2 ¢
Major 14-mosstep M14ms 4L + 10s 646.2 ¢ to 685.7 ¢
15-mosstep Perfect 15-mosstep P15ms 4L + 11s 685.7 ¢ to 692.3 ¢
Augmented 15-mosstep A15ms 5L + 10s 692.3 ¢ to 857.1 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 685.7 ¢ to 738.5 ¢
Major 16-mosstep M16ms 5L + 11s 738.5 ¢ to 857.1 ¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 685.7 ¢ to 784.6 ¢
Major 17-mosstep M17ms 5L + 12s 784.6 ¢ to 857.1 ¢
18-mosstep Minor 18-mosstep m18ms 4L + 14s 685.7 ¢ to 830.8 ¢
Major 18-mosstep M18ms 5L + 13s 830.8 ¢ to 857.1 ¢
19-mosstep Minor 19-mosstep m19ms 5L + 14s 857.1 ¢ to 876.9 ¢
Major 19-mosstep M19ms 6L + 13s 876.9 ¢ to 1028.6 ¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 857.1 ¢ to 923.1 ¢
Major 20-mosstep M20ms 6L + 14s 923.1 ¢ to 1028.6 ¢
21-mosstep Minor 21-mosstep m21ms 5L + 16s 857.1 ¢ to 969.2 ¢
Major 21-mosstep M21ms 6L + 15s 969.2 ¢ to 1028.6 ¢
22-mosstep Minor 22-mosstep m22ms 5L + 17s 857.1 ¢ to 1015.4 ¢
Major 22-mosstep M22ms 6L + 16s 1015.4 ¢ to 1028.6 ¢
23-mosstep Minor 23-mosstep m23ms 6L + 17s 1028.6 ¢ to 1061.5 ¢
Major 23-mosstep M23ms 7L + 16s 1061.5 ¢ to 1200.0 ¢
24-mosstep Minor 24-mosstep m24ms 6L + 18s 1028.6 ¢ to 1107.7 ¢
Major 24-mosstep M24ms 7L + 17s 1107.7 ¢ to 1200.0 ¢
25-mosstep Minor 25-mosstep m25ms 6L + 19s 1028.6 ¢ to 1153.8 ¢
Major 25-mosstep M25ms 7L + 18s 1153.8 ¢ to 1200.0 ¢
26-mosstep Perfect 26-mosstep P26ms 7L + 19s 1200.0 ¢

Generator chain

Generator chain of 7L 19s
Bright gens Scale degree Abbrev.
32 Augmented 14-mosdegree A14md
31 Augmented 3-mosdegree A3md
30 Augmented 18-mosdegree A18md
29 Augmented 7-mosdegree A7md
28 Augmented 22-mosdegree A22md
27 Augmented 11-mosdegree A11md
26 Augmented 0-mosdegree A0md
25 Augmented 15-mosdegree A15md
24 Major 4-mosdegree M4md
23 Major 19-mosdegree M19md
22 Major 8-mosdegree M8md
21 Major 23-mosdegree M23md
20 Major 12-mosdegree M12md
19 Major 1-mosdegree M1md
18 Major 16-mosdegree M16md
17 Major 5-mosdegree M5md
16 Major 20-mosdegree M20md
15 Major 9-mosdegree M9md
14 Major 24-mosdegree M24md
13 Major 13-mosdegree M13md
12 Major 2-mosdegree M2md
11 Major 17-mosdegree M17md
10 Major 6-mosdegree M6md
9 Major 21-mosdegree M21md
8 Major 10-mosdegree M10md
7 Major 25-mosdegree M25md
6 Major 14-mosdegree M14md
5 Major 3-mosdegree M3md
4 Major 18-mosdegree M18md
3 Major 7-mosdegree M7md
2 Major 22-mosdegree M22md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 26-mosdegree		 P0md
P26md
−1 Perfect 15-mosdegree P15md
−2 Minor 4-mosdegree m4md
−3 Minor 19-mosdegree m19md
−4 Minor 8-mosdegree m8md
−5 Minor 23-mosdegree m23md
−6 Minor 12-mosdegree m12md
−7 Minor 1-mosdegree m1md
−8 Minor 16-mosdegree m16md
−9 Minor 5-mosdegree m5md
−10 Minor 20-mosdegree m20md
−11 Minor 9-mosdegree m9md
−12 Minor 24-mosdegree m24md
−13 Minor 13-mosdegree m13md
−14 Minor 2-mosdegree m2md
−15 Minor 17-mosdegree m17md
−16 Minor 6-mosdegree m6md
−17 Minor 21-mosdegree m21md
−18 Minor 10-mosdegree m10md
−19 Minor 25-mosdegree m25md
−20 Minor 14-mosdegree m14md
−21 Minor 3-mosdegree m3md
−22 Minor 18-mosdegree m18md
−23 Minor 7-mosdegree m7md
−24 Minor 22-mosdegree m22md
−25 Diminished 11-mosdegree d11md
−26 Diminished 26-mosdegree d26md
−27 Diminished 15-mosdegree d15md
−28 Diminished 4-mosdegree d4md
−29 Diminished 19-mosdegree d19md
−30 Diminished 8-mosdegree d8md
−31 Diminished 23-mosdegree d23md
−32 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 7L 19s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
25|0 1 LssLsssLsssLssLsssLsssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
24|1 12 LssLsssLsssLsssLssLsssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
23|2 23 LsssLssLsssLsssLssLsssLsss Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
22|3 8 LsssLssLsssLsssLsssLssLsss Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
21|4 19 LsssLsssLssLsssLsssLssLsss Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|5 4 LsssLsssLssLsssLsssLsssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf.
19|6 15 LsssLsssLsssLssLsssLsssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf.
18|7 26 sLssLsssLsssLssLsssLsssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf.
17|8 11 sLssLsssLsssLsssLssLsssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf.
16|9 22 sLsssLssLsssLsssLssLsssLss Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf.
15|10 7 sLsssLssLsssLsssLsssLssLss Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Perf.
14|11 18 sLsssLsssLssLsssLsssLssLss Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Perf.
13|12 3 sLsssLsssLssLsssLsssLsssLs Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf.
12|13 14 sLsssLsssLsssLssLsssLsssLs Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf.
11|14 25 ssLssLsssLsssLssLsssLsssLs Perf. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf.
10|15 10 ssLssLsssLsssLsssLssLsssLs Perf. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf.
9|16 21 ssLsssLssLsssLsssLssLsssLs Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf.
8|17 6 ssLsssLssLsssLsssLsssLssLs Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Perf.
7|18 17 ssLsssLsssLssLsssLsssLssLs Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Perf.
6|19 2 ssLsssLsssLssLsssLsssLsssL Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf.
5|20 13 ssLsssLsssLsssLssLsssLsssL Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf.
4|21 24 sssLssLsssLsssLssLsssLsssL Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf.
3|22 9 sssLssLsssLsssLsssLssLsssL Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Perf.
2|23 20 sssLsssLssLsssLsssLssLsssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Perf.
1|24 5 sssLsssLssLsssLsssLsssLssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
0|25 16 sssLsssLsssLssLsssLsssLssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 7L 19s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\26 507.692 692.308 1:1 1.000 Equalized 7L 19s
69\163 507.975 692.025 7:6 1.167
58\137 508.029 691.971 6:5 1.200
105\248 508.065 691.935 11:9 1.222
47\111 508.108 691.892 5:4 1.250
130\307 508.143 691.857 14:11 1.273
83\196 508.163 691.837 9:7 1.286
119\281 508.185 691.815 13:10 1.300
36\85 508.235 691.765 4:3 1.333 Supersoft 7L 19s
133\314 508.280 691.720 15:11 1.364
97\229 508.297 691.703 11:8 1.375
158\373 508.311 691.689 18:13 1.385
61\144 508.333 691.667 7:5 1.400
147\347 508.357 691.643 17:12 1.417
86\203 508.374 691.626 10:7 1.429
111\262 508.397 691.603 13:9 1.444
25\59 508.475 691.525 3:2 1.500 Soft 7L 19s
114\269 508.550 691.450 14:9 1.556
89\210 508.571 691.429 11:7 1.571
153\361 508.587 691.413 19:12 1.583
64\151 508.609 691.391 8:5 1.600
167\394 508.629 691.371 21:13 1.615
103\243 508.642 691.358 13:8 1.625
142\335 508.657 691.343 18:11 1.636
39\92 508.696 691.304 5:3 1.667 Semisoft 7L 19s
131\309 508.738 691.262 17:10 1.700
92\217 508.756 691.244 12:7 1.714
145\342 508.772 691.228 19:11 1.727
53\125 508.800 691.200 7:4 1.750
120\283 508.834 691.166 16:9 1.778
67\158 508.861 691.139 9:5 1.800
81\191 508.901 691.099 11:6 1.833
14\33 509.091 690.909 2:1 2.000 Basic 7L 19s
Scales with tunings softer than this are proper
73\172 509.302 690.698 11:5 2.200
59\139 509.353 690.647 9:4 2.250
104\245 509.388 690.612 16:7 2.286
45\106 509.434 690.566 7:3 2.333
121\285 509.474 690.526 19:8 2.375
76\179 509.497 690.503 12:5 2.400
107\252 509.524 690.476 17:7 2.429
31\73 509.589 690.411 5:2 2.500 Semihard 7L 19s
110\259 509.653 690.347 18:7 2.571
79\186 509.677 690.323 13:5 2.600
127\299 509.699 690.301 21:8 2.625
48\113 509.735 690.265 8:3 2.667
113\266 509.774 690.226 19:7 2.714
65\153 509.804 690.196 11:4 2.750
82\193 509.845 690.155 14:5 2.800
17\40 510.000 690.000 3:1 3.000 Hard 7L 19s
71\167 510.180 689.820 13:4 3.250
54\127 510.236 689.764 10:3 3.333
91\214 510.280 689.720 17:5 3.400
37\87 510.345 689.655 7:2 3.500
94\221 510.407 689.593 18:5 3.600
57\134 510.448 689.552 11:3 3.667
77\181 510.497 689.503 15:4 3.750
20\47 510.638 689.362 4:1 4.000 Superhard 7L 19s
63\148 510.811 689.189 13:3 4.333
43\101 510.891 689.109 9:2 4.500
66\155 510.968 689.032 14:3 4.667
23\54 511.111 688.889 5:1 5.000
49\115 511.304 688.696 11:2 5.500
26\61 511.475 688.525 6:1 6.000
29\68 511.765 688.235 7:1 7.000
3\7 514.286 685.714 1:0 → ∞ Collapsed 7L 19s
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