7L 17s: Difference between revisions

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This is the MOS where the large steps divide the small steps into groups of 3-2-3-2-3-2-2. Its generator is a neutral third of up to 7/24edo (350 cents), which serves as an approxiamte 11/9; with 38edo (the low estimate for the boundary of "practicality") giving this ratio almost exactly.
{{Infobox MOS}}
{{MOS intro}}
 
The [[dark]] generator serves as an approximate [[11/9]] (347{{c}}), with [[38edo|11\38]] – the low estimate for the boundary of "practicality" – giving this ratio almost exactly.
 
Notable [[harmonic entropy]] minima are [[mohajira]] and [[migration]], two alternative extensions of the [[Subgroup|2.3.5.11]] temperament [[mohaha]] to the full [[11-limit]], merging in [[31edo]].
 
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum}}


{| class="wikitable"
|-
| | 7/24
| |
| |
| |
| |
| | 350
|-
| |
| |
| |
| |
| | 30/103
| | 349.515
|-
| |
| |
| |
| | 23/79
| |
| | 349.367
|-
| |
| |
| |
| |
| | 39/134
| | 349.236
|-
| |
| |
| | 16/55
| |
| |
| | 349.091
|-
| |
| |
| |
| |
| |
| | 348.981
|-
| |
| |
| |
| |
| | 41/141
| | 348.936
|-
| |
| |
| |
| |
| |
| | 348.909
|-
| |
| |
| |
| | 25/86
| |
| | 348.837
|-
| |
| |
| |
| |
| |
| | 348.743
|-
| |
| |
| |
| |
| | 34/117
| | 348.72
|-
| |
| | 9/31
| |
| |
| |
| | 348.387
|-
| |
| |
| |
| |
| | 29/100
| | 348
|-
| |
| |
| |
| | 20/69
| |
| | 347.826
|-
| |
| |
| |
| |
| |
| | 347.71
|-
| |
| |
| |
| |
| | 31/107
| | 347.664
|-
| |
| |
| |
| |
| |
| | 347.615
|-
| |
| |
| | 11/38
| |
| |
| | 347.368
|-
| |
| |
| |
| |
| |
| | 347.254
|-
| |
| |
| |
| |
| | 24/83
| | 346.988
|-
| |
| |
| |
| | 13/45
| |
| | 346 2/3
|-
| |
| |
| |
| |
| | 15/52
| | 346 2/13
|-
| | 2/7
| |
| |
| |
| |
| | 342 6/7
|}
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Latest revision as of 14:01, 5 May 2025

↖ 6L 16s ↑ 7L 16s 8L 16s ↗
← 6L 17s 7L 17s 8L 17s →
↙ 6L 18s ↓ 7L 18s 8L 18s ↘ 
┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐
│║││║││║│││║││║│││║││║││││
││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLsssLssLsssLssLsss
sssLssLsssLssLsssLssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 17\24 to 5\7 (850.0 ¢ to 857.1 ¢)
Dark 2\7 to 7\24 (342.9 ¢ to 350.0 ¢)
TAMNAMS information
Related to 7L 3s (dicoid)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 7L 10s
Sister 17L 7s
Daughters 24L 7s, 7L 24s
Neutralized 14L 10s
2-Flought 31L 17s, 7L 41s
Equal tunings
Equalized (L:s = 1:1) 17\24 (850.0 ¢)
Supersoft (L:s = 4:3) 56\79 (850.6 ¢)
Soft (L:s = 3:2) 39\55 (850.9 ¢)
Semisoft (L:s = 5:3) 61\86 (851.2 ¢)
Basic (L:s = 2:1) 22\31 (851.6 ¢)
Semihard (L:s = 5:2) 49\69 (852.2 ¢)
Hard (L:s = 3:1) 27\38 (852.6 ¢)
Superhard (L:s = 4:1) 32\45 (853.3 ¢)
Collapsed (L:s = 1:0) 5\7 (857.1 ¢)

7L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 17 small steps, repeating every octave. 7L 17s is a grandchild scale of 7L 3s, expanding it by 14 tones. Generators that produce this scale range from 850 ¢ to 857.1 ¢, or from 342.9 ¢ to 350 ¢.

The dark generator serves as an approximate 11/9 (347 ¢), with 11\38 – the low estimate for the boundary of "practicality" – giving this ratio almost exactly.

Notable harmonic entropy minima are mohajira and migration, two alternative extensions of the 2.3.5.11 temperament mohaha to the full 11-limit, merging in 31edo.

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 17s
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 50.0 ¢
Major 1-mosstep M1ms L 50.0 ¢ to 171.4 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 100.0 ¢
Major 2-mosstep M2ms L + s 100.0 ¢ to 171.4 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 150.0 ¢
Major 3-mosstep M3ms L + 2s 150.0 ¢ to 171.4 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4 ¢ to 200.0 ¢
Major 4-mosstep M4ms 2L + 2s 200.0 ¢ to 342.9 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 171.4 ¢ to 250.0 ¢
Major 5-mosstep M5ms 2L + 3s 250.0 ¢ to 342.9 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 171.4 ¢ to 300.0 ¢
Major 6-mosstep M6ms 2L + 4s 300.0 ¢ to 342.9 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 342.9 ¢ to 350.0 ¢
Augmented 7-mosstep A7ms 3L + 4s 350.0 ¢ to 514.3 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 342.9 ¢ to 400.0 ¢
Major 8-mosstep M8ms 3L + 5s 400.0 ¢ to 514.3 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 342.9 ¢ to 450.0 ¢
Major 9-mosstep M9ms 3L + 6s 450.0 ¢ to 514.3 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 342.9 ¢ to 500.0 ¢
Major 10-mosstep M10ms 3L + 7s 500.0 ¢ to 514.3 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 514.3 ¢ to 550.0 ¢
Major 11-mosstep M11ms 4L + 7s 550.0 ¢ to 685.7 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 514.3 ¢ to 600.0 ¢
Major 12-mosstep M12ms 4L + 8s 600.0 ¢ to 685.7 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 514.3 ¢ to 650.0 ¢
Major 13-mosstep M13ms 4L + 9s 650.0 ¢ to 685.7 ¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 685.7 ¢ to 700.0 ¢
Major 14-mosstep M14ms 5L + 9s 700.0 ¢ to 857.1 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 685.7 ¢ to 750.0 ¢
Major 15-mosstep M15ms 5L + 10s 750.0 ¢ to 857.1 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 685.7 ¢ to 800.0 ¢
Major 16-mosstep M16ms 5L + 11s 800.0 ¢ to 857.1 ¢
17-mosstep Diminished 17-mosstep d17ms 4L + 13s 685.7 ¢ to 850.0 ¢
Perfect 17-mosstep P17ms 5L + 12s 850.0 ¢ to 857.1 ¢
18-mosstep Minor 18-mosstep m18ms 5L + 13s 857.1 ¢ to 900.0 ¢
Major 18-mosstep M18ms 6L + 12s 900.0 ¢ to 1028.6 ¢
19-mosstep Minor 19-mosstep m19ms 5L + 14s 857.1 ¢ to 950.0 ¢
Major 19-mosstep M19ms 6L + 13s 950.0 ¢ to 1028.6 ¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 857.1 ¢ to 1000.0 ¢
Major 20-mosstep M20ms 6L + 14s 1000.0 ¢ to 1028.6 ¢
21-mosstep Minor 21-mosstep m21ms 6L + 15s 1028.6 ¢ to 1050.0 ¢
Major 21-mosstep M21ms 7L + 14s 1050.0 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 6L + 16s 1028.6 ¢ to 1100.0 ¢
Major 22-mosstep M22ms 7L + 15s 1100.0 ¢ to 1200.0 ¢
23-mosstep Minor 23-mosstep m23ms 6L + 17s 1028.6 ¢ to 1150.0 ¢
Major 23-mosstep M23ms 7L + 16s 1150.0 ¢ to 1200.0 ¢
24-mosstep Perfect 24-mosstep P24ms 7L + 17s 1200.0 ¢

Generator chain

Generator chain of 7L 17s
Bright gens Scale degree Abbrev.
30 Augmented 6-mosdegree A6md
29 Augmented 13-mosdegree A13md
28 Augmented 20-mosdegree A20md
27 Augmented 3-mosdegree A3md
26 Augmented 10-mosdegree A10md
25 Augmented 17-mosdegree A17md
24 Augmented 0-mosdegree A0md
23 Augmented 7-mosdegree A7md
22 Major 14-mosdegree M14md
21 Major 21-mosdegree M21md
20 Major 4-mosdegree M4md
19 Major 11-mosdegree M11md
18 Major 18-mosdegree M18md
17 Major 1-mosdegree M1md
16 Major 8-mosdegree M8md
15 Major 15-mosdegree M15md
14 Major 22-mosdegree M22md
13 Major 5-mosdegree M5md
12 Major 12-mosdegree M12md
11 Major 19-mosdegree M19md
10 Major 2-mosdegree M2md
9 Major 9-mosdegree M9md
8 Major 16-mosdegree M16md
7 Major 23-mosdegree M23md
6 Major 6-mosdegree M6md
5 Major 13-mosdegree M13md
4 Major 20-mosdegree M20md
3 Major 3-mosdegree M3md
2 Major 10-mosdegree M10md
1 Perfect 17-mosdegree P17md
0 Perfect 0-mosdegree
Perfect 24-mosdegree		 P0md
P24md
−1 Perfect 7-mosdegree P7md
−2 Minor 14-mosdegree m14md
−3 Minor 21-mosdegree m21md
−4 Minor 4-mosdegree m4md
−5 Minor 11-mosdegree m11md
−6 Minor 18-mosdegree m18md
−7 Minor 1-mosdegree m1md
−8 Minor 8-mosdegree m8md
−9 Minor 15-mosdegree m15md
−10 Minor 22-mosdegree m22md
−11 Minor 5-mosdegree m5md
−12 Minor 12-mosdegree m12md
−13 Minor 19-mosdegree m19md
−14 Minor 2-mosdegree m2md
−15 Minor 9-mosdegree m9md
−16 Minor 16-mosdegree m16md
−17 Minor 23-mosdegree m23md
−18 Minor 6-mosdegree m6md
−19 Minor 13-mosdegree m13md
−20 Minor 20-mosdegree m20md
−21 Minor 3-mosdegree m3md
−22 Minor 10-mosdegree m10md
−23 Diminished 17-mosdegree d17md
−24 Diminished 24-mosdegree d24md
−25 Diminished 7-mosdegree d7md
−26 Diminished 14-mosdegree d14md
−27 Diminished 21-mosdegree d21md
−28 Diminished 4-mosdegree d4md
−29 Diminished 11-mosdegree d11md
−30 Diminished 18-mosdegree d18md

Modes

Scale degrees of the modes of 7L 17s
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
23|0 1 LssLssLsssLssLsssLssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
22|1 18 LssLsssLssLssLsssLssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
21|2 11 LssLsssLssLsssLssLssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|3 4 LssLsssLssLsssLssLsssLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf.
19|4 21 LsssLssLssLsssLssLsssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf.
18|5 14 LsssLssLsssLssLssLsssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf.
17|6 7 LsssLssLsssLssLsssLssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
16|7 24 sLssLssLsssLssLsssLssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
15|8 17 sLssLsssLssLssLsssLssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
14|9 10 sLssLsssLssLsssLssLssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
13|10 3 sLssLsssLssLsssLssLsssLs Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf.
12|11 20 sLsssLssLssLsssLssLsssLs Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf.
11|12 13 sLsssLssLsssLssLssLsssLs Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf.
10|13 6 sLsssLssLsssLssLsssLssLs Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
9|14 23 ssLssLssLsssLssLsssLssLs Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
8|15 16 ssLssLsssLssLssLsssLssLs Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
7|16 9 ssLssLsssLssLsssLssLssLs Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
6|17 2 ssLssLsssLssLsssLssLsssL Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Perf.
5|18 19 ssLsssLssLssLsssLssLsssL Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Perf.
4|19 12 ssLsssLssLsssLssLssLsssL Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Perf.
3|20 5 ssLsssLssLsssLssLsssLssL Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
2|21 22 sssLssLssLsssLssLsssLssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|22 15 sssLssLsssLssLssLsssLssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|23 8 sssLssLsssLssLsssLssLssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 7L 17s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\24 850.000 350.000 1:1 1.000 Equalized 7L 17s
90\127 850.394 349.606 6:5 1.200
73\103 850.485 349.515 5:4 1.250
129\182 850.549 349.451 9:7 1.286
56\79 850.633 349.367 4:3 1.333 Supersoft 7L 17s
151\213 850.704 349.296 11:8 1.375
95\134 850.746 349.254 7:5 1.400
134\189 850.794 349.206 10:7 1.429
39\55 850.909 349.091 3:2 1.500 Soft 7L 17s
139\196 851.020 348.980 11:7 1.571
100\141 851.064 348.936 8:5 1.600
161\227 851.101 348.899 13:8 1.625
61\86 851.163 348.837 5:3 1.667 Semisoft 7L 17s
144\203 851.232 348.768 12:7 1.714
83\117 851.282 348.718 7:4 1.750
105\148 851.351 348.649 9:5 1.800
22\31 851.613 348.387 2:1 2.000 Basic 7L 17s
Scales with tunings softer than this are proper
93\131 851.908 348.092 9:4 2.250
71\100 852.000 348.000 7:3 2.333
120\169 852.071 347.929 12:5 2.400
49\69 852.174 347.826 5:2 2.500 Semihard 7L 17s
125\176 852.273 347.727 13:5 2.600
76\107 852.336 347.664 8:3 2.667
103\145 852.414 347.586 11:4 2.750
27\38 852.632 347.368 3:1 3.000 Hard 7L 17s
86\121 852.893 347.107 10:3 3.333
59\83 853.012 346.988 7:2 3.500
91\128 853.125 346.875 11:3 3.667
32\45 853.333 346.667 4:1 4.000 Superhard 7L 17s
69\97 853.608 346.392 9:2 4.500
37\52 853.846 346.154 5:1 5.000
42\59 854.237 345.763 6:1 6.000
5\7 857.143 342.857 1:0 → ∞ Collapsed 7L 17s
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