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17L 2s

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↖ 16L 1s ↑ 17L 1s 18L 1s ↗
← 16L 2s 17L 2s 18L 2s →
↙ 16L 3s ↓ 17L 3s 18L 3s ↘ 
┌╥╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║║│║║║║║║║║││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLLsLLLLLLLLs
sLLLLLLLLsLLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\19 to 9\17 (631.6 ¢ to 635.3 ¢)
Dark 8\17 to 9\19 (564.7 ¢ to 568.4 ¢)
TAMNAMS information
Related to 2L 7s (balzano)
With tunings 5:1 to 6:1
Related MOS scales
Parent 2L 15s
Sister 2L 17s
Daughters 19L 17s, 17L 19s
Neutralized 15L 4s
2-Flought 36L 2s, 17L 21s
Equal tunings
Equalized (L:s = 1:1) 10\19 (631.6 ¢)
Supersoft (L:s = 4:3) 39\74 (632.4 ¢)
Soft (L:s = 3:2) 29\55 (632.7 ¢)
Semisoft (L:s = 5:3) 48\91 (633.0 ¢)
Basic (L:s = 2:1) 19\36 (633.3 ¢)
Semihard (L:s = 5:2) 47\89 (633.7 ¢)
Hard (L:s = 3:1) 28\53 (634.0 ¢)
Superhard (L:s = 4:1) 37\70 (634.3 ¢)
Collapsed (L:s = 1:0) 9\17 (635.3 ¢)

17L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 2 small steps, repeating every octave. 17L 2s is related to 2L 7s, expanding it by 10 tones. Generators that produce this scale range from 631.6 ¢ to 635.3 ¢, or from 564.7 ¢ to 568.4 ¢.

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 17L 2s
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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 70.6 ¢
2-mosstep Minor 2-mosstep m2ms L + s 70.6 ¢ to 126.3 ¢
Major 2-mosstep M2ms 2L 126.3 ¢ to 141.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 141.2 ¢ to 189.5 ¢
Major 3-mosstep M3ms 3L 189.5 ¢ to 211.8 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 211.8 ¢ to 252.6 ¢
Major 4-mosstep M4ms 4L 252.6 ¢ to 282.4 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 282.4 ¢ to 315.8 ¢
Major 5-mosstep M5ms 5L 315.8 ¢ to 352.9 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 352.9 ¢ to 378.9 ¢
Major 6-mosstep M6ms 6L 378.9 ¢ to 423.5 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 423.5 ¢ to 442.1 ¢
Major 7-mosstep M7ms 7L 442.1 ¢ to 494.1 ¢
8-mosstep Minor 8-mosstep m8ms 7L + s 494.1 ¢ to 505.3 ¢
Major 8-mosstep M8ms 8L 505.3 ¢ to 564.7 ¢
9-mosstep Perfect 9-mosstep P9ms 8L + s 564.7 ¢ to 568.4 ¢
Augmented 9-mosstep A9ms 9L 568.4 ¢ to 635.3 ¢
10-mosstep Diminished 10-mosstep d10ms 8L + 2s 564.7 ¢ to 631.6 ¢
Perfect 10-mosstep P10ms 9L + s 631.6 ¢ to 635.3 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 635.3 ¢ to 694.7 ¢
Major 11-mosstep M11ms 10L + s 694.7 ¢ to 705.9 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 705.9 ¢ to 757.9 ¢
Major 12-mosstep M12ms 11L + s 757.9 ¢ to 776.5 ¢
13-mosstep Minor 13-mosstep m13ms 11L + 2s 776.5 ¢ to 821.1 ¢
Major 13-mosstep M13ms 12L + s 821.1 ¢ to 847.1 ¢
14-mosstep Minor 14-mosstep m14ms 12L + 2s 847.1 ¢ to 884.2 ¢
Major 14-mosstep M14ms 13L + s 884.2 ¢ to 917.6 ¢
15-mosstep Minor 15-mosstep m15ms 13L + 2s 917.6 ¢ to 947.4 ¢
Major 15-mosstep M15ms 14L + s 947.4 ¢ to 988.2 ¢
16-mosstep Minor 16-mosstep m16ms 14L + 2s 988.2 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 15L + s 1010.5 ¢ to 1058.8 ¢
17-mosstep Minor 17-mosstep m17ms 15L + 2s 1058.8 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 16L + s 1073.7 ¢ to 1129.4 ¢
18-mosstep Minor 18-mosstep m18ms 16L + 2s 1129.4 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 17L + s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 17L + 2s 1200.0 ¢

Generator chain

Generator chain of 17L 2s
Bright gens Scale degree Abbrev.
35 Augmented 8-mosdegree A8md
34 Augmented 17-mosdegree A17md
33 Augmented 7-mosdegree A7md
32 Augmented 16-mosdegree A16md
31 Augmented 6-mosdegree A6md
30 Augmented 15-mosdegree A15md
29 Augmented 5-mosdegree A5md
28 Augmented 14-mosdegree A14md
27 Augmented 4-mosdegree A4md
26 Augmented 13-mosdegree A13md
25 Augmented 3-mosdegree A3md
24 Augmented 12-mosdegree A12md
23 Augmented 2-mosdegree A2md
22 Augmented 11-mosdegree A11md
21 Augmented 1-mosdegree A1md
20 Augmented 10-mosdegree A10md
19 Augmented 0-mosdegree A0md
18 Augmented 9-mosdegree A9md
17 Major 18-mosdegree M18md
16 Major 8-mosdegree M8md
15 Major 17-mosdegree M17md
14 Major 7-mosdegree M7md
13 Major 16-mosdegree M16md
12 Major 6-mosdegree M6md
11 Major 15-mosdegree M15md
10 Major 5-mosdegree M5md
9 Major 14-mosdegree M14md
8 Major 4-mosdegree M4md
7 Major 13-mosdegree M13md
6 Major 3-mosdegree M3md
5 Major 12-mosdegree M12md
4 Major 2-mosdegree M2md
3 Major 11-mosdegree M11md
2 Major 1-mosdegree M1md
1 Perfect 10-mosdegree P10md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 9-mosdegree P9md
−2 Minor 18-mosdegree m18md
−3 Minor 8-mosdegree m8md
−4 Minor 17-mosdegree m17md
−5 Minor 7-mosdegree m7md
−6 Minor 16-mosdegree m16md
−7 Minor 6-mosdegree m6md
−8 Minor 15-mosdegree m15md
−9 Minor 5-mosdegree m5md
−10 Minor 14-mosdegree m14md
−11 Minor 4-mosdegree m4md
−12 Minor 13-mosdegree m13md
−13 Minor 3-mosdegree m3md
−14 Minor 12-mosdegree m12md
−15 Minor 2-mosdegree m2md
−16 Minor 11-mosdegree m11md
−17 Minor 1-mosdegree m1md
−18 Diminished 10-mosdegree d10md
−19 Diminished 19-mosdegree d19md
−20 Diminished 9-mosdegree d9md
−21 Diminished 18-mosdegree d18md
−22 Diminished 8-mosdegree d8md
−23 Diminished 17-mosdegree d17md
−24 Diminished 7-mosdegree d7md
−25 Diminished 16-mosdegree d16md
−26 Diminished 6-mosdegree d6md
−27 Diminished 15-mosdegree d15md
−28 Diminished 5-mosdegree d5md
−29 Diminished 14-mosdegree d14md
−30 Diminished 4-mosdegree d4md
−31 Diminished 13-mosdegree d13md
−32 Diminished 3-mosdegree d3md
−33 Diminished 12-mosdegree d12md
−34 Diminished 2-mosdegree d2md
−35 Diminished 11-mosdegree d11md

Modes

Scale degrees of the modes of 17L 2s
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
18|0 1 LLLLLLLLLsLLLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|1 11 LLLLLLLLsLLLLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|2 2 LLLLLLLLsLLLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf.
15|3 12 LLLLLLLsLLLLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf.
14|4 3 LLLLLLLsLLLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf.
13|5 13 LLLLLLsLLLLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf.
12|6 4 LLLLLLsLLLLLLLLsLLL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Perf.
11|7 14 LLLLLsLLLLLLLLLsLLL Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Perf.
10|8 5 LLLLLsLLLLLLLLsLLLL Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Perf.
9|9 15 LLLLsLLLLLLLLLsLLLL Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Perf.
8|10 6 LLLLsLLLLLLLLsLLLLL Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Min. Perf.
7|11 16 LLLsLLLLLLLLLsLLLLL Perf. Maj. Maj. Maj. Min. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Min. Perf.
6|12 7 LLLsLLLLLLLLsLLLLLL Perf. Maj. Maj. Maj. Min. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Min. Min. Min. Min. Min. Min. Perf.
5|13 17 LLsLLLLLLLLLsLLLLLL Perf. Maj. Maj. Min. Min. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Min. Min. Min. Min. Min. Min. Perf.
4|14 8 LLsLLLLLLLLsLLLLLLL Perf. Maj. Maj. Min. Min. Min. Min. Min. Min. Perf. Perf. Maj. Min. Min. Min. Min. Min. Min. Min. Perf.
3|15 18 LsLLLLLLLLLsLLLLLLL Perf. Maj. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Maj. Min. Min. Min. Min. Min. Min. Min. Perf.
2|16 9 LsLLLLLLLLsLLLLLLLL Perf. Maj. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
1|17 19 sLLLLLLLLLsLLLLLLLL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
0|18 10 sLLLLLLLLsLLLLLLLLL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

  Todo: complete table

Add temperaments to table — see the corresponding Talk page for a beta version of this.

Scale tree and tuning spectrum of 17L 2s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
10\19 631.579 568.421 1:1 1.000 Equalized 17L 2s
59\112 632.143 567.857 6:5 1.200
49\93 632.258 567.742 5:4 1.250
88\167 632.335 567.665 9:7 1.286
39\74 632.432 567.568 4:3 1.333 Supersoft 17L 2s
107\203 632.512 567.488 11:8 1.375
68\129 632.558 567.442 7:5 1.400
97\184 632.609 567.391 10:7 1.429
29\55 632.727 567.273 3:2 1.500 Soft 17L 2s
106\201 632.836 567.164 11:7 1.571
77\146 632.877 567.123 8:5 1.600
125\237 632.911 567.089 13:8 1.625
48\91 632.967 567.033 5:3 1.667 Semisoft 17L 2s
115\218 633.028 566.972 12:7 1.714
67\127 633.071 566.929 7:4 1.750
86\163 633.129 566.871 9:5 1.800
19\36 633.333 566.667 2:1 2.000 Basic 17L 2s
Scales with tunings softer than this are proper
85\161 633.540 566.460 9:4 2.250
66\125 633.600 566.400 7:3 2.333
113\214 633.645 566.355 12:5 2.400
47\89 633.708 566.292 5:2 2.500 Semihard 17L 2s
122\231 633.766 566.234 13:5 2.600
75\142 633.803 566.197 8:3 2.667
103\195 633.846 566.154 11:4 2.750
28\53 633.962 566.038 3:1 3.000 Hard 17L 2s
93\176 634.091 565.909 10:3 3.333
65\123 634.146 565.854 7:2 3.500
102\193 634.197 565.803 11:3 3.667
37\70 634.286 565.714 4:1 4.000 Superhard 17L 2s
83\157 634.395 565.605 9:2 4.500
46\87 634.483 565.517 5:1 5.000
55\104 634.615 565.385 6:1 6.000
9\17 635.294 564.706 1:0 → ∞ Collapsed 17L 2s


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