17L 2s
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Step pattern
LLLLLLLLLsLLLLLLLLs
sLLLLLLLLsLLLLLLLLL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
10\19 to 9\17 (631.6 ¢ to 635.3 ¢)
Dark
8\17 to 9\19 (564.7 ¢ to 568.4 ¢)
Descends from
2L 7s (balzano)
Ancestor's step ratio range
5:1 to 6:1
Parent
2L 15s
Sister
2L 17s
Daughters
19L 17s, 17L 19s
Neutralized
15L 4s
2-Flought
36L 2s, 17L 21s
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 ¢)
| ↖ 16L 1s | ↑ 17L 1s | 18L 1s ↗ |
| ← 16L 2s | 17L 2s | 18L 2s → |
| ↙ 16L 3s | ↓ 17L 3s | 18L 3s ↘ |
┌╥╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║│║║║║║║║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLLLLLLLLsLLLLLLLLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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 diatonic interval categories.
Intervals
The intervals of 17L 2s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 19-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.
| 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
A chain of bright generators, each a perfect 10-mosstep, produces the following scale degrees. A chain of 19 bright generators contains the scale degrees of one of the modes of 17L 2s. Expanding the chain to 36 scale degrees produces the modes of either 19L 17s (for soft-of-basic tunings) or 17L 19s (for hard-of-basic tunings).
| 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
| 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
| 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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