21L 1s
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| ← 20L 1s | 21L 1s | 22L 1s → |
| ↙ 20L 2s | ↓ 21L 2s | 22L 2s ↘ |
┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║║║║║║║║║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLLLLLLLLLLLLLLLLLLLLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
21L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 21 large steps and 1 small step, repeating every octave. 21L 1s is related to 1L 9s, expanding it by 12 tones. Generators that produce this scale range from 54.5 ¢ to 57.1 ¢, or from 1142.9 ¢ to 1145.5 ¢. Scales of this form are always proper because there is only one small step. Eliora proposes the name escapist for this pattern, referencing the escapade temperament which is supported by both 21edo and 22edo, thus covering the entire tuning spectrum; Lériendil proposes noletic for similar reasons, as 9 generators reach a diatonic 4/3, supporting the scale 9ed4/3 known also as "noleta".
Moremajorthanmajor proposes the name tricesimoprimal quartertonic for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960—the tricesimoprimal quartertones being equated with each other. In addition, both 21edo and 22edo, extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.
Tuning ranges
The scale's approach to standard harmony can be considered based on the mode.
Brighter modes
Diatonic fifth and 65edo (Ultrasoft and supersoft)
Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In 65edo, the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of 5edo, and thus is the exact boundary between a fifth proper and a fifth-sixth.
If the pure 32/31 is used as a generator, the resulting fifth is 714.53756 cents, which puts it in the category around Ultrapyth.
Fifth-sixth (hard of supersoft)
From 1\21 to 3\65, 13 steps amount to a fifth-sixth.
If the pure 31/30 is used as a generator, the resulting fifth-sixth is 737.96915 cents, which puts it in the category around father/petritri/aurora.
Darker modes
If instead the small step is stacked down, this enables the scale to approximate the standard 4:5:6 and 10:12:15 triads, as the escapade temperament does.
The escapade temperament reaches 4/3 in 9 gensteps, meaning that modes from Hermit (12|9) onward support a perfect fifth from the tonic. This also enables the modes from Hermit through Temperance (7|14) to support the major triad, 4:5:6, and from Devil (6|15) onward to support the minor triad, 10:12:15. The 700 cent fifth is supported in 108edo, stacking steps of 5\108 downward.
Relation to other equal divisions
2 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out.
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 | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0 ¢ |
| 1-mosstep | Diminished 1-mosstep | d1ms | s | 0.0 ¢ to 54.5 ¢ |
| Perfect 1-mosstep | P1ms | L | 54.5 ¢ to 57.1 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 57.1 ¢ to 109.1 ¢ |
| Major 2-mosstep | M2ms | 2L | 109.1 ¢ to 114.3 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 114.3 ¢ to 163.6 ¢ |
| Major 3-mosstep | M3ms | 3L | 163.6 ¢ to 171.4 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 171.4 ¢ to 218.2 ¢ |
| Major 4-mosstep | M4ms | 4L | 218.2 ¢ to 228.6 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 228.6 ¢ to 272.7 ¢ |
| Major 5-mosstep | M5ms | 5L | 272.7 ¢ to 285.7 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 285.7 ¢ to 327.3 ¢ |
| Major 6-mosstep | M6ms | 6L | 327.3 ¢ to 342.9 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 342.9 ¢ to 381.8 ¢ |
| Major 7-mosstep | M7ms | 7L | 381.8 ¢ to 400.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 7L + s | 400.0 ¢ to 436.4 ¢ |
| Major 8-mosstep | M8ms | 8L | 436.4 ¢ to 457.1 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 8L + s | 457.1 ¢ to 490.9 ¢ |
| Major 9-mosstep | M9ms | 9L | 490.9 ¢ to 514.3 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 9L + s | 514.3 ¢ to 545.5 ¢ |
| Major 10-mosstep | M10ms | 10L | 545.5 ¢ to 571.4 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 10L + s | 571.4 ¢ to 600.0 ¢ |
| Major 11-mosstep | M11ms | 11L | 600.0 ¢ to 628.6 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 11L + s | 628.6 ¢ to 654.5 ¢ |
| Major 12-mosstep | M12ms | 12L | 654.5 ¢ to 685.7 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 12L + s | 685.7 ¢ to 709.1 ¢ |
| Major 13-mosstep | M13ms | 13L | 709.1 ¢ to 742.9 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 13L + s | 742.9 ¢ to 763.6 ¢ |
| Major 14-mosstep | M14ms | 14L | 763.6 ¢ to 800.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 14L + s | 800.0 ¢ to 818.2 ¢ |
| Major 15-mosstep | M15ms | 15L | 818.2 ¢ to 857.1 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 15L + s | 857.1 ¢ to 872.7 ¢ |
| Major 16-mosstep | M16ms | 16L | 872.7 ¢ to 914.3 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 16L + s | 914.3 ¢ to 927.3 ¢ |
| Major 17-mosstep | M17ms | 17L | 927.3 ¢ to 971.4 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 17L + s | 971.4 ¢ to 981.8 ¢ |
| Major 18-mosstep | M18ms | 18L | 981.8 ¢ to 1028.6 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 18L + s | 1028.6 ¢ to 1036.4 ¢ |
| Major 19-mosstep | M19ms | 19L | 1036.4 ¢ to 1085.7 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 19L + s | 1085.7 ¢ to 1090.9 ¢ |
| Major 20-mosstep | M20ms | 20L | 1090.9 ¢ to 1142.9 ¢ | |
| 21-mosstep | Perfect 21-mosstep | P21ms | 20L + s | 1142.9 ¢ to 1145.5 ¢ |
| Augmented 21-mosstep | A21ms | 21L | 1145.5 ¢ to 1200.0 ¢ | |
| 22-mosstep | Perfect 22-mosstep | P22ms | 21L + s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 42 | Augmented 20-mosdegree | A20md |
| 41 | Augmented 19-mosdegree | A19md |
| 40 | Augmented 18-mosdegree | A18md |
| 39 | Augmented 17-mosdegree | A17md |
| 38 | Augmented 16-mosdegree | A16md |
| 37 | Augmented 15-mosdegree | A15md |
| 36 | Augmented 14-mosdegree | A14md |
| 35 | Augmented 13-mosdegree | A13md |
| 34 | Augmented 12-mosdegree | A12md |
| 33 | Augmented 11-mosdegree | A11md |
| 32 | Augmented 10-mosdegree | A10md |
| 31 | Augmented 9-mosdegree | A9md |
| 30 | Augmented 8-mosdegree | A8md |
| 29 | Augmented 7-mosdegree | A7md |
| 28 | Augmented 6-mosdegree | A6md |
| 27 | Augmented 5-mosdegree | A5md |
| 26 | Augmented 4-mosdegree | A4md |
| 25 | Augmented 3-mosdegree | A3md |
| 24 | Augmented 2-mosdegree | A2md |
| 23 | Augmented 1-mosdegree | A1md |
| 22 | Augmented 0-mosdegree | A0md |
| 21 | Augmented 21-mosdegree | A21md |
| 20 | Major 20-mosdegree | M20md |
| 19 | Major 19-mosdegree | M19md |
| 18 | Major 18-mosdegree | M18md |
| 17 | Major 17-mosdegree | M17md |
| 16 | Major 16-mosdegree | M16md |
| 15 | Major 15-mosdegree | M15md |
| 14 | Major 14-mosdegree | M14md |
| 13 | Major 13-mosdegree | M13md |
| 12 | Major 12-mosdegree | M12md |
| 11 | Major 11-mosdegree | M11md |
| 10 | Major 10-mosdegree | M10md |
| 9 | Major 9-mosdegree | M9md |
| 8 | Major 8-mosdegree | M8md |
| 7 | Major 7-mosdegree | M7md |
| 6 | Major 6-mosdegree | M6md |
| 5 | Major 5-mosdegree | M5md |
| 4 | Major 4-mosdegree | M4md |
| 3 | Major 3-mosdegree | M3md |
| 2 | Major 2-mosdegree | M2md |
| 1 | Perfect 1-mosdegree | P1md |
| 0 | Perfect 0-mosdegree Perfect 22-mosdegree |
P0md P22md |
| −1 | Perfect 21-mosdegree | P21md |
| −2 | Minor 20-mosdegree | m20md |
| −3 | Minor 19-mosdegree | m19md |
| −4 | Minor 18-mosdegree | m18md |
| −5 | Minor 17-mosdegree | m17md |
| −6 | Minor 16-mosdegree | m16md |
| −7 | Minor 15-mosdegree | m15md |
| −8 | Minor 14-mosdegree | m14md |
| −9 | Minor 13-mosdegree | m13md |
| −10 | Minor 12-mosdegree | m12md |
| −11 | Minor 11-mosdegree | m11md |
| −12 | Minor 10-mosdegree | m10md |
| −13 | Minor 9-mosdegree | m9md |
| −14 | Minor 8-mosdegree | m8md |
| −15 | Minor 7-mosdegree | m7md |
| −16 | Minor 6-mosdegree | m6md |
| −17 | Minor 5-mosdegree | m5md |
| −18 | Minor 4-mosdegree | m4md |
| −19 | Minor 3-mosdegree | m3md |
| −20 | Minor 2-mosdegree | m2md |
| −21 | Diminished 1-mosdegree | d1md |
| −22 | Diminished 22-mosdegree | d22md |
| −23 | Diminished 21-mosdegree | d21md |
| −24 | Diminished 20-mosdegree | d20md |
| −25 | Diminished 19-mosdegree | d19md |
| −26 | Diminished 18-mosdegree | d18md |
| −27 | Diminished 17-mosdegree | d17md |
| −28 | Diminished 16-mosdegree | d16md |
| −29 | Diminished 15-mosdegree | d15md |
| −30 | Diminished 14-mosdegree | d14md |
| −31 | Diminished 13-mosdegree | d13md |
| −32 | Diminished 12-mosdegree | d12md |
| −33 | Diminished 11-mosdegree | d11md |
| −34 | Diminished 10-mosdegree | d10md |
| −35 | Diminished 9-mosdegree | d9md |
| −36 | Diminished 8-mosdegree | d8md |
| −37 | Diminished 7-mosdegree | d7md |
| −38 | Diminished 6-mosdegree | d6md |
| −39 | Diminished 5-mosdegree | d5md |
| −40 | Diminished 4-mosdegree | d4md |
| −41 | Diminished 3-mosdegree | d3md |
| −42 | Diminished 2-mosdegree | d2md |
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 | 20 | 21 | 22 | |||
| 21|0 | 1 | LLLLLLLLLLLLLLLLLLLLLs | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Perf. |
| 20|1 | 2 | LLLLLLLLLLLLLLLLLLLLsL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 19|2 | 3 | LLLLLLLLLLLLLLLLLLLsLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Perf. | Perf. |
| 18|3 | 4 | LLLLLLLLLLLLLLLLLLsLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Perf. | Perf. |
| 17|4 | 5 | LLLLLLLLLLLLLLLLLsLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Perf. | Perf. |
| 16|5 | 6 | LLLLLLLLLLLLLLLLsLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 15|6 | 7 | LLLLLLLLLLLLLLLsLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 14|7 | 8 | LLLLLLLLLLLLLLsLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 13|8 | 9 | LLLLLLLLLLLLLsLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 12|9 | 10 | LLLLLLLLLLLLsLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 11|10 | 11 | LLLLLLLLLLLsLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 10|11 | 12 | LLLLLLLLLLsLLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 9|12 | 13 | LLLLLLLLLsLLLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 8|13 | 14 | LLLLLLLLsLLLLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 7|14 | 15 | LLLLLLLsLLLLLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 6|15 | 16 | LLLLLLsLLLLLLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 5|16 | 17 | LLLLLsLLLLLLLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 4|17 | 18 | LLLLsLLLLLLLLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 3|18 | 19 | LLLsLLLLLLLLLLLLLLLLLL | Perf. | Perf. | Maj. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 2|19 | 20 | LLsLLLLLLLLLLLLLLLLLLL | Perf. | Perf. | Maj. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 1|20 | 21 | LsLLLLLLLLLLLLLLLLLLLL | Perf. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 0|21 | 22 | sLLLLLLLLLLLLLLLLLLLLL | Perf. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
Proposed mode names =
The author proposes naming the modes after Tarot Major Arcana adjectivals based on how many generators down there is since there are 22 of them.
| Mode | Name |
|---|---|
| 21|0 | Foolish |
| 20|1 | Magical |
| 19|2 | High Priestess's |
| 18|3 | Empress's |
| … | … |
| 3|19 | Lunar |
| 2|19 | Solar |
| 1|20 | Judgemental |
| 0|21 | Worldwide |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0 ¢ |
| 1-mosstep | Diminished 1-mosstep | d1ms | s | 0.0 ¢ to 54.5 ¢ |
| Perfect 1-mosstep | P1ms | L | 54.5 ¢ to 57.1 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 57.1 ¢ to 109.1 ¢ |
| Major 2-mosstep | M2ms | 2L | 109.1 ¢ to 114.3 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 114.3 ¢ to 163.6 ¢ |
| Major 3-mosstep | M3ms | 3L | 163.6 ¢ to 171.4 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 171.4 ¢ to 218.2 ¢ |
| Major 4-mosstep | M4ms | 4L | 218.2 ¢ to 228.6 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 228.6 ¢ to 272.7 ¢ |
| Major 5-mosstep | M5ms | 5L | 272.7 ¢ to 285.7 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 285.7 ¢ to 327.3 ¢ |
| Major 6-mosstep | M6ms | 6L | 327.3 ¢ to 342.9 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 342.9 ¢ to 381.8 ¢ |
| Major 7-mosstep | M7ms | 7L | 381.8 ¢ to 400.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 7L + s | 400.0 ¢ to 436.4 ¢ |
| Major 8-mosstep | M8ms | 8L | 436.4 ¢ to 457.1 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 8L + s | 457.1 ¢ to 490.9 ¢ |
| Major 9-mosstep | M9ms | 9L | 490.9 ¢ to 514.3 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 9L + s | 514.3 ¢ to 545.5 ¢ |
| Major 10-mosstep | M10ms | 10L | 545.5 ¢ to 571.4 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 10L + s | 571.4 ¢ to 600.0 ¢ |
| Major 11-mosstep | M11ms | 11L | 600.0 ¢ to 628.6 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 11L + s | 628.6 ¢ to 654.5 ¢ |
| Major 12-mosstep | M12ms | 12L | 654.5 ¢ to 685.7 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 12L + s | 685.7 ¢ to 709.1 ¢ |
| Major 13-mosstep | M13ms | 13L | 709.1 ¢ to 742.9 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 13L + s | 742.9 ¢ to 763.6 ¢ |
| Major 14-mosstep | M14ms | 14L | 763.6 ¢ to 800.0 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 14L + s | 800.0 ¢ to 818.2 ¢ |
| Major 15-mosstep | M15ms | 15L | 818.2 ¢ to 857.1 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 15L + s | 857.1 ¢ to 872.7 ¢ |
| Major 16-mosstep | M16ms | 16L | 872.7 ¢ to 914.3 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 16L + s | 914.3 ¢ to 927.3 ¢ |
| Major 17-mosstep | M17ms | 17L | 927.3 ¢ to 971.4 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 17L + s | 971.4 ¢ to 981.8 ¢ |
| Major 18-mosstep | M18ms | 18L | 981.8 ¢ to 1028.6 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 18L + s | 1028.6 ¢ to 1036.4 ¢ |
| Major 19-mosstep | M19ms | 19L | 1036.4 ¢ to 1085.7 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 19L + s | 1085.7 ¢ to 1090.9 ¢ |
| Major 20-mosstep | M20ms | 20L | 1090.9 ¢ to 1142.9 ¢ | |
| 21-mosstep | Perfect 21-mosstep | P21ms | 20L + s | 1142.9 ¢ to 1145.5 ¢ |
| Augmented 21-mosstep | A21ms | 21L | 1145.5 ¢ to 1200.0 ¢ | |
| 22-mosstep | Perfect 22-mosstep | P22ms | 21L + s | 1200.0 ¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\22 | 54.545 | 1145.455 | 1:1 | 1.000 | Equalized 21L 1s | |||||
| 6\131 | 54.962 | 1145.038 | 6:5 | 1.200 | ||||||
| 5\109 | 55.046 | 1144.954 | 5:4 | 1.250 | ||||||
| 9\196 | 55.102 | 1144.898 | 9:7 | 1.286 | ||||||
| 4\87 | 55.172 | 1144.828 | 4:3 | 1.333 | Supersoft 21L 1s | |||||
| 11\239 | 55.230 | 1144.770 | 11:8 | 1.375 | ||||||
| 7\152 | 55.263 | 1144.737 | 7:5 | 1.400 | ||||||
| 10\217 | 55.300 | 1144.700 | 10:7 | 1.429 | ||||||
| 3\65 | 55.385 | 1144.615 | 3:2 | 1.500 | Soft 21L 1s | |||||
| 11\238 | 55.462 | 1144.538 | 11:7 | 1.571 | ||||||
| 8\173 | 55.491 | 1144.509 | 8:5 | 1.600 | ||||||
| 13\281 | 55.516 | 1144.484 | 13:8 | 1.625 | ||||||
| 5\108 | 55.556 | 1144.444 | 5:3 | 1.667 | Semisoft 21L 1s | |||||
| 12\259 | 55.598 | 1144.402 | 12:7 | 1.714 | ||||||
| 7\151 | 55.629 | 1144.371 | 7:4 | 1.750 | ||||||
| 9\194 | 55.670 | 1144.330 | 9:5 | 1.800 | ||||||
| 2\43 | 55.814 | 1144.186 | 2:1 | 2.000 | Basic 21L 1s | |||||
| 9\193 | 55.959 | 1144.041 | 9:4 | 2.250 | ||||||
| 7\150 | 56.000 | 1144.000 | 7:3 | 2.333 | ||||||
| 12\257 | 56.031 | 1143.969 | 12:5 | 2.400 | ||||||
| 5\107 | 56.075 | 1143.925 | 5:2 | 2.500 | Semihard 21L 1s | |||||
| 13\278 | 56.115 | 1143.885 | 13:5 | 2.600 | ||||||
| 8\171 | 56.140 | 1143.860 | 8:3 | 2.667 | ||||||
| 11\235 | 56.170 | 1143.830 | 11:4 | 2.750 | ||||||
| 3\64 | 56.250 | 1143.750 | 3:1 | 3.000 | Hard 21L 1s | |||||
| 10\213 | 56.338 | 1143.662 | 10:3 | 3.333 | ||||||
| 7\149 | 56.376 | 1143.624 | 7:2 | 3.500 | ||||||
| 11\234 | 56.410 | 1143.590 | 11:3 | 3.667 | ||||||
| 4\85 | 56.471 | 1143.529 | 4:1 | 4.000 | Superhard 21L 1s | |||||
| 9\191 | 56.545 | 1143.455 | 9:2 | 4.500 | ||||||
| 5\106 | 56.604 | 1143.396 | 5:1 | 5.000 | ||||||
| 6\127 | 56.693 | 1143.307 | 6:1 | 6.000 | ||||||
| 1\21 | 57.143 | 1142.857 | 1:0 | → ∞ | Collapsed 21L 1s | |||||