5L 2s
| ↖4L 1s | ↑5L 1s | 6L 1s↗ |
| ←4L 2s | 5L 2s | 6L 2s→ |
| ↙4L 3s | ↓5L 3s | 6L 3s↘ |
5L 2s, named diatonic, is an octave-equivalent moment of symmetry scale containing 5 large steps and 2 small steps, repeating every octave. Modes of this scale are rotations of the step pattern LLLsLLs. Generators that produce this scale range from 685.714¢ to 720¢, or from 480¢ to 514.286¢.
The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, takes on a generalized form of LLsLLLs, where the large and small steps – denoted as L's and s's – represent whole number step sizes, thus producing different edos. These step ratios affect the sizes of the diatonic scale's intervals and correspond to different tuning systems.
Among the most well-known forms of this scale are the diatonic scale of 12edo, the Pythagorean diatonic scale, and scales produced by meantone systems.
Name
TAMNAMS suggests the temperament-agnostic name diatonic for this scale, which commonly refers to a scale with 5 whole steps and 2 half steps. Under TAMNAMS and for all scale pattern pages on the wiki, the term diatonic exclusively refers to 5L 2s.
The term diatonic may also refer to scales that have more than one size of whole step, such as those produced using tetrachords or just intonation. Such diatonic-like scales, such as Zarlino, blackdye and diasem, are called detempered diatonic scales (for an RTT-based philosophy) or deregularized diatonic scales (for an RTT-agnostic philosophy). The terms diatonic-like or diatonic-based may also be used to refer such scales, depending on what's contextually the most appropriate.
Notation
- This article assumes TAMNAMS for naming step ratios.
Intervals
Intervals are identical to that of standard notation. As such, the usual interval qualities of major/minor and augmented/perfect/diminished apply here.
| Interval classes | Specific intervals | Size
(in ascending order) |
Abbrev. |
|---|---|---|---|
| 0-mosstep (unison) | Perfect 0-mosstep | 0 | P0ms |
| 1-mosstep | Minor 1-mosstep | s | m1ms |
| Major 1-mosstep | L | M1ms | |
| 2-mosstep | Minor 2-mosstep | L + s | m2ms |
| Major 2-mosstep | 2L | M2ms | |
| 3-mosstep | Perfect 3-mosstep | 2L + s | P3ms |
| Augmented 3-mosstep | 3L | A3ms | |
| 4-mosstep | Diminished 4-mosstep | 2L + 2s | d4ms |
| Perfect 4-mosstep | 3L + s | P4ms | |
| 5-mosstep | Minor 5-mosstep | 3L + 2s | m5ms |
| Major 5-mosstep | 4L + s | M5ms | |
| 6-mosstep | Minor 6-mosstep | 4L + 2s | m6ms |
| Major 6-mosstep | 5L + s | M6ms | |
| 7-mosstep (octave) | Perfect 7-mosstep | 5L + 2s | P7ms |
Note names
Note names are identical to that of standard notation. Thus, the basic gamut for 5L 2s is the following:
C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B, C
Theory
Temperament interpretations
- Main article: 5L 2s/Temperaments
5L 2s has several rank-2 temperament interpretations, such as:
- Meantone, with generators around 696.2¢. This includes:
- Flattone, with generators around 693.7¢.
- Schismic, with generators around 702¢.
- Parapyth, with generators around 704.7¢.
- Archy, with generators around 709.3¢. This includes:
- Supra, with generators around 707.2¢
- Superpyth, with generators around 710.3¢
- Ultrapyth, with generators around 713.7¢.
Tuning ranges
Simple tunings
17edo and 19edo are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.
| Scale degree | 12edo (Basic, L:s = 2:1) | 17edo (Hard, L:s = 3:1) | 19edo (Soft, L:s = 3:2) | Approx. JI Ratios | |||
|---|---|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | Steps | Cents | ||
| Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-diadegree | 1 | 100 | 1 | 70.6 | 2 | 126.3 | |
| Major 1-diadegree | 2 | 200 | 3 | 211.8 | 3 | 189.5 | |
| Minor 2-diadegree | 3 | 300 | 4 | 282.4 | 5 | 315.8 | |
| Major 2-diadegree | 4 | 400 | 6 | 423.5 | 6 | 378.9 | |
| Perfect 3-diadegree | 5 | 500 | 7 | 494.1 | 8 | 505.3 | |
| Augmented 3-diadegree | 6 | 600 | 9 | 635.3 | 9 | 568.4 | |
| Diminished 4-diadegree | 6 | 600 | 8 | 564.7 | 10 | 631.6 | |
| Perfect 4-diadegree | 7 | 700 | 10 | 705.9 | 11 | 694.7 | |
| Minor 5-diadegree | 8 | 800 | 11 | 776.5 | 13 | 821.1 | |
| Major 5-diadegree | 9 | 900 | 13 | 917.6 | 14 | 884.2 | |
| Minor 6-diadegree | 10 | 1000 | 14 | 988.2 | 16 | 1010.5 | |
| Major 6-diadegree | 11 | 1100 | 16 | 1129.4 | 17 | 1073.7 | |
| Perfect 7-diadegree (octave) | 12 | 1200 | 17 | 1200 | 19 | 1200 | 2/1 (exact) |
Parasoft tunings
- Main article: Flattone
Parasoft diatonic tunings (4:3 to 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths (3/2, flat of 702¢) to produce major 3rds that are flatter than 5/4 (386¢).
Edos include 19edo, 26edo, 45edo, and 64edo.
| Scale degree | 19edo (Soft, L:s = 3:2) | 26edo (Supersoft, L:s = 4:3) | 45edo (L:s = 7:5) | 64edo (L:s = 10:7) | Approx. JI Ratios | ||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | Steps | Cents | Steps | Cents | ||
| Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-diadegree | 2 | 126.3 | 3 | 138.5 | 5 | 133.3 | 7 | 131.3 | |
| Major 1-diadegree | 3 | 189.5 | 4 | 184.6 | 7 | 186.7 | 10 | 187.5 | |
| Minor 2-diadegree | 5 | 315.8 | 7 | 323.1 | 12 | 320 | 17 | 318.8 | |
| Major 2-diadegree | 6 | 378.9 | 8 | 369.2 | 14 | 373.3 | 20 | 375 | |
| Perfect 3-diadegree | 8 | 505.3 | 11 | 507.7 | 19 | 506.7 | 27 | 506.2 | |
| Augmented 3-diadegree | 9 | 568.4 | 12 | 553.8 | 21 | 560 | 30 | 562.5 | |
| Diminished 4-diadegree | 10 | 631.6 | 14 | 646.2 | 24 | 640 | 34 | 637.5 | |
| Perfect 4-diadegree | 11 | 694.7 | 15 | 692.3 | 26 | 693.3 | 37 | 693.8 | |
| Minor 5-diadegree | 13 | 821.1 | 18 | 830.8 | 31 | 826.7 | 44 | 825 | |
| Major 5-diadegree | 14 | 884.2 | 19 | 876.9 | 33 | 880 | 47 | 881.2 | |
| Minor 6-diadegree | 16 | 1010.5 | 22 | 1015.4 | 38 | 1013.3 | 54 | 1012.5 | |
| Major 6-diadegree | 17 | 1073.7 | 23 | 1061.5 | 40 | 1066.7 | 57 | 1068.8 | |
| Perfect 7-diadegree (octave) | 19 | 1200 | 26 | 1200 | 45 | 1200 | 64 | 1200 | 2/1 (exact) |
Hyposoft tunings
- Main article: Meantone
Hyposoft diatonic tunings (3:2 to 2:1) correspond to meantone temperaments, characterized by flattened perfect 5ths (flat of 702¢) to produce diatonic major 3rds that approximate 5/4 (386¢).
Edos include 19edo, 31edo, 43edo, and 50edo.
| Scale degree | 19edo (Soft, L:s = 3:2) | 31edo (Semisoft, L:s = 5:3) | 43edo (L:s = 7:4) | 50edo (L:s = 8:5) | Approx. JI Ratios | ||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | Steps | Cents | Steps | Cents | ||
| Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-diadegree | 2 | 126.3 | 3 | 116.1 | 4 | 111.6 | 5 | 120 | |
| Major 1-diadegree | 3 | 189.5 | 5 | 193.5 | 7 | 195.3 | 8 | 192 | |
| Minor 2-diadegree | 5 | 315.8 | 8 | 309.7 | 11 | 307 | 13 | 312 | |
| Major 2-diadegree | 6 | 378.9 | 10 | 387.1 | 14 | 390.7 | 16 | 384 | |
| Perfect 3-diadegree | 8 | 505.3 | 13 | 503.2 | 18 | 502.3 | 21 | 504 | |
| Augmented 3-diadegree | 9 | 568.4 | 15 | 580.6 | 21 | 586 | 24 | 576 | |
| Diminished 4-diadegree | 10 | 631.6 | 16 | 619.4 | 22 | 614 | 26 | 624 | |
| Perfect 4-diadegree | 11 | 694.7 | 18 | 696.8 | 25 | 697.7 | 29 | 696 | |
| Minor 5-diadegree | 13 | 821.1 | 21 | 812.9 | 29 | 809.3 | 34 | 816 | |
| Major 5-diadegree | 14 | 884.2 | 23 | 890.3 | 32 | 893 | 37 | 888 | |
| Minor 6-diadegree | 16 | 1010.5 | 26 | 1006.5 | 36 | 1004.7 | 42 | 1008 | |
| Major 6-diadegree | 17 | 1073.7 | 28 | 1083.9 | 39 | 1088.4 | 45 | 1080 | |
| Perfect 7-diadegree (octave) | 19 | 1200 | 31 | 1200 | 43 | 1200 | 50 | 1200 | 2/1 (exact) |
Hypohard tunings
- Main article: Pythagorean tuning and schismatic temperament
The range of hypohard tunings can be divided into a minihard range (2:1 to 5:2) and quasihard range (5:2 to 3:1).
Minihard tunings
Minihard diatonic tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in a major 3rd of 81/64 (407¢).
| Scale degree | 41edo (L:s = 7:3) | 53edo (L:s = 9:4) | Approx. JI Ratios | ||
|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | ||
| Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-diadegree | 3 | 87.8 | 4 | 90.6 | |
| Major 1-diadegree | 7 | 204.9 | 9 | 203.8 | |
| Minor 2-diadegree | 10 | 292.7 | 13 | 294.3 | |
| Major 2-diadegree | 14 | 409.8 | 18 | 407.5 | |
| Perfect 3-diadegree | 17 | 497.6 | 22 | 498.1 | |
| Augmented 3-diadegree | 21 | 614.6 | 27 | 611.3 | |
| Diminished 4-diadegree | 20 | 585.4 | 26 | 588.7 | |
| Perfect 4-diadegree | 24 | 702.4 | 31 | 701.9 | |
| Minor 5-diadegree | 27 | 790.2 | 35 | 792.5 | |
| Major 5-diadegree | 31 | 907.3 | 40 | 905.7 | |
| Minor 6-diadegree | 34 | 995.1 | 44 | 996.2 | |
| Major 6-diadegree | 38 | 1112.2 | 49 | 1109.4 | |
| Perfect 7-diadegree (octave) | 41 | 1200 | 53 | 1200 | 2/1 (exact) |
Quasihard tunings
Quasihard diatonic tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of 32/27 (294¢).
Edos include 17edo, 29edo, and 46edo. 17edo is considered to be on the sharper end of the neogothic spectrum, with a major 3rd that is more discordant than flatter neogothic tunings.
| Scale degree | 17edo (Hard, L:s = 3:1) | 29edo (Semihard, L:s = 5:2) | 46edo (L:s = 8:3) | Approx. JI Ratios | |||
|---|---|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | Steps | Cents | ||
| Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-diadegree | 1 | 70.6 | 2 | 82.8 | 3 | 78.3 | |
| Major 1-diadegree | 3 | 211.8 | 5 | 206.9 | 8 | 208.7 | |
| Minor 2-diadegree | 4 | 282.4 | 7 | 289.7 | 11 | 287 | |
| Major 2-diadegree | 6 | 423.5 | 10 | 413.8 | 16 | 417.4 | |
| Perfect 3-diadegree | 7 | 494.1 | 12 | 496.6 | 19 | 495.7 | |
| Augmented 3-diadegree | 9 | 635.3 | 15 | 620.7 | 24 | 626.1 | |
| Diminished 4-diadegree | 8 | 564.7 | 14 | 579.3 | 22 | 573.9 | |
| Perfect 4-diadegree | 10 | 705.9 | 17 | 703.4 | 27 | 704.3 | |
| Minor 5-diadegree | 11 | 776.5 | 19 | 786.2 | 30 | 782.6 | |
| Major 5-diadegree | 13 | 917.6 | 22 | 910.3 | 35 | 913 | |
| Minor 6-diadegree | 14 | 988.2 | 24 | 993.1 | 38 | 991.3 | |
| Major 6-diadegree | 16 | 1129.4 | 27 | 1117.2 | 43 | 1121.7 | |
| Perfect 7-diadegree (octave) | 17 | 1200 | 29 | 1200 | 46 | 1200 | 2/1 (exact) |
Parahard and ultrahard tunings
- Main article: Archy
Parahard (3:1 to 4:1) and ultrahard (4:1 to 1:0) diatonic tunings correspond to archy systems, with perfect 5ths that are significantly sharper than than 702¢.
Edos include 17edo, 22edo, 27edo, and 32edo, among others.
| Scale degree | 17edo (Hard, L:s = 3:1) | 22edo (Superhard, L:s = 4:1) | 27edo (L:s = 5:1) | 32edo (L:s = 6:1) | Approx. JI Ratios | ||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | Steps | Cents | Steps | Cents | ||
| Perfect 0-diadegree (unison) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-diadegree | 1 | 70.6 | 1 | 54.5 | 1 | 44.4 | 1 | 37.5 | |
| Major 1-diadegree | 3 | 211.8 | 4 | 218.2 | 5 | 222.2 | 6 | 225 | |
| Minor 2-diadegree | 4 | 282.4 | 5 | 272.7 | 6 | 266.7 | 7 | 262.5 | |
| Major 2-diadegree | 6 | 423.5 | 8 | 436.4 | 10 | 444.4 | 12 | 450 | |
| Perfect 3-diadegree | 7 | 494.1 | 9 | 490.9 | 11 | 488.9 | 13 | 487.5 | |
| Augmented 3-diadegree | 9 | 635.3 | 12 | 654.5 | 15 | 666.7 | 18 | 675 | |
| Diminished 4-diadegree | 8 | 564.7 | 10 | 545.5 | 12 | 533.3 | 14 | 525 | |
| Perfect 4-diadegree | 10 | 705.9 | 13 | 709.1 | 16 | 711.1 | 19 | 712.5 | |
| Minor 5-diadegree | 11 | 776.5 | 14 | 763.6 | 17 | 755.6 | 20 | 750 | |
| Major 5-diadegree | 13 | 917.6 | 17 | 927.3 | 21 | 933.3 | 25 | 937.5 | |
| Minor 6-diadegree | 14 | 988.2 | 18 | 981.8 | 22 | 977.8 | 26 | 975 | |
| Major 6-diadegree | 16 | 1129.4 | 21 | 1145.5 | 26 | 1155.6 | 31 | 1162.5 | |
| Perfect 7-diadegree (octave) | 17 | 1200 | 22 | 1200 | 27 | 1200 | 32 | 1200 | 2/1 (exact) |
Modes
Diatonic modes have standard names from classical music theory.
| UDP | Step pattern | Mode names |
|---|---|---|
| 6|0 | LLLsLLs | Lydian |
| 5|1 | LLsLLLs | Ionian (major) |
| 4|2 | LLsLLsL | Mixolydian |
| 3|3 | LsLLLsL | Dorian |
| 2|4 | LsLLsLL | Aeolian (minor) |
| 1|5 | sLLLsLL | Phrygian |
| 0|6 | sLLsLLL | Locrian |
Each mode has the following scale degrees, reached by raising or lowering certain naturals by a chroma.
| Mode | Scale degree (on C) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| UDP | Step pattern | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th |
| 6|0 | LLLsLLs | Perfect (C) | Major (D) | Major (E) | Augmented (F#) | Perfect (G) | Major (A) | Major (B) | Perfect (C) |
| 5|1 | LLsLLLs | Perfect (C) | Major (D) | Major (E) | Perfect (F) | Perfect (G) | Major (A) | Major (B) | Perfect (C) |
| 4|2 | LLsLLsL | Perfect (C) | Major (D) | Major (E) | Perfect (F) | Perfect (G) | Major (A) | Minor (Bb) | Perfect (C) |
| 3|3 | LsLLLsL | Perfect (C) | Major (D) | Minor (Eb) | Perfect (F) | Perfect (G) | Major (A) | Minor (Bb) | Perfect (C) |
| 2|4 | LsLLsLL | Perfect (C) | Major (D) | Minor (Eb) | Perfect (F) | Perfect (G) | Minor (Ab) | Minor (Bb) | Perfect (C) |
| 1|5 | sLLLsLL | Perfect (C) | Minor (Db) | Minor (Eb) | Perfect (F) | Perfect (G) | Minor (Ab) | Minor (Bb) | Perfect (C) |
| 0|6 | sLLsLLL | Perfect (C) | Minor (Db) | Minor (Eb) | Perfect (F) | Diminished (Gb) | Minor (Ab) | Minor (Bb) | Perfect (C) |
Scales
Subset and superset scales
5L 2s has a parent scale of 2L 3s, a pentatonic scale, meaning 2L 3s is a subset. 5L 2s also has two child scales, which are supersets of 5L 2s:
- 7L 5s, a chromatic scale produced using soft-of-basic step ratios.
- 5L 7s, a chromatic scale produced using hard-of-basic step ratios.
12edo, the equalized form of both 7L 5s and 5L 7s, is also a superset of 5L 2s.
MODMOS scales and muddles
- Main article: 5L 2s MODMOSes and 5L 2s Muddles
Scala files
- Meantone7 – 19edo and 31edo tunings
- Nestoria7 – 171edo tuning
- Pythagorean7 – Pythagorean tuning
- Garibaldi7 – 94edo tuning
- Cotoneum7 – 217edo tuning
- Pepperoni7 – 271edo tuning
- Supra7 – 56edo tuning
- Archy7 – 472edo tuning
Scale tree
| Steps of ED | Generator in cents | Step ratio | Comments | ||
|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | ||
| 4\7 | 685.714 | 514.286 | 1:1 | 1 | Equalized 5L 2s |
| 27\47 | 689.362 | 510.638 | 7:6 | 1.167 | |
| 23\40 | 690 | 510 | 6:5 | 1.2 | |
| 42\73 | 690.411 | 509.589 | 11:9 | 1.222 | |
| 19\33 | 690.909 | 509.091 | 5:4 | 1.25 | |
| 53\92 | 691.304 | 508.696 | 14:11 | 1.273 | |
| 34\59 | 691.525 | 508.475 | 9:7 | 1.286 | |
| 49\85 | 691.765 | 508.235 | 13:10 | 1.3 | |
| 15\26 | 692.308 | 507.692 | 4:3 | 1.333 | Supersoft 5L 2s |
| 56\97 | 692.784 | 507.216 | 15:11 | 1.364 | |
| 41\71 | 692.958 | 507.042 | 11:8 | 1.375 | |
| 67\116 | 693.103 | 506.897 | 18:13 | 1.385 | |
| 26\45 | 693.333 | 506.667 | 7:5 | 1.4 | Flattone is in this region |
| 63\109 | 693.578 | 506.422 | 17:12 | 1.417 | |
| 37\64 | 693.75 | 506.25 | 10:7 | 1.429 | |
| 48\83 | 693.976 | 506.024 | 13:9 | 1.444 | |
| 11\19 | 694.737 | 505.263 | 3:2 | 1.5 | Soft 5L 2s |
| 51\88 | 695.455 | 504.545 | 14:9 | 1.556 | |
| 40\69 | 695.652 | 504.348 | 11:7 | 1.571 | |
| 69\119 | 695.798 | 504.202 | 19:12 | 1.583 | |
| 29\50 | 696 | 504 | 8:5 | 1.6 | |
| 76\131 | 696.183 | 503.817 | 21:13 | 1.615 | Golden meantone (696.2145¢) |
| 47\81 | 696.296 | 503.704 | 13:8 | 1.625 | |
| 65\112 | 696.429 | 503.571 | 18:11 | 1.636 | |
| 18\31 | 696.774 | 503.226 | 5:3 | 1.667 | Semisoft 5L 2s Meantone is in this region |
| 61\105 | 697.143 | 502.857 | 17:10 | 1.7 | |
| 43\74 | 697.297 | 502.703 | 12:7 | 1.714 | |
| 68\117 | 697.436 | 502.564 | 19:11 | 1.727 | |
| 25\43 | 697.674 | 502.326 | 7:4 | 1.75 | |
| 57\98 | 697.959 | 502.041 | 16:9 | 1.778 | |
| 32\55 | 698.182 | 501.818 | 9:5 | 1.8 | |
| 39\67 | 698.507 | 501.493 | 11:6 | 1.833 | |
| 7\12 | 700 | 500 | 2:1 | 2 | Basic 5L 2s (Generators smaller than this are proper) |
| 38\65 | 701.538 | 498.462 | 11:5 | 2.2 | |
| 31\53 | 701.887 | 498.113 | 9:4 | 2.25 | The generator closest to a just 3/2 for EDOs less than 200 |
| 55\94 | 702.128 | 497.872 | 16:7 | 2.286 | Garibaldi / Cassandra |
| 24\41 | 702.439 | 497.561 | 7:3 | 2.333 | |
| 65\111 | 702.703 | 497.297 | 19:8 | 2.375 | |
| 41\70 | 702.857 | 497.143 | 12:5 | 2.4 | |
| 58\99 | 703.03 | 496.97 | 17:7 | 2.429 | |
| 17\29 | 703.448 | 496.552 | 5:2 | 2.5 | Semihard 5L 2s |
| 61\104 | 703.846 | 496.154 | 18:7 | 2.571 | |
| 44\75 | 704 | 496 | 13:5 | 2.6 | |
| 71\121 | 704.132 | 495.868 | 21:8 | 2.625 | Golden neogothic (704.0956¢) |
| 27\46 | 704.348 | 495.652 | 8:3 | 2.667 | Neogothic is in this region |
| 64\109 | 704.587 | 495.413 | 19:7 | 2.714 | |
| 37\63 | 704.762 | 495.238 | 11:4 | 2.75 | |
| 47\80 | 705 | 495 | 14:5 | 2.8 | |
| 10\17 | 705.882 | 494.118 | 3:1 | 3 | Hard 5L 2s |
| 43\73 | 706.849 | 493.151 | 13:4 | 3.25 | |
| 33\56 | 707.143 | 492.857 | 10:3 | 3.333 | |
| 56\95 | 707.368 | 492.632 | 17:5 | 3.4 | |
| 23\39 | 707.692 | 492.308 | 7:2 | 3.5 | |
| 59\100 | 708 | 492 | 18:5 | 3.6 | |
| 36\61 | 708.197 | 491.803 | 11:3 | 3.667 | |
| 49\83 | 708.434 | 491.566 | 15:4 | 3.75 | |
| 13\22 | 709.091 | 490.909 | 4:1 | 4 | Superhard 5L 2s Archy is in this region |
| 42\71 | 709.859 | 490.141 | 13:3 | 4.333 | |
| 29\49 | 710.204 | 489.796 | 9:2 | 4.5 | |
| 45\76 | 710.526 | 489.474 | 14:3 | 4.667 | |
| 16\27 | 711.111 | 488.889 | 5:1 | 5 | |
| 35\59 | 711.864 | 488.136 | 11:2 | 5.5 | |
| 19\32 | 712.5 | 487.5 | 6:1 | 6 | |
| 22\37 | 713.514 | 486.486 | 7:1 | 7 | |
| 3\5 | 720 | 480 | 1:0 | → ∞ | Collapsed 5L 2s |
Step ratio diagram
