53edo
| ← 52edo | 53edo | 54edo → |
(convergent)
53 equal divisions of the octave (abbreviated 53edo or 53ed2), also called 53-tone equal temperament (53tet) or 53 equal temperament (53et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 53 equal parts of about 22.6 ¢ each. Each step represents a frequency ratio of 21/53, or the 53rd root of 2.
Theory
53edo is notable as an excellent 5-limit system, a fact apparently first noted by Isaac Newton[1], notably tempering out Mercator's comma (353/284), the schisma (32805/32768), kleisma (15625/15552), and amity comma (1600000/1594323). In the 7-limit it tempers out the marvel comma (225/224), orwellisma (1728/1715), gariboh comma (3125/3087), and ragisma (4375/4374). In the 11-limit, it tempers out 99/98 and 121/120 (in addition to their difference, 540/539), and is the optimal patent val for big brother temperament, which tempers out both, as well as 11-limit orwell temperament, which also tempers out the 11-limit commas 176/175 and 385/384. In the 13-limit, it tempers out 169/168, 275/273, 325/324, 625/624, 676/675, 1001/1000, 2080/2079, and 4096/4095, and gives the optimal patent val for athene temperament. It is the seventh strict zeta edo. It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 23-odd-limit.
53edo has also found a certain dissemination as an edo tuning for Arabic, Turkish, and Persian music. It can also be used as an extended Pythagorean tuning, since its fifths are almost indistinguishable from just.
53edo's step is sometimes called the "Holdrian comma", despite the 53rd root of 2 being an irrational number; the step's role as a "comma" comes from it being an approximation of the Pythagorean comma and syntonic comma.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.07 | -1.41 | +4.76 | -7.92 | -2.79 | +8.25 | -3.17 | +5.69 | -10.71 | +9.68 | -2.29 | +1.13 |
| Relative (%) | +0.0 | -0.3 | -6.2 | +21.0 | -35.0 | -12.3 | +36.4 | -14.0 | +25.1 | -47.3 | +42.8 | -10.1 | +5.0 | |
| Steps (reduced) |
53 (0) |
84 (31) |
123 (17) |
149 (43) |
183 (24) |
196 (37) |
217 (5) |
225 (13) |
240 (28) |
257 (45) |
263 (51) |
276 (11) |
284 (19) | |
53edo also has reasonably good approximations to a number of higher primes such as 71, 73, 79 and 83. See #Approximation to JI.
Subsets and supersets
53edo is the 16th prime edo, following 47edo and coming before 59edo.
Many of its multiples such as 159edo, 212edo, 742edo, 901edo and 954edo have good consistency limits and are each of their own interest. The mercator family comprises rank-2 temperaments with 1/53-octave periods.
Intervals
| # | Cents | Approximate Ratios[note 1] | Ups and Downs Notation | Solfeges | |||
|---|---|---|---|---|---|---|---|
| 0 | 0.00 | 1/1 | P1 | unison | D | Da | Do |
| 1 | 22.64 | 81/80, 64/63, 50/49 | ^1 | up unison | ^D | Du | Di |
| 2 | 45.28 | 49/48, 36/35, 33/32, 128/125 | ^^1, vvm2 | dup unison, dudminor 2nd | ^^D, vvEb | Di / Fre | Daw |
| 3 | 67.92 | 25/24, 28/27, 22/21, 27/26, 26/25 | vvA1, vm2 | dudaug 1sn, downminor 2nd | vvD#, vEb | Fro | Ro |
| 4 | 90.57 | 19/18, 20/19, 21/20, 256/243 | vA1, m2 | downaug 1sn, minor 2nd | vD#, Eb | Fra | Rih |
| 5 | 113.21 | 16/15, 15/14 | A1, ^m2 | aug 1sn, upminor 2nd | D#, ^Eb | Fru | Ra |
| 6 | 135.85 | 14/13, 13/12, 27/25 | ^^m2 | dupminor 2nd | ^^Eb | Fri | Ru |
| 7 | 158.49 | 35/32, 12/11, 11/10, 57/52, 800/729 | vvM2 | dudmajor 2nd | vvE | Re | Ruh |
| 8 | 181.13 | 10/9 | vM2 | downmajor 2nd | vE | Ro | Reh |
| 9 | 203.77 | 9/8 | M2 | major 2nd | E | Ra | Re |
| 10 | 226.42 | 8/7, 256/225 | ^M2 | upmajor 2nd | ^E | Ru | Ri |
| 11 | 249.06 | 15/13, 144/125, 125/108 | ^^M2, vvm3 | dupmajor 2nd, dudminor 3rd | ^^E, vvF | Ri / Ne | Raw |
| 12 | 271.70 | 7/6, 75/64 | vm3 | downminor 3rd | vF | No | Ma |
| 13 | 294.34 | 13/11, 19/16, 32/27 | m3 | minor 3rd | F | Na | Meh |
| 14 | 316.98 | 6/5 | ^m3 | upminor 3rd | ^F | Nu | Me |
| 15 | 339.62 | 11/9, 243/200 | ^^m3 | dupminor 3rd | ^^F | Ni | Mu |
| 16 | 362.26 | 16/13, 100/81 | vvM3 | dudmajor 3rd | vvF# | Me | Muh |
| 17 | 384.91 | 5/4 | vM3 | downmajor 3rd | vF# | Mo | Mi |
| 18 | 407.55 | 19/15, 24/19, 81/64 | M3 | major 3rd | F# | Ma | Maa |
| 19 | 430.19 | 9/7, 14/11 | ^M3 | upmajor 3rd | ^F# | Mu | Mo |
| 20 | 452.83 | 13/10, 125/96, 162/125 | ^^M3, vv4 | dupmajor 3rd, dud 4th | ^^F#, vvG | Mi / Fe | Maw |
| 21 | 475.47 | 21/16, 25/19, 675/512, 320/243 | v4 | down 4th | vG | Fo | Fe |
| 22 | 498.11 | 4/3 | P4 | perfect 4th | G | Fa | Fa |
| 23 | 520.75 | 27/20 | ^4 | up 4th | ^G | Fu | Fih |
| 24 | 543.40 | 11/8, 15/11, 26/19 | ^^4 | dup 4th | ^^G | Fi / She | Fu |
| 25 | 566.04 | 18/13 | vvA4, vd5 | dudaug 4th, downdim 5th | vvG#, vAb | Pe / Sho | Fuh |
| 26 | 588.68 | 7/5, 45/32 | vA4, d5 | downaug 4th, dim 5th | vG#, Ab | Po / Sha | Fi |
| 27 | 611.32 | 10/7, 64/45 | A4, ^d5 | aug 4th, updim 5th | G#, ^Ab | Pa / Shu | Se |
| 28 | 633.96 | 13/9 | ^A4, ^^d5 | upaug 4th, dupdim 5th | ^G#, ^^Ab | Pu / Shi | Suh |
| 29 | 656.60 | 16/11, 19/13, 22/15 | vv5 | dud 5th | vvA | Pi / Se | Su |
| 30 | 679.25 | 40/27 | v5 | down 5th | vA | So | Sih |
| 31 | 701.89 | 3/2 | P5 | perfect 5th | A | Sa | Sol |
| 32 | 724.53 | 32/21, 38/25, 243/160, 1024/675 | ^5 | up 5th | ^A | Su | Si |
| 33 | 747.17 | 20/13, 192/125, 125/81 | ^^5, vvm6 | dup 5th, dudminor 6th | ^^A, vvBb | Si / Fle | Saw |
| 34 | 769.81 | 14/9, 25/16, 11/7 | vm6 | downminor 6th | vBb | Flo | Lo |
| 35 | 792.45 | 19/12, 30/19, 128/81 | m6 | minor 6th | Bb | Fla | Leh |
| 36 | 815.09 | 8/5 | ^m6 | upminor 6th | ^Bb | Flu | Le |
| 37 | 837.74 | 13/8, 81/50 | ^^m6 | dupminor 6th | ^^Bb | Fli | Lu |
| 38 | 860.38 | 18/11, 400/243 | vvM6 | dudmajor 6th | vvB | Le | Luh |
| 39 | 883.02 | 5/3 | vM6 | downmajor 6th | vB | Lo | La |
| 40 | 905.66 | 22/13, 27/16, 32/19 | M6 | major 6th | B | La | Laa |
| 41 | 928.30 | 12/7 | ^M6 | upmajor 6th | ^B | Lu | Li |
| 42 | 950.94 | 26/15, 125/72, 216/125 | ^^M6, vvm7 | dupmajor 6th, dudminor 7th | ^^B, vvC | Li / The | Law |
| 43 | 973.58 | 7/4 | vm7 | downminor 7th | vC | Tho | Ta |
| 44 | 996.23 | 16/9 | m7 | minor 7th | C | Tha | Teh |
| 45 | 1018.87 | 9/5 | ^m7 | upminor 7th | ^C | Thu | Te |
| 46 | 1041.51 | 64/35, 11/6, 20/11, 729/400 | ^^m7 | dupminor 7th | ^^C | Thi | Tu |
| 47 | 1064.15 | 13/7, 24/13, 50/27 | vvM7 | dudmajor 7th | vvC# | Te | Tuh |
| 48 | 1086.79 | 15/8 | vM7 | downmajor 7th | vC# | To | Ti |
| 49 | 1109.43 | 19/10, 36/19, 40/21, 243/128 | M7 | major 7th | C# | Ta | Tih |
| 50 | 1132.08 | 48/25, 27/14, 21/11, 52/27, 25/13 | ^M7 | upmajor 7th | ^C# | Tu | To |
| 51 | 1154.72 | 96/49, 35/18, 64/33, 125/64 | ^^M7, vv8 | dupmajor 7th, dud 8ve | ^^C#, vvD | Ti / De | Taw |
| 52 | 1177.36 | 160/81, 63/32, 49/25 | v8 | down 8ve | vD | Do | Da |
| 53 | 1200.00 | 2/1 | P8 | perfect 8ve | D | Da | Do |
Interval quality and chord names in color notation
Combining ups and downs notation with color notation, qualities can be loosely associated with colors:
| Quality | Color | Monzo Format | Examples |
|---|---|---|---|
| downminor | zo | (a, b, 0, 1) | 7/6, 7/4 |
| minor | fourthward wa | (a, b) with b < -1 | 32/27, 16/9 |
| upminor | gu | (a, b, -1) | 6/5, 9/5 |
| dupminor | ilo | (a, b, 0, 0, 1) | 11/9, 11/6 |
| dudmajor | lu | (a, b, 0, 0, -1) | 12/11, 18/11 |
| downmajor | yo | (a, b, 1) | 5/4, 5/3 |
| major | fifthward wa | (a, b) with b > 1 | 9/8, 27/16 |
| upmajor | ru | (a, b, 0, -1) | 9/7, 12/7 |
All 53edo chords can be named using ups and downs. An up, down or mid after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are.
Here are the zo, gu, ilo, lu, yo and ru triads:
| Color of the 3rd | JI Chord | Notes as Edosteps | Notes of C Chord | Written Name | Spoken Name |
|---|---|---|---|---|---|
| zo | 6:7:9 | 0-12-31 | C vEb G | Cvm | C downminor |
| gu | 10:12:15 | 0-14-31 | C ^Eb G | C^m | C upminor |
| ilo | 18:22:27 | 0-15-31 | C ^^Eb G | C^^m | C dupminor |
| lu | 22:27:33 | 0-16-31 | C vvE G | Cvv | C dudmajor or C dud |
| yo | 4:5:6 | 0-17-31 | C vE G | Cv | C downmajor or C down |
| ru | 14:18:21 | 0-19-31 | C ^E G | C^ | C upmajor or C up |
For a more complete list, see Ups and downs notation #Chords and Chord Progressions.
Notation
Ups and downs notation
Using Helmholtz–Ellis accidentals, 53edo can be notated using ups and downs notation:
| Step Offset | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Sharp Symbol |  |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
| Flat Symbol |  |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
Here, a sharp raises by five steps (commas), and a flat lowers by five steps, so single and double arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, then in some cases certain notes may be best spelled with triple arrows.
Sagittal
The following table shows sagittal notation accidentals in one apotome for 53edo.
| Steps | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Symbol | 
|
|
|
|
|
|
Relationship to 12edo
Whereas 12edo has a circle of twelve 5ths, 53edo has a spiral of twelve 5ths (since 31\53 is on the 7\12 kite in the scale tree). This shows 53edo in a 12edo-friendly format. Excellent for introducing 53edo to musicians unfamiliar with microtonal music. The two innermost and two outermost intervals on the spiral are duplicates.
Approximation to JI
53edo provides excellent approximations for the classic 5-limit just chords and scales, such as the Ptolemy-Zarlino "just major" scale.
| Interval | Ratio | Size | Difference |
|---|---|---|---|
| Perfect fifth | 3/2 | 31 | −0.07 cents |
| Major third | 5/4 | 17 | −1.40 cents |
| Minor third | 6/5 | 14 | +1.34 cents |
| Major second | 9/8 | 9 | −0.14 cents |
| 10/9 | 8 | −1.27 cents | |
| Minor second | 16/15 | 5 | +1.48 cents |
Because the 5th is so accurate, 53edo also offers good approximations for Pythagorean thirds. In addition, the 43\53 interval is only 4.8 cents wider than 7/4, so 53edo can also be used for 7-limit harmony, in which it tempers out the septimal kleisma, 225/224.
15-odd-limit interval mappings
The following tables show how 15-odd-limit intervals are represented in 53edo. Prime harmonics are in bold; inconsistent intervals are in italics.
| Interval and complement | Error (abs, ¢) | Error (rel, %) |
|---|---|---|
| 1/1, 2/1 | 0.000 | 0.0 |
| 3/2, 4/3 | 0.068 | 0.3 |
| 9/8, 16/9 | 0.136 | 0.6 |
| 9/5, 10/9 | 1.272 | 5.6 |
| 15/13, 26/15 | 1.316 | 5.8 |
| 5/3, 6/5 | 1.340 | 5.9 |
| 13/10, 20/13 | 1.384 | 6.1 |
| 5/4, 8/5 | 1.408 | 6.2 |
| 15/8, 16/15 | 1.476 | 6.5 |
| 13/9, 18/13 | 2.655 | 11.7 |
| 13/12, 24/13 | 2.724 | 12.0 |
| 13/8, 16/13 | 2.792 | 12.3 |
| 7/4, 8/7 | 4.759 | 21.0 |
| 7/6, 12/7 | 4.827 | 21.3 |
| 9/7, 14/9 | 4.895 | 21.6 |
| 13/11, 22/13 | 5.130 | 22.7 |
| 7/5, 10/7 | 6.167 | 27.2 |
| 15/14, 28/15 | 6.235 | 27.5 |
| 15/11, 22/15 | 6.445 | 28.5 |
| 11/10, 20/11 | 6.514 | 28.8 |
| 13/7, 14/13 | 7.551 | 33.3 |
| 11/9, 18/11 | 7.785 | 34.4 |
| 11/6, 12/11 | 7.854 | 34.7 |
| 11/8, 16/11 | 7.922 | 35.0 |
| 11/7, 14/11 | 9.961 | 44.0 |
| Interval and complement | Error (abs, ¢) | Error (rel, %) |
|---|---|---|
| 1/1, 2/1 | 0.000 | 0.0 |
| 3/2, 4/3 | 0.068 | 0.3 |
| 9/8, 16/9 | 0.136 | 0.6 |
| 9/5, 10/9 | 1.272 | 5.6 |
| 15/13, 26/15 | 1.316 | 5.8 |
| 5/3, 6/5 | 1.340 | 5.9 |
| 13/10, 20/13 | 1.384 | 6.1 |
| 5/4, 8/5 | 1.408 | 6.2 |
| 15/8, 16/15 | 1.476 | 6.5 |
| 13/9, 18/13 | 2.655 | 11.7 |
| 13/12, 24/13 | 2.724 | 12.0 |
| 13/8, 16/13 | 2.792 | 12.3 |
| 7/4, 8/7 | 4.759 | 21.0 |
| 7/6, 12/7 | 4.827 | 21.3 |
| 9/7, 14/9 | 4.895 | 21.6 |
| 13/11, 22/13 | 5.130 | 22.7 |
| 7/5, 10/7 | 6.167 | 27.2 |
| 15/14, 28/15 | 6.235 | 27.5 |
| 15/11, 22/15 | 6.445 | 28.5 |
| 11/10, 20/11 | 6.514 | 28.8 |
| 13/7, 14/13 | 7.551 | 33.3 |
| 11/9, 18/11 | 7.785 | 34.4 |
| 11/6, 12/11 | 7.854 | 34.7 |
| 11/8, 16/11 | 7.922 | 35.0 |
| 11/7, 14/11 | 12.681 | 56.0 |
Higher-limit JI
There is also a cluster of usable higher primes starting at 71; even 89 (4.84 ¢ flat), 97 (4.63 ¢ sharp) and 101 (2.6 ¢ sharp) are usable if placed in just the right context.
| Harmonic | 71 | 73 | 79 | 83 | |
|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.44 | -1.37 | -2.27 | +2.78 |
| Relative (%) | +6.3 | -6.1 | -10.0 | +12.3 | |
| Steps (reduced) |
326 (8) |
328 (10) |
334 (16) |
338 (20) | |
This make 53edo excellent (for its size) in the 2.3.5.7.11.13.19.23.37.41.71.73.79.83 subgroup, although some higher error primes like 11 and 23 require the right context to be convincing.
Note that the high primes, in rooted (/2n) position, essentially act as alternate interpretations of LCJI intervals, if you want to force a rooted interpretation; namely: 71/64 as ~10/9, 73/64 as ~8/7, 79/64 as ~16/13, and perhaps most questionably in the context of 53edo, 83/64 as ~13/10.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-84 53⟩ | [⟨53 84]] | +0.022 | 0.022 | 0.10 |
| 2.3.5 | 15625/15552, 32805/32768 | [⟨53 84 123]] | +0.216 | 0.276 | 1.22 |
| 2.3.5.7 | 225/224, 1728/1715, 3125/3087 | [⟨53 84 123 149]] | −0.262 | 0.861 | 3.81 |
| 2.3.5.7.11 | 99/98, 121/120, 176/175, 2200/2187 | [⟨53 84 123 149 183]] | +0.248 | 1.279 | 5.64 |
| 2.3.5.7.11.13 | 99/98, 121/120, 169/168, 176/175, 275/273 | [⟨53 84 123 149 183 196]] | +0.332 | 1.183 | 5.22 |
| 2.3.5.7.11.13.19 | 99/98, 121/120, 169/168, 176/175, 209/208, 275/273 | [⟨53 84 123 149 183 196 225]] | +0.391 | 1.105 | 4.88 |
- 53et is lower in relative error than any previous equal temperaments in the 3-, 5-, and 13-limit. The next equal temperaments doing better in these subgroups are 306, 118, and 58, respectively. It is even more prominent in the 2.3.5.7.13.19 and 2.3.5.7.13.19.23 subgroups, and the next equal temperament doing better in either subgroup is 130.
Commas
Commas that 53edo tempers out using its patent val, ⟨53 84 123 149 183 196 225], include:
| Prime Limit |
Ratio[note 2] | Monzo | Cents | Color name | Name(s) |
|---|---|---|---|---|---|
| 3 | (52 digits) | [-84 53⟩ | 3.62 | Tribilawa | 53-comma, Mercator's comma |
| 5 | (14 digits) | [-21 3 7⟩ | 10.06 | Lasepyo | Semicomma |
| 5 | 15625/15552 | [-6 -5 6⟩ | 8.11 | Tribiyo | Kleisma |
| 5 | (14 digits) | [9 -13 5⟩ | 6.15 | Saquinyo | Amity comma |
| 5 | (22 digits) | [24 -21 4⟩ | 4.20 | Sasaquadyo | Vulture comma |
| 5 | 32805/32768 | [-15 8 1⟩ | 1.95 | Layo | Schisma |
| 7 | 3125/3087 | [0 -2 5 -3⟩ | 21.18 | Triru-aquinyo | Gariboh comma |
| 7 | 1728/1715 | [6 3 -1 -3⟩ | 13.07 | Triru-agu | Orwellisma |
| 7 | 225/224 | [-5 2 2 -1⟩ | 7.71 | Ruyoyo | Marvel comma, septimal kleisma |
| 7 | 4375/4374 | [-1 -7 4 1⟩ | 0.40 | Zoquadyo | Ragisma |
| 11 | 99/98 | [-1 2 0 -2 1⟩ | 17.58 | Loruru | Mothwellsma |
| 11 | 121/120 | [-3 -1 -1 0 2⟩ | 14.37 | Lologu | Biyatisma |
| 11 | 176/175 | [4 0 -2 -1 1⟩ | 9.86 | Lorugugu | Valinorsma |
| 11 | (22 digits) | [33 -23 0 0 1⟩ | 6.35 | Trisalo | Pythrabian comma |
| 11 | 385/384 | [-7 -1 1 1 1⟩ | 4.50 | Lozoyo | Keenanisma |
| 11 | 540/539 | [2 3 1 -2 -1⟩ | 3.21 | Lururuyo | Swetisma |
| 13 | 275/273 | [0 -1 2 -1 1 -1⟩ | 12.64 | Thuloruyoyo | Gassorma |
| 13 | 169/168 | [-3 -1 0 -1 0 2⟩ | 10.27 | Thothoru | Buzurgisma, dhanvantarisma |
| 13 | 625/624 | [-4 -1 4 0 0 -1⟩ | 2.77 | Thuquadyo | Tunbarsma |
| 13 | 676/675 | [2 -3 -2 0 0 2⟩ | 2.56 | Bithogu | Island comma, parizeksma |
| 13 | 1001/1000 | [-3 0 -3 1 1 1⟩ | 1.73 | Tholozotrigu | Fairytale comma, sinbadma |
| 13 | 2080/2079 | [5 -3 1 -1 -1 1⟩ | 0.83 | Tholuruyo | Ibnsinma, sinaisma |
| 13 | 4096/4095 | [12 -2 -1 -1 0 -1⟩ | 0.42 | Sathurugu | Schismina |
Linear temperaments
| Periods per 8ve |
Generator | Cents | Associated Ratio |
Temperament |
|---|---|---|---|---|
| 1 | 2\53 | 45.28 | 36/35 | Quartonic |
| 1 | 5\53 | 113.21 | 16/15 | Misneb |
| 1 | 7\53 | 158.49 | 11/10 | Hemikleismic |
| 1 | 9\53 | 203.77 | 9/8 | Baldy |
| 1 | 10\53 | 226.42 | 8/7 | Semaja |
| 1 | 11\53 | 249.06 | 15/13 | Hemischis / hemigari |
| 1 | 12\53 | 271.70 | 7/6 | Orwell |
| 1 | 13\53 | 294.34 | 25/21 | Kleiboh |
| 1 | 14\53 | 316.98 | 6/5 | Hanson / catakleismic / countercata |
| 1 | 15\53 | 339.62 | 11/9 | Amity / houborizic |
| 1 | 16\53 | 362.26 | 16/13 | Submajor |
| 1 | 18\53 | 407.55 | 1225/972 | Ditonic / coditone |
| 1 | 19\53 | 430.19 | 9/7 | Hamity |
| 1 | 21\53 | 475.47 | 21/16 | Vulture / buzzard |
| 1 | 22\53 | 498.11 | 4/3 | Garibaldi / pontiac |
| 1 | 23\53 | 520.75 | 4/3 | Mavila (53bbcc) |
| 1 | 25\53 | 566.04 | 18/13 | Tricot |
| 1 | 26\53 | 588.68 | 45/32 | Untriton / aufo |
Scales
MOS scales
While there is only one possible generator for the diatonic mos scale supported by this edo, there are a greater number of generators for other mosses such as the antidiatonic scale.
Scales approximated from JI
- The eagle 53 scale described by John O'Sullivan
- Ptolmey—Zarlino justly-intonated major: 9 8 5 9 8 9 5
- Ptolmey—Zarlino justly-intonated minor: 9 5 8 9 5 9 8
- Composite Cliffedge (approximated from 60afdo): 12 10 9 19 3
- Composite Deja Vu (approximated from 101afdo): 14 17 5 9 8
- Composite Dungeon (approximated from 30afdo): 17 5 9 4 18
- Composite Freeway (approximated from 6afdo): 12 10 9 8 7 7
- Composite Geode (approximated from 6afdo): 12 10 9 15 7
- Composite Labyrinth (approximated from 30afdo): 7 7 17 5 17
- Composite Mushroom (approximated from 30afdo): 12 10 9 3 19
- Composite Underpass (approximated from 10afdo): 14 17 10 4 8
- Spectral Arcade (approximated from 32afdo): 17 4 10 12 10
- Spectral Mechanical (approximated from 16afdo): 13 4 14 12 10
- Spectral Moonbeam (approximated from 16afdo): 9 4 18 17 5
- Spectral Springwater (approximated from 8afdo): 9 8 14 12 10
- Spectral Starship (approximated from 68ifdo): 4 13 4 10 12 10
- Spectral Volcanic (approximated from 16afdo): 5 12 14 12 10
Other scales
Music
- See also: Category:53edo tracks
Modern renderings
- "Jesus bleibet meine Freude" from Herz und Mund und Tat und Leben, BWV 147 (1723) – tuned in 53edo, rendered by Claudi Meneghin (2021)
- Prelude and Fugue in C Major, No. 1, BWV 846, from The Well-Tempered Clavier, Book I (1722) – rendered by Mykhaylo Khramov
- "Contrapunctus 4" from The Art of Fugue, BWV 1080 (1742–1749) – rendered by Claudi Meneghin (2024)
- "Contrapunctus 11" from The Art of Fugue, BWV 1080 (1742–1749) – rendered by Claudi Meneghin (2024)
- Prelude in E Minor "The Great" – rendered by Claudi Meneghin (2023)
- Prelude in E Minor "The Little" – rendered by Claudi Meneghin (2024)
- Suite in D minor HWV 428 for Harpsichord - Allemande (1720) – rendered by Claudi Meneghin (2024)
- Maple Leaf Rag (1899) – arranged for harpsichord and rendered by Claudi Meneghin (2024)
- Maple Leaf Rag (1899) – with syntonic comma adjustment, arranged for harpsichord and rendered by Claudi Meneghin (2024)
- Qui veut faire l'ange fait la bete – rendered by MortisTheneRd (2024)
- Bande-announce – rendered by MortisTheneRd (2024)
21st century
- Space Race (2022)
- "strange worlds" from hope in dark times (2024) – Spotify | Bandcamp | YouTube – hanson[11] in 53edo
- Blasphemous Rumors (2024) – blackdye in 53edo
- Like Uminari (2021)
- Whisper Song (2007) – blog | play | SoundCloud
- mothers (2014)
- Hero (2023)
- Ficta (2021)
- "Taking Flight" from Nano Particular (2019) – Spotify | Bandcamp | YouTube
- "Detective Duckweed" from Jazzbeetle (2023) – Spotify | Bandcamp | YouTube – jazzy big band electronic hybrid
Instruments
Notes
- ↑ Based on treating 53edo as a no-17's 19-limit temperament; other approaches are also possible. Italics represent inconsistent intervals which are mapped by the 19-limit patent val to their second-closest (as opposed to closest) approximation in 53edo.
- ↑ Ratios longer than 10 digits are presented by placeholders with informative hints.