53edo: Difference between revisions
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added a 53-edo spiral pic, also updated the ups and down notation (Cv --> vC) |
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| Line 92: | Line 92: | ||
| style="text-align:center;" | ^1 | | style="text-align:center;" | ^1 | ||
| style="text-align:center;" | up unison | | style="text-align:center;" | up unison | ||
| style="text-align:center;" | D | | style="text-align:center;" | ^D | ||
| | | | | | ||
|- | |- | ||
| Line 107: | Line 107: | ||
double-down minor 2nd | double-down minor 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^D, | ||
vvEb | |||
| | [[Quartonic|Quartonic]] | | | [[Quartonic|Quartonic]] | ||
|- | |- | ||
| Line 120: | Line 120: | ||
| style="text-align:center;" | vm2 | | style="text-align:center;" | vm2 | ||
| style="text-align:center;" | downminor 2nd | | style="text-align:center;" | downminor 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | vEb | ||
| | | | | | ||
|- | |- | ||
| Line 142: | Line 142: | ||
| style="text-align:center;" | ^m2 | | style="text-align:center;" | ^m2 | ||
| style="text-align:center;" | upminor 2nd | | style="text-align:center;" | upminor 2nd | ||
| style="text-align:center;" | Eb | | style="text-align:center;" | ^Eb | ||
| | | | | | ||
|- | |- | ||
| Line 153: | Line 153: | ||
| style="text-align:center;" | v~2 | | style="text-align:center;" | v~2 | ||
| style="text-align:center;" | downmid 2nd | | style="text-align:center;" | downmid 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^Eb | ||
| | | | | | ||
|- | |- | ||
| Line 164: | Line 164: | ||
| style="text-align:center;" | ^~2 | | style="text-align:center;" | ^~2 | ||
| style="text-align:center;" | upmid 2nd | | style="text-align:center;" | upmid 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | vvE | ||
| | [[Hemikleismic|Hemikleismic]] | | | [[Hemikleismic|Hemikleismic]] | ||
|- | |- | ||
| Line 175: | Line 175: | ||
| style="text-align:center;" | vM2 | | style="text-align:center;" | vM2 | ||
| style="text-align:center;" | downmajor 2nd | | style="text-align:center;" | downmajor 2nd | ||
| style="text-align:center;" | | | style="text-align:center;" | vE | ||
| | | | | | ||
|- | |- | ||
| Line 197: | Line 197: | ||
| style="text-align:center;" | ^M2 | | style="text-align:center;" | ^M2 | ||
| style="text-align:center;" | upmajor 2nd | | style="text-align:center;" | upmajor 2nd | ||
| style="text-align:center;" | E | | style="text-align:center;" | ^E | ||
| | | | | | ||
|- | |- | ||
| Line 212: | Line 212: | ||
double-down minor 3rd | double-down minor 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^E, | ||
vvF | |||
| | [[Hemischis|Hemischis]] | | | [[Hemischis|Hemischis]] | ||
|- | |- | ||
| Line 225: | Line 225: | ||
| style="text-align:center;" | vm3 | | style="text-align:center;" | vm3 | ||
| style="text-align:center;" | downminor 3rd | | style="text-align:center;" | downminor 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | vF | ||
| | [[Orwell|Orwell]] | | | [[Orwell|Orwell]] | ||
|- | |- | ||
| Line 247: | Line 247: | ||
| style="text-align:center;" | ^m3 | | style="text-align:center;" | ^m3 | ||
| style="text-align:center;" | upminor 3rd | | style="text-align:center;" | upminor 3rd | ||
| style="text-align:center;" | F | | style="text-align:center;" | ^F | ||
| | [[Hanson|Hanson]]/[[catakleismic|Catakleismic]] | | | [[Hanson|Hanson]]/[[catakleismic|Catakleismic]] | ||
|- | |- | ||
| Line 258: | Line 258: | ||
| style="text-align:center;" | v~3 | | style="text-align:center;" | v~3 | ||
| style="text-align:center;" | downmid 3rd | | style="text-align:center;" | downmid 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^F | ||
| | [[Amity|Amity]]/[[Hitchcock|Hitchcock]] | | | [[Amity|Amity]]/[[Hitchcock|Hitchcock]] | ||
|- | |- | ||
| Line 269: | Line 269: | ||
| style="text-align:center;" | ^~3 | | style="text-align:center;" | ^~3 | ||
| style="text-align:center;" | upmid 3rd | | style="text-align:center;" | upmid 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | vvF# | ||
| | | | | | ||
|- | |- | ||
| Line 280: | Line 280: | ||
| style="text-align:center;" | vM3 | | style="text-align:center;" | vM3 | ||
| style="text-align:center;" | downmajor 3rd | | style="text-align:center;" | downmajor 3rd | ||
| style="text-align:center;" | | | style="text-align:center;" | vF# | ||
| | | | | | ||
|- | |- | ||
| Line 302: | Line 302: | ||
| style="text-align:center;" | ^M3 | | style="text-align:center;" | ^M3 | ||
| style="text-align:center;" | upmajor 3rd | | style="text-align:center;" | upmajor 3rd | ||
| style="text-align:center;" | F# | | style="text-align:center;" | ^F# | ||
| | [[Hamity|Hamity]] | | | [[Hamity|Hamity]] | ||
|- | |- | ||
| Line 317: | Line 317: | ||
double-down 4th | double-down 4th | ||
| style="text-align:center;" | F# | | style="text-align:center;" | ^^F#, | ||
vvG | |||
| | | | | | ||
|- | |- | ||
| Line 330: | Line 330: | ||
| style="text-align:center;" | v4 | | style="text-align:center;" | v4 | ||
| style="text-align:center;" | down 4th | | style="text-align:center;" | down 4th | ||
| style="text-align:center;" | | | style="text-align:center;" | vG | ||
| | [[Vulture|Vulture]]/[[Buzzard|Buzzard]] | | | [[Vulture|Vulture]]/[[Buzzard|Buzzard]] | ||
|- | |- | ||
| Line 352: | Line 352: | ||
| style="text-align:center;" | ^4 | | style="text-align:center;" | ^4 | ||
| style="text-align:center;" | up 4th | | style="text-align:center;" | up 4th | ||
| style="text-align:center;" | G | | style="text-align:center;" | ^G | ||
| | | | | | ||
|- | |- | ||
| Line 361: | Line 361: | ||
|695.55 (2B7.8C<sub>16</sub>) | |695.55 (2B7.8C<sub>16</sub>) | ||
| style="text-align:center;" | 11/8, 15/11 | | style="text-align:center;" | 11/8, 15/11 | ||
| style="text-align:center;" | | | style="text-align:center;" | v~4 | ||
| style="text-align:center;" | | | style="text-align:center;" | downmid 4th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^G | ||
| | | | | | ||
|- | |- | ||
| Line 372: | Line 372: | ||
|724.53 (2D4.87<sub>16</sub>) | |724.53 (2D4.87<sub>16</sub>) | ||
| style="text-align:center;" | 18/13 | | style="text-align:center;" | 18/13 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^~4, | ||
vd5 | vd5 | ||
| style="text-align:center;" | | | style="text-align:center;" | upmid 4th, | ||
downdim 5th | downdim 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvG#, | ||
vAb | |||
| | [[Tricot|Tricot]] | | | [[Tricot|Tricot]] | ||
|- | |- | ||
| Line 395: | Line 395: | ||
dim 5th | dim 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vG#, | ||
Ab | Ab | ||
| Line 414: | Line 414: | ||
| style="text-align:center;" | G#, | | style="text-align:center;" | G#, | ||
Ab | ^Ab | ||
| | | | | | ||
|- | |- | ||
| Line 425: | Line 425: | ||
| style="text-align:center;" | ^A4, | | style="text-align:center;" | ^A4, | ||
v~5 | |||
| style="text-align:center;" | upaug 4th, | | style="text-align:center;" | upaug 4th, | ||
downmid 5th | |||
| style="text-align:center;" | G# | | style="text-align:center;" | ^G#, | ||
^^Ab | |||
| | | | | | ||
|- | |- | ||
| Line 440: | Line 440: | ||
|840.45 (348.74<sub>16</sub>) | |840.45 (348.74<sub>16</sub>) | ||
| style="text-align:center;" | 16/11, 22/15 | | style="text-align:center;" | 16/11, 22/15 | ||
| style="text-align:center;" | | | style="text-align:center;" | ^~5 | ||
| style="text-align:center;" | | | style="text-align:center;" | upmid 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvA | ||
| | | | | | ||
|- | |- | ||
| Line 453: | Line 453: | ||
| style="text-align:center;" | v5 | | style="text-align:center;" | v5 | ||
| style="text-align:center;" | down 5th | | style="text-align:center;" | down 5th | ||
| style="text-align:center;" | | | style="text-align:center;" | vA | ||
| | | | | | ||
|- | |- | ||
| Line 475: | Line 475: | ||
| style="text-align:center;" | ^5 | | style="text-align:center;" | ^5 | ||
| style="text-align:center;" | up 5th | | style="text-align:center;" | up 5th | ||
| style="text-align:center;" | A | | style="text-align:center;" | ^A | ||
| | | | | | ||
|- | |- | ||
| Line 490: | Line 490: | ||
double-down minor 6th | double-down minor 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^A, | ||
vvBb | |||
| | | | | | ||
|- | |- | ||
| Line 503: | Line 503: | ||
| style="text-align:center;" | vm6 | | style="text-align:center;" | vm6 | ||
| style="text-align:center;" | downminor 6th | | style="text-align:center;" | downminor 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | vBb | ||
| | | | | | ||
|- | |- | ||
| Line 525: | Line 525: | ||
| style="text-align:center;" | ^m6 | | style="text-align:center;" | ^m6 | ||
| style="text-align:center;" | upminor 6th | | style="text-align:center;" | upminor 6th | ||
| style="text-align:center;" | Bb | | style="text-align:center;" | ^Bb | ||
| | | | | | ||
|- | |- | ||
| Line 536: | Line 536: | ||
| style="text-align:center;" | v~6 | | style="text-align:center;" | v~6 | ||
| style="text-align:center;" | downmid 6th | | style="text-align:center;" | downmid 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^Bb | ||
| | | | | | ||
|- | |- | ||
| Line 547: | Line 547: | ||
| style="text-align:center;" | ^~6 | | style="text-align:center;" | ^~6 | ||
| style="text-align:center;" | upmid 6th | | style="text-align:center;" | upmid 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvB | ||
| | | | | | ||
|- | |- | ||
| Line 558: | Line 558: | ||
| style="text-align:center;" | vM6 | | style="text-align:center;" | vM6 | ||
| style="text-align:center;" | downmajor 6th | | style="text-align:center;" | downmajor 6th | ||
| style="text-align:center;" | | | style="text-align:center;" | vB | ||
| | | | | | ||
|- | |- | ||
| Line 580: | Line 580: | ||
| style="text-align:center;" | ^M6 | | style="text-align:center;" | ^M6 | ||
| style="text-align:center;" | upmajor 6th | | style="text-align:center;" | upmajor 6th | ||
| style="text-align:center;" | B | | style="text-align:center;" | ^B | ||
| | | | | | ||
|- | |- | ||
| Line 595: | Line 595: | ||
double-down minor 7th | double-down minor 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^B, | ||
vvC | |||
| | | | | | ||
|- | |- | ||
| Line 608: | Line 608: | ||
| style="text-align:center;" | vm7 | | style="text-align:center;" | vm7 | ||
| style="text-align:center;" | downminor 7th | | style="text-align:center;" | downminor 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | vC | ||
| | | | | | ||
|- | |- | ||
| Line 630: | Line 630: | ||
| style="text-align:center;" | ^m7 | | style="text-align:center;" | ^m7 | ||
| style="text-align:center;" | upminor 7th | | style="text-align:center;" | upminor 7th | ||
| style="text-align:center;" | C | | style="text-align:center;" | ^C | ||
| | | | | | ||
|- | |- | ||
| Line 641: | Line 641: | ||
| style="text-align:center;" | v~7 | | style="text-align:center;" | v~7 | ||
| style="text-align:center;" | downmid 7th | | style="text-align:center;" | downmid 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | ^^C | ||
| | | | | | ||
|- | |- | ||
| Line 652: | Line 652: | ||
| style="text-align:center;" | ^~7 | | style="text-align:center;" | ^~7 | ||
| style="text-align:center;" | upmid 7th | | style="text-align:center;" | upmid 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | vvC# | ||
| | | | | | ||
|- | |- | ||
| Line 663: | Line 663: | ||
| style="text-align:center;" | vM7 | | style="text-align:center;" | vM7 | ||
| style="text-align:center;" | downmajor 7th | | style="text-align:center;" | downmajor 7th | ||
| style="text-align:center;" | | | style="text-align:center;" | vC# | ||
| | | | | | ||
|- | |- | ||
| Line 685: | Line 685: | ||
| style="text-align:center;" | ^M7 | | style="text-align:center;" | ^M7 | ||
| style="text-align:center;" | upmajor 7th | | style="text-align:center;" | upmajor 7th | ||
| style="text-align:center;" | C# | | style="text-align:center;" | ^C# | ||
| | | | | | ||
|- | |- | ||
| Line 700: | Line 700: | ||
double-down 8ve | double-down 8ve | ||
| style="text-align:center;" | C# | | style="text-align:center;" | ^^C#, | ||
vvD | |||
| | | | | | ||
|- | |- | ||
| Line 713: | Line 713: | ||
| style="text-align:center;" | v8 | | style="text-align:center;" | v8 | ||
| style="text-align:center;" | down 8ve | | style="text-align:center;" | down 8ve | ||
| style="text-align:center;" | | | style="text-align:center;" | vD | ||
| | | | | | ||
|- | |- | ||
| Line 738: | Line 738: | ||
| style="text-align:center;" | downminor | | style="text-align:center;" | downminor | ||
| style="text-align:center;" | zo | | style="text-align:center;" | zo | ||
| style="text-align:center;" | | | style="text-align:center;" | (a, b, 0, 1) | ||
| style="text-align:center;" | 7/6, 7/4 | | style="text-align:center;" | 7/6, 7/4 | ||
|- | |- | ||
| style="text-align:center;" | minor | | style="text-align:center;" | minor | ||
| style="text-align:center;" | fourthward wa | | style="text-align:center;" | fourthward wa | ||
| style="text-align:center;" | | | style="text-align:center;" | (a, b) with b < -1 | ||
| style="text-align:center;" | 32/27, 16/9 | | style="text-align:center;" | 32/27, 16/9 | ||
|- | |- | ||
| style="text-align:center;" | upminor | | style="text-align:center;" | upminor | ||
| style="text-align:center;" | gu | | style="text-align:center;" | gu | ||
| style="text-align:center;" | | | style="text-align:center;" | (a, b, -1) | ||
| style="text-align:center;" | 6/5, 9/5 | | style="text-align:center;" | 6/5, 9/5 | ||
|- | |- | ||
| style="text-align:center;" | downmid | | style="text-align:center;" | downmid | ||
| style="text-align:center;" | ilo | | style="text-align:center;" | ilo | ||
| style="text-align:center;" | | | style="text-align:center;" | (a, b, 0, 0, 1) | ||
| style="text-align:center;" | 11/9, 11/6 | | style="text-align:center;" | 11/9, 11/6 | ||
|- | |- | ||
| style="text-align:center;" | upmid | | style="text-align:center;" | upmid | ||
| style="text-align:center;" | lu | | style="text-align:center;" | lu | ||
| style="text-align:center;" | | | style="text-align:center;" | (a, b, 0, 0, -1) | ||
| style="text-align:center;" | 12/11, 18/11 | | style="text-align:center;" | 12/11, 18/11 | ||
|- | |- | ||
| style="text-align:center;" | downmajor | | style="text-align:center;" | downmajor | ||
| style="text-align:center;" | yo | | style="text-align:center;" | yo | ||
| style="text-align:center;" | | | style="text-align:center;" | (a, b, 1) | ||
| style="text-align:center;" | 5/4, 5/3 | | style="text-align:center;" | 5/4, 5/3 | ||
|- | |- | ||
| style="text-align:center;" | major | | style="text-align:center;" | major | ||
| style="text-align:center;" | fifthward wa | | style="text-align:center;" | fifthward wa | ||
| style="text-align:center;" | | | style="text-align:center;" | (a, b) with b > 1 | ||
| style="text-align:center;" | 9/8, 27/16 | | style="text-align:center;" | 9/8, 27/16 | ||
|- | |- | ||
| style="text-align:center;" | upmajor | | style="text-align:center;" | upmajor | ||
| style="text-align:center;" | ru | | style="text-align:center;" | ru | ||
| style="text-align:center;" | | | style="text-align:center;" | (a, b, 0, -1) | ||
| style="text-align:center;" | 9/7, 12/7 | | style="text-align:center;" | 9/7, 12/7 | ||
|} | |} | ||
All 53edo chords can be named using ups and downs. Here are the zo, gu, ilo, yo and ru triads: | All 53edo chords can be named using ups and downs. Here are the zo, gu, ilo, lu, yo and ru triads: | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 790: | Line 790: | ||
| style="text-align:center;" | 6:7:9 | | style="text-align:center;" | 6:7:9 | ||
| style="text-align:center;" | 0-12-31 | | style="text-align:center;" | 0-12-31 | ||
| style="text-align:center;" | C | | style="text-align:center;" | C vEb G | ||
| style="text-align:center;" | | | style="text-align:center;" | Cvm | ||
| style="text-align:center;" | C downminor | | style="text-align:center;" | C downminor | ||
|- | |- | ||
| Line 797: | Line 797: | ||
| style="text-align:center;" | 10:12:15 | | style="text-align:center;" | 10:12:15 | ||
| style="text-align:center;" | 0-14-31 | | style="text-align:center;" | 0-14-31 | ||
| style="text-align:center;" | C Eb | | style="text-align:center;" | C ^Eb G | ||
| style="text-align:center;" | C | | style="text-align:center;" | C^m | ||
| style="text-align:center;" | C upminor | | style="text-align:center;" | C upminor | ||
|- | |- | ||
| Line 804: | Line 804: | ||
| style="text-align:center;" | 18:22:27 | | style="text-align:center;" | 18:22:27 | ||
| style="text-align:center;" | 0-15-31 | | style="text-align:center;" | 0-15-31 | ||
| style="text-align:center;" | C | | style="text-align:center;" | C ^^Eb G | ||
| style="text-align:center;" | | | style="text-align:center;" | Cv~ | ||
| style="text-align:center;" | C downmid | | style="text-align:center;" | C downmid | ||
|- | |||
| style="text-align:center;" | lu | |||
| style="text-align:center;" | 22:27:33 | |||
| style="text-align:center;" | 0-16-31 | |||
| style="text-align:center;" | C vvE G | |||
| style="text-align:center;" | C^~ | |||
| style="text-align:center;" | C upmid | |||
|- | |- | ||
| style="text-align:center;" | yo | | style="text-align:center;" | yo | ||
| style="text-align:center;" | 4:5:6 | | style="text-align:center;" | 4:5:6 | ||
| style="text-align:center;" | 0-17-31 | | style="text-align:center;" | 0-17-31 | ||
| style="text-align:center;" | C | | style="text-align:center;" | C vE G | ||
| style="text-align:center;" | | | style="text-align:center;" | Cv | ||
| style="text-align:center;" | C downmajor or C | | style="text-align:center;" | C downmajor or C down | ||
|- | |- | ||
| style="text-align:center;" | ru | | style="text-align:center;" | ru | ||
| style="text-align:center;" | 14:18:27 | | style="text-align:center;" | 14:18:27 | ||
| style="text-align:center;" | 0-19-31 | | style="text-align:center;" | 0-19-31 | ||
| style="text-align:center;" | C E | | style="text-align:center;" | C ^E G | ||
| style="text-align:center;" | C | | style="text-align:center;" | C^ | ||
| style="text-align:center;" | C upmajor or C | | style="text-align:center;" | C upmajor or C up | ||
|} | |} | ||
For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | ||
This chart shows 53-edo in a 12-edo-friendly format. | |||
[[File:53-edo spiral.png|702x702px]] | |||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
Revision as of 20:32, 2 September 2019
Theory
The famous 53 equal division divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a 5-limit system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, 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 comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for athene temperament. It is the eighth zeta integral edo and the 16th prime edo, following 47edo and coming before 59edo.
53EDO has also found a certain dissemination as an EDO tuning for Arabic/Turkish/Persian music.
It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit.
Linear temperaments
List of edo-distinct 53et rank two temperaments
Just Approximation
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 tone | 9/8 | 9 | −0.14 cents |
| minor tone | 10/9 | 8 | −1.27 cents |
| diat. semitone | 16/15 | 5 | +1.48 cents |
One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the septimal kleisma, 225/224.
Intervals
| degree | solfege | cents | pions | 7mus | approximate ratios | ups and downs notation | generator for | ||
|---|---|---|---|---|---|---|---|---|---|
| 0 | do | 0.00 | 1/1 | P1 | unison | D | |||
| 1 | di | 22.64 | 24 | 28.98 (1C.FB16) | 81/80, 64/63, 50/49 | ^1 | up unison | ^D | |
| 2 | daw | 45.28 | 48 | 57.96 (39.F616) | 49/48, 36/35, 33/32, 128/125 | ^^1,
vvm2 |
double-up unison,
double-down minor 2nd |
^^D,
vvEb |
Quartonic |
| 3 | ro | 67.925 | 72 | 86.94 (56.F1816) | 27/26, 26/25, 25/24, 22/21 | vm2 | downminor 2nd | vEb | |
| 4 | rih | 90.57 | 96 | 115.925 (73.EC16) | 21/20, 256/243 | m2 | minor 2nd | Eb | |
| 5 | ra | 113.21 | 120 | 144.91 (90.E816) | 16/15, 15/14 | ^m2 | upminor 2nd | ^Eb | |
| 6 | ru | 135.85 | 144 | 173.89 (AD.E316) | 14/13, 13/12, 27/25 | v~2 | downmid 2nd | ^^Eb | |
| 7 | ruh | 158.49 | 168 | 202.87 (CA.DE16) | 12/11, 11/10, 800/729 | ^~2 | upmid 2nd | vvE | Hemikleismic |
| 8 | reh | 181.13 | 192 | 231.85 (E7.D916) | 10/9 | vM2 | downmajor 2nd | vE | |
| 9 | re | 203.77 | 216 | 260.83 (104.D4816) | 9/8 | M2 | major 2nd | E | |
| 10 | ri | 226.42 | 240 | 289.81 (121.D16) | 8/7, 256/225 | ^M2 | upmajor 2nd | ^E | |
| 11 | raw | 249.06 | 264 | 318.79 (13E.CB16) | 15/13, 144/125 | ^^M2,
vvm3 |
double-up major 2nd,
double-down minor 3rd |
^^E,
vvF |
Hemischis |
| 12 | ma | 271.70 | 288 | 347.77 (15B.C616) | 7/6, 75/64 | vm3 | downminor 3rd | vF | Orwell |
| 13 | meh | 294.34 | 312 | 376.755 (178.C116) | 13/11, 32/27 | m3 | minor 3rd | F | |
| 14 | me | 316.98 | 336 | 405.74 (195.BC16) | 6/5 | ^m3 | upminor 3rd | ^F | Hanson/Catakleismic |
| 15 | mu | 339.62 | 360 | 434.72 (1B2.B816) | 11/9, 243/200 | v~3 | downmid 3rd | ^^F | Amity/Hitchcock |
| 16 | muh | 362.26 | 384 | 463.7 (1CF.B316) | 16/13, 100/81 | ^~3 | upmid 3rd | vvF# | |
| 17 | mi | 384.91 | 408 | 492.68 (1EC.AE16) | 5/4 | vM3 | downmajor 3rd | vF# | |
| 18 | maa | 407.55 | 432 | 521.66 (209.A916) | 81/64 | M3 | major 3rd | F# | |
| 19 | mo | 430.19 | 456 | 550.64 (226.A416) | 9/7, 14/11 | ^M3 | upmajor 3rd | ^F# | Hamity |
| 20 | maw | 452.83 | 480 | 579.62 (243.9F16) | 13/10, 125/96 | ^^M3,
vv4 |
double-up major 3rd,
double-down 4th |
^^F#,
vvG |
|
| 21 | fe | 475.47 | 504 | 608.6 (260.9B16) | 21/16, 675/512, 320/243 | v4 | down 4th | vG | Vulture/Buzzard |
| 22 | fa | 498.11 | 528 | 637.585 (27D.9616) | 4/3 | P4 | perfect 4th | G | |
| 23 | fih | 520.75 | 552 | 666.57 (29A.9116) | 27/20 | ^4 | up 4th | ^G | |
| 24 | fu | 543.40 | 576 | 695.55 (2B7.8C16) | 11/8, 15/11 | v~4 | downmid 4th | ^^G | |
| 25 | fuh | 566.04 | 600 | 724.53 (2D4.8716) | 18/13 | ^~4,
vd5 |
upmid 4th,
downdim 5th |
vvG#,
vAb |
Tricot |
| 26 | fi | 588.68 | 624 | 753.51 (2F1.8216) | 7/5, 45/32 | vA4,
d5 |
downaug 4th,
dim 5th |
vG#,
Ab |
|
| 27 | se | 611.32 | 648 | 782.49 (30E.7E16) | 10/7, 64/45 | A4,
^d5 |
aug 4th,
updim 5th |
G#,
^Ab |
|
| 28 | suh | 633.96 | 672 | 811.47 (32B.7916) | 13/9 | ^A4,
v~5 |
upaug 4th,
downmid 5th |
^G#,
^^Ab |
|
| 29 | su | 656.60 | 696 | 840.45 (348.7416) | 16/11, 22/15 | ^~5 | upmid 5th | vvA | |
| 30 | sih | 679.25 | 720 | 869.43 (365.6F16) | 40/27 | v5 | down 5th | vA | |
| 31 | sol | 701.89 | 744 | 898.415 (382.6A16) | 3/2 | P5 | perfect 5th | A | Helmholtz/Garibaldi |
| 32 | si | 724.53 | 768 | 927.4 (39F.6516) | 32/21, 243/160, 1024/675 | ^5 | up 5th | ^A | |
| 33 | saw | 747.17 | 792 | 956.38 (3BC.6116) | 20/13, 192/125 | ^^5,
vvm6 |
double-up 5th,
double-down minor 6th |
^^A,
vvBb |
|
| 34 | lo | 769.81 | 816 | 985.36 (3D9.5C16) | 14/9, 25/16, 11/7 | vm6 | downminor 6th | vBb | |
| 35 | leh | 792.45 | 840 | 1014.34 (3F6.5716) | 128/81 | m6 | minor 6th | Bb | |
| 36 | le | 815.09 | 864 | 1043.32 (413.5216) | 8/5 | ^m6 | upminor 6th | ^Bb | |
| 37 | lu | 837.74 | 888 | 1072.3 (430.4D16) | 13/8, 81/50 | v~6 | downmid 6th | ^^Bb | |
| 38 | luh | 860.38 | 912 | 1101.28 (44D.4816) | 18/11, 400/243 | ^~6 | upmid 6th | vvB | |
| 39 | la | 883.02 | 936 | 1130.26 (46A.4416) | 5/3 | vM6 | downmajor 6th | vB | |
| 40 | laa | 905.66 | 960 | 1159.245 (487.3F16) | 22/13, 27/16 | M6 | major 6th | B | |
| 41 | lo | 928.30 | 984 | 1188.23 (4A4.3A16) | 12/7 | ^M6 | upmajor 6th | ^B | |
| 42 | law | 950.94 | 1008 | 1217.21 (4C1.3516) | 26/15, 125/72 | ^^M6
vvm7 |
double-up major 6th,
double-down minor 7th |
^^B,
vvC |
|
| 43 | ta | 973.58 | 1032 | 1246.19 (4DE.316) | 7/4 | vm7 | downminor 7th | vC | |
| 44 | teh | 996.23 | 1056 | 1275.17 (4FB.2B816) | 16/9 | m7 | minor 7th | C | |
| 45 | te | 1018.87 | 1080 | 1304.15 (518.2716) | 9/5 | ^m7 | upminor 7th | ^C | |
| 46 | tu | 1041.51 | 1104 | 1333.13 (535.2216) | 11/6, 20/11, 729/400 | v~7 | downmid 7th | ^^C | |
| 47 | tuh | 1064.15 | 1128 | 1362.11 (552.1D16) | 13/7, 24/13, 50/27 | ^~7 | upmid 7th | vvC# | |
| 48 | ti | 1086.79 | 1152 | 1391.09 (56F.1816) | 15/8 | vM7 | downmajor 7th | vC# | |
| 49 | tih | 1109.43 | 1176 | 1420.075 (58C.1316) | 40/21, 243/128 | M7 | major 7th | C# | |
| 50 | to | 1132.08 | 1200 | 1449.06 (5A9.0E816) | 48/25, 27/14 | ^M7 | upmajor 7th | ^C# | |
| 51 | taw | 1154.72 | 1224 | 1478.04 (5C6.0A16) | 125/64 | ^^M7,
vv8 |
double-up major 7th,
double-down 8ve |
^^C#,
vvD |
|
| 52 | da | 1177.36 | 1248 | 1507.02 (5E3.0516) | 160/81 | v8 | down 8ve | vD | |
| 53 | do | 1200 | 1272 | 1536 (60016) | 2/1 | P8 | perfect 8ve | D | |
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 |
| downmid | ilo | (a, b, 0, 0, 1) | 11/9, 11/6 |
| upmid | 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. 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 | Cv~ | C downmid |
| lu | 22:27:33 | 0-16-31 | C vvE G | C^~ | C upmid |
| yo | 4:5:6 | 0-17-31 | C vE G | Cv | C downmajor or C down |
| ru | 14:18:27 | 0-19-31 | C ^E G | C^ | C upmajor or C up |
For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.
This chart shows 53-edo in a 12-edo-friendly format.
Selected just intervals by error
The following table shows how some prominent just intervals are represented in 53edo (ordered by absolute error).
| Interval, complement | Error (abs., in cents) |
| 4/3, 3/2 | 0.068 |
| 9/8, 16/9 | 0.136 |
| 10/9, 9/5 | 1.272 |
| 15/13, 26/15 | 1.316 |
| 6/5, 5/3 | 1.340 |
| 13/10, 20/13 | 1.384 |
| 5/4, 8/5 | 1.408 |
| 16/15, 15/8 | 1.476 |
| 18/13, 13/9 | 2.655 |
| 13/12, 24/13 | 2.724 |
| 16/13, 13/8 | 2.792 |
| 8/7, 7/4 | 4.759 |
| 7/6, 12/7 | 4.827 |
| 9/7, 14/9 | 4.895 |
| 13/11, 22/13 | 5.130 |
| 7/5, 10/7 | 6.167 |
| 15/14, 28/15 | 6.235 |
| 15/11, 22/15 | 6.445 |
| 11/10, 20/11 | 6.514 |
| 14/13, 13/7 | 7.551 |
| 11/9, 18/11 | 7.785 |
| 12/11, 11/6 | 7.854 |
| 11/8, 16/11 | 7.922 |
| 14/11, 11/7 | 9.961 |
Compositions
Bach WTC1 Prelude 1 in 53 by Bach and Mykhaylo Khramov
Bach WTC1 Fugue 1 in 53 by Bach and Mykhaylo Khramov
Whisper Song in 53EDO play by Prent Rodgers
Trio in Orwell play by Gene Ward Smith
Desert Prayer by Aaron Krister Johnson
Whisper Song in 53 EDO by Prent Rodgers
Elf Dine on Ho Ho play and Spun play by Andrew Heathwaite
The Fallen of Kleismic15play by Chris Vaisvil
mothers by Cam Taylor