45edo
45edo divides the octave into 45 equal parts of 26.667 cents. It is the optimal patent val for flattone temperament, the 7-limit 525/512 planar avicennmic temperament, the 11-limit calliope temperament tempering out 45/44 and 81/80, and the rank four temperament tempering out 45/44. It tempers out 81/80, 3125/3087, 525/512, 875/864 and 45/44. It is a flat-tending system in the 7-limit, with 3, 5 and 7 all flat, but the 11 is sharp. Also supports messed-up ennealimmal, if you want. Since 45 is a multiple of 5 and 9, it can be used to model Indonesian music in both Slendro (~ 5edo) and Pelog (~ modes of 9edo) tunings.
| Step # | ET | Just | Difference (ET minus Just) |
Ups and Downs Notation | |||
| Cents | Interval | Cents | |||||
| 0 | 0¢ | unison | 1 | D | |||
| 1 | 26.666 | ||||||
| 2 | 53.333 | 21:20 | 84.47 | 1.24 | double-up 1sn, double-down 2nd | ^^1, vv2 | ^^D, vvE |
| 3 | 14:13 | 128.3 | 0.27 | down 2nd | v2 | vE | |
| 4 | 11:10 | 165 | 6.43 | 2nd | 2 | E | |
| 5 | 17:15 | 216.69 | -2.40 | up 2nd | ^2 | ^E | |
| 6 | 7:6 | 266.87 | -9.73 | double-up 2nd, double-down 3rd | ^^2, vv3 | ^^E, vvF | |
| 7 | 6:5 | 315.64 | -15.64 | down 3rd | v3 | vF | |
| 8 | 11:9 | 347.41 | -4.55 | 3rd | 3 | F | |
| 9 | 5:4 | 386.31 | -0.60 | up 3rd | ^3 | ^F | |
| 10 | 9:7 | 435.08 | -6.51 | double-up 3rd, double-down 4th | ^^3, vv4 | ^^F, vvG | |
| 11 | 21:16 | 470.78 | 0.65 | down 4th | v4 | vG | |
| 12 | 4:3 | 498.045 | 16.245 | 4th | 4 | G | |
| 13 | 11:8 | 551.32 | 5.82 | up 4th | ^4 | ^G | |
| 14 | 7:5 | 582.51 | 17.49 | double-up 4th, double-down 5th | ^^4, vv5 | ^^G, vvA | |
| 15 | 16:11 | 648.68 | -5.82 | down 5th | v5 | vA | |
| 16 | 3:2 | 701.955 | -16.245 | 5th | 5 | A | |
| 17 | 32:21 | 729.22 | -0.65 | up 5th | ^5 | ^A | |
| 18 | 14:9 | 764.92 | 6.51 | double-up 5th, double-down 6th | ^^5, vv6 | ^^A, vvB | |
| 19 | 8:5 | 813.68 | 0.61 | down 6th | v6 | vB | |
| 20 | 18:11 | 852.59 | 4.55 | 6th | 6 | B | |
| 21 | 5:3 | 884.36 | 15.64 | up 6th | ^6 | ^B | |
| 22 | 12:7 | 933.13 | 9.73 | double-up 6th, double-down 7th | ^^6, vv7 | ^^B, vvC | |
| 23 | 30:17 | 983.31 | 2.40 | down 7th | v7 | vC | |
| 24 | 20:11 | 1035 | -6.43 | 7th | 7 | C | |
| 25 | 13:7 | 1071.70 | -0.27 | up 7th | ^7 | ^C | |
| 26 | 40:21 | 1115.53 | -1.24 | double-up 7th, double-down 8ve | ^^7, vv8 | ^^C, vvD | |
| 27 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 28 | |||||||
| 29 | 1157.14 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD |
| 30 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 31 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 32 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 33 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 34 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 35 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 36 | 80:41 | -0.12 | down 8ve | v8 | vD | ||
| 37 | 80:41 | -0.12 | down 8ve | v8 | vD | ||
| 38 | 80:41 | -0.12 | down 8ve | v8 | vD | ||
| 39 | 80:41 | -0.12 | down 8ve | v8 | vD | ||
| 40 | 80:41 | -0.12 | down 8ve | v8 | vD | ||
| 41 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 42 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 43 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 44 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |
| 45 | 80:41 | 1157.26 | -0.12 | down 8ve | v8 | vD | |