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 | ||||||
| 3 | 80.0 | ||||||
| 4 | 106.666 | ||||||
| 5 | 133.333 | ||||||
| 6 | 160 | ||||||
| 7 | 186.666 | ||||||
| 8 | 213.333 | ||||||
| 9 | 240 | ||||||
| 10 | 266.666 | ||||||
| 11 | 293.333 | ||||||
| 12 | 320 | ||||||
| 13 | 346.666 | ||||||
| 14 | 373.333 | ||||||
| 15 | 400 | ||||||
| 16 | 426.666 | ||||||
| 17 | 453.333 | ||||||
| 18 | 480 | ||||||
| 19 | 506.666 | ||||||
| 20 | 533.333 | ||||||
| 21 | 560 | ||||||
| 22 | 586.666 | ||||||
| 23 | 613.333 | ||||||
| 24 | 640 | ||||||
| 25 | 666.666 | ||||||
| 26 | 693.333 | ||||||
| 27 | 720 | ||||||
| 28 | 746.666 | ||||||
| 29 | 773.333 | ||||||
| 30 | 800 | ||||||
| 31 | 826.666 | ||||||
| 32 | 853.333 | ||||||
| 33 | 880 | ||||||
| 34 | 906.666 | ||||||
| 35 | 933.333 | ||||||
| 36 | 960 | ||||||
| 37 | 986.666 | ||||||
| 38 | 1013.333 | ||||||
| 39 | 1040 | ||||||
| 40 | 1066.666 | ||||||
| 41 | 1093.333 | ||||||
| 42 | 1120 | ||||||
| 43 | 1146.666 | ||||||
| 44 | 1173.333 | ||||||
| 45 | 1200 | Octave | D | ||||