45edo
45edo divides the octave into 45 equal parts of 26.667 cents. It has two major thirds, each almost equally far from Just, but as the flat one is slightly closer, it qualifies as a meantone temperament, forming a good approximation to 2/5 comma meantone. 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¢ | 1:1 | 0 | 0 | Unison | 1 | D |
| 1 | 26.666 | 65:64 | 26.841 | -0.174 | Up unison | D^ | |
| 2 | 53.333 | 33:32 | 53.273 | 0.060 | Downminor 2nd | D# | |
| 3 | 80.0 | 22:21 | 80.537 | -0.537 | Minor 2nd | D#^ | |
| 4 | 106.666 | 17:16 | 104.955 | 1.7112 | Upminor 2nd | Ebv | |
| 5 | 133.333 | 27:25 | 133.238 | 0.095 | Downmid 2nd | Eb | |
| 6 | 160 | 11:10 | 165.004 | -5.004 | Downmajor 2nd | Ev | |
| 7 | 186.666 | 10:9 | 182.404 | 4.262 | Major 2nd | E | |
| 8 | 213.333 | 9:8 | 203.910 | 9.423 | Upmajor 2nd | E^ | |
| 9 | 240 | 8:7 | 231.174 | 8.826 | 2nd/3rd | E# | |
| 10 | 266.666 | 7:6 | 266.871 | -0.205 | Flat Third | Fb | |
| 11 | 293.333 | 32:27 | 294.135 | -0.802 | Downminor Third | Fv | |
| 12 | 320 | 6:5 | 315.641 | 4.359 | Minor Third | F | |
| 13 | 346.666 | 11:9 | 347.408 | -0.741 | Mid Third | F^ | |
| 14 | 373.333 | 5:4- | 386.314 | -12.980 | Downmajor Third | F# | |
| 15 | 400 | 5:4+ | 386.314 | 13.686 | Upmajor Third | F#^ | |
| 16 | 426.666 | 9:7 | 435.084 | -8.418 | Sharp Third | Gbv | |
| 17 | 453.333 | 13:10 | 454.294 | -0.961 | Diminished 4th | Gb | |
| 18 | 480 | 21:16 | 470.781 | 9.219 | Blackwood 4th | Gv | |
| 19 | 506.666 | 4:3 | 498.045 | 8.622 | perfect 4th | G | |
| 20 | 533.333 | 49:36 | 533.742 | -0.409 | Up 4th | G^ | |
| 21 | 560 | 18:13 | 563.382 | -3.382 | Downmid 4th | G# | |
| 22 | 586.666 | 7:5 | 582.512 | 4.155 | Mid 4th | G#^ | |
| 23 | 613.333 | 10:7 | 617.488 | -4.155 | Mid 5th | Abv | |
| 24 | 640 | 13:9 | 636.618 | 3.382 | Upmid 5th | Ab | |
| 25 | 666.666 | 72:49 | 66.258 | 0.409 | Down 5th | Av | |
| 26 | 693.333 | 3:2 | 701.955 | -8.622 | Perfect 5th | A | |
| 27 | 720 | 32:21 | 729.219 | -9.219 | Blackwood 5th | A^ | |
| 28 | 746.666 | 20:13 | 745.786 | 0.961 | Augmented 5th | A# | |
| 29 | 773.333 | 14:9 | 764.916 | 8.418 | Flat 6th | A#^ | |
| 30 | 800 | 8:5- | 813.686 | -13.686 | Downminor 6th | Bbv | |
| 31 | 826.666 | 8:5+ | 813.686 | 12.980 | Upminor 6th | Bb | |
| 32 | 853.333 | 18:11 | 852.592 | 0.741 | Mid 6th | Bv | |
| 33 | 880 | 5:3 | 884.359 | -4.359 | Major 6th | B | |
| 34 | 906.666 | 27:16 | 905.865 | 0.802 | Upmajor 6th | B^ | |
| 35 | 933.333 | 12:7 | 933.129 | 0.205 | Sharp 6th | B# | |
| 36 | 960 | 7:4 | 968.826 | -8.826 | 6th/7th | Cb | |
| 37 | 986.666 | 16:9 | 996.089 | -9.423 | Downminor 7th | Cv | |
| 38 | 1013.333 | 9:5 | 1017.596 | -4.262 | Minor 7th | C | |
| 39 | 1040 | 20:11 | 1034.996 | 5.004 | Upminor 7th | C^ | |
| 40 | 1066.666 | 50:27 | 1066.762 | -0.095 | Mid 7th | C# | |
| 41 | 1093.333 | 32:17 | 1095.044 | -1.7112 | Downmajor 7th | C#^ | |
| 42 | 1120 | 21:11 | 1119.463 | 0.537 | Major 7th | Dbv | |
| 43 | 1146.666 | 64:33 | 1146.727 | -0.060 | Upmajor 7th | Db | |
| 44 | 1173.333 | 128:65 | 1173.158 | 0.174 | Down 8ve | Dv | |
| 45 | 1200 | 2:1 | 1200 | 0 | Octave | D | |