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 a very inaccurate version of ennealimmal, if you want to view it that way. 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.
| ← 44edo | 45edo | 46edo → |
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.6 | -13.0 | -8.8 | +9.4 | +8.7 | +12.8 | +5.1 | +1.7 | -4.2 | +9.2 | +11.7 |
| Relative (%) | -32.3 | -48.7 | -33.1 | +35.3 | +32.6 | +48.0 | +19.0 | +6.4 | -15.7 | +34.6 | +44.0 | |
| Steps (reduced) |
71 (26) |
104 (14) |
126 (36) |
143 (8) |
156 (21) |
167 (32) |
176 (41) |
184 (4) |
191 (11) |
198 (18) |
204 (24) | |
Intervals
| Step # | ET | Just (JI) | Error (ET−JI) |
Ups and Downs Notation | |||
|---|---|---|---|---|---|---|---|
| Cents | Interval | Cents | |||||
| 0 | 0.000 | 1/1 | 0.000 | 0.000 | Perfect Unison | D | |
| 1 | 26.666 | 65/64 | 26.841 | -0.174 | Up unison | ^D | |
| 2 | 53.333 | 33/32 | 53.273 | 0.060 | Augmented Unison | D# | |
| 3 | 80.000 | 22/21 | 80.537 | -0.537 | Diminished 2nd | Ebb | |
| 4 | 106.666 | 17/16 | 104.955 | 1.711 | Downminor 2nd | vEb | |
| 5 | 133.333 | 27/25 | 133.238 | 0.095 | Minor 2nd | Eb | |
| 6 | 160.000 | 11/10 | 165.004 | -5.004 | Mid 2nd | vE | |
| 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 | 240.000 | 8/7 | 231.174 | 8.826 | Augmented 2nd | E# | |
| 10 | 266.666 | 7/6 | 266.871 | -0.205 | Diminished 3rd | Fb | |
| 11 | 293.333 | 32/27 | 294.135 | -0.802 | Downminor 3rd | vF | |
| 12 | 320.000 | 6/5 | 315.641 | 4.359 | Minor 3rd | F | |
| 13 | 346.666 | 11/9 | 347.408 | -0.741 | Mid 3rd | ^F | |
| 14 | 373.333 | 5/4- | 386.314 | -12.980 | Major 3rd | F# | |
| 15 | 400.000 | 5/4+ | 386.314 | 13.686 | Upmajor 3rd | ^F# | |
| 16 | 426.666 | 9/7 | 435.084 | -8.418 | Augmented 3rd | Fx | |
| 17 | 453.333 | 13/10 | 454.294 | -0.961 | Diminished 4th | Gb | |
| 18 | 480.000 | 21/16 | 470.781 | 9.219 | Down 4th | vG | |
| 19 | 506.666 | 4/3 | 498.045 | 8.622 | Perfect 4th | G | |
| 20 | 533.333 | 49/36 | 533.742 | -0.409 | Up 4th or Mid 4th | ^G | |
| 21 | 560.000 | 18/13 | 563.382 | -3.382 | Augmented 4th | G# | |
| 22 | 586.666 | 7/5 | 582.512 | 4.155 | Upaugmented 4th | ^G# | |
| 23 | 613.333 | 10/7 | 617.488 | -4.155 | Downdiminshed 5th | vAb | |
| 24 | 640.000 | 13/9 | 636.618 | 3.382 | Diminished 5th | Ab | |
| 25 | 666.666 | 72/49 | 666.258 | 0.409 | Down 5th or Mid 5th | vA | |
| 26 | 693.333 | 3/2 | 701.955 | -8.622 | Perfect 5th | A | |
| 27 | 720.000 | 32/21 | 729.219 | -9.219 | Up 5th | ^A | |
| 28 | 746.666 | 20/13 | 745.786 | 0.961 | Augmented 5th | A# | |
| 29 | 773.333 | 14/9 | 764.916 | 8.418 | Diminished 6th | Bbb | |
| 30 | 800.000 | 8/5- | 813.686 | -13.686 | Downminor 6th | vBb | |
| 31 | 826.666 | 8/5+ | 813.686 | 12.980 | Minor 6th | Bb | |
| 32 | 853.333 | 18/11 | 852.592 | 0.741 | Mid 6th | vB | |
| 33 | 880.000 | 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 | Augmented 6th | B# | |
| 36 | 960.000 | 7/4 | 968.826 | -8.826 | Diminished 7th | Cb | |
| 37 | 986.666 | 16/9 | 996.089 | -9.423 | Downminor 7th | vC | |
| 38 | 1013.333 | 9/5 | 1017.596 | -4.262 | Minor 7th | C | |
| 39 | 1040.000 | 20/11 | 1034.996 | 5.004 | Mid 7th | ^C | |
| 40 | 1066.666 | 50/27 | 1066.762 | -0.095 | Major 7th | C# | |
| 41 | 1093.333 | 32/17 | 1095.044 | -1.711 | Upmajor 7th | ^C# | |
| 42 | 1120.000 | 21/11 | 1119.463 | 0.537 | Augmented 7th | Cx | |
| 43 | 1146.666 | 64/33 | 1146.727 | -0.060 | Diminished 8ve | Db | |
| 44 | 1173.333 | 128/65 | 1173.158 | 0.174 | Down 8ve | vD | |
| 45 | 1200.000 | 2/1 | 1200.000 | 0.000 | Perfect Octave | D | |