45edo: Difference between revisions
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Still adding intervals. |
Finally finished intervals. |
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Revision as of 08:10, 9 July 2020
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 | D^ | ||
| 2 | 53.333 | 33:32 | 53.273 | 0.060 | D# | ||
| 3 | 80.0 | 22:21 | 80.537 | -0.537 | D#^ | ||
| 4 | 106.666 | 17:16 | 104.955 | 1.7112 | Ebv | ||
| 5 | 133.333 | 27:25 | 133.238 | 0.095 | Eb | ||
| 6 | 160 | 11:10 | 165.004 | -5.004 | Ev | ||
| 7 | 186.666 | 10:9 | 182.404 | 4.262 | E | ||
| 8 | 213.333 | 9:8 | 203.910 | 9.423 | E^ | ||
| 9 | 240 | 8:7 | 231.174 | 8.826 | E# | ||
| 10 | 266.666 | 7:6 | 266.871 | -0.205 | Fb | ||
| 11 | 293.333 | 32:27 | 294.135 | -0.802 | Fv | ||
| 12 | 320 | 6:5 | 315.641 | 4.359 | F | ||
| 13 | 346.666 | 11:9 | 347.408 | -0.741 | F^ | ||
| 14 | 373.333 | 5:4- | 386.314 | -12.980 | F# | ||
| 15 | 400 | 5:4+ | 386.314 | 13.686 | F#^ | ||
| 16 | 426.666 | 9:7 | 435.084 | -8.418 | Gbv | ||
| 17 | 453.333 | 13:10 | 454.294 | -0.961 | Gb | ||
| 18 | 480 | 21:16 | 470.781 | 9.219 | Gv | ||
| 19 | 506.666 | 4:3 | 498.045 | 8.622 | G | ||
| 20 | 533.333 | 49:36 | 533.742 | -0.409 | G^ | ||
| 21 | 560 | 18:13 | 563.382 | -3.382 | G# | ||
| 22 | 586.666 | 7:5 | 582.512 | 4.155 | G#^ | ||
| 23 | 613.333 | 10:7 | 617.488 | -4.155 | Abv | ||
| 24 | 640 | 13:9 | 636.618 | 3.382 | Ab | ||
| 25 | 666.666 | 72:49 | 66.258 | 0.409 | Av | ||
| 26 | 693.333 | 3:2 | 701.955 | -8.622 | A | ||
| 27 | 720 | 32:21 | 729.219 | -9.219 | A^ | ||
| 28 | 746.666 | 20:13 | 745.786 | 0.961 | A# | ||
| 29 | 773.333 | 14:9 | 764.916 | 8.418 | A#^ | ||
| 30 | 800 | 8:5- | 813.686 | -13.686 | Bbv | ||
| 31 | 826.666 | 8:5+ | 813.686 | 12.980 | Bb | ||
| 32 | 853.333 | 18:11 | 852.592 | 0.741 | Bv | ||
| 33 | 880 | 5:3 | 884.359 | -4.359 | B | ||
| 34 | 906.666 | 27:16 | 905.865 | 0.802 | B^ | ||
| 35 | 933.333 | 12:7 | 933.129 | 0.205 | B# | ||
| 36 | 960 | 7:4 | 968.826 | -8.826 | Cb | ||
| 37 | 986.666 | 16:9 | 996.089 | -9.423 | Cv | ||
| 38 | 1013.333 | 9:5 | 1017.596 | -4.262 | C | ||
| 39 | 1040 | 20:11 | 1034.996 | 5.004 | C^ | ||
| 40 | 1066.666 | 50:27 | 1066.762 | -0.095 | C# | ||
| 41 | 1093.333 | 32:17 | 1095.044 | -1.7112 | C#^ | ||
| 42 | 1120 | 21:11 | 1119.463 | 0.537 | Dbv | ||
| 43 | 1146.666 | 64:33 | 1146.727 | -0.060 | Db | ||
| 44 | 1173.333 | 128:65 | 1173.158 | 0.174 | Dv | ||
| 45 | 1200 | 2:1 | 1200 | 0 | Octave | D | |