45edo

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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 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