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
Step #	Cents	Interval	Cents
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						Eb
6	160	11:10		-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		4.359			F
13	346.666	11:9					F^
14	373.333	5:4-		-12.980			F#
15	400	5:4+		13.686			F#^
16	426.666						Gbv
17	453.333						Gb
18	480						Gv
19	506.666	4:3	498.045	8.622			G
20	533.333						G^
21	560	18:13					G#
22	586.666	7:5					G#^
23	613.333	10:7					Abv
24	640	13:9					Ab
25	666.666						Av
26	693.333	3:2	701.955	-8.622			A
27	720						A^
28	746.666						A#
29	773.333						A#^
30	800						Bbv
31	826.666						Bb
32	853.333						Bv
33	880						B
34	906.666						B^
35	933.333						B#
36	960						Cb
37	986.666						Cv
38	1013.333						C
39	1040						C^
40	1066.666						C#
41	1093.333						C#^
42	1120						Dbv
43	1146.666						Db
44	1173.333						Dv
45	1200	2:1	1200	0	Octave		D