45edo: Difference between revisions

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Line 40: Line 40:
| 2
| 2
| 53.333
| 53.333
| 21:20
|
| 84.47
|
| 1.24
|
| double-up 1sn, double-down 2nd
|
| ^^1, vv2
|
| ^^D, vvE
|
|-
|-
| 3
| 3
|  
|  
| 14:13
|
| 128.3
|
| 0.27
|
| down 2nd
|
| v2
|
| vE
|
|-
|-
| 4
| 4
|  
|  
| 11:10
|
| 165
|
| 6.43
|
| 2nd
|
| 2
|
| E
|
|-
|-
| 5
| 5
|  
|  
| 17:15
|
| 216.69
|
| -2.40
|
| up 2nd
|
| ^2
|
| ^E
|
|-
|-
| 6
| 6
|  
|  
| 7:6
|
| 266.87
|
| -9.73
|
| double-up 2nd, double-down 3rd
|
| ^^2, vv3
|
| ^^E, vvF
|
|-
|-
| 7
| 7
|  
|  
| 6:5
|
| 315.64
|
| -15.64
|
| down 3rd
|
| v3
|
| vF
|
|-
|-
| 8
| 8
|  
|  
| 11:9
|
| 347.41
|
| -4.55
|
| 3rd
|
| 3
|
| F
|
|-
|-
| 9
| 9
|  
|  
| 5:4
|
| 386.31
|
| -0.60
|
| up 3rd
|
| ^3
|
| ^F
|
|-
|-
| 10
| 10
|  
|  
| 9:7
|
| 435.08
|
| -6.51
|
| double-up 3rd, double-down 4th
|
| ^^3, vv4
|
| ^^F, vvG
|
|-
|-
| 11
| 11
|  
|  
| 21:16
|
| 470.78
|
| 0.65
|
| down 4th
|
| v4
|
| vG
|
|-
|-
| 12
| 12
|  
|  
| 4:3
|
| 498.045
|
| 16.245
|
| 4th
|
| 4
|  
| G
|
|-
|-
| 13
| 13
|  
|  
| 11:8
|
| 551.32
|
| 5.82
|
| up 4th
|
| ^4
|
| ^G
|
|-
|-
| 14
| 14
|  
|  
| 7:5
|
| 582.51
|
| 17.49
|
| double-up 4th, double-down 5th
|
| ^^4, vv5
|
| ^^G, vvA
|
|-
|-
| 15
| 15
|  
|  
| 16:11
|
| 648.68
|
| -5.82
|
| down 5th
|
| v5
|
| vA
|
|-
|-
| 16
| 16
|  
|  
| 3:2
|
| 701.955
|
| -16.245
|
| 5th
|
| 5
|
| A
|
|-
|-
| 17
| 17
|  
|  
| 32:21
|
| 729.22
|
| -0.65
|
| up 5th
|
| ^5
|
| ^A
|
|-
|-
| 18
| 18
|  
|  
| 14:9
|
| 764.92
|
| 6.51
|
| double-up 5th, double-down 6th
|
| ^^5, vv6
|
| ^^A, vvB
|
|-
|-
| 19
| 19
|
|
| 8:5
|
| 813.68
|
| 0.61
|
| down 6th
|
| v6
|
| vB
|
|-
|-
| 20
| 20
|  
|  
| 18:11
|
| 852.59
|
| 4.55
|
| 6th
|
| 6
|
| B
|
|-
|-
| 21
| 21
|  
|  
| 5:3
|
| 884.36
|
| 15.64
|
| up 6th
|
| ^6
|
| ^B
|
|-
|-
| 22
| 22
|  
|  
| 12:7
|
| 933.13
|
| 9.73
|
| double-up 6th, double-down 7th
|
| ^^6, vv7
|
| ^^B, vvC
|
|-
|-
| 23
| 23
|  
|  
| 30:17
|
| 983.31
|
| 2.40
|
| down 7th
|
| v7
|
| vC
|
|-
|-
| 24
| 24
|  
|  
| 20:11
|
| 1035
|
| -6.43
|
| 7th
|
| 7
|
| C
|
|-
|-
| 25
| 25
|  
|  
| 13:7
|
| 1071.70
|
| -0.27
|
| up 7th
|
| ^7
|
| ^C
|
|-
|-
| 26
| 26
|  
|  
| 40:21
|
| 1115.53
|
| -1.24
|
| double-up 7th, double-down 8ve
|
| ^^7, vv8
|
| ^^C, vvD
|
|-
|-
| 27
| 27
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 28
| 28
Line 282: Line 282:
|-
|-
| 29
| 29
| 1157.14
|
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 30
| 30
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 31
| 31
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 32
| 32
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 33
| 33
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 34
| 34
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 35
| 35
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 36
| 36
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
|  
|  
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 37
| 37
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
|  
|  
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 38
| 38
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
|  
|  
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 39
| 39
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
|  
|  
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 40
| 40
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
|  
|  
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 41
| 41
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 42
| 42
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 43
| 43
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 44
| 44
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|-
|-
| 45
| 45
|  
|  
| style="text-align:center;" |80:41
| style="text-align:center;" |
| 1157.26
|
| -0.12
|
| down 8ve
|
| v8
|
| vD
|
|}
|}

Revision as of 19:49, 8 July 2020

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
Cents Interval Cents
0 0¢ unison 1 D
1 26.666
2 53.333
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
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