45edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Jkarimak (talk | contribs)
191 edits
m Added links
Yourmusic Productions (talk | contribs)
autopatrolled, emailconfirmed
1,896 edits
Start creating intervals table
Line 3: Line 3:
[[Category:Edo]]
[[Category:Edo]]
[[Category:Theory]]
[[Category:Theory]]
{| class="wikitable center-all"
|-
| rowspan="2" | Step #
| style="text-align:center;" | ET
| colspan="2" | Just
| Difference <br> (ET minus Just)
| colspan="3" | [[Ups and Downs Notation]]
|-
| Cents
| Interval
| Cents
|
|
|
|
|-
| 0
| 0¢
|
|
|
| unison
| 1
| D
|-
| 1
| 26.666
|
|
|
|
|
|
|-
| 2
| 53.333
| 21:20
| 84.47
| 1.24
| double-up 1sn, double-down 2nd
| ^^1, vv2
| ^^D, vvE
|-
| 3
|
| 14:13
| 128.3
| 0.27
| down 2nd
| v2
| vE
|-
| 4
|
| 11:10
| 165
| 6.43
| 2nd
| 2
| E
|-
| 5
|
| 17:15
| 216.69
| -2.40
| up 2nd
| ^2
| ^E
|-
| 6
|
| 7:6
| 266.87
| -9.73
| double-up 2nd, double-down 3rd
| ^^2, vv3
| ^^E, vvF
|-
| 7
|
| 6:5
| 315.64
| -15.64
| down 3rd
| v3
| vF
|-
| 8
|
| 11:9
| 347.41
| -4.55
| 3rd
| 3
| F
|-
| 9
|
| 5:4
| 386.31
| -0.60
| up 3rd
| ^3
| ^F
|-
| 10
|
| 9:7
| 435.08
| -6.51
| double-up 3rd, double-down 4th
| ^^3, vv4
| ^^F, vvG
|-
| 11
|
| 21:16
| 470.78
| 0.65
| down 4th
| v4
| vG
|-
| 12
|
| 4:3
| 498.045
| 16.245
| 4th
| 4
| G
|-
| 13
|
| 11:8
| 551.32
| 5.82
| up 4th
| ^4
| ^G
|-
| 14
|
| 7:5
| 582.51
| 17.49
| double-up 4th, double-down 5th
| ^^4, vv5
| ^^G, vvA
|-
| 15
|
| 16:11
| 648.68
| -5.82
| down 5th
| v5
| vA
|-
| 16
|
| 3:2
| 701.955
| -16.245
| 5th
| 5
| A
|-
| 17
|
| 32:21
| 729.22
| -0.65
| up 5th
| ^5
| ^A
|-
| 18
|
| 14:9
| 764.92
| 6.51
| double-up 5th, double-down 6th
| ^^5, vv6
| ^^A, vvB
|-
| 19
|
| 8:5
| 813.68
| 0.61
| down 6th
| v6
| vB
|-
| 20
|
| 18:11
| 852.59
| 4.55
| 6th
| 6
| B
|-
| 21
|
| 5:3
| 884.36
| 15.64
| up 6th
| ^6
| ^B
|-
| 22
|
| 12:7
| 933.13
| 9.73
| double-up 6th, double-down 7th
| ^^6, vv7
| ^^B, vvC
|-
| 23
|
| 30:17
| 983.31
| 2.40
| down 7th
| v7
| vC
|-
| 24
|
| 20:11
| 1035
| -6.43
| 7th
| 7
| C
|-
| 25
|
| 13:7
| 1071.70
| -0.27
| up 7th
| ^7
| ^C
|-
| 26
|
| 40:21
| 1115.53
| -1.24
| double-up 7th, double-down 8ve
| ^^7, vv8
| ^^C, vvD
|-
| 27
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 28
|
|
|
|
|
|
|
|-
| 29
| 1157.14
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 30
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 31
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 32
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 33
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 34
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 35
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 36
|
| style="text-align:center;" |80:41
|
| -0.12
| down 8ve
| v8
| vD
|-
| 37
|
| style="text-align:center;" |80:41
|
| -0.12
| down 8ve
| v8
| vD
|-
| 38
|
| style="text-align:center;" |80:41
|
| -0.12
| down 8ve
| v8
| vD
|-
| 39
|
| style="text-align:center;" |80:41
|
| -0.12
| down 8ve
| v8
| vD
|-
| 40
|
| style="text-align:center;" |80:41
|
| -0.12
| down 8ve
| v8
| vD
|-
| 41
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 42
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 43
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 44
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|-
| 45
|
| style="text-align:center;" |80:41
| 1157.26
| -0.12
| down 8ve
| v8
| vD
|}

Revision as of 19:44, 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 21:20 84.47 1.24 double-up 1sn, double-down 2nd ^^1, vv2 ^^D, vvE
3 14:13 128.3 0.27 down 2nd v2 vE
4 11:10 165 6.43 2nd 2 E
5 17:15 216.69 -2.40 up 2nd ^2 ^E
6 7:6 266.87 -9.73 double-up 2nd, double-down 3rd ^^2, vv3 ^^E, vvF
7 6:5 315.64 -15.64 down 3rd v3 vF
8 11:9 347.41 -4.55 3rd 3 F
9 5:4 386.31 -0.60 up 3rd ^3 ^F
10 9:7 435.08 -6.51 double-up 3rd, double-down 4th ^^3, vv4 ^^F, vvG
11 21:16 470.78 0.65 down 4th v4 vG
12 4:3 498.045 16.245 4th 4 G
13 11:8 551.32 5.82 up 4th ^4 ^G
14 7:5 582.51 17.49 double-up 4th, double-down 5th ^^4, vv5 ^^G, vvA
15 16:11 648.68 -5.82 down 5th v5 vA
16 3:2 701.955 -16.245 5th 5 A
17 32:21 729.22 -0.65 up 5th ^5 ^A
18 14:9 764.92 6.51 double-up 5th, double-down 6th ^^5, vv6 ^^A, vvB
19 8:5 813.68 0.61 down 6th v6 vB
20 18:11 852.59 4.55 6th 6 B
21 5:3 884.36 15.64 up 6th ^6 ^B
22 12:7 933.13 9.73 double-up 6th, double-down 7th ^^6, vv7 ^^B, vvC
23 30:17 983.31 2.40 down 7th v7 vC
24 20:11 1035 -6.43 7th 7 C
25 13:7 1071.70 -0.27 up 7th ^7 ^C
26 40:21 1115.53 -1.24 double-up 7th, double-down 8ve ^^7, vv8 ^^C, vvD
27 80:41 1157.26 -0.12 down 8ve v8 vD
28
29 1157.14 80:41 1157.26 -0.12 down 8ve v8 vD
30 80:41 1157.26 -0.12 down 8ve v8 vD
31 80:41 1157.26 -0.12 down 8ve v8 vD
32 80:41 1157.26 -0.12 down 8ve v8 vD
33 80:41 1157.26 -0.12 down 8ve v8 vD
34 80:41 1157.26 -0.12 down 8ve v8 vD
35 80:41 1157.26 -0.12 down 8ve v8 vD
36 80:41 -0.12 down 8ve v8 vD
37 80:41 -0.12 down 8ve v8 vD
38 80:41 -0.12 down 8ve v8 vD
39 80:41 -0.12 down 8ve v8 vD
40 80:41 -0.12 down 8ve v8 vD
41 80:41 1157.26 -0.12 down 8ve v8 vD
42 80:41 1157.26 -0.12 down 8ve v8 vD
43 80:41 1157.26 -0.12 down 8ve v8 vD
44 80:41 1157.26 -0.12 down 8ve v8 vD
45 80:41 1157.26 -0.12 down 8ve v8 vD
Retrieved from "https://en.xen.wiki/index.php?title=45edo&oldid=47524"