65edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Jkarimak (talk | contribs)
191 edits
m →Intervals: style
TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
added ups and downs names
Line 13: Line 13:
! [[Degree|Degree]]
! [[Degree|Degree]]
![[cent|Cents]]
![[cent|Cents]]
! colspan="2" |[[Ups and Downs Notation|Ups and Downs]]
|-
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:right;" | 0.0000
| style="text-align:right;" | 0.0000
|P1
|D
|-
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:right;" | 18.4615
| style="text-align:right;" | 18.4615
|^1
|^D
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:right;" | 36.9231
| style="text-align:right;" | 36.9231
|^^1
|^^D
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:right;" | 55.3846
| style="text-align:right;" | 55.3846
|vvm2
|vvEb
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:right;" | 73.84615
| style="text-align:right;" | 73.84615
|vm2
|vEb
|-
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:right;" | 92.3077
| style="text-align:right;" | 92.3077
|m2
|Eb
|-
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| style="text-align:right;" | 110.7692
| style="text-align:right;" | 110.7692
|A1/^m2
|D#/^Eb
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| style="text-align:right;" | 129.2308
| style="text-align:right;" | 129.2308
|v~2
|^^Eb
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:right;" | 147.6923
| style="text-align:right;" | 147.6923
|~2
|vvvE
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| style="text-align:right;" | 166.15385
| style="text-align:right;" | 166.15385
|^~2
|vvE
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| style="text-align:right;" | 184.6154
| style="text-align:right;" | 184.6154
|vM2
|vE
|-
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| style="text-align:right;" | 203.0769
| style="text-align:right;" | 203.0769
|M2
|E
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| style="text-align:right;" | 221.5385
| style="text-align:right;" | 221.5385
|^M2
|^E
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| style="text-align:right;" | 240
| style="text-align:right;" | 240
|^^M2
|^^E
|-
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| style="text-align:right;" | 258.4615
| style="text-align:right;" | 258.4615
|vvm3
|vvF
|-
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 15
| style="text-align:right;" | 276.9231
| style="text-align:right;" | 276.9231
|vm3
|vF
|-
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| style="text-align:right;" | 295.3846
| style="text-align:right;" | 295.3846
|m3
|F
|-
|-
| style="text-align:center;" | 17
| style="text-align:center;" | 17
| style="text-align:right;" | 313.84615
| style="text-align:right;" | 313.84615
|^m3
|^F
|-
|-
| style="text-align:center;" | 18
| style="text-align:center;" | 18
| style="text-align:right;" | 332.3077
| style="text-align:right;" | 332.3077
|v~3
|^^F
|-
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 19
| style="text-align:right;" | 350.7692
| style="text-align:right;" | 350.7692
|~3
|^^^F
|-
|-
| style="text-align:center;" | 20
| style="text-align:center;" | 20
| style="text-align:right;" | 369.2308
| style="text-align:right;" | 369.2308
|^~3
|vvF#
|-
|-
| style="text-align:center;" | 21
| style="text-align:center;" | 21
| style="text-align:right;" | 387.6923
| style="text-align:right;" | 387.6923
|vM3
|vF#
|-
|-
| style="text-align:center;" | 22
| style="text-align:center;" | 22
| style="text-align:right;" | 406.15385
| style="text-align:right;" | 406.15385
|M3
|F#
|-
|-
| style="text-align:center;" | 23
| style="text-align:center;" | 23
| style="text-align:right;" | 424.6154
| style="text-align:right;" | 424.6154
|^M3
|^F#
|-
|-
| style="text-align:center;" | 24
| style="text-align:center;" | 24
| style="text-align:right;" | 443.0769
| style="text-align:right;" | 443.0769
|^^M3
|^^F#
|-
|-
| style="text-align:center;" | 25
| style="text-align:center;" | 25
| style="text-align:right;" | 461.5385
| style="text-align:right;" | 461.5385
|vv4
|vvG
|-
|-
| style="text-align:center;" | 26
| style="text-align:center;" | 26
| style="text-align:right;" | 480
| style="text-align:right;" | 480
|v4
|vG
|-
|-
| style="text-align:center;" | 27
| style="text-align:center;" | 27
| style="text-align:right;" | 498.4615
| style="text-align:right;" | 498.4615
|P4
|G
|-
|-
| style="text-align:center;" | 28
| style="text-align:center;" | 28
| style="text-align:right;" | 516.9231
| style="text-align:right;" | 516.9231
|^4
|^G
|-
|-
| style="text-align:center;" | 29
| style="text-align:center;" | 29
| style="text-align:right;" | 535.3846
| style="text-align:right;" | 535.3846
|v~4
|^^G
|-
|-
| style="text-align:center;" | 30
| style="text-align:center;" | 30
| style="text-align:right;" | 553.84615
| style="text-align:right;" | 553.84615
|~4
|^^^G
|-
|-
| style="text-align:center;" | 31
| style="text-align:center;" | 31
| style="text-align:right;" | 572.3077
| style="text-align:right;" | 572.3077
|^~4/vd5
|vvG#/vAb
|-
|-
| style="text-align:center;" | 32
| style="text-align:center;" | 32
| style="text-align:right;" | 590.7692
| style="text-align:right;" | 590.7692
|vA4/d5
|vG#/Ab
|-
|-
| style="text-align:center;" | 33
| style="text-align:center;" | 33
| style="text-align:right;" | 609.2308
| style="text-align:right;" | 609.2308
|A4/^d5
|G#/^Ab
|-
|-
| style="text-align:center;" | 34
| style="text-align:center;" | 34
| style="text-align:right;" | 627.6923
| style="text-align:right;" | 627.6923
|^A4/v~5
|^G#/^^Ab
|-
|-
| style="text-align:center;" | 35
| style="text-align:center;" | 35
| style="text-align:right;" | 646.1538
| style="text-align:right;" | 646.1538
|~5
|vvvA
|-
|-
| style="text-align:center;" | 36
| style="text-align:center;" | 36
| style="text-align:right;" | 664.6154
| style="text-align:right;" | 664.6154
|^~5
|vvA
|-
|-
| style="text-align:center;" | 37
| style="text-align:center;" | 37
| style="text-align:right;" | 683.0769
| style="text-align:right;" | 683.0769
|v5
|vA
|-
|-
| style="text-align:center;" | 38
| style="text-align:center;" | 38
| style="text-align:right;" | 701.5385
| style="text-align:right;" | 701.5385
|P5
|A
|-
|-
| style="text-align:center;" | 39
| style="text-align:center;" | 39
| style="text-align:right;" | 720
| style="text-align:right;" | 720
|^5
|^A
|-
|-
| style="text-align:center;" | 40
| style="text-align:center;" | 40
| style="text-align:right;" | 738.4615
| style="text-align:right;" | 738.4615
|^^5
|^^A
|-
|-
| style="text-align:center;" | 41
| style="text-align:center;" | 41
| style="text-align:right;" | 756.9231
| style="text-align:right;" | 756.9231
|vvm6
|vvBb
|-
|-
| style="text-align:center;" | 42
| style="text-align:center;" | 42
| style="text-align:right;" | 775.3846
| style="text-align:right;" | 775.3846
|vm6
|vBb
|-
|-
| style="text-align:center;" | 43
| style="text-align:center;" | 43
| style="text-align:right;" | 793.84615
| style="text-align:right;" | 793.84615
|m6
|Bb
|-
|-
| style="text-align:center;" | 44
| style="text-align:center;" | 44
| style="text-align:right;" | 812.3077
| style="text-align:right;" | 812.3077
|^m6
|^Bb
|-
|-
| style="text-align:center;" | 45
| style="text-align:center;" | 45
| style="text-align:right;" | 830.7692
| style="text-align:right;" | 830.7692
|v~6
|^^Bb
|-
|-
| style="text-align:center;" | 46
| style="text-align:center;" | 46
| style="text-align:right;" | 849.2308
| style="text-align:right;" | 849.2308
|~6
|vvvB
|-
|-
| style="text-align:center;" | 47
| style="text-align:center;" | 47
| style="text-align:right;" | 867.6923
| style="text-align:right;" | 867.6923
|^~6
|vvB
|-
|-
| style="text-align:center;" | 48
| style="text-align:center;" | 48
| style="text-align:right;" | 886.15385
| style="text-align:right;" | 886.15385
|vM6
|vB
|-
|-
| style="text-align:center;" | 49
| style="text-align:center;" | 49
| style="text-align:right;" | 904.6154
| style="text-align:right;" | 904.6154
|M6
|B
|-
|-
| style="text-align:center;" | 50
| style="text-align:center;" | 50
| style="text-align:right;" | 923.0769
| style="text-align:right;" | 923.0769
|^M6
|^B
|-
|-
| style="text-align:center;" | 51
| style="text-align:center;" | 51
| style="text-align:right;" | 941.5385
| style="text-align:right;" | 941.5385
|^^M6
|^^B
|-
|-
| style="text-align:center;" | 52
| style="text-align:center;" | 52
| style="text-align:right;" | 960
| style="text-align:right;" | 960
|vvm7
|vvC
|-
|-
| style="text-align:center;" | 53
| style="text-align:center;" | 53
| style="text-align:right;" | 978.4615
| style="text-align:right;" | 978.4615
|vm7
|vC
|-
|-
| style="text-align:center;" | 54
| style="text-align:center;" | 54
| style="text-align:right;" | 996.9231
| style="text-align:right;" | 996.9231
|m7
|C
|-
|-
| style="text-align:center;" | 55
| style="text-align:center;" | 55
| style="text-align:right;" | 1015.3846
| style="text-align:right;" | 1015.3846
|^m7
|^C
|-
|-
| style="text-align:center;" | 56
| style="text-align:center;" | 56
| style="text-align:right;" | 1033.84615
| style="text-align:right;" | 1033.84615
|v~7
|^^C
|-
|-
| style="text-align:center;" | 57
| style="text-align:center;" | 57
| style="text-align:right;" | 1052.3077
| style="text-align:right;" | 1052.3077
|~7
|^^^C
|-
|-
| style="text-align:center;" | 58
| style="text-align:center;" | 58
| style="text-align:right;" | 1070.7692
| style="text-align:right;" | 1070.7692
|^~7
|vvC#
|-
|-
| style="text-align:center;" | 59
| style="text-align:center;" | 59
| style="text-align:right;" | 1089.2308
| style="text-align:right;" | 1089.2308
|vM7
|vC#
|-
|-
| style="text-align:center;" | 60
| style="text-align:center;" | 60
| style="text-align:right;" | 1107.6923
| style="text-align:right;" | 1107.6923
|M7
|C#
|-
|-
| style="text-align:center;" | 61
| style="text-align:center;" | 61
| style="text-align:right;" | 1126.15385
| style="text-align:right;" | 1126.15385
|^M7
|^C#
|-
|-
| style="text-align:center;" | 62
| style="text-align:center;" | 62
| style="text-align:right;" | 1144.6154
| style="text-align:right;" | 1144.6154
|^^M7
|^^C#
|-
|-
| style="text-align:center;" | 63
| style="text-align:center;" | 63
| style="text-align:right;" | 1163.0769
| style="text-align:right;" | 1163.0769
|vv8
|vvD
|-
|-
| style="text-align:center;" | 64
| style="text-align:center;" | 64
| style="text-align:right;" | 1181.5385
| style="text-align:right;" | 1181.5385
|v8
|vD
|-
|-
| style="text-align:center;" | 65
| style="text-align:center;" | 65
| style="text-align:right;" | 1200
| style="text-align:right;" | 1200
|P8
|D
|}
|}


Revision as of 22:57, 5 July 2020

65 tone equal temperament

65edo divides the octave into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the schisma, 32805/32768, the sensipent comma, 78732/78125, and the wuerschmidt comma. In the 7-limit, there are two different maps; the first is <65 103 151 182|, tempering out 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the 5-limit over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit wuerschmidt temperament (wurschmidt and worschmidt) these two mappings provide.

65edo approximates the intervals 3/2, 5/4, 11/8 and 19/16 well, so that it does a good job representing the 2.3.5.11.19 just intonation subgroup. To this one may want to add 13/8 and 17/16, giving the 19-limit no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit 2*65 subgroup 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as 130edo.

65edo contains 13edo as a subset. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see Rubble: a Xenuke Unfolded.

Intervals

Degree Cents Ups and Downs
0 0.0000 P1 D
1 18.4615 ^1 ^D
2 36.9231 ^^1 ^^D
3 55.3846 vvm2 vvEb
4 73.84615 vm2 vEb
5 92.3077 m2 Eb
6 110.7692 A1/^m2 D#/^Eb
7 129.2308 v~2 ^^Eb
8 147.6923 ~2 vvvE
9 166.15385 ^~2 vvE
10 184.6154 vM2 vE
11 203.0769 M2 E
12 221.5385 ^M2 ^E
13 240 ^^M2 ^^E
14 258.4615 vvm3 vvF
15 276.9231 vm3 vF
16 295.3846 m3 F
17 313.84615 ^m3 ^F
18 332.3077 v~3 ^^F
19 350.7692 ~3 ^^^F
20 369.2308 ^~3 vvF#
21 387.6923 vM3 vF#
22 406.15385 M3 F#
23 424.6154 ^M3 ^F#
24 443.0769 ^^M3 ^^F#
25 461.5385 vv4 vvG
26 480 v4 vG
27 498.4615 P4 G
28 516.9231 ^4 ^G
29 535.3846 v~4 ^^G
30 553.84615 ~4 ^^^G
31 572.3077 ^~4/vd5 vvG#/vAb
32 590.7692 vA4/d5 vG#/Ab
33 609.2308 A4/^d5 G#/^Ab
34 627.6923 ^A4/v~5 ^G#/^^Ab
35 646.1538 ~5 vvvA
36 664.6154 ^~5 vvA
37 683.0769 v5 vA
38 701.5385 P5 A
39 720 ^5 ^A
40 738.4615 ^^5 ^^A
41 756.9231 vvm6 vvBb
42 775.3846 vm6 vBb
43 793.84615 m6 Bb
44 812.3077 ^m6 ^Bb
45 830.7692 v~6 ^^Bb
46 849.2308 ~6 vvvB
47 867.6923 ^~6 vvB
48 886.15385 vM6 vB
49 904.6154 M6 B
50 923.0769 ^M6 ^B
51 941.5385 ^^M6 ^^B
52 960 vvm7 vvC
53 978.4615 vm7 vC
54 996.9231 m7 C
55 1015.3846 ^m7 ^C
56 1033.84615 v~7 ^^C
57 1052.3077 ~7 ^^^C
58 1070.7692 ^~7 vvC#
59 1089.2308 vM7 vC#
60 1107.6923 M7 C#
61 1126.15385 ^M7 ^C#
62 1144.6154 ^^M7 ^^C#
63 1163.0769 vv8 vvD
64 1181.5385 v8 vD
65 1200 P8 D

Scales

photia7

photia12

Retrieved from "https://en.xen.wiki/index.php?title=65edo&oldid=47473"