39ed5: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,024 edits
No edit summary
Tags: Mobile edit Mobile web edit
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,024 edits
No edit summary
Tags: Mobile edit Mobile web edit
Line 1: Line 1:
'''[[Ed5|Division of the 5th harmonic]] into 39 equal parts''' (39ed5) is a good [[hyperpyth]] tuning. The step size about 71.4439 cents. It is similar to every fifth step of [[84edo]], but with the 5/1 rather than the 2/1 being just.
'''[[Ed5|Division of the 5th harmonic]] into 39 equal parts''' (39ed5) is a good [[hyperpyth]] tuning. The step size about 71.4439 cents. It is compared to every fifth step of [[84edo]], but with the 5/1 rather than the 2/1 being just.


{| class="wikitable"
{| class="wikitable"
Line 21: Line 21:
| | 142.8879
| | 142.8879
| | 38/35, 25/23
| | 38/35, 25/23
| | +9.7 cents from 27/25
| |  
|-
|-
| | 3
| | 3
Line 36: Line 36:
| | 357.2197
| | 357.2197
| | [[16/13]]
| | [[16/13]]
| | -15.2 cents from 31/25
| |  
|-
|-
| | 6
| | 6
Line 46: Line 46:
| | 500.1076
| | 500.1076
| | [[4/3]]
| | [[4/3]]
| | +19.5 cents from 33/25
| |  
|-
|-
| | 8
| | 8
Line 66: Line 66:
| | 785.8834
| | 785.8834
| | [[11/7]]
| | [[11/7]]
| | +16.0 cents from 39/25
| |  
|-
|-
| | 12
| | 12
| | 857.3273
| | 857.3273
| | 41/25, 23/14
| | 41/25, 23/14
| | +0.9 cents from 41/25
| |  
|-
|-
| | 13
| | 13
| | 928.7712
| | 928.7712
| | 70/41, 65/38
| | 70/41, 65/38
| | -10.1 cents from 43/25
| |  
|-
|-
| | 14
| | 14
Line 86: Line 86:
| | 1071.6591
| | 1071.6591
| | [[13/7]]
| | [[13/7]]
| | -21.2 cents from 47/25
| |  
|-
|-
| | 16
| | 16
| | 1143.1031
| | 1143.1031
| | 29/15, 31/16
| | 29/15, 31/16
| | -21.9 cents from 49/25
| |  
|-
|-
| | 17
| | 17
| | 1214.5470
| | 1214.5470
| | 125/62, 115/57, 105/52
| | 125/62, 115/57, 105/52
| | -19.7 cents from 51/25
| |  
|-
|-
| | 18
| | 18
| | 1285.9909
| | 1285.9909
| | [[21/20|21/10]]
| | [[21/20|21/10]]
| | -14.9 cents from 53/25
| |  
|-
|-
| | 19
| | 19
Line 111: Line 111:
| | 1428.8788
| | 1428.8788
| | 57/25, 105/46, 16/7
| | 57/25, 105/46, 16/7
| | +2.0 cents from 57/25
| |  
|-
|-
| | 21
| | 21
| | 1500.3228
| | 1500.3228
| | [[25/21|50/21]]
| | [[25/21|50/21]]
| | +13.8 cents from 59/25
| |  
|-
|-
| | 22
| | 22
| | 1571.7667
| | 1571.7667
| | 52/21, 57/23, 62/25
| | 52/21, 57/23, 62/25
| | -28.3 cents from 63/25
| |  
|-
|-
| | 23
| | 23
Line 131: Line 131:
| | 1714.6546
| | 1714.6546
| | 35/13
| | 35/13
| | +8.0 cents from 67/25
| |  
|-
|-
| | 25
| | 25
| | 1786.0985
| | 1786.0985
| | 115/41, 160/57
| | 115/41, 160/57
| | -21.0 cents from 71/25
| |  
|-
|-
| | 26
| | 26
| | 1857.5425
| | 1857.5425
| | [[19/13|38/13]], 41/14
| | [[19/13|38/13]], 41/14
| | +2.4 cents from 73/25
| |  
|-
|-
| | 27
| | 27

Revision as of 11:30, 17 January 2019

Division of the 5th harmonic into 39 equal parts (39ed5) is a good hyperpyth tuning. The step size about 71.4439 cents. It is compared to every fifth step of 84edo, but with the 5/1 rather than the 2/1 being just.

degree cents value corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 71.4439 25/24, 24/23
2 142.8879 38/35, 25/23
3 214.3318 26/23, 43/38, 60/53, 17/15
4 285.7758 33/28, 46/39, 13/11
5 357.2197 16/13
6 428.6636 32/25, 41/32, 50/39
7 500.1076 4/3
8 571.5515 25/18 -11.0 cents from 7/5
9 642.9955 45/31
10 714.4394 80/53, 77/51, 68/45, 65/43
11 785.8834 11/7
12 857.3273 41/25, 23/14
13 928.7712 70/41, 65/38
14 1000.2152 57/32, 98/55, 41/23 -17.4 cents from 9/5
15 1071.6591 13/7
16 1143.1031 29/15, 31/16
17 1214.5470 125/62, 115/57, 105/52
18 1285.9909 21/10
19 1357.4349 35/16, 46/21, 125/57 -7.6 cents from 11/5
20 1428.8788 57/25, 105/46, 16/7
21 1500.3228 50/21
22 1571.7667 52/21, 57/23, 62/25
23 1643.2107 80/31, 75/29 -11.0 cents from 13/5
24 1714.6546 35/13
25 1786.0985 115/41, 160/57
26 1857.5425 38/13, 41/14
27 1928.9864 70/23 +27.0 cents from 3/1
28 2000.4304 35/11
29 2071.8743 43/13, 53/16
30 2143.3182 31/9 +24.7 cents from 17/5
31 2214.7622 18/5
32 2286.2061 15/4 -25.0 cents from 19/5
33 2357.6501 39/10
34 2429.0940 65/16
35 2500.5379 55/13 +16.1 cents from 21/5
36 2571.9819 75/17, 53/12, 190/43, 115/26
37 2643.4258 23/5 +1.5 cents from 23/5
38 2714.8698 24/5
39 2786.3137 exact 5/1 just major third plus two octaves
Retrieved from "https://en.xen.wiki/index.php?title=39ed5&oldid=39598"