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Created page with "'''Division of the 5th harmonic into 29 equal parts''' (29ED5) is compared to every other step of 25EDO, but with the 5/1 rather than the 2/1 being just. The..." |
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{{Infobox ET}} | |||
'''[[Ed5|Division of the 5th harmonic]] into 29 equal parts''' (29ED5) is compared to every other step of [[25edo|25EDO]], but with the 5/1 rather than the 2/1 being just. The step size is about 96.0798 cents, corresponding to 12.4896 [[EDO]]. | '''[[Ed5|Division of the 5th harmonic]] into 29 equal parts''' (29ED5) is compared to every other step of [[25edo|25EDO]], but with the 5/1 rather than the 2/1 being just. The step size is about 96.0798 cents, corresponding to 12.4896 [[EDO]]. | ||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 41: | Line 43: | ||
| | 576.4787 | | | 576.4787 | ||
| | 53/38, 60/43 | | | 53/38, 60/43 | ||
| | | | | -6.0 cents from [[7/5]] | ||
|- | |- | ||
| | 7 | | | 7 | ||
| Line 159: | Line 161: | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 29 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 29 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
[[Category:Hyperpyth]] | [[Category:Hyperpyth]] | ||
{{todo|expand}} | |||
Latest revision as of 19:21, 1 August 2025
| ← 28ed5 | 29ed5 | 30ed5 → |
Division of the 5th harmonic into 29 equal parts (29ED5) is compared to every other step of 25EDO, but with the 5/1 rather than the 2/1 being just. The step size is about 96.0798 cents, corresponding to 12.4896 EDO.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 96.0798 | 18/17, 19/18 | |
| 2 | 192.1596 | 19/17 | |
| 3 | 288.2393 | 13/11 | |
| 4 | 384.3191 | 5/4 | |
| 5 | 480.3989 | 33/25 | |
| 6 | 576.4787 | 53/38, 60/43 | -6.0 cents from 7/5 |
| 7 | 672.5585 | 28/19 | |
| 8 | 768.6383 | 14/9 | |
| 9 | 864.7180 | 28/17 | |
| 10 | 960.7978 | 54/31 | |
| 11 | 1056.8776 | 46/25 | +39.3 cents from 9/5 |
| 12 | 1152.9574 | 35/18, 37/19, 72/37 | |
| 13 | 1249.0372 | 35/17, 37/18, 72/35 | |
| 14 | 1345.1170 | 50/23 | |
| 15 | 1441.1967 | 23/10 | |
| 16 | 1537.2765 | 17/7 | |
| 17 | 1633.3563 | 18/7 | -20.9 cents from 13/5 |
| 18 | 1729.4361 | 19/7 | |
| 19 | 1825.5159 | ||
| 20 | 1921.5957 | 88/29 | +19.6 cents from 3/1 |
| 21 | 2017.6754 | ||
| 22 | 2113.7552 | -4.9 cents from 17/5 | |
| 23 | 2209.8350 | ||
| 24 | 2305.9148 | 72/19 | -5.3 cents from 19/5 |
| 25 | 2401.9946 | 4/1 | |
| 26 | 2498.0744 | 72/17 | +13.6 cents from 21/5 |
| 27 | 2594.1541 | -47.8 cents from 23/5 | |
| 28 | 2690.2339 | 52/11 | |
| 29 | 2786.3137 | exact 5/1 | just major third plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -47.0 | +19.6 | +2.0 | +0.0 | -27.4 | -6.0 | -45.0 | +39.3 | -47.0 | -19.9 | +21.6 |
| Relative (%) | -49.0 | +20.4 | +2.1 | +0.0 | -28.5 | -6.3 | -46.9 | +40.9 | -49.0 | -20.7 | +22.5 | |
| Steps (reduced) |
12 (12) |
20 (20) |
25 (25) |
29 (0) |
32 (3) |
35 (6) |
37 (8) |
40 (11) |
41 (12) |
43 (14) |
45 (16) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.9 | +43.0 | +19.6 | +4.0 | -4.9 | -7.8 | -5.3 | +2.0 | +13.6 | +29.1 | -47.8 |
| Relative (%) | -21.7 | +44.8 | +20.4 | +4.2 | -5.1 | -8.1 | -5.5 | +2.1 | +14.2 | +30.3 | -49.8 | |
| Steps (reduced) |
46 (17) |
48 (19) |
49 (20) |
50 (21) |
51 (22) |
52 (23) |
53 (24) |
54 (25) |
55 (26) |
56 (27) |
56 (27) | |