12ed5: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
m Removing from Category:Edonoi using Cat-a-lot |
||
| (5 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
'''[[Ed5|Division of the 5th harmonic]] into 12 equal parts''' (12ed5) is related to the [[Meantone family|mothra temperament]] and the [[Semicomma family|quadrawell temperament]]. The step size about 232.1928 cents, corresponding to 5.1681 [[edo]]. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. | {{Infobox ET}} | ||
'''[[Ed5|Division of the 5th harmonic]] into 12 equal parts''' (12ed5) is related to the [[Meantone family|mothra temperament]] and the [[Semicomma family|quadrawell temperament]]. The step size about 232.1928 cents, corresponding to 5.1681 [[edo]], very nearly every 6th step of [[31edo]]. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. | |||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 74: | Line 76: | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 12 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 12 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 19:20, 1 August 2025
| ← 11ed5 | 12ed5 | 13ed5 → |
Division of the 5th harmonic into 12 equal parts (12ed5) is related to the mothra temperament and the quadrawell temperament. The step size about 232.1928 cents, corresponding to 5.1681 edo, very nearly every 6th step of 31edo. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 232.1928 | 8/7 | |
| 2 | 464.3856 | 17/13 | |
| 3 | 696.5784 | meantone fifth (pseudo-3/2) | |
| 4 | 928.7712 | 65/38 | |
| 5 | 1160.9640 | 45/23 | |
| 6 | 1393.1569 | 38/17, 85/38 | meantone major second plus an octave |
| 7 | 1625.3497 | 23/9 | |
| 8 | 1857.5425 | 38/13 | |
| 9 | 2089.7353 | meantone major sixth plus an octave (pseudo-10/3) | |
| 10 | 2321.9281 | 65/17 | |
| 11 | 2554.1209 | 35/8 | |
| 12 | 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 (¢) | -39 | -44 | -78 | +0 | -83 | +114 | +115 | -89 | -39 | +28 | +110 |
| Relative (%) | -16.8 | -19.1 | -33.6 | +0.0 | -35.9 | +49.1 | +49.6 | -38.3 | -16.8 | +12.1 | +47.2 | |
| Steps (reduced) |
5 (5) |
8 (8) |
10 (10) |
12 (0) |
13 (1) |
15 (3) |
16 (4) |
16 (4) |
17 (5) |
18 (6) |
19 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -29 | +75 | -44 | +76 | -29 | +104 | +11 | -78 | +70 | -11 | -88 |
| Relative (%) | -12.4 | +32.3 | -19.1 | +32.8 | -12.4 | +44.9 | +4.6 | -33.6 | +30.0 | -4.7 | -37.8 | |
| Steps (reduced) |
19 (7) |
20 (8) |
20 (8) |
21 (9) |
21 (9) |
22 (10) |
22 (10) |
22 (10) |
23 (11) |
23 (11) |
23 (11) | |