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Created page with "'''Division of the 7th harmonic into 20 equal parts''' (20ed7) is related to the meantone temperament. The step size is about 168.4413 cents, corre..." Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | |||
'''[[Ed7|Division of the 7th harmonic]] into 20 equal parts''' (20ed7) is related to the [[Meantone family|meantone temperament]]. The step size is about 168.4413 cents, corresponding to 7.1241 [[edo]]. | '''[[Ed7|Division of the 7th harmonic]] into 20 equal parts''' (20ed7) is related to the [[Meantone family|meantone temperament]]. The step size is about 168.4413 cents, corresponding to 7.1241 [[edo]]. | ||
==Intervals== | |||
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==Harmonics== | |||
{{Harmonics in equal|20|7|1|intervals=prime}} | |||
{{Harmonics in equal|20|7|1|intervals=prime|collapsed=1|start=12}} | |||
{{stub}} | |||
Latest revision as of 19:20, 1 August 2025
| ← 19ed7 | 20ed7 | 21ed7 → |
Division of the 7th harmonic into 20 equal parts (20ed7) is related to the meantone temperament. The step size is about 168.4413 cents, corresponding to 7.1241 edo.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 168.4413 | 11/10 | |
| 2 | 336.8826 | 17/14 | |
| 3 | 505.3239 | 91/68 | |
| 4 | 673.7652 | 28/19, 96/65, 65/44, 34/23 | |
| 5 | 842.2065 | 13/8 | |
| 6 | 1010.6478 | 70/39 | |
| 7 | 1179.0891 | 77/39 | |
| 8 | 1347.5304 | 24/11 | |
| 9 | 1515.9717 | 12/5 | |
| 10 | 1684.4130 | 119/45, 45/17 | |
| 11 | 1852.8542 | 35/12 | |
| 12 | 2021.2955 | 77/24 | |
| 13 | 2189.7368 | 39/11 | |
| 14 | 2358.1781 | 39/10 | |
| 15 | 2526.6194 | 56/13 | |
| 16 | 2695.0607 | 19/4 | |
| 17 | 2863.5020 | 68/13 | |
| 18 | 3031.9433 | 98/17 | |
| 19 | 3200.3846 | 70/11 | |
| 20 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.9 | -49.1 | +77.2 | +0.0 | +59.7 | -61.1 | -20.2 | -44.3 | -38.2 | +65.9 | -49.6 |
| Relative (%) | -12.4 | -29.2 | +45.8 | +0.0 | +35.5 | -36.2 | -12.0 | -26.3 | -22.7 | +39.1 | -29.4 | |
| Steps (reduced) |
7 (7) |
11 (11) |
17 (17) |
20 (0) |
25 (5) |
26 (6) |
29 (9) |
30 (10) |
32 (12) |
35 (15) |
35 (15) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -19.0 | -28.3 | +57.7 | +72.1 | +32.6 | +15.4 | -42.4 | -36.3 | +31.7 | -16.4 | +15.3 |
| Relative (%) | -11.3 | -16.8 | +34.3 | +42.8 | +19.3 | +9.1 | -25.1 | -21.6 | +18.8 | -9.7 | +9.1 | |
| Steps (reduced) |
37 (17) |
38 (18) |
39 (19) |
40 (0) |
41 (1) |
42 (2) |
42 (2) |
43 (3) |
44 (4) |
44 (4) |
45 (5) | |
|
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