17ed7: Difference between revisions
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'''[[Ed7|Division of the 7th harmonic]] into 17 equal parts''' (17ed7) is related to [[6edo|6 edo]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 198.1662 cents. | '''[[Ed7|Division of the 7th harmonic]] into 17 equal parts''' (17ed7) is related to [[6edo|6 edo]], but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 198.1662 cents. | ||
== Intervals == | |||
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== Harmonics == | |||
{{Harmonics in equal|14|7|1|intervals=prime}} | |||
{{Harmonics in equal|14|7|1|intervals=prime|collapsed=1|start=12}} | |||
{{stub}} | |||
[[Category:Ed7]] | [[Category:Ed7]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 23:40, 22 December 2024
| ← 16ed7 | 17ed7 | 18ed7 → |
(semiconvergent)
Division of the 7th harmonic into 17 equal parts (17ed7) is related to 6 edo, but with the 7/1 rather than the 2/1 being just. The octave is about 11.0026 cents compressed and the step size is about 198.1662 cents.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 198.1662 | 28/25 | |
| 2 | 396.3325 | 49/39, 34/27 | pseudo-5/4 |
| 3 | 594.4987 | 24/17 | |
| 4 | 792.6649 | 30/19, 128/81 | |
| 5 | 990.8311 | 85/48, 39/22 | |
| 6 | 1188.9974 | 143/72, 175/88 | pseudo-octave |
| 7 | 1387.1636 | 49/22 | |
| 8 | 1585.3298 | 5/2 | |
| 9 | 1783.4961 | 14/5 | |
| 10 | 1981.6623 | 22/7 | |
| 11 | 2179.8285 | 88/25 | |
| 12 | 2377.9948 | 154/39, 320/81, 336/85 | pseudo-4/1 |
| 13 | 2576.1610 | 133/30 | |
| 14 | 2774.3272 | 119/24 | pseudo-5/1 |
| 15 | 2972.4934 | 39/7 | |
| 16 | 3170.6597 | 25/4 | |
| 17 | 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 (¢) | +3 | +23 | +101 | +0 | -61 | -109 | -92 | -44 | +106 | -54 | +71 |
| Relative (%) | +1.3 | +9.6 | +42.1 | +0.0 | -25.2 | -45.4 | -38.4 | -18.4 | +44.1 | -22.6 | +29.4 | |
| Steps (reduced) |
5 (5) |
8 (8) |
12 (12) |
14 (0) |
17 (3) |
18 (4) |
20 (6) |
21 (7) |
23 (9) |
24 (10) |
25 (11) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5 | +68 | -14 | +72 | +105 | -81 | +102 | -60 | +80 | +32 | -105 |
| Relative (%) | +2.1 | +28.2 | -6.0 | +30.0 | +43.5 | -33.6 | +42.4 | -25.1 | +33.2 | +13.2 | -43.6 | |
| Steps (reduced) |
26 (12) |
27 (13) |
27 (13) |
28 (0) |
29 (1) |
29 (1) |
30 (2) |
30 (2) |
31 (3) |
31 (3) |
31 (3) | |
|
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