14ed7: Difference between revisions
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Created page with "{{Infobox ET}} '''Division of the 7th harmonic into 14 equal parts''' (14ed7) is closely related to 5edo. == Harmonics == {{Harmonics in equal|14|7|1}} {{Stub}}" |
m Intro intervals harmonics |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} It is closely related to [[5edo]]. | |||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | == Harmonics == | ||
{{Harmonics in equal| | {{Harmonics in equal | ||
{{ | | steps = 17 | ||
| num = 7 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 14 | |||
| num = 7 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Revision as of 03:43, 5 October 2024
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| ← 13ed7 | 14ed7 | 15ed7 → |
(convergent)
14 equal divisions of the 7th harmonic (abbreviated 14ed7) is a nonoctave tuning system that divides the interval of 7/1 into 14 equal parts of about 241 ¢ each. Each step represents a frequency ratio of 71/14, or the 14th root of 7. It is closely related to 5edo.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 240.6 | 8/7, 22/19, 23/20 |
| 2 | 481.3 | 4/3, 17/13, 21/16 |
| 3 | 721.9 | 3/2, 23/15 |
| 4 | 962.5 | 7/4, 19/11 |
| 5 | 1203.2 | 2/1 |
| 6 | 1443.8 | 7/3, 16/7, 23/10 |
| 7 | 1684.4 | 8/3, 21/8 |
| 8 | 1925 | 3/1 |
| 9 | 2165.7 | 7/2 |
| 10 | 2406.3 | 4/1 |
| 11 | 2646.9 | 14/3, 23/5 |
| 12 | 2887.6 | 16/3, 21/4 |
| 13 | 3128.2 | |
| 14 | 3368.8 | 7/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.0 | +79.7 | -22.0 | -12.0 | +68.7 | +0.0 | -33.0 | -38.8 | -23.0 | +10.2 | +57.7 |
| Relative (%) | -5.6 | +40.2 | -11.1 | -6.0 | +34.7 | +0.0 | -16.7 | -19.6 | -11.6 | +5.1 | +29.1 | |
| Steps (reduced) |
6 (6) |
10 (10) |
12 (12) |
14 (14) |
16 (16) |
17 (0) |
18 (1) |
19 (2) |
20 (3) |
21 (4) |
22 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -109 | +3 | -116 | +13 | -92 | +49 | -44 | +108 | +23 | -57 | +106 |
| Relative (%) | -45.4 | +1.3 | -48.3 | +5.2 | -38.4 | +20.5 | -18.4 | +44.7 | +9.6 | -23.9 | +44.1 | |
| Steps (reduced) |
18 (4) |
19 (5) |
19 (5) |
20 (6) |
20 (6) |
21 (7) |
21 (7) |
22 (8) |
22 (8) |
22 (8) |
23 (9) | |