4ed6: Difference between revisions
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4ed6 notably approximates the [[23/1|23rd harmonic]] with incredible accuracy, less than 0.15 cents off. | |||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|4|6|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|4|6|1| | {{Harmonics in equal|4|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 4ed6 (continued)}} | ||
{{Harmonics in equal|4|6|1| | |||
Revision as of 12:54, 23 May 2025
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Template:Niche is deprecated. Please use Template:Mathematical interest instead. |
| ← 3ed6 | 4ed6 | 5ed6 → |
4 equal divisions of the 6th harmonic (abbreviated 4ed6) is a nonoctave tuning system that divides the interval of 6/1 into 4 equal parts of about 775 ¢ each. Each step represents a frequency ratio of 61/4, or the 4th root of 6.
4ed6 notably approximates the 23rd harmonic with incredible accuracy, less than 0.15 cents off.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +351 | -351 | -74 | +316 | +0 | -267 | +277 | +74 | -109 | -274 | +351 |
| Relative (%) | +45.3 | -45.3 | -9.5 | +40.7 | +0.0 | -34.4 | +35.8 | +9.5 | -14.0 | -35.3 | +45.3 | |
| Steps (reduced) |
2 (2) |
2 (2) |
3 (3) |
4 (0) |
4 (0) |
4 (0) |
5 (1) |
5 (1) |
5 (1) |
5 (1) |
6 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +212 | +84 | -35 | -147 | -252 | -351 | +331 | +242 | +158 | +77 | +0 | -74 |
| Relative (%) | +27.4 | +10.8 | -4.6 | -19.0 | -32.5 | -45.3 | +42.7 | +31.2 | +20.3 | +9.9 | +0.0 | -9.5 | |
| Steps (reduced) |
6 (2) |
6 (2) |
6 (2) |
6 (2) |
6 (2) |
6 (2) |
7 (3) |
7 (3) |
7 (3) |
7 (3) |
7 (3) |
7 (3) | |