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{{Mathematical interest}} | |||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | |||
=== Harmonics === | |||
{{Harmonics in equal|1|4|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|1|4|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 1ed4 (continued)}} | |||
== Intervals == | |||
* 2400 cents | |||
* 4800 cents | |||
* 7200 cents | |||
* etc… | |||
Latest revision as of 09:05, 9 September 2025
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| 1ed4 | 3ed4 → |
1 equal division of the 4th harmonic (abbreviated 1ed4) is a nonoctave tuning system that uses equal steps of 4/1, or exactly 2400 ¢.
Theory
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1200 | +498 | +0 | -386 | -702 | -969 | +1200 | +996 | +814 | +649 | +498 |
| Relative (%) | +50.0 | +20.8 | +0.0 | -16.1 | -29.2 | -40.4 | +50.0 | +41.5 | +33.9 | +27.0 | +20.8 | |
| Step | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +359 | +231 | +112 | +0 | -105 | -204 | -298 | -386 | -471 | -551 | -628 | -702 |
| Relative (%) | +15.0 | +9.6 | +4.7 | +0.0 | -4.4 | -8.5 | -12.4 | -16.1 | -19.6 | -23.0 | -26.2 | -29.2 | |
| Step | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |
Intervals
- 2400 cents
- 4800 cents
- 7200 cents
- etc…