2ed5: Difference between revisions
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m →Interval table: Replaced auto-generated table of intervals with manually curated table |
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{{Harmonics in equal|2|5|1}} | {{Harmonics in equal|2|5|1}} | ||
== Interval table == | == Interval table == | ||
{ | {| class="wikitable" | ||
!Steps | |||
!Cents | |||
!Approximate Ratios | |||
|- | |||
|0 | |||
|0 | |||
|[[1/1]] | |||
|- | |||
|1 | |||
|1393.157 | |||
|[[9/4]] | |||
|- | |||
|2 | |||
|2786.314 | |||
|[[5/1]] | |||
|} | |||
Revision as of 20:21, 3 October 2024
| ← 1ed5 | 2ed5 | 3ed5 → |
(convergent)
(semiconvergent)
2 equal divisions of the 5th harmonic (abbreviated 2ed5) is a nonoctave tuning system that divides the interval of 5/1 into 2 equal parts of about 1390 ¢ each. Each step represents a frequency ratio of 51/2, or the 2nd root of 5.
Theory
Odd harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +193 | -509 | +386 | +0 | -316 | -583 | +579 | +376 | +193 | +28 | -122 |
| Relative (%) | +13.9 | -36.5 | +27.7 | +0.0 | -22.7 | -41.8 | +41.6 | +27.0 | +13.9 | +2.0 | -8.8 | |
| Steps (reduced) |
1 (1) |
1 (1) |
2 (0) |
2 (0) |
2 (0) |
2 (0) |
3 (1) |
3 (1) |
3 (1) |
3 (1) |
3 (1) | |
Interval table
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 1393.157 | 9/4 |
| 2 | 2786.314 | 5/1 |