3558edo: Difference between revisions
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{{ | {{Infobox ET}} | ||
{{ED intro}} | |||
== Theory == | |||
3558edo is only [[consistent]] to the [[5-odd-limit]]. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|3558}} | |||
=== Subsets and supersets === | |||
Since 3558 factors into {{factorization|3558}}, 3558edo has subset edos 2, 3, 6, 593, 1186, and 1779. | |||
== Scales == | |||
Some MOS scales: | Some MOS scales: | ||
* [[ | * [[Terrain9|Terrain[9]]] | ||
* [[ | * [[Terrain15|Terrain[15]]] | ||
[[Category:Terrain]] | [[Category:Terrain]] | ||
Latest revision as of 14:46, 20 February 2025
| ← 3557edo | 3558edo | 3559edo → |
3558 equal divisions of the octave (abbreviated 3558edo or 3558ed2), also called 3558-tone equal temperament (3558tet) or 3558 equal temperament (3558et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3558 equal parts of about 0.337 ¢ each. Each step represents a frequency ratio of 21/3558, or the 3558th root of 2.
Theory
3558edo is only consistent to the 5-odd-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.100 | -0.142 | +0.145 | +0.137 | +0.115 | -0.055 | +0.096 | -0.065 | -0.043 | +0.045 | +0.056 |
| Relative (%) | -29.7 | -42.0 | +43.1 | +40.7 | +34.2 | -16.5 | +28.3 | -19.3 | -12.6 | +13.5 | +16.7 | |
| Steps (reduced) |
5639 (2081) |
8261 (1145) |
9989 (2873) |
11279 (605) |
12309 (1635) |
13166 (2492) |
13901 (3227) |
14543 (311) |
15114 (882) |
15628 (1396) |
16095 (1863) | |
Subsets and supersets
Since 3558 factors into 2 × 3 × 593, 3558edo has subset edos 2, 3, 6, 593, 1186, and 1779.
Scales
Some MOS scales: