458edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | |||
458edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[5/1|5]] is about halfway between its steps. It is most notable for [[tempering out]] the kleisma, [[15625/15552]], in the 5-limit and provides the [[optimal patent val]] for the 5-limit [[kleismic]] temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|458}} | |||
=== Subsets and supersets === | |||
Since 458 factors into {{factorization|458}}, 458edo contains [[2edo]] and [[229edo]] as subsets. | |||
[[Category:Kleismic]] | [[Category:Kleismic]] | ||
Latest revision as of 14:58, 20 February 2025
| ← 457edo | 458edo | 459edo → |
458 equal divisions of the octave (abbreviated 458edo or 458ed2), also called 458-tone equal temperament (458tet) or 458 equal temperament (458et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 458 equal parts of about 2.62 ¢ each. Each step represents a frequency ratio of 21/458, or the 458th root of 2.
458edo is inconsistent to the 5-odd-limit and harmonic 5 is about halfway between its steps. It is most notable for tempering out the kleisma, 15625/15552, in the 5-limit and provides the optimal patent val for the 5-limit kleismic temperament.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.23 | -1.16 | +0.61 | -1.10 | +0.52 | -0.15 | +1.18 | +0.55 | +0.12 | -0.06 |
| Relative (%) | +0.0 | +8.7 | -44.3 | +23.1 | -42.0 | +19.9 | -5.8 | +44.9 | +20.9 | +4.5 | -2.2 | |
| Steps (reduced) |
458 (0) |
726 (268) |
1063 (147) |
1286 (370) |
1584 (210) |
1695 (321) |
1872 (40) |
1946 (114) |
2072 (240) |
2225 (393) |
2269 (437) | |
Subsets and supersets
Since 458 factors into 2 × 229, 458edo contains 2edo and 229edo as subsets.