1258edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
1258edo is consistent in the 11-odd-limit and it is a strong no-7s 19-limit tuning, with errors less than 15%. Despite inconsistency, it provides the [[optimal patent val]] for the [[abigail]] temperament in the 13-limit. | 1258edo is consistent in the 11-odd-limit and it is a strong no-7s 19-limit tuning, with errors less than 15%. Despite inconsistency, it provides the [[optimal patent val]] for the [[abigail]] temperament in the 13-limit. | ||
In 5-limit, it is a tuning for [[lafa]] and [[chlorine]], tempering out the [[septendecima]] in light of being a multiple of 17. | In 5-limit, it is a tuning for [[lafa]] and [[chlorine]], tempering out the [[septendecima]] in light of being a multiple of 17. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{harmonics in equal|1258}} | {{harmonics in equal|1258}} | ||
=== Divisors === | === Divisors === | ||
1258edo has subset edos {{EDOs|1, 2, 17, 34, 37, 74, 629}}. | 1258edo has subset edos {{EDOs|1, 2, 17, 34, 37, 74, 629}}. | ||
[[Category:Abigail]] | [[Category:Abigail]] | ||
[[Category:Chlorine]] | [[Category:Chlorine]] | ||
Latest revision as of 13:25, 21 February 2025
| ← 1257edo | 1258edo | 1259edo → |
1258 equal divisions of the octave (abbreviated 1258edo or 1258ed2), also called 1258-tone equal temperament (1258tet) or 1258 equal temperament (1258et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1258 equal parts of about 0.954 ¢ each. Each step represents a frequency ratio of 21/1258, or the 1258th root of 2.
1258edo is consistent in the 11-odd-limit and it is a strong no-7s 19-limit tuning, with errors less than 15%. Despite inconsistency, it provides the optimal patent val for the abigail temperament in the 13-limit.
In 5-limit, it is a tuning for lafa and chlorine, tempering out the septendecima in light of being a multiple of 17.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.112 | +0.014 | +0.331 | +0.033 | -0.146 | -0.027 | +0.102 | +0.343 | -0.324 | -0.361 |
| Relative (%) | +0.0 | +11.7 | +1.4 | +34.8 | +3.5 | -15.3 | -2.8 | +10.7 | +35.9 | -34.0 | -37.9 | |
| Steps (reduced) |
1258 (0) |
1994 (736) |
2921 (405) |
3532 (1016) |
4352 (578) |
4655 (881) |
5142 (110) |
5344 (312) |
5691 (659) |
6111 (1079) |
6232 (1200) | |