506edo: Difference between revisions
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{{EDO intro|506}} | {{EDO intro|506}} | ||
506edo is a strong 5-limit system, correcting [[253edo]]'s mapping for 5. It tunes a number of strong 5-limit temperaments like [[vishnu]], [[monzismic]], and [[lafa]]. It also tunes [[stockhausenic]] and [[geb]] temperaments. 506e val tempers out the [[swetisma]] and tunes [[hades]]. | 506edo is a strong 5-limit system, correcting [[253edo]]'s mapping for 5. It tunes a number of strong 5-limit temperaments like [[vishnu]], [[monzismic]], and [[lafa]]. It also tunes [[stockhausenic]] and [[geb]] temperaments. The 506e [[val]] [[tempering out|tempers out]] the [[swetisma]] and tunes [[hades]]. | ||
506edo tempers out the [[ | 506edo tempers out the [[major arcana]] comma, tempering out which divides the octave in 22 parts, and it is the only patent val supporting the 7-limit extension of this temperament, though 506edo's 7th harmonic is with a large error. It also tunes the [[palladium]] temperament in the 5-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|506}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
[[1012edo]], which is a zeta edo, provides correction for the 13-limit. | Since 506 factors into {{factorization|506}}, 506edo has subset edos {{EDOs| 2, 11, 22, 23, 46, and 253 }}. [[1012edo]], which is a [[zeta edo]], provides correction for the 13-limit. | ||
Revision as of 13:52, 2 November 2023
| ← 505edo | 506edo | 507edo → |
506edo is a strong 5-limit system, correcting 253edo's mapping for 5. It tunes a number of strong 5-limit temperaments like vishnu, monzismic, and lafa. It also tunes stockhausenic and geb temperaments. The 506e val tempers out the swetisma and tunes hades.
506edo tempers out the major arcana comma, tempering out which divides the octave in 22 parts, and it is the only patent val supporting the 7-limit extension of this temperament, though 506edo's 7th harmonic is with a large error. It also tunes the palladium temperament in the 5-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.02 | +0.25 | +1.13 | -1.12 | -1.00 | -0.61 | -1.07 | +0.18 | -0.33 | +0.42 |
| Relative (%) | +0.0 | +0.9 | +10.4 | +47.8 | -47.2 | -42.2 | -25.6 | -45.1 | +7.8 | -13.8 | +17.7 | |
| Steps (reduced) |
506 (0) |
802 (296) |
1175 (163) |
1421 (409) |
1750 (232) |
1872 (354) |
2068 (44) |
2149 (125) |
2289 (265) |
2458 (434) |
2507 (483) | |
Subsets and supersets
Since 506 factors into 2 × 11 × 23, 506edo has subset edos 2, 11, 22, 23, 46, and 253. 1012edo, which is a zeta edo, provides correction for the 13-limit.