506edo

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← 505edo506edo507edo →
Prime factorization 2 × 11 × 23
Step size 2.37154¢ 
Fifth 296\506 (701.976¢) (→148\253)
Semitones (A1:m2) 48:38 (113.8¢ : 90.12¢)
Consistency limit 9
Distinct consistency limit 9

506 equal divisions of the octave (abbreviated 506edo or 506ed2), also called 506-tone equal temperament (506tet) or 506 equal temperament (506et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 506 equal parts of about 2.37 ¢ each. Each step represents a frequency ratio of 21/506, or the 506th root of 2.

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, providing the optimal patent val for 11- and 17-limit stockhausenic. 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. It also tunes the palladium temperament in the 5-limit.

Prime harmonics

Approximation of prime harmonics in 506edo
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.