486edo: Difference between revisions

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== Theory ==

486edo is contorted in the 7-limit, with the same tuning as [[243edo]], but it corrects the [[11/1|11]]th harmonic. However, due to the doubling of [[relative error]] on the fifth, it is in[[consistent]] to the [[9-odd-limit]]. Its approximation of most harmonics are poor for its size, with all odd harmonics from 3 to 23 having more than 25% relative error, but the ratios between harmonics are approximated better. Using the patent val, it [[tempering out|tempers out]] 2401/2400, 3025/3024, and 4375/4374 in the 11-limit, and 625/624, 729/728, and 1575/1573 in the 13-limit. The 486g val with a strong flat tendency is the best way to extend it further, tempering out 833/832 and 1701/1700 in the 17-limit, 513/512 and 1521/1520 in the 19-limit, and 897/896 and 1105/1104 in the 23-limit.

486edo is contorted in the 7-limit, with the same tuning as [[243edo]], but it corrects the [[11/1|11]]th harmonic. However, due to the doubling of [[relative interval error|relative error]] on the fifth, it is in[[consistent]] to the [[9-odd-limit]]. Its approximation of most harmonics are poor for its size, with all odd harmonics from 3 to 23 having more than 25% relative error, but the ratios between harmonics are approximated better. Using the patent val, it [[tempering out|tempers out]] 2401/2400, 3025/3024, and 4375/4374 in the 11-limit, and 625/624, 729/728, and 1575/1573 in the 13-limit. The 486g val with a strong flat tendency is the best way to extend it further, tempering out 833/832 and 1701/1700 in the 17-limit, 513/512 and 1521/1520 in the 19-limit, and 897/896 and 1105/1104 in the 23-limit.

=== Prime harmonics ===

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 == Theory ==
-edo is contorted in the 7-limit, with the same tuning as [[243edo]], but it corrects the [[11/1|11]]th harmonic. However, due to the doubling of [[relative error]] on the fifth, it is in[[consistent]] to the [[9-odd-limit]]. Its approximation of most harmonics are poor for its size, with all odd harmonics from 3 to 23 having more than 25% relative error, but the ratios between harmonics are approximated better. Using the patent val, it [[tempering out|tempers out]] 2401/2400, 3025/3024, and 4375/4374 in the 11-limit, and 625/624, 729/728, and 1575/1573 in the 13-limit. The 486g val with a strong flat tendency is the best way to extend it further, tempering out 833/832 and 1701/1700 in the 17-limit, 513/512 and 1521/1520 in the 19-limit, and 897/896 and 1105/1104 in the 23-limit.
+edo is contorted in the 7-limit, with the same tuning as [[243edo]], but it corrects the [[11/1|11]]th harmonic. However, due to the doubling of [[relative interval error|relative error]] on the fifth, it is in[[consistent]] to the [[9-odd-limit]]. Its approximation of most harmonics are poor for its size, with all odd harmonics from 3 to 23 having more than 25% relative error, but the ratios between harmonics are approximated better. Using the patent val, it [[tempering out|tempers out]] 2401/2400, 3025/3024, and 4375/4374 in the 11-limit, and 625/624, 729/728, and 1575/1573 in the 13-limit. The 486g val with a strong flat tendency is the best way to extend it further, tempering out 833/832 and 1701/1700 in the 17-limit, 513/512 and 1521/1520 in the 19-limit, and 897/896 and 1105/1104 in the 23-limit.
 === Prime harmonics ===
 {{Harmonics in equal|486|columns=15}}