486edo - Revision history

Overthink: /* Theory */ correct link

2026-02-11T05:27:38Z

Theory: correct link

← Older revision		Revision as of 05:27, 11 February 2026
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	== Theory ==		== 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 ===		=== Prime harmonics ===
	{{Harmonics in equal\|486\|columns=15}}		{{Harmonics in equal\|486\|columns=15}}

Overthink: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 486edo is contorted in the 7-limit, with the same tuning as 243edo, but it corrects the 11th harmonic. However, due to the doubling of relative error on the fifth, it is inconsistent 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 paten..."

2025-09-15T05:06:50Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 486edo is contorted in the 7-limit, with the same tuning as 243edo, but it corrects the 11th harmonic. However, due to the doubling of relative error on the fifth, it is inconsistent 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 paten..."

New page

{{Infobox ET}}
{{ED intro}}

== 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.

=== Prime harmonics ===
{{Harmonics in equal|486|columns=15}}