210edo: Difference between revisions

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== Theory ==

Since {{nowrap|210 {{=}} 3 ~~×~~ 70}}, 210edo shares its [[3/2|fifth]] with [[70edo]]. It is [[consistent]] to the [[9-odd-limit]], but there is a sharp tendency in the lower [[harmonic]]s. The equal temperament [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; [[3136/3125]], [[5120/5103]], and 118098/117649 in the 7-limit.

Since {{nowrap|210 {{=}} 3 × 70}}, 210edo shares its [[3/2|fifth]] with [[70edo]]. It is [[consistent]] to the [[9-odd-limit]], but there is a sharp tendency in the lower [[harmonic]]s. The equal temperament [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; [[3136/3125]], [[5120/5103]], and 118098/117649 in the 7-limit.

Using the 210e val, which does the best, it tempers out [[540/539]], [[4000/3993]], 6912/6875, and 15488/15435 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], [[2197/2187]], and 3584/3575 in the 13-limit. Using the patent val, it tempers out [[176/175]], 1375/1372, [[8019/8000]], and 41503/41472 in the 11-limit; [[351/350]], [[352/351]], [[847/845]], 2197/2187, and 16900/16807 in the 13-limit.

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| [[Countdown]] (210e)

|}

<nowiki />* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

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 {{Infobox ET}}
-{{EDO intro|210}}
+{{ED intro}}
 == Theory ==
-Since {{nowrap|210 {{=}} 3 &times; 70}}, 210edo shares its [[3/2|fifth]] with [[70edo]]. It is [[consistent]] to the [[9-odd-limit]], but there is a sharp tendency in the lower [[harmonic]]s. The equal temperament [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; [[3136/3125]], [[5120/5103]], and 118098/117649 in the 7-limit.
+Since {{nowrap|210 {{=}} 3 × 70}}, 210edo shares its [[3/2|fifth]] with [[70edo]]. It is [[consistent]] to the [[9-odd-limit]], but there is a sharp tendency in the lower [[harmonic]]s. The equal temperament [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; [[3136/3125]], [[5120/5103]], and 118098/117649 in the 7-limit.
 Using the 210e val, which does the best, it tempers out [[540/539]], [[4000/3993]], 6912/6875, and 15488/15435 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], [[2197/2187]], and 3584/3575 in the 13-limit. Using the patent val, it tempers out [[176/175]], 1375/1372, [[8019/8000]], and 41503/41472 in the 11-limit; [[351/350]], [[352/351]], [[847/845]], 2197/2187, and 16900/16807 in the 13-limit.
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 | [[Countdown]] (210e)
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct