402edo: Difference between revisions

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== Theory ==

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* {{val| 402 637 '''934''' 1129 }} (402c)

Using the patent val, it tempers out the [[semicomma]] in the 5-limit; [[4375/4374]], 7381125/7340032 and 3200000/3176523 in the 7-limit~~. It~~ [[support]]s [[~~abigail~~]].

Using the patent val, it tempers out the [[semicomma]] in the 5-limit and [[4375/4374]], 7381125/7340032, and 3200000/3176523 in the 7-limit, [[support]]ing [[Abigail]].

Using the 402d val, it tempers out [[250047/250000]], 1500625/1492992 and 2460375/2458624 in the 7-limit.

Using the 402d val, it tempers out [[250047/250000]], and 1500625/1492992 and 2460375/2458624 in the 7-limit.

Using the 402c val, it tempers out the [[schisma]] in the 5-limit; and [[3136/3125]], 321489/320000 and 13060694016/12867859375 in the 7-limit~~. It supports~~ [[bischismic]].

Using the 402c val, it tempers out the [[schisma]] in the 5-limit; and [[3136/3125]], 321489/320000, and 13060694016/12867859375 in the 7-limit, supporting [[bischismic]].

=== Odd harmonics ===

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=== Subsets and supersets ===

Since 402 factors into 2 × 3 × 67, 402edo has subset edos {{EDOs| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the harmonics 5 and 7.

Since 402 factors into {{nowrap|2 × 3 × 67}}, 402edo has subset edos {{EDOs| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the harmonics 5 and 7.

== Regular temperament properties ==

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| [[Bischismic]] (402c, 7-limit)

|}

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

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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|402}}
+{{ED intro}}
 == Theory ==
@@ Line 8: / Line 8: @@
 * {{val| 402 637 '''934''' 1129 }} (402c)
-Using the patent val, it tempers out the [[semicomma]] in the 5-limit; [[4375/4374]], 7381125/7340032 and 3200000/3176523 in the 7-limit. It [[support]]s [[abigail]].
+Using the patent val, it tempers out the [[semicomma]] in the 5-limit and [[4375/4374]], 7381125/7340032, and 3200000/3176523 in the 7-limit, [[support]]ing [[Abigail]].
-Using the 402d val, it tempers out [[250047/250000]], 1500625/1492992 and 2460375/2458624 in the 7-limit.
+Using the 402d val, it tempers out [[250047/250000]], and 1500625/1492992 and 2460375/2458624 in the 7-limit.
-Using the 402c val, it tempers out the [[schisma]] in the 5-limit; and [[3136/3125]], 321489/320000 and 13060694016/12867859375 in the 7-limit. It supports [[bischismic]].
+Using the 402c val, it tempers out the [[schisma]] in the 5-limit; and [[3136/3125]], 321489/320000, and 13060694016/12867859375 in the 7-limit, supporting [[bischismic]].
 === Odd harmonics ===
@@ Line 18: / Line 18: @@
 === Subsets and supersets ===
-Since 402 factors into 2 × 3 × 67, 402edo has subset edos {{EDOs| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the harmonics 5 and 7.
+Since 402 factors into {{nowrap|2 × 3 × 67}}, 402edo has subset edos {{EDOs| 2, 3, 6, 67, 134, and 201 }}. [[804edo]], which doubles it, gives a good correction to the harmonics 5 and 7.
 == Regular temperament properties ==
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 | [[Bischismic]] (402c, 7-limit)
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct