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 ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~Stretch~~ (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

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=== Rank-2 temperaments ===

{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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|-

| 2

| 167\402 (34\402)

| 167\402 (34\402)

| 498.51 (101.49)

| 498.51 (101.49)

| 4/3 (200/189)

| 4/3 (200/189)

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

|}

<nowiki>*~~</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 ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
@@ Line 48: / Line 49: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 74: / Line 76: @@
 |-
 | 2
-| 167\402<br>(34\402)
+| 167\402<br />(34\402)
-| 498.51<br>(101.49)
+| 498.51<br />(101.49)
-| 4/3<br>(200/189)
+| 4/3<br />(200/189)
 | [[Bischismic]] (402c, 7-limit)
 |}
-<nowiki>*</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