229edo: Difference between revisions

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The '''229 equal divisions of the octave''' ('''229edo'''), or the '''229(-tone) equal temperament''' ('''229tet''', '''229et'''), is the [[EDO|equal division of the octave]] into 229 parts of 5.~~2402~~ [[cent]]s each.

{{Infobox ET

| Prime factorization = 229 (prime)

| Step size = 5.24017¢

| Fifth = 134\229 (702.18¢)

| Semitones = 22:17 (115.28¢ : 89.08¢)

| Consistency = 11

}}

The '''229 equal divisions of the octave''' ('''229edo'''), or the '''229(-tone) equal temperament''' ('''229tet''', '''229et'''), is the [[EDO|equal division of the octave]] into 229 parts of about 5.24 [[cent]]s each.

== Theory ==

While not highly accurate for its size, 229et is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out 393216/390625 ([[würschmidt comma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, and using the [[patent val]], [[351/350]], [[2080/2079]], and [[4096/4095]] in the 13-limit, notably supporting [[hemiwürschmidt]], [[newt]], and [[trident]].

The 229b val supports a [[septimal meantone]] close to the [[CTE tuning]].

229edo is the 50th [[prime EDO]].

@@ Line 1: / Line 1: @@
-The '''229 equal divisions of the octave''' ('''229edo'''), or the '''229(-tone) equal temperament''' ('''229tet''', '''229et'''), is the [[EDO|equal division of the octave]] into 229 parts of 5.2402 [[cent]]s each.
+{{Infobox ET
+| Prime factorization = 229 (prime)
+| Step size = 5.24017¢
+| Fifth = 134\229 (702.18¢)
+| Semitones = 22:17 (115.28¢ : 89.08¢)
+| Consistency = 11
+}}
+The '''229 equal divisions of the octave''' ('''229edo'''), or the '''229(-tone) equal temperament''' ('''229tet''', '''229et'''), is the [[EDO|equal division of the octave]] into 229 parts of about 5.24 [[cent]]s each.
 == Theory ==
 While not highly accurate for its size, 229et is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out 393216/390625 ([[würschmidt comma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, and using the [[patent val]], [[351/350]], [[2080/2079]], and [[4096/4095]] in the 13-limit, notably supporting [[hemiwürschmidt]], [[newt]], and [[trident]].
+The 229b val supports a [[septimal meantone]] close to the [[CTE tuning]].
 edo is the 50th [[prime EDO]].