181edo: Difference between revisions

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'''181edo''' is the [[EDO|equal division of the octave]] into 181 parts of 6.~~6298 cents~~ each.

{{Infobox ET

| Prime factorization = 181 (prime)

| Step size = 6.62983¢

| Fifth = 106\181 (702.76¢)

| Semitones = 18:13 (119.34¢ : 86.19¢)

| Consistency = 7

}}

The '''181 equal divisions of the octave''' ('''181edo'''), or the '''181(-tone) equal temperament''' ('''181tet''', '''181et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 181 parts of about 6.63 [[cent]]s each.

== Theory ==

181et tempers out 2109375/2097152 ([[semicomma]]) and ~~32000000000/31381059609~~ in the 5-limit; [[2401/2400]], [[5120/5103]], and 390625/387072 in the 7-limit (supporting the [[hemififths]] and the [[cotritone]]). Using the patent val, it tempers out [[385/384]], 1375/1372, [[2200/~~2197]]~~, and [[4000/3993]] in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1575/1573]] in the 13-limit.

181et tempers out 2109375/2097152 ([[semicomma]]) and {{monzo| 14 -22 9 }} in the 5-limit; [[2401/2400]], [[5120/5103]], and 390625/387072 in the 7-limit (supporting the [[hemififths]] and the [[cotritone]]). Using the patent val, it tempers out [[385/384]], 1375/1372, 2200/2187, and [[4000/3993]] in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1575/1573]] in the 13-limit.

181edo is the 42nd [[prime ~~EDO~~]].

181edo is the 42nd [[prime edo]].

=== Prime harmonics ===

@@ Line 1: / Line 1: @@
-'''181edo''' is the [[EDO|equal division of the octave]] into 181 parts of 6.6298 cents each.
+{{Infobox ET
+| Prime factorization = 181 (prime)
+| Step size = 6.62983¢
+| Fifth = 106\181 (702.76¢)
+| Semitones = 18:13 (119.34¢ : 86.19¢)
+| Consistency = 7
+}}
+The '''181 equal divisions of the octave''' ('''181edo'''), or the '''181(-tone) equal temperament''' ('''181tet''', '''181et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 181 parts of about 6.63 [[cent]]s each.
 == Theory ==
-et tempers out 2109375/2097152 ([[semicomma]]) and 32000000000/31381059609 in the 5-limit; [[2401/2400]], [[5120/5103]], and 390625/387072 in the 7-limit (supporting the [[hemififths]] and the [[cotritone]]). Using the patent val, it tempers out [[385/384]], 1375/1372, [[2200/2197]], and [[4000/3993]] in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1575/1573]] in the 13-limit.
+et tempers out 2109375/2097152 ([[semicomma]]) and {{monzo| 14 -22 9 }} in the 5-limit; [[2401/2400]], [[5120/5103]], and 390625/387072 in the 7-limit (supporting the [[hemififths]] and the [[cotritone]]). Using the patent val, it tempers out [[385/384]], 1375/1372, 2200/2187, and [[4000/3993]] in the 11-limit; [[325/324]], [[352/351]], [[847/845]], and [[1575/1573]] in the 13-limit.
-edo is the 42nd [[prime EDO]].
+edo is the 42nd [[prime edo]].
 === Prime harmonics ===