161edo: Difference between revisions

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The '''161 equal ~~division~~''' ~~divides~~ the ~~octave into~~ 161 equal ~~parts of 7.453 cents each. It tempers out the~~ [[~~Würschmidt comma~~]], ~~393216/390625, in~~ the ~~5-limit;~~ [[~~3136/3125~~]], [[~~6144/6125~~]] ~~and [[2401/2400]] in the~~ 7~~-limit; [[243/242]], [[441/440]], [[540/539]] and 5632/5625 in the 11-limit; and [[1188/1183]], [[351/350]], [[847/845]], [[1575/1573]], [[1001/1000]] and [[1716/1715]] in the 13-limit~~. ~~It serves as the~~ [[~~optimal patent val~~]] ~~for the [[mintone]] temperament in the 5-, 7-, 11- and 13-limits~~.

{{Infobox ET

| Prime factorization = 7 × 23

| Step size = 7.45324¢

| Fifth = 94\161 (700.62¢)

| Semitones = 14:13 (104.35¢ : 96.89)

| Consistency = 7

}}

The '''161 equal divisions of the octave''' ('''161edo'''), or the '''161(-tone) equal temperament''' ('''161tet''', '''161et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 161 [[equal]] parts of about 7.45 [[cent]]s each.

== Prime harmonics ==

== Theory ==

161edo tempers out the [[Würschmidt comma]], 393216/390625, in the 5-limit; [[3136/3125]], [[6144/6125]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]] and 5632/5625 in the 11-limit; and [[1188/1183]], [[351/350]], [[847/845]], [[1575/1573]], [[1001/1000]] and [[1716/1715]] in the 13-limit. It serves as the [[optimal patent val]] for the [[mintone]] temperament in the 5-, 7-, 11- and 13-limits.

=== Prime harmonics ===

161edo is notable as being low in [[29-limit]] relative error in the 100 to 200 range.

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-The '''161 equal division''' divides the octave into 161 equal parts of 7.453 cents each. It tempers out the [[Würschmidt comma]], 393216/390625, in the 5-limit; [[3136/3125]], [[6144/6125]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]] and 5632/5625 in the 11-limit; and [[1188/1183]], [[351/350]], [[847/845]], [[1575/1573]], [[1001/1000]] and [[1716/1715]] in the 13-limit. It serves as the [[optimal patent val]] for the [[mintone]] temperament in the 5-, 7-, 11- and 13-limits.
+{{Infobox ET
+| Prime factorization = 7 × 23
+| Step size = 7.45324¢
+| Fifth = 94\161 (700.62¢)
+| Semitones = 14:13 (104.35¢ : 96.89)
+| Consistency = 7
+}}
+The '''161 equal divisions of the octave''' ('''161edo'''), or the '''161(-tone) equal temperament''' ('''161tet''', '''161et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 161 [[equal]] parts of about 7.45 [[cent]]s each.
-== Prime harmonics ==
+== Theory ==
+edo tempers out the [[Würschmidt comma]], 393216/390625, in the 5-limit; [[3136/3125]], [[6144/6125]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]] and 5632/5625 in the 11-limit; and [[1188/1183]], [[351/350]], [[847/845]], [[1575/1573]], [[1001/1000]] and [[1716/1715]] in the 13-limit. It serves as the [[optimal patent val]] for the [[mintone]] temperament in the 5-, 7-, 11- and 13-limits.
+=== Prime harmonics ===
 edo is notable as being low in [[29-limit]] relative error in the 100 to 200 range.
 {{Harmonics in equal|161}}