125edo: Difference between revisions
+prime error table, +temperament section |
Expansion on 13-limit interpretation |
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The '''125 equal temperament''' divides the octave into 125 equal parts of exactly 9.6 cents each. | The '''125 equal temperament''' divides the octave into 125 equal parts of exactly 9.6 cents each. Being the cube closest to division of the octave by the Germanic [[Wikipedia: Long hundred|long hundred]], 125edo has a unit step which is the cubic (fine) relative cent of [[1edo]]. | ||
== Theory == | == Theory == | ||
125edo defines the [[optimal patent val]] for 7- and 11-limit [[slender]] temperament. It tempers out [[15625/15552]] in the 5-limit; [[225/224]] and [[4375/4374]] in the 7-limit; [[385/384]] | 125edo defines the [[optimal patent val]] for 7- and 11-limit [[slender]] temperament. It tempers out [[15625/15552]] in the 5-limit; [[225/224]] and [[4375/4374]] in the 7-limit; [[385/384]] and [[540/539]] in the 11-limit. In the 13-limit the 125f val {{val| 125 198 290 351 432 462 }} does a better job, where it tempers out [[169/168]], [[325/324]], [[351/350]], [[625/624]] and [[676/675]], providing a good tuning for [[catakleismic]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||