125edo: Difference between revisions
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+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 === | ||
Revision as of 07:59, 5 July 2021
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 long hundred, 125edo has a unit step which is the cubic (fine) relative cent of 1edo.
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 and 540/539 in the 11-limit. In the 13-limit the 125f 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
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Regular temperament properties
| Periods per octave |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 4\125 | 38.4 | 49/48 | Slender |
| 1 | 19\125 | 182.4 | 10/9 | Mitonic |
| 1 | 24\125 | 230.4 | 8/7 | Gamera |
| 1 | 33\125 | 316.8 | 6/5 | Hanson / catakleismic |
| 1 | 52\125 | 499.2 | 4/3 | Gracecordial |
| 1 | 61\125 | 585.6 | 7/5 | Merman |