125edo: Difference between revisions

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-The ''125 equal temperament'' divides the octave into 125 equal parts of exactly 9.6 cents each. It defines the [[Optimal_patent_val|optimal patent val]] for 7- and 11-limit [[Marvel_temperaments|slender temperament]]. It tempers out 15625/15552 in the 5-limit; 225/224 and 4375/4374 in the 7-limit; 385/384 in the 11-limit; and 275/273 in the 13-limit. Being the cube closest to division of the octave by the Germanic [https://en.wikipedia.org/wiki/Long_hundred long hundred], it has a unit step which is the cubic (fine) relative cent of [[1edo]].
+The '''125 equal temperament''' divides the octave into 125 equal parts of exactly 9.6 cents each.
+== Theory ==
+edo 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]] in the 11-limit; and [[275/273]] in the 13-limit. Being the cube closest to division of the octave by the Germanic [[Wikipedia: Long hundred|long hundred]], it has a unit step which is the cubic (fine) relative cent of [[1edo]].
+=== Prime harmonics ===
+{{Primes in edo|125|prec=2}}
+== Regular temperament properties ==
+{| class="wikitable center-all left-5"
+|+Table of rank-2 temperaments by generator
+! Periods<br>per octave
+! Generator<br>(reduced)
+! Cents<br>(reduced)
+! Associated<br>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]]
+|}
 [[Category:Equal divisions of the octave]]
-[[Category:theory]]
+[[Category:Theory]]
+[[Category:Catakleismic]]