125edo: Difference between revisions
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m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot |
+prime error table, +temperament section |
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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. | ||
== 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]] 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:Equal divisions of the octave]] | ||
[[Category: | [[Category:Theory]] | ||
[[Category:Catakleismic]] | |||
Revision as of 07:54, 5 July 2021
The 125 equal temperament divides the octave into 125 equal parts of exactly 9.6 cents each.
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 in the 11-limit; and 275/273 in the 13-limit. Being the cube closest to division of the octave by the Germanic long hundred, it has a unit step which is the cubic (fine) relative cent of 1edo.
Prime harmonics
Script error: No such module "primes_in_edo".
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 |