125edo: Difference between revisions
→Regular temperament properties: cleanup and update |
→Theory: +octave stretch |
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|125}} | {{Harmonics in equal|125}} | ||
=== Octave stretch === | |||
125edo's approximated harmonics 3, 5, and 13 can be improved, and moreover the approximated harmonic 11 can be brought to consistency, by slightly [[stretched and compressed tuning|stretching the octave]], though it comes at the expense of somewhat less accurate approximations of 7, 17, and 19. Tunings such as [[198edt]] and [[323ed6]] are great demonstrations of this. | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 125 factors into | Since 125 factors into primes as 5<sup>3</sup>, 125edo contains [[5edo]] and [[25edo]] as subset edos. Being the cube closest to division of the octave by the Germanic {{w|long hundred}}, 125edo has a unit step which is the cubic (fine) relative cent of [[1edo]]. Using every 9th step, or [[1ed86.4c]] still encapsulates many of its best-tuned harmonics. | ||
== Regular temperament properties == | == Regular temperament properties == | ||