27edo: Difference between revisions

Octave compression: unify section titles
Octave stretch or compression: restore the entirety of the summary, which is helpful if the reader can't bother to check the data below
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== Octave stretch or compression ==
== Octave stretch or compression ==
Since the harmonics whose intervals it approximates well (3, 5, 7, 13, and 19) are all tuned sharp of just, 27edo is a prime candidate for [[stretched and compressed tuning|octave compression]]. Narrowing the steps to between 44.2 and 44.35{{c}} might be better in theory.
Since the harmonics whose intervals it approximates well (3, 5, 7, 13, and 19) are all tuned sharp of just, 27edo is a prime candidate for [[stretched and compressed tuning|octave compression]]. The local zeta peak around 27 is at 27.086614, which corresponds to a step size of 44.3023{{c}}. More generally, narrowing the steps to between 44.2 and 44.35{{c}} would be better in theory; [[43edt]], [[70ed6]], [[90ed10]], and [[97ed12]] are good options if octave compression is acceptable, and these narrow the octaves by 5.75, 3.53, 4.11, and 2.55{{c}}, respectively.


What follows is a comparison of compressed-octave 27edo tunings.
What follows is a comparison of compressed-octave 27edo tunings.