27edo: Difference between revisions
Contribution (talk | contribs) Note that 97ed12 gives a poorer approximation of the local zeta peak than 70ed6, 76ed7, or 90ed10. |
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=== Octave stretch === | === Octave stretch === | ||
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, and 2.55{{c}}, respectively. | 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]]<ref group="note">Note that [[97ed12]] gives a poorer approximation of the local zeta peak than [[70ed6]], [[76ed7]], or [[90ed10]].</ref> are good options if octave compression is acceptable, and these narrow the octaves by 5.75, 3.53, and 2.55{{c}}, respectively. | ||
=== Subsets and supersets === | === Subsets and supersets === | ||