31edo: Difference between revisions
→Notation: Stein–Zimmermann is an instance of neutral chain-of-fifths notation |
→Theory: +octave stretch; some additions to subsets and supersets |
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{{Harmonics in equal|31|columns=9}} | {{Harmonics in equal|31|columns=9}} | ||
{{Harmonics in equal|31|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 31edo (continued)}} | {{Harmonics in equal|31|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 31edo (continued)}} | ||
=== Octave stretch === | |||
31edo can benefit from slightly [[stretched and compressed tuning|stretching the octave]] especially when using it as an 11-limit equal temperament. With the right amount of stretch we can find a slightly better 3rd harmonic and more importantly a way better 11th harmonic at the expense of somewhat less accurate 5th and 7th harmonics. Tunings such as [[80ed6]] and [[111ed12]] are great demonstrations of this. | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
31edo is the 11th [[prime edo]], following [[29edo]] and coming before [[37edo]]. | 31edo is the 11th [[prime edo]], following [[29edo]] and coming before [[37edo]]. It does not contain any nontrivial subset edos, though it contains [[31ed4]]. [[62edo]], which doubles it, provides an alternative way to extend the temperament to the 13- and 17- and 19-limit. | ||
== Intervals == | == Intervals == | ||