87edo: Difference between revisions

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== Theory ==

87edo is solid as both a [[13-limit]] (or [[15-odd-limit]]) and as a [[5-limit]] system, and does well enough in any limit in between. It is the smallest edo that is distinctly [[consistent]] in the [[13-odd-limit]] [[tonality diamond]], the smallest edo that is [[purely consistent]] in the 15-odd-limit, and also the smallest edo with [[relative interval error]]s of no greater than 25% on all of the first 16 harmonics of the [[harmonic series]]. It is also a [[zeta peak integer edo]].

87edo is solid as both a [[13-limit]] (or [[15-odd-limit]]) and as a [[5-limit]] system, and does well enough in any limit in between. It is the smallest edo that is distinctly [[consistent]] in the [[13-odd-limit]] [[tonality diamond]], the smallest edo that is [[purely consistent]]{{idiosyncratic}} in the 15-odd-limit, and also the smallest edo with [[relative interval error]]s of no greater than 25% on all of the first 16 harmonics of the [[harmonic series]]. It is also a [[zeta peak integer edo]].

87edo also shows some potential in limits beyond 13. The next four prime harmonics [[17/1|17]], [[19/1|19]], [[23/1|23]] and [[29/1|29]] are all near-critically sharp, but the feature of it is that the overtones and undertones are distinct, and most intervals are usable as long as they do not combine with [[7/1|7]], which is flat. Actually, as a no-sevens system, it is consistent in the 33-odd-limit.

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 == Theory ==
-edo is solid as both a [[13-limit]] (or [[15-odd-limit]]) and as a [[5-limit]] system, and does well enough in any limit in between. It is the smallest edo that is distinctly [[consistent]] in the [[13-odd-limit]] [[tonality diamond]], the smallest edo that is [[purely consistent]] in the 15-odd-limit, and also the smallest edo with [[relative interval error]]s of no greater than 25% on all of the first 16 harmonics of the [[harmonic series]]. It is also a [[zeta peak integer edo]].
+edo is solid as both a [[13-limit]] (or [[15-odd-limit]]) and as a [[5-limit]] system, and does well enough in any limit in between. It is the smallest edo that is distinctly [[consistent]] in the [[13-odd-limit]] [[tonality diamond]], the smallest edo that is [[purely consistent]]{{idiosyncratic}} in the 15-odd-limit, and also the smallest edo with [[relative interval error]]s of no greater than 25% on all of the first 16 harmonics of the [[harmonic series]]. It is also a [[zeta peak integer edo]].
 edo also shows some potential in limits beyond 13. The next four prime harmonics [[17/1|17]], [[19/1|19]], [[23/1|23]] and [[29/1|29]] are all near-critically sharp, but the feature of it is that the overtones and undertones are distinct, and most intervals are usable as long as they do not combine with [[7/1|7]], which is flat. Actually, as a no-sevens system, it is consistent in the 33-odd-limit.