428edt: Difference between revisions

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== Theory ==

428edt is related to [[270edo]], but with the [[3/1|twelfth]] rather than the [[2/1|octave]] being just. The octave is about 0.169 cents compressed. 428edt is [[consistent]] to the [[integer limit|22-integer-limit]]; in comparison, 270edo is only consistent up to the 16-integer-limit. It fixes 270edo's inconsistently mapped [[17/13]], which is 270edo's only inconsistently mapped interval in the [[21-odd-limit]]. However, this comes at the cost of a flat-tending tuning profile, with [[harmonic]]s 1–22 all tuned flat except for [[17/1|17]].

428edt is related to [[270edo]], but with the [[3/1|twelfth]] rather than the [[2/1|octave]] being just. The octave is about 0.169 cents compressed. 428edt is [[consistent]] to the [[integer limit|22-integer-limit]]; in comparison, 270edo is only consistent up to the 16-integer-limit. It fixes 270edo's inconsistently mapped [[17/13]], which is 270edo's only inconsistently mapped interval in the [[21-odd-limit]]. However, this comes at the cost of a flat-tending tuning profile, with [[harmonic]]s 1–22 all tuned flat except for [[17/1|17]] and perfect powers of 3.

=== Harmonics ===

{{Harmonics in equal|428|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 428edt (continued)}}

=== Subsets and supersets ===

Since 428 factors into primes as {{nowrap| 2<sup>2</sup> × 107 }}, 428edt has subset edts {{EDTs| 2, 4, 107, and 214 }}.

== See also ==

* [[270edo]] – relative edo

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 == Theory ==
-edt is related to [[270edo]], but with the [[3/1|twelfth]] rather than the [[2/1|octave]] being just. The octave is about 0.169 cents compressed. 428edt is [[consistent]] to the [[integer limit|22-integer-limit]]; in comparison, 270edo is only consistent up to the 16-integer-limit. It fixes 270edo's inconsistently mapped [[17/13]], which is 270edo's only inconsistently mapped interval in the [[21-odd-limit]]. However, this comes at the cost of a flat-tending tuning profile, with [[harmonic]]s 1–22 all tuned flat except for [[17/1|17]].
+edt is related to [[270edo]], but with the [[3/1|twelfth]] rather than the [[2/1|octave]] being just. The octave is about 0.169 cents compressed. 428edt is [[consistent]] to the [[integer limit|22-integer-limit]]; in comparison, 270edo is only consistent up to the 16-integer-limit. It fixes 270edo's inconsistently mapped [[17/13]], which is 270edo's only inconsistently mapped interval in the [[21-odd-limit]]. However, this comes at the cost of a flat-tending tuning profile, with [[harmonic]]s 1–22 all tuned flat except for [[17/1|17]] and perfect powers of 3.
 === Harmonics ===
 {{Harmonics in equal|428|3|1|columns=11}}
 {{Harmonics in equal|428|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 428edt (continued)}}
+=== Subsets and supersets ===
+Since 428 factors into primes as {{nowrap| 2<sup>2</sup> × 107 }}, 428edt has subset edts {{EDTs| 2, 4, 107, and 214 }}.
 == See also ==
 * [[270edo]] – relative edo