58edf: Difference between revisions

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'''[[EDF|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo|99 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). It is consistent to the [[11-odd-limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit|10-integer-limit]].

~~Lookalikes:~~ [[99edo]], [[~~157edt~~]]

== Theory ==

58edf corresponds to 99.1517…edo. It is related to [[99edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|compressed]] by about 1.84 cents. 58edf is [[consistent]] to the [[integer limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 58edf has a flat tendency, with [[prime harmonic]]s 2, [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] all tuned flat of just.

[[~~Category:Edf~~]]

=== Harmonics ===

[[~~Category:Edonoi~~]]

{{Harmonics in equal|58|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edf (continued)}}

=== Subsets and supersets ===

Since 58 factors into primes as {{nowrap| 2 × 29 }}, 58edf contains [[2edf]] and [[29edf]] as subset edts.

== See also ==

* [[99edo]] – relative edo

* [[157edt]] – relative edt

* [[256ed6]] – relative ed6

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-'''[[EDF|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo|99 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). It is consistent to the [[11-odd-limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit|10-integer-limit]].
+{{Infobox ET}}
+{{ED intro}}
-Lookalikes: [[99edo]], [[157edt]]
+== Theory ==
+edf corresponds to 99.1517…edo. It is related to [[99edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|compressed]] by about 1.84 cents. 58edf is [[consistent]] to the [[integer limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 58edf has a flat tendency, with [[prime harmonic]]s 2, [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] all tuned flat of just.
-[[Category:Edf]]
+=== Harmonics ===
-[[Category:Edonoi]]
+{{Harmonics in equal|58|3|2|intervals=integer|columns=11}}
+{{Harmonics in equal|58|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edf (continued)}}
+=== Subsets and supersets ===
+Since 58 factors into primes as {{nowrap| 2 × 29 }}, 58edf contains [[2edf]] and [[29edf]] as subset edts.
+== See also ==
+* [[99edo]] – relative edo
+* [[157edt]] – relative edt
+* [[256ed6]] – relative ed6