187edt: Difference between revisions

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== Theory ==

187edt is nearly identical to [[118edo]], but with the [[3/1|perfect twelfth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 0.164 cents. Like 118edo, 187edt is [[consistent]] to the [[integer limit|12-integer-limit]]. It preserves the 5-limit [[microtemperament|microtempering]] quality of 118edo, and the approximated [[prime harmonic]]s [[7/1|7]], [[11/1|11]], [[17/1|17]], and [[19/1|19]] are slighly improved.

=== Harmonics ===

{{Harmonics in equal|187|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 187edt (continued)}}

=== Subsets and supersets ===

Since 187 factors into primes as {{nowrap| 11 × 17 }}, 187edt contains [[11edt]] and [[17edt]] as subset edts.

== See also ==

* [[69edf]] – relative edf

* [[118edo]] – relative edo

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 {{Infobox ET}}
+{{ED intro}}
+== Theory ==
+edt is nearly identical to [[118edo]], but with the [[3/1|perfect twelfth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 0.164 cents. Like 118edo, 187edt is [[consistent]] to the [[integer limit|12-integer-limit]]. It preserves the 5-limit [[microtemperament|microtempering]] quality of 118edo, and the approximated [[prime harmonic]]s [[7/1|7]], [[11/1|11]], [[17/1|17]], and [[19/1|19]] are slighly improved.
+=== Harmonics ===
+{{Harmonics in equal|187|3|1|intervals=integer|columns=11}}
+{{Harmonics in equal|187|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 187edt (continued)}}
+=== Subsets and supersets ===
+Since 187 factors into primes as {{nowrap| 11 × 17 }}, 187edt contains [[11edt]] and [[17edt]] as subset edts.
+== See also ==
+* [[69edf]] – relative edf
+* [[118edo]] – relative edo