186ed6: Difference between revisions

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== Theory ==

186ed6 is closely related to [[72edo]], but with the 6th harmonic rather than the [[~~2/1|~~octave]] being just, which results in the octaves being stretched by about 0.757{{c}}. Like 72edo, 186ed6 is [[consistent]] to the [[integer limit|18-integer-limit]], and significantly ~~improves on~~ 72edo~~'s approximation to 13~~.

186ed6 is closely related to [[72edo]], but with the 6th harmonic rather than the [[octave]] being just, which results in the octaves being stretched by about 0.757{{c}}. Like 72edo, 186ed6 is [[consistent]] to the [[integer limit|18-integer-limit]]. While it tunes 2 and [[11/1|11]] sharp, the [[3/1|3]] and [[5/1|5]] remain flat as in 72edo but less so, and the [[7/1|7]] is practically pure. Moreover, the [[13/1|13]] and [[17/1|17]] are significantly improved compared to 72edo, although the [[19/1|19]] becomes worse.

=== Harmonics ===

{{Harmonics in equal|186|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 186ed6 (continued)}}

=== Subsets and supersets ===

Since 186 factors into primes as {{nowrap| 2 × 3 × 31 }}, 186ed6 contains subset ed6's {{EDs|equave=6| 2, 3, 6, 31, 62, and 93 }}.

== See also ==

* [[72edo]] – relative edo

* [[114edt]] – relative edt

* [[258ed12]] – relative ed12

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 == Theory ==
-ed6 is closely related to [[72edo]], but with the 6th harmonic rather than the [[2/1|octave]] being just, which results in the octaves being stretched by about 0.757{{c}}. Like 72edo, 186ed6 is [[consistent]] to the [[integer limit|18-integer-limit]], and significantly improves on 72edo's approximation to 13.
+ed6 is closely related to [[72edo]], but with the 6th harmonic rather than the [[octave]] being just, which results in the octaves being stretched by about 0.757{{c}}. Like 72edo, 186ed6 is [[consistent]] to the [[integer limit|18-integer-limit]]. While it tunes 2 and [[11/1|11]] sharp, the [[3/1|3]] and [[5/1|5]] remain flat as in 72edo but less so, and the [[7/1|7]] is practically pure. Moreover, the [[13/1|13]] and [[17/1|17]] are significantly improved compared to 72edo, although the [[19/1|19]] becomes worse.
 === Harmonics ===
 {{Harmonics in equal|186|6|1|intervals=integer|columns=11}}
 {{Harmonics in equal|186|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 186ed6 (continued)}}
+=== Subsets and supersets ===
+Since 186 factors into primes as {{nowrap| 2 × 3 × 31 }}, 186ed6 contains subset ed6's {{EDs|equave=6| 2, 3, 6, 31, 62, and 93 }}.
 == See also ==
 * [[72edo]] – relative edo
 * [[114edt]] – relative edt
+* [[258ed12]] – relative ed12