186ed6: Difference between revisions

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'''[[Ed6|Division of the sixth harmonic]] into 186 equal parts''' (186ED6) is related to [[72edo|72 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the 18-[[integer-limit]], and significantly improves on 72edo's approximation to 13.

~~Lookalikes:~~ [[72edo]], [[~~114edt~~]]

== 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]]. 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 ===

{{Harmonics in equal|186|6|1|intervals=~~prime~~|~~collapsed~~=1|start=12}}

{{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 }}.

~~{{stub}}~~

== See also ==

[[~~Category:Edonoi~~]]

* [[72edo]] – relative edo

* [[114edt]] – relative edt

* [[258ed12]] – relative ed12

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 {{Infobox ET}}
-'''[[Ed6|Division of the sixth harmonic]] into 186 equal parts''' (186ED6) is related to [[72edo|72 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the 18-[[integer-limit]], and significantly improves on 72edo's approximation to 13.
+{{ED intro}}
-Lookalikes: [[72edo]], [[114edt]]
+== 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]]. 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 ===
-{{Harmonics in equal|186|6|1|intervals=prime}}
+{{Harmonics in equal|186|6|1|intervals=integer|columns=11}}
-{{Harmonics in equal|186|6|1|intervals=prime|collapsed=1|start=12}}
+{{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 }}.
-{{stub}}
+== See also ==
-[[Category:Edonoi]]
+* [[72edo]] – relative edo
+* [[114edt]] – relative edt
+* [[258ed12]] – relative ed12