186ed6: Difference between revisions

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~~186ED6~~ is related to [[72edo~~|72 edo~~]], but with the ~~6/1~~ rather than the ~~2/1~~ being just, which results in the octaves being stretched by about 1.~~2347~~{{c}}. It is consistent to the 18-[[integer-limit]], and significantly ~~improves on~~ 72edo~~'s approximation to 13~~.

== Theory ==

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.

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

=== Harmonics ===

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

== ~~Harmonics~~ ==

=== 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 }}.

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

== See also ==

~~{{stub}}~~

* [[72edo]] – relative edo

[[~~Category:Edonoi~~]]

* [[114edt]] – relative edt

* [[258ed12]] – relative ed12

@@ Line 2: / Line 2: @@
 {{ED intro}}
-ED6 is related to [[72edo|72 edo]], but with the 6/1 rather than the 2/1 being just, which results in the octaves being stretched by about 1.2347{{c}}. It is consistent to the 18-[[integer-limit]], and significantly improves on 72edo's approximation to 13.
+== Theory ==
+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.
-Lookalikes: [[72edo]], [[114edt]]
+=== 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)}}
-== Harmonics ==
+=== Subsets and supersets ===
-{{Harmonics in equal|186|6|1|intervals=prime}}
+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 }}.
-{{Harmonics in equal|186|6|1|intervals=prime|collapsed=1|start=12}}
+== See also ==
-{{stub}}
+* [[72edo]] – relative edo
-[[Category:Edonoi]]
+* [[114edt]] – relative edt
+* [[258ed12]] – relative ed12