31ed6: Difference between revisions

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'''[[Ed6|Division of the sixth harmonic]] into 31 equal parts''' (31ED6) is very nearly identical to [[12edo|12 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 0.7568 [[cent]]s stretched and the step size is about 100.0631 cents.

==~~Harmonics~~==

== Theory ==

~~{{Harmonics in equal|31|~~6|1~~|prec=~~2~~|columns=15}}~~

31ed6 is not a true xenharmonic tuning; it is a slightly stretched version (with an octave of 1200.8 cents) of the normal [[12edo]], similar to [[19ed3]]. It is very nearly identical to [[12edo]], but with the [[6/1]] rather than the 2/1 being just.

== ~~Division of~~ 6/1 ~~into~~ 31 ~~equal parts~~ ==

=== Harmonics ===

~~Note: 31 equal divisions~~ of ~~the hexatave is not a "real" xenharmonic tuning; it is a slightly stretched version~~ (~~with an octave of 1200.8 cents~~) of the ~~normal~~ [[~~12edo~~|~~12-tone scale~~]], ~~similar to~~ [[~~19ed3|19ED3~~]].

{{Harmonics in equal|31|6|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 31ed6 (continued)}}

=== Subsets and supersets ===

31ed6 is the 11th [[prime equal division|prime ed6]], following [[29ed6]] and before [[37ed6]].

== See also ==

* [[12edo~~|12EDO~~]] ~~–~~ relative ~~EDO~~

* [[7edf]] – relative edf

* [[19ed3~~|19ED3~~]] ~~–~~ relative ~~ED3~~

* [[12edo]] – relative edo

* [[28ed5~~|28ED5~~]] ~~–~~ relative ~~ED5~~

* [[19ed3]] – relative ed3

* [[34ed7~~|34ED7~~]] ~~–~~ relative ~~ED7~~

* [[28ed5]] – relative ed5

* [[40ed10~~|40ED10~~]] ~~–~~ relative ~~ED10~~

* [[34ed7]] – relative ed7

* [[43ed12|~~43ED12~~]] ~~–~~ relative ~~ED12~~

* [[40ed10]] – relative ed10

* [[43ed12]] – relative ed12

* [[76ed80]] – close to the zeta-optimized tuning for 12edo

* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]

[[Category:~~Ed6]]~~

[[Category:12edo]]

~~[[Category:Edonoi]]~~

~~[[category:Macrotonal~~]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''[[Ed6|Division of the sixth harmonic]] into 31 equal parts''' (31ED6) is very nearly identical to [[12edo|12 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 0.7568 [[cent]]s stretched and the step size is about 100.0631 cents.
+{{ED intro}}
-==Harmonics==
+== Theory ==
-{{Harmonics in equal|31|6|1|prec=2|columns=15}}
+ed6 is not a true xenharmonic tuning; it is a slightly stretched version (with an octave of 1200.8 cents) of the normal [[12edo]], similar to [[19ed3]]. It is very nearly identical to [[12edo]], but with the [[6/1]] rather than the 2/1 being just.
-== Division of 6/1 into 31 equal parts ==
+=== Harmonics ===
-Note: 31 equal divisions of the hexatave is not a "real" xenharmonic tuning; it is a slightly stretched version (with an octave of 1200.8 cents) of the normal [[12edo|12-tone scale]], similar to [[19ed3|19ED3]].
+{{Harmonics in equal|31|6|1|columns=12}}
+{{Harmonics in equal|31|6|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 31ed6 (continued)}}
+=== Subsets and supersets ===
+ed6 is the 11th [[prime equal division|prime ed6]], following [[29ed6]] and before [[37ed6]].
 == See also ==
-* [[12edo|12EDO]] &ndash; relative EDO
+* [[7edf]] – relative edf
-* [[19ed3|19ED3]] &ndash; relative ED3
+* [[12edo]] – relative edo
-* [[28ed5|28ED5]] &ndash; relative ED5
+* [[19ed3]] – relative ed3
-* [[34ed7|34ED7]] &ndash; relative ED7
+* [[28ed5]] – relative ed5
-* [[40ed10|40ED10]] &ndash; relative ED10
+* [[34ed7]] – relative ed7
-* [[43ed12|43ED12]] &ndash; relative ED12
+* [[40ed10]] – relative ed10
+* [[43ed12]] – relative ed12
+* [[76ed80]] – close to the zeta-optimized tuning for 12edo
+* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]
-[[Category:Ed6]]
+[[Category:12edo]]
-[[Category:Edonoi]]
-[[category:Macrotonal]]