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.
+{{Infobox ET}}
+{{ED intro}}
-== Division of 6/1 into 31 equal parts ==
+== Theory ==
+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.
-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]].
+=== Harmonics ===
+{{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 ==
+* [[7edf]] – relative edf
+* [[12edo]] – relative edo
+* [[19ed3]] – relative ed3
+* [[28ed5]] – relative ed5
+* [[34ed7]] – relative ed7
+* [[40ed10]] – relative ed10
+* [[43ed12]] – relative ed12
+* [[76ed80]] – close to the zeta-optimized tuning for 12edo
+* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]
-* [[12edo]]: relative EDO
+[[Category:12edo]]
-* [[19ed3]]: relative ED3
-* [[28ed5]]: relative ED5
-* [[34ed7]]: relative ED7
-* [[40ed10]]: relative ED10
-[[Category:Ed6]]
-[[Category:edonoi]]
-[[category:macrotonal]]