106ed6: Difference between revisions

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'''[[ed6|Division of the sixth harmonic]] into 106 equal parts''' (106ED6) is related to [[41edo|41 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 0.19 cents compressed and the step size is about 29.26 cents. It is consistent to the [[15-odd-limit|16-integer-limit]].

~~Lookalikes:~~ [[~~24edf~~]], [[41edo]], [[~~65edt~~]], [[~~95ed5~~]]

== Theory ==

106ed6 is very nearly identical to [[41edo]], but with the 6th harmonic rather than the [[2/1|octave]] being just. The octave is about 0.187 cents compressed. Like 41edo, 106ed6 is [[consistent]] to the [[integer limit|16-integer-limit]], and in comparison, it slightly improves the intonation of primes 3, [[11/1|11]], [[13/1|13]], and [[17/1|17]] at the expense of barely less accurate intonations of 2, [[5/1|5]], [[7/1|7]], and [[19/1|19]], commending itself as a suitable tuning for [[13-limit|13-]] and [[17-limit]]-focused harmonies.

[[Category:~~Edonoi~~]]

=== Harmonics ===

{{Harmonics in equal|106|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 106ed6 (continued)}}

=== Subsets and supersets ===

Since 106 factors into primes as {{nowrap| 2 × 53 }}, 106ed6 contains [[2ed6]] and [[53ed6]] as subset ed6's.

== See also ==

* [[24edf]] – relative edf

* [[41edo]] – relative edo

* [[65edt]] – relative edt

* [[95ed5]] – relative ed5

* [[147ed12]] – relative ed12

* [[361ed448]] – close to the zeta-optimized tuning for 41edo

[[Category:41edo]]

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 {{Infobox ET}}
-'''[[ed6|Division of the sixth harmonic]] into 106 equal parts''' (106ED6) is related to [[41edo|41 edo]], but with the 6/1 rather than the 2/1 being just. The octave is about 0.19 cents compressed and the step size is about 29.26 cents. It is consistent to the [[15-odd-limit|16-integer-limit]].
+{{ED intro}}
-Lookalikes: [[24edf]], [[41edo]], [[65edt]], [[95ed5]]
+== Theory ==
+ed6 is very nearly identical to [[41edo]], but with the 6th harmonic rather than the [[2/1|octave]] being just. The octave is about 0.187 cents compressed. Like 41edo, 106ed6 is [[consistent]] to the [[integer limit|16-integer-limit]], and in comparison, it slightly improves the intonation of primes 3, [[11/1|11]], [[13/1|13]], and [[17/1|17]] at the expense of barely less accurate intonations of 2, [[5/1|5]], [[7/1|7]], and [[19/1|19]], commending itself as a suitable tuning for [[13-limit|13-]] and [[17-limit]]-focused harmonies.
-[[Category:Edonoi]]
+=== Harmonics ===
+{{Harmonics in equal|106|6|1|intervals=integer}}
+{{Harmonics in equal|106|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 106ed6 (continued)}}
+=== Subsets and supersets ===
+Since 106 factors into primes as {{nowrap| 2 × 53 }}, 106ed6 contains [[2ed6]] and [[53ed6]] as subset ed6's.
+== See also ==
+* [[24edf]] – relative edf
+* [[41edo]] – relative edo
+* [[65edt]] – relative edt
+* [[95ed5]] – relative ed5
+* [[147ed12]] – relative ed12
+* [[361ed448]] – close to the zeta-optimized tuning for 41edo
+[[Category:41edo]]