106ed6: Difference between revisions

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== Theory ==

106ed6 is very nearly identical to [[41edo]], but with the ~~6/1~~ rather than the [[2/1]] being just. The octave is about 0.19 cents compressed. Like 41edo, 106ed6 is consistent to the [[integer limit|16-integer-limit]].

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.

=== 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 ==

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* [[65edt]] – relative edt

* [[95ed5]] – relative ed5

* [[147ed12]] – relative ed12

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

[[Category:41edo]]

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 == Theory ==
-ed6 is very nearly identical to [[41edo]], but with the 6/1 rather than the [[2/1]] being just. The octave is about 0.19 cents compressed. Like 41edo, 106ed6 is consistent to the [[integer limit|16-integer-limit]].
+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.
 === 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 ==
@@ Line 14: / Line 17: @@
 * [[65edt]] – relative edt
 * [[95ed5]] – relative ed5
+* [[147ed12]] – relative ed12
+* [[361ed448]] – close to the zeta-optimized tuning for 41edo
+[[Category:41edo]]