44ed6: Difference between revisions

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~~'''~~44ed6~~''' divides the perfect nineteenth (6:1 ratio) into 44 equal tones of 70.499 [[cents]] each. It~~ is closely related to [[17edo]] and [[27edt]], and like them is an excellent [[No-fives subgroup temperaments|no-~~fives~~]] ~~tuning in the~~ [[13 ~~odd~~ limit]]. It also has good matches for the 23rd and 25th ~~harmonics~~. Like 27edt, its [[~~octave~~]]s are slightly flat, albeit less so. The octave of 44ed6 is 1198.48 cents: about a cent and a half flat. The ~~third harmonic (~~[[~~tritave~~]]) is sharp by the same amount, while the 7th, 11th, and 13th harmonics are all sharp by 15, 8, and 0.9 cents, respectively.

== Theory ==

44ed6 is closely related to [[17edo]] and [[27edt]], and like them is an excellent [[no-fives subgroup temperaments|no-5]] [[13-limit]] tuning. It also has good matches for the [[23/1|23rd]] and [[25/1|25th]] [[harmonic]]s. Like 27edt, its [[2/1|octaves]] are slightly flat, albeit less so. The octave of 44ed6 is 1198.48 cents: about a cent and a half flat. The [[3/1|3rd harmonic]] is sharp by the same amount, while the [[7/1|7th]], [[11/1|11th]], and [[13/1|13th harmonics]] are all sharp by 15.1, 8.1, and 0.9 cents, respectively.

=== Harmonics ===

{{Harmonics in equal|44|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 44ed6 (continued)}}

=== Subsets and supersets ===

Since 44 factors into primes as {{nowrap| 2<sup>2</sup> × 11 }}, 44ed6 has subset ed6's {{EDs|equave=6| 2, 4, 11, and 22 }}.

== Intervals ==

== ~~Harmonics~~ ==

== See also ==

~~{{Harmonics in equal~~

* [[10edf]] – relative edf

~~| steps = 44~~

* [[17edo]] – relative edo

~~| num = 6~~

* [[27edt]] – relative edt

~~| denom = 1~~

}}

~~{{Harmonics in equal~~

~~| steps = 44~~

~~| num = 6~~

~~| denom = 1~~

~~| start = 12~~

~~| collapsed = 1~~

}}

[[~~Category:17edo~~]]

[[~~Category:27edt~~]]

[[~~Category:Ed6~~]]

~~{{todo|expand}}~~

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 {{Infobox ET}}
-'''44ed6''' divides the perfect nineteenth (6:1 ratio) into 44 equal tones of 70.499 [[cents]] each. It is closely related to [[17edo]] and [[27edt]], and like them is an excellent [[No-fives subgroup temperaments|no-fives]] tuning in the [[13 odd limit]]. It also has good matches for the 23rd and 25th harmonics. Like 27edt, its [[octave]]s are slightly flat, albeit less so. The octave of 44ed6 is 1198.48 cents: about a cent and a half flat. The third harmonic ([[tritave]]) is sharp by the same amount, while the 7th, 11th, and 13th harmonics are all sharp by 15, 8, and 0.9 cents, respectively.
+{{ED intro}}
+== Theory ==
+ed6 is closely related to [[17edo]] and [[27edt]], and like them is an excellent [[no-fives subgroup temperaments|no-5]] [[13-limit]] tuning. It also has good matches for the [[23/1|23rd]] and [[25/1|25th]] [[harmonic]]s. Like 27edt, its [[2/1|octaves]] are slightly flat, albeit less so. The octave of 44ed6 is 1198.48 cents: about a cent and a half flat. The [[3/1|3rd harmonic]] is sharp by the same amount, while the [[7/1|7th]], [[11/1|11th]], and [[13/1|13th harmonics]] are all sharp by 15.1, 8.1, and 0.9 cents, respectively.
+=== Harmonics ===
+{{Harmonics in equal|44|6|1|intervals=integer|columns=11}}
+{{Harmonics in equal|44|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 44ed6 (continued)}}
+=== Subsets and supersets ===
+Since 44 factors into primes as {{nowrap| 2<sup>2</sup> × 11 }}, 44ed6 has subset ed6's {{EDs|equave=6| 2, 4, 11, and 22 }}.
 == Intervals ==
 {{Interval table}}
-== Harmonics ==
+== See also ==
-{{Harmonics in equal
+* [[10edf]] – relative edf
-| steps = 44
+* [[17edo]] – relative edo
-| num = 6
+* [[27edt]] – relative edt
-| denom = 1
-}}
-{{Harmonics in equal
-| steps = 44
-| num = 6
-| denom = 1
-| start = 12
-| collapsed = 1
-}}
-[[Category:17edo]]
-[[Category:27edt]]
-[[Category:Ed6]]
-{{todo|expand}}