7edt: Difference between revisions

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~~'''7edt''' (short for '''7''' '''e'''qual '''d'''ivision of '''t'''ritave) divides the interval [[3/1]] it into 7 equal parts of 271.708 [[cent]]s each, corresponding to 4.4165 edo.~~

~~__FORCETOC__~~

== Theory ==

== ~~Properties~~ ==

Since one step of 7edt approximates a [[7/6]] subminor third (4.84 cents sharp) quite nicely, three steps are almost exactly [[8/5]] (tempering out [[1728/1715]], the orwellisma), and four steps are very nearly [[15/8]] (tempering out [[2430/2401]], the nuwell comma). 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony, along with some elements of the [[11-limit]], such as the [[11/8]] major fourth. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.

~~The~~ step ~~size is~~ very ~~close to~~ the ~~271~~.~~509 cents~~ of 7-limit [[~~Orwell|orwell temperament~~]] ~~and also close~~ to the ~~271.426 cents~~ of [[~~11-limit~~]] ~~orwell~~. It is almost identical to 12\53, the [[53edo]] orwell generator ~~which is~~ 271.698 cents. 7edt is a good tuning for [[Electra]] temperament, with ~~its second degree~~ being a close approximation to [[15/11]].

Due to the proximity of the step size with 7/6, 7edt supports [[orwell]] temperament. One step of 7edt is almost identical to 12\53, the [[53edo]] orwell generator, at about 271.698 cents. 7edt is also a good tuning for [[Electra]] temperament, with two steps of 7edt being a close approximation to [[15/11]].

=== Harmonics ===

=== Prime harmonics ===

== Scale degrees of 7edt ==

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! Degrees

! Cents

!~~hekts~~

! [[Hekt]]s

! Approximate Ratio

! [[Electra]] notation (J = 1/1)

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|}

Since one step of 7edt is a sharp subminor ([[7/6]]) third, three steps are almost exactly [[8/5]], four steps are very nearly [[15/8]] and six steps are a bit flat of [[18/7]], 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the [[eric]] [[comma]].

~~== Prime harmonics ==~~

~~{{Harmonics in equal|7|3|1|intervals=prime}}~~

~~== 7n-edt Family ==~~

* [[14edt]]

* [[21edt]]

* [[28edt]]

* [[56edt]]

[[category:macrotonal]]

~~[[Category:53edo]]~~

[[Category:orwell]]

[[Category:subminor third]]

[[Category:Edt]]

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 {{Infobox ET}}
-'''7edt''' (short for '''7''' '''e'''qual '''d'''ivision of '''t'''ritave) divides the interval [[3/1]] it into 7 equal parts of 271.708 [[cent]]s each, corresponding to 4.4165 edo.
+{{EDO intro}}
-__FORCETOC__
+== Theory ==
-== Properties ==
+Since one step of 7edt approximates a [[7/6]] subminor third (4.84 cents sharp) quite nicely, three steps are almost exactly [[8/5]] (tempering out [[1728/1715]], the orwellisma), and four steps are very nearly [[15/8]] (tempering out [[2430/2401]], the nuwell comma). 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony, along with some elements of the [[11-limit]], such as the [[11/8]] major fourth. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.
-The step size is very close to the 271.509 cents of 7-limit [[Orwell|orwell temperament]] and also close to the 271.426 cents of [[11-limit]] orwell. It is almost identical to 12\53, the [[53edo]] orwell generator which is 271.698 cents. 7edt is a good tuning for [[Electra]] temperament, with its second degree being a close approximation to [[15/11]].
+Due to the proximity of the step size with 7/6, 7edt supports [[orwell]] temperament. One step of 7edt is almost identical to 12\53, the [[53edo]] orwell generator, at about 271.698 cents. 7edt is also a good tuning for [[Electra]] temperament, with two steps of 7edt being a close approximation to [[15/11]].
+=== Harmonics ===
+{{Harmonics in equal|7|3|1|}}
+=== Prime harmonics ===
+{{Harmonics in equal|7|3|1|intervals=prime}}
 == Scale degrees of 7edt ==
@@ Line 11: / Line 18: @@
 ! Degrees
 ! Cents
-!hekts
+! [[Hekt]]s
 ! Approximate Ratio
 ! [[Electra]] notation (J = 1/1)
@@ Line 62: / Line 69: @@
 |}
-Since one step of 7edt is a sharp subminor ([[7/6]]) third, three steps are almost exactly [[8/5]], four steps are very nearly [[15/8]] and six steps are a bit flat of [[18/7]], 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the [[eric]] [[comma]].
-== Prime harmonics ==
-{{Harmonics in equal|7|3|1|intervals=prime}}
-== 7n-edt Family ==
-* [[14edt]]
-* [[21edt]]
-* [[28edt]]
-* [[56edt]]
 [[category:macrotonal]]
-[[Category:53edo]]
 [[Category:orwell]]
 [[Category:subminor third]]
 [[Category:Edt]]