7edt: Difference between revisions

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-__FORCETOC__
+{{Infobox ET}}
-=Properties=
+{{ED intro}}
-[[category:macrotonal]]
-The 7 equal division of 3, the tritave, divides it into 7 equal parts  of 271.708 cents each, corresponding to 4.4165 edo. 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|53edo]] orwell generator which is 271.698 cents.
-=Scale degrees of 7edt=
+== Theory ==
+Since one step of 7edt approximates a [[7/6]] subminor third (4.84{{c}} 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.
-{| class="wikitable"
+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|columns=15}}
+=== Subsets and supersets ===
+edt is the 4th [[prime equal division|prime edt]], after [[5edt]] and before [[11edt]].
+== Intervals ==
+{| class="wikitable center-1 right-2 right-3"
 |-
-| | Degrees
+! #
-| | Cents
+! Cents
-| | Approximate Ratio
+! [[Hekt]]s
+! Approximate ratios
+! [[Electra]] notation<br>({{nowrap|J {{=}} 1/1}})
 |-
-| | 0
+| 0
-| | 0
+| 0
-| | [[1/1|1/1]]
+| 0
+| [[1/1]]
+| J
 |-
-| | 1
+| 1
-| | 271.708
+| 272
-| | [[7/6|7/6]]
+| 186
+| [[7/6]]
+| K
 |-
-| | 2
+| 2
-| | 543.416
+| 543
-| | [[15/11|15/11]], [[11/8|11/8]]
+| 371
+| [[11/8]], [[15/11]]
+| L
 |-
-| | 3
+| 3
-| | 815.124
+| 815
-| | [[8/5|8/5]]
+| 557
+| [[8/5]]
+| M
 |-
-| | 4
+| 4
-| | 1086.831
+| 1087
-| | [[15/8|15/8]]
+| 743
+| [[15/8]]
+| N
 |-
-| | 5
+| 5
-| | 1358.539
+| 1359
-| | 11/5 ([[11/10|11/10]] plus an octave)
+| 929
+| [[11/5]]
+| O
 |-
-| | 6
+| 6
-| | 1630.247
+| 1630
-| | 18/7 ([[9/7|9/7]] plus an octave)
+| 1114
+| [[18/7]]
+| P
 |-
-| | 7
+| 7
-| | 1901.955
+| 1902
-| | 3/1
+| 1300
+| [[3/1]]
+| J
 |}
-Since one step of 7edt is a sharp subminor (7/6) third, three steps are almost exactlty 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.
+[[Category:Orwell]]
+[[Category:Subminor third]]
-=7n-edt Family=
-[[14edt|14edt]]
-[[21edt|21edt]]
-[[28edt|28edt]]
-...
-[[Category:53edo]]
-[[Category:orwell]]
-[[Category:subminor_third]]