7edt: Difference between revisions

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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.
+{{ED intro}}
-__FORCETOC__
+== Theory ==
-== Properties ==
+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.
-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, being the equalized version of it's [[4L 3s<3/1>|4L 3s]] MOS scale.
-== Scale degrees of 7edt ==
+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]].
-{| class="wikitable"
+=== Harmonics ===
-! Degrees
+{{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"
+|-
+! #
 ! Cents
-!hekts
+! [[Hekt]]s
-! Approximate Ratio
+! Approximate ratios
+! [[Electra]] notation<br>({{nowrap|J {{=}} 1/1}})
 |-
-! colspan="3" | 0
+| 0
+| 0
+| 0
 | [[1/1]]
+| J
 |-
 | 1
-| 271.708
+| 272
-|185.714
+| 186
 | [[7/6]]
+| K
 |-
 | 2
-| 543.416
+| 543
-|371.429
+| 371
-| [[15/11]], [[11/8]]
+| [[11/8]], [[15/11]]
+| L
 |-
 | 3
-| 815.124
+| 815
-|557.143
+| 557
 | [[8/5]]
+| M
 |-
 | 4
-| 1086.831
+| 1087
-|742.857
+| 743
 | [[15/8]]
+| N
 |-
 | 5
-| 1358.539
+| 1359
-|928.571
+| 929
-| [[11/5]] ([[11/10]] plus an octave)
+| [[11/5]]
+| O
 |-
 | 6
-| 1630.247
+| 1630
-|1114.286
+| 1114
-| [[18/7]] ([[9/7]] plus an octave)
+| [[18/7]]
+| P
 |-
 | 7
-| 1901.955
+| 1902
-|1300
+| 1300
 | [[3/1]]
+| J
 |}
-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]].
+[[Category:Orwell]]
+[[Category:Subminor third]]
-== 7n-edt Family ==
-* [[14edt]]
-* [[21edt]]
-* [[28edt]]
-* [[56edt]]
-[[category:macrotonal]]
-[[Category:53edo]]
-[[Category:orwell]]
-[[Category:subminor third]]
-[[Category:Edt]]