Xenharmonic Wiki

7edt: Difference between revisions

← Older edit
VisualWikitext
CompactStar (talk | contribs)
5,020 edits
No edit summary
+subsets and supersets; cleanup; -redundant categories
 
(6 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{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, with its second degree being a close approximation to [[15/11]].


== 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 ===
7edt is the 4th [[prime equal division|prime edt]], after [[5edt]] and before [[11edt]].
 
== Intervals ==
{| class="wikitable center-1 right-2 right-3"
|-
! #
! Cents
! Cents
!hekts
! [[Hekt]]s
! Approximate Ratio
! Approximate ratios
! [[Electra]] notation (J = 1/1)
! [[Electra]] notation<br>({{nowrap|J {{=}} 1/1}})
|-
|-
! colspan="3" | 0
| 0
| 0
| 0
| [[1/1]]
| [[1/1]]
| J
| J
|-
|-
| 1
| 1
| 271.708
| 272
|185.714
| 186
| [[7/6]]
| [[7/6]]
| K
| K
|-
|-
| 2
| 2
| 543.416
| 543
|371.429
| 371
| [[15/11]], [[11/8]]
| [[11/8]], [[15/11]]
| L
| L
|-
|-
| 3
| 3
| 815.124
| 815
|557.143
| 557
| [[8/5]]
| [[8/5]]
| M
| M
|-
|-
| 4
| 4
| 1086.831
| 1087
|742.857
| 743
| [[15/8]]
| [[15/8]]
| N
| N
|-
|-
| 5
| 5
| 1358.539
| 1359
|928.571
| 929
| [[11/5]] ([[11/10]] plus an octave)
| [[11/5]]
| O
| O
|-
|-
| 6
| 6
| 1630.247
| 1630
|1114.286
| 1114
| [[18/7]] ([[9/7]] plus an octave)
| [[18/7]]
| P
| P
|-
|-
| 7
| 7
| 1901.955
| 1902
|1300
| 1300
| [[3/1]]
| [[3/1]]
| J
| 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]]
Retrieved from "https://en.xen.wiki/w/7edt"