Xenharmonic Wiki

7edt: Difference between revisions

← Older editNewer edit →
VisualWikitext
No edit summary
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
reworked wiki syntax and heading levels (H1 -> H2), links added, spelling fix(es), all categories at the end
Line 1: Line 1:
'''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__
__FORCETOC__
=Properties=
== Properties ==
[[category:macrotonal]]
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.
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=
== Scale degrees of 7edt ==


{| class="wikitable"
{| class="wikitable"
! Degrees
! Cents
! Approximate Ratio
|-
|-
| | Degrees
| 0
| | Cents
| 0
| | Approximate Ratio
| [[1/1]]
|-
| | 0
| | 0
| | [[1/1|1/1]]
|-
|-
| | 1
| 1
| | 271.708
| 271.708
| | [[7/6|7/6]]
| [[7/6]]
|-
|-
| | 2
| 2
| | 543.416
| 543.416
| | [[15/11|15/11]], [[11/8|11/8]]
| [[15/11]], [[11/8]]
|-
|-
| | 3
| 3
| | 815.124
| 815.124
| | [[8/5|8/5]]
| [[8/5]]
|-
|-
| | 4
| 4
| | 1086.831
| 1086.831
| | [[15/8|15/8]]
| [[15/8]]
|-
|-
| | 5
| 5
| | 1358.539
| 1358.539
| | 11/5 ([[11/10|11/10]] plus an octave)
| [[11/5]] ([[11/10]] plus an octave)
|-
|-
| | 6
| 6
| | 1630.247
| 1630.247
| | 18/7 ([[9/7|9/7]] plus an octave)
| [[18/7]] ([[9/7]] plus an octave)
|-
|-
| | 7
| 7
| | 1901.955
| 1901.955
| | 3/1
| [[3/1]]
|}
|}


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.
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]].


=7n-edt Family=
== 7n-edt Family ==
[[14edt|14edt]]
* [[14edt]]
* [[21edt]]
* [[28edt]]
* [[56edt]]


[[21edt|21edt]]
[[category:macrotonal]]
 
[[28edt|28edt]]
 
...
[[Category:53edo]]
[[Category:53edo]]
[[Category:orwell]]
[[Category:orwell]]
[[Category:subminor_third]]
[[Category:subminor third]]
[[Category:Edt]]
Retrieved from "https://en.xen.wiki/w/7edt"