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__ | __FORCETOC__ | ||
=Properties= | == Properties == | ||
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. | |||
=Scale degrees of 7edt= | == Scale degrees of 7edt == | ||
{| class="wikitable" | {| class="wikitable" | ||
! Degrees | |||
! Cents | |||
! Approximate Ratio | |||
|- | |- | ||
| 0 | |||
| 0 | |||
| [[1/1]] | |||
|- | |- | ||
| 1 | |||
| 271.708 | |||
| [[7/6]] | |||
|- | |- | ||
| 2 | |||
| 543.416 | |||
| [[15/11]], [[11/8]] | |||
|- | |- | ||
| 3 | |||
| 815.124 | |||
| [[8/5]] | |||
|- | |- | ||
| 4 | |||
| 1086.831 | |||
| [[15/8]] | |||
|- | |- | ||
| 5 | |||
| 1358.539 | |||
| | | [[11/5]] ([[11/10]] plus an octave) | ||
|- | |- | ||
| 6 | |||
| 1630.247 | |||
| | | [[18/7]] ([[9/7]] plus an octave) | ||
|- | |- | ||
| 7 | |||
| 1901.955 | |||
| | | [[3/1]] | ||
|} | |} | ||
Since one step of 7edt is a sharp subminor (7/6) third, three steps are almost | 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]] | ||
* [[21edt]] | |||
* [[28edt]] | |||
* [[56edt]] | |||
[[ | [[category:macrotonal]] | ||
[[Category:53edo]] | [[Category:53edo]] | ||
[[Category:orwell]] | [[Category:orwell]] | ||
[[Category: | [[Category:subminor third]] | ||
[[Category:Edt]] | |||
Revision as of 12:00, 2 October 2018
7edt (short for 7 equal division of tritave) divides the interval 3/1 it into 7 equal parts of 271.708 cents each, corresponding to 4.4165 edo.
Properties
The step size is very close to the 271.509 cents of 7-limit 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.
Scale degrees of 7edt
| Degrees | Cents | Approximate Ratio |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 271.708 | 7/6 |
| 2 | 543.416 | 15/11, 11/8 |
| 3 | 815.124 | 8/5 |
| 4 | 1086.831 | 15/8 |
| 5 | 1358.539 | 11/5 (11/10 plus an octave) |
| 6 | 1630.247 | 18/7 (9/7 plus an octave) |
| 7 | 1901.955 | 3/1 |
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.