7edt: Difference between revisions
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| Line 13: | Line 13: | ||
!hekts | !hekts | ||
! Approximate Ratio | ! Approximate Ratio | ||
! [[Electra]] notation | |||
|- | |- | ||
! colspan="3" | 0 | ! colspan="3" | 0 | ||
| Line 21: | Line 22: | ||
|185.714 | |185.714 | ||
| [[7/6]] | | [[7/6]] | ||
| K | |||
|- | |- | ||
| 2 | | 2 | ||
| Line 26: | Line 28: | ||
|371.429 | |371.429 | ||
| [[15/11]], [[11/8]] | | [[15/11]], [[11/8]] | ||
| L | |||
|- | |- | ||
| 3 | | 3 | ||
| Line 31: | Line 34: | ||
|557.143 | |557.143 | ||
| [[8/5]] | | [[8/5]] | ||
| M | |||
|- | |- | ||
| 4 | | 4 | ||
| Line 36: | Line 40: | ||
|742.857 | |742.857 | ||
| [[15/8]] | | [[15/8]] | ||
| N | |||
|- | |- | ||
| 5 | | 5 | ||
| Line 41: | Line 46: | ||
|928.571 | |928.571 | ||
| [[11/5]] ([[11/10]] plus an octave) | | [[11/5]] ([[11/10]] plus an octave) | ||
| O | |||
|- | |- | ||
| 6 | | 6 | ||
| Line 46: | Line 52: | ||
|1114.286 | |1114.286 | ||
| [[18/7]] ([[9/7]] plus an octave) | | [[18/7]] ([[9/7]] plus an octave) | ||
| P | |||
|- | |- | ||
| 7 | | 7 | ||
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|1300 | |1300 | ||
| [[3/1]] | | [[3/1]] | ||
| J | |||
|} | |} | ||
Revision as of 02:18, 5 March 2023
| ← 6edt | 7edt | 8edt → |
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. 7edt is a good tuning for Electra temperament, with its second degree being a close approximation to 15/11.
Scale degrees of 7edt
| Degrees | Cents | hekts | Approximate Ratio | Electra notation |
|---|---|---|---|---|
| 0 | 1/1 | |||
| 1 | 271.708 | 185.714 | 7/6 | K |
| 2 | 543.416 | 371.429 | 15/11, 11/8 | L |
| 3 | 815.124 | 557.143 | 8/5 | M |
| 4 | 1086.831 | 742.857 | 15/8 | N |
| 5 | 1358.539 | 928.571 | 11/5 (11/10 plus an octave) | O |
| 6 | 1630.247 | 1114.286 | 18/7 (9/7 plus an octave) | P |
| 7 | 1901.955 | 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.