7edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
Since one step of 7edt approximates a [[7/6]] subminor third (4.84 | 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. | ||
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]]. | 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]]. | ||
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== Scale degrees of 7edt == | == Scale degrees of 7edt == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |||
! Degrees | ! Degrees | ||
! Cents | ! Cents | ||
! [[Hekt]]s | ! [[Hekt]]s | ||
! Approximate Ratio | ! Approximate Ratio | ||
! [[Electra]] notation (J = 1/1) | ! [[Electra]] notation ({{nowrap|J {{=}} 1/1}}) | ||
|- | |- | ||
! colspan="3" | 0 | ! colspan="3" | 0 | ||
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| 1 | | 1 | ||
| 271.708 | | 271.708 | ||
|185.714 | | 185.714 | ||
| [[7/6]] | | [[7/6]] | ||
| K | | K | ||
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| 2 | | 2 | ||
| 543.416 | | 543.416 | ||
|371.429 | | 371.429 | ||
| [[15/11]], [[11/8]] | | [[15/11]], [[11/8]] | ||
| L | | L | ||
| Line 40: | Line 40: | ||
| 3 | | 3 | ||
| 815.124 | | 815.124 | ||
|557.143 | | 557.143 | ||
| [[8/5]] | | [[8/5]] | ||
| M | | M | ||
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| 4 | | 4 | ||
| 1086.831 | | 1086.831 | ||
|742.857 | | 742.857 | ||
| [[15/8]] | | [[15/8]] | ||
| N | | N | ||
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| 5 | | 5 | ||
| 1358.539 | | 1358.539 | ||
|928.571 | | 928.571 | ||
| [[11/5]] ([[11/10]] plus an octave) | | [[11/5]] ([[11/10]] plus an octave) | ||
| O | | O | ||
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| 6 | | 6 | ||
| 1630.247 | | 1630.247 | ||
|1114.286 | | 1114.286 | ||
| [[18/7]] ([[9/7]] plus an octave) | | [[18/7]] ([[9/7]] plus an octave) | ||
| P | | P | ||
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| 7 | | 7 | ||
| 1901.955 | | 1901.955 | ||
|1300 | | 1300 | ||
| [[3/1]] | | [[3/1]] | ||
| J | | J | ||
|} | |} | ||
[[category:Macrotonal]] | |||
[[category: | [[Category:Orwell]] | ||
[[Category: | [[Category:Subminor third]] | ||
[[Category: | |||
[[Category:Edt]] | [[Category:Edt]] | ||