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{{ED intro}} | |||
== Harmonics == | == Theory == | ||
7ed5 is related to [[3edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 6 cents compressed and the step size is about 398 cents. It is present (though possibly tempered) in any [[regular temperament]] which [[tempering out|tempers out]] [[441/440]] and 244515348/244140625 in the [[11-limit]], such as [[equal temperament]]s [[3edo|3]], [[12edo|12]], [[15edo|15]], [[175edo|175]], [[190edo|190]], [[202edo|202]], and [[217edo]]. | |||
Due to [[Kirnberger's atom]], its step is 100.0002¢ flat of [[4/3]]{{clarify}}. | |||
=== Harmonics === | |||
{{Harmonics in equal|7|5|1}} | {{Harmonics in equal|7|5|1}} | ||
{{Harmonics in equal|7|5|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 7ed5 (contined)}} | |||
=== Subsets and supersets === | |||
7ed5 is the 4th [[prime equal division|prime ed5]], past [[5ed5]] and before [[11ed5]]. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable center-1 right-2" | |||
{| class="wikitable" | |||
|- | |- | ||
! | ! # | ||
! | ! Cents | ||
! | ! Approximate ratios | ||
|- | |- | ||
| 0 | |||
| 0 | |||
| | | [[1/1]] | ||
|- | |- | ||
| 1 | |||
| 398 | |||
| [[5/4]], 34/27 | |||
| | |||
|- | |- | ||
| 2 | |||
| 796 | |||
| [[19/12]] | |||
|- | |- | ||
| | | 3 | ||
| 1194 | |||
| | | [[2/1]], 255/128 | ||
|- | |- | ||
| 4 | |||
| 1592 | |||
| [[5/2]], 128/51 | |||
| | |||
|- | |- | ||
| 5 | |||
| 1990 | |||
| 60/19 | |||
|- | |- | ||
| | | 6 | ||
| 2388 | |||
| [[4/1]], 135/34 | |||
| | |||
|- | |- | ||
| 7 | |||
| 2786 | |||
| | | [[5/1]] | ||
|} | |} | ||