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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | |||
== | 7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just, which stretches the octave by 3.3514{{c}}. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13. It forms as a decent approximation to stretched-octave tuning on pianos, since pianos' strings have overtones that tend slightly sharp and are thus often tuned with stretched octaves. | ||
{| | |||
| | === Harmonics === | ||
{{Harmonics in equal|7|3|2|prec=2|columns=15}} | |||
=== Subsets and supersets === | |||
7edf is the 4th [[prime equal division|prime edf]], after [[5edf]] and before [[11edf]]. | |||
== Intervals == | |||
{| class="wikitable center-1 right-2 center-3" | |||
|- | |- | ||
! | ! # | ||
! | ! Cents | ||
! Approximate ratios | |||
! 12edo notation | |||
|- | |- | ||
| | | 0 | ||
| | | 0 | ||
| | | exact 1/1 | ||
| C | |||
| | |||
|- | |- | ||
| | | 1 | ||
| | | 100.3 | ||
| | | 18/17, 17/16 | ||
| C#, Db | |||
| | |||
|- | |- | ||
| | | 2 | ||
| | | 200.6 | ||
| | | 9/8 | ||
| D | |||
| | |||
|- | |- | ||
| | | 3 | ||
| | | 300.8 | ||
| | | 19/16, 44/37 | ||
| D#, Eb | |||
| | |||
|- | |- | ||
| | | 4 | ||
| | | 401.1 | ||
| | | 63/50 | ||
| E | |||
| | |||
|- | |- | ||
| | | 5 | ||
| | | 501.4 | ||
| | |4/3 | ||
| F | |||
| | |||
|- | |- | ||
| | | 6 | ||
| | | 601.7 | ||
| 64/45 | |||
| F#, Gb | |||
| | |||
| | |||
|- | |- | ||
| | | 7 | ||
| | | 702.0 | ||
| | | exact 3/2 | ||
| G | |||
| | |||
|- | |- | ||
| | | 8 | ||
| | | 802.2 | ||
| | | 100/63 | ||
| G#, Ab | |||
| | |||
|- | |- | ||
| | | 9 | ||
| | | 902.5 | ||
| | | 27/16 | ||
| A | |||
| | |||
|- | |- | ||
| | | 10 | ||
| | | 1002.8 | ||
| | | 16/9 | ||
| A#, Bb | |||
| | |||
|- | |- | ||
| | | 11 | ||
| | | 1103.1 | ||
| | | 17/9 | ||
| B | |||
| | |||
|- | |- | ||
| | | 12 | ||
| | | 1203.4 | ||
| | | 2/1 | ||
| C | |||
| | |||
|- | |- | ||
| | | 13 | ||
| | | 1303.6 | ||
| | | 17/8 | ||
| | | C#, Db | ||
| | |- | ||
| | | 14 | ||
| | | 1403.9 | ||
| | | exact 9/4 | ||
| D | |||
|} | |} | ||
[[ | |||
[[ | == See also == | ||
[[Category: | * [[12edo]] – relative edo | ||
* [[19edt]] – relative edt | |||
* [[28ed5]] – relative ed5 | |||
* [[31ed6]] – relative ed6 | |||
* [[34ed7]] – relative ed7 | |||
* [[40ed10]] – relative ed10 | |||
* [[43ed12]] – relative ed12 | |||
* [[76ed80]] – close to the zeta-optimized tuning for 12edo | |||
* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]] | |||
{{Todo|expand}} | |||
[[Category:12edo]] | |||