7edf: Difference between revisions
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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 === | ||
[[Category: | {{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 == | |||
* [[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]] | |||