7edf: Difference between revisions
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{{Infobox ET}} | {{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 === | ||
{{Harmonics in equal|7|3|2|prec=2|columns=15}} | {{Harmonics in equal|7|3|2|prec=2|columns=15}} | ||
==Intervals== | === Subsets and supersets === | ||
{| class="wikitable" | 7edf is the 4th [[prime equal division|prime edf]], after [[5edf]] and before [[11edf]]. | ||
== Intervals == | |||
{| class="wikitable center-1 right-2 center-3" | |||
|- | |- | ||
! # | ! # | ||
! Cents | ! Cents | ||
! Approximate ratios | |||
! 12edo notation | ! 12edo notation | ||
|- | |||
| 0 | |||
| 0 | |||
| exact 1/1 | |||
| C | |||
|- | |- | ||
| 1 | | 1 | ||
| 100. | | 100.3 | ||
| 18/17, 17/16 | |||
| C#, Db | | C#, Db | ||
|- | |- | ||
| 2 | | 2 | ||
| 200. | | 200.6 | ||
| 9/8 | |||
| D | | D | ||
|- | |- | ||
| 3 | | 3 | ||
| 300. | | 300.8 | ||
| 19/16, 44/37 | |||
| D#, Eb | | D#, Eb | ||
|- | |- | ||
| 4 | | 4 | ||
| 401. | | 401.1 | ||
| 63/50 | |||
| E | | E | ||
|- | |- | ||
| 5 | | 5 | ||
| 501. | | 501.4 | ||
|4/3 | |||
| F | | F | ||
|- | |- | ||
| 6 | | 6 | ||
| 601. | | 601.7 | ||
| 64/45 | |||
| F#, Gb | | F#, Gb | ||
|- | |- | ||
| 7 | | 7 | ||
| | | 702.0 | ||
| exact 3/2 | |||
| G | | G | ||
|- | |- | ||
| 8 | | 8 | ||
| 802. | | 802.2 | ||
| 100/63 | |||
| G#, Ab | | G#, Ab | ||
|- | |- | ||
| 9 | | 9 | ||
| 902. | | 902.5 | ||
| 27/16 | |||
| A | | A | ||
|- | |- | ||
| 10 | | 10 | ||
| 1002. | | 1002.8 | ||
| 16/9 | |||
| A#, Bb | | A#, Bb | ||
|- | |- | ||
| 11 | | 11 | ||
| 1103. | | 1103.1 | ||
| 17/9 | |||
| B | | B | ||
|- | |- | ||
| 12 | | 12 | ||
| 1203. | | 1203.4 | ||
| 2/1 | |||
| C | | C | ||
|- | |- | ||
| 13 | | 13 | ||
| 1303. | | 1303.6 | ||
| 17/8 | |||
| C#, Db | | C#, Db | ||
|- | |- | ||
| 14 | | 14 | ||
| 1403. | | 1403.9 | ||
| exact 9/4 | |||
| D | | 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]] | |||