7edf: Difference between revisions
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== Theory == | == Theory == | ||
7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just | 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 === | ||
| Line 16: | Line 16: | ||
! # | ! # | ||
! Cents | ! Cents | ||
!Approximate ratios | ! Approximate ratios | ||
! 12edo notation | ! 12edo notation | ||
|- | |- | ||
| 0 | | 0 | ||
| 0 | | 0 | ||
|exact 1/1 | | exact 1/1 | ||
| C | | C | ||
|- | |- | ||
| 1 | | 1 | ||
| 100.3 | | 100.3 | ||
|18/17, 17/16 | | 18/17, 17/16 | ||
| C#, Db | | C#, Db | ||
|- | |- | ||
| 2 | | 2 | ||
| 200.6 | | 200.6 | ||
|9/8 | | 9/8 | ||
| D | | D | ||
|- | |- | ||
| 3 | | 3 | ||
| 300.8 | | 300.8 | ||
|19/16, 44/37 | | 19/16, 44/37 | ||
| D#, Eb | | D#, Eb | ||
|- | |- | ||
| 4 | | 4 | ||
| 401.1 | | 401.1 | ||
|63/50 | | 63/50 | ||
| E | | E | ||
|- | |- | ||
| 5 | | 5 | ||
| 501.4 | | 501.4 | ||
|4/3 | |4/3 | ||
| F | | F | ||
|- | |- | ||
| 6 | | 6 | ||
| 601.7 | | 601.7 | ||
|64/45 | | 64/45 | ||
| F#, Gb | | F#, Gb | ||
|- | |- | ||
| 7 | | 7 | ||
| 702.0 | | 702.0 | ||
|exact 3/2 | | exact 3/2 | ||
| G | | G | ||
|- | |- | ||
| 8 | | 8 | ||
| 802.2 | | 802.2 | ||
|100/63 | | 100/63 | ||
| G#, Ab | | G#, Ab | ||
|- | |- | ||
| 9 | | 9 | ||
| 902.5 | | 902.5 | ||
|27/16 | | 27/16 | ||
| A | | A | ||
|- | |- | ||
| 10 | | 10 | ||
| 1002.8 | | 1002.8 | ||
|16/9 | | 16/9 | ||
| A#, Bb | | A#, Bb | ||
|- | |- | ||
| 11 | | 11 | ||
| 1103.1 | | 1103.1 | ||
|17/9 | | 17/9 | ||
| B | | B | ||
|- | |- | ||
| 12 | | 12 | ||
| 1203.4 | | 1203.4 | ||
|2/1 | | 2/1 | ||
| C | | C | ||
|- | |- | ||
| 13 | | 13 | ||
| 1303.6 | | 1303.6 | ||
|17/8 | | 17/8 | ||
| C#, Db | | C#, Db | ||
|- | |- | ||
| 14 | | 14 | ||
| 1403.9 | | 1403.9 | ||
|exact 9/4 | | exact 9/4 | ||
| D | | D | ||
|} | |} | ||
| Line 103: | Line 103: | ||
* [[40ed10]] – relative ed10 | * [[40ed10]] – relative ed10 | ||
* [[43ed12]] – relative ed12 | * [[43ed12]] – relative ed12 | ||
* [[76ed80]] – close to the zeta-optimized tuning for 12edo | |||
* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]] | |||
{{Todo|expand}} | {{Todo|expand}} | ||
[[Category:12edo]] | |||