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| '''[[EDF|Division of the just perfect fifth]] into 7 equal parts''' (7EDF) is related to [[12edo|12 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.
| | {{Infobox ET}} |
| | {{ED intro}} |
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| |
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| Lookalikes: [[12edo]], [[19ED3|19ed3]], [[31ed6]]
| | == Theory == |
| ==Intervals== | | 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. |
| {| class="wikitable" | | |
| |+ | | === Harmonics === |
| ! rowspan="2" |
| | {{Harmonics in equal|7|3|2|prec=2|columns=15}} |
| ! rowspan="2" |''ed233\420-5¢''
| | |
| ! rowspan="2" |ed31\54
| | === Subsets and supersets === |
| ! rowspan="2" |ed121/81 (~ed11\19)
| | 7edf is the 4th [[prime equal division|prime edf]], after [[5edf]] and before [[11edf]]. |
| ! rowspan="2" |ed696¢
| | |
| ! rowspan="2" |ed3/2
| | == Intervals == |
| ! colspan="2" |Pyrite
| | {| class="wikitable center-1 right-2 center-3" |
| ! rowspan="2" |ed708¢
| |
| ! rowspan="2" |ed122/81 (~ed13\22)
| |
| ! rowspan="2" |ed34\57
| |
| ! rowspan="2" |''ed37\60+5¢''
| |
| |- | | |- |
| !(~ed17\29) | | ! # |
| !(~ed10\17) | | ! Cents |
| | ! Approximate ratios |
| | ! 12edo notation |
| |- | | |- |
| |1 | | | 0 |
| |''94.3878-95.102'' | | | 0 |
| |98.4127 | | | exact 1/1 |
| |99.2594
| | | C |
| |99.4286
| |
| |100.2793
| |
| |100.5194
| |
| |100.8365
| |
| |101.1429
| |
| |101.295
| |
| |102.2556
| |
| |''105.7143-106.4286'' | |
| |- | | |- |
| |2 | | | 1 |
| |''188.7755-190.2041'' | | | 100.3 |
| |196.8254
| | | 18/17, 17/16 |
| |198.5188
| | | C#, Db |
| |198.8571
| |
| |200.5586
| |
| |201.0389
| |
| |201.673
| |
| |202.2857
| |
| |202.5899 | |
| |204.5113 | |
| |''211.4286-212.8571''
| |
| |- | | |- |
| |3 | | | 2 |
| |''283.1633-285.3061'' | | | 200.6 |
| |295.238
| | | 9/8 |
| |297.7782
| | | D |
| |298.2857
| |
| |300.8379
| |
| |301.5583
| |
| |302.5095
| |
| |303.4286
| |
| |303.8849 | |
| |306.7669 | |
| |''317.1429-319.2857''
| |
| |- | | |- |
| |4 | | | 3 |
| |''377.551-380.4082'' | | | 300.8 |
| |393.6508
| | | 19/16, 44/37 |
| |397.03765
| | | D#, Eb |
| |397.7143
| |
| |401.1171
| |
| |402.0777
| |
| |403.346
| |
| |404.5714
| |
| |405.1799 | |
| |409.0226 | |
| |''422.8571-425.7143''
| |
| |- | | |- |
| |5 | | | 4 |
| |''471.9388-475.5102'' | | | 401.1 |
| |492.0635
| | | 63/50 |
| |496.2971
| | | E |
| |497.1429
| |
| |501.3964
| |
| |502.5972
| |
| |504.1825
| |
| |505.7143
| |
| |506.4749 | |
| |511.2781 | |
| |''528.5714-532.1429''
| |
| |- | | |- |
| |6 | | | 5 |
| |''566.3265-570.6122'' | | | 501.4 |
| |590.476
| | |4/3 |
| |595.5565
| | | F |
| |596.5714
| |
| |601.6757
| |
| |603.1166
| |
| |605.019
| |
| |606.8571
| |
| |607.7698 | |
| |613.5338 | |
| |''634.2857-638.5714''
| |
| |- | | |- |
| |7 | | | 6 |
| |''660.7143-665.714''3 | | | 601.7 |
| |688.8889
| | | 64/45 |
| |694.8158
| | | F#, Gb |
| |696
| |
| |701.955
| |
| |703.636
| |
| |705.85545 | |
| |708
| |
| |709.0648
| |
| |715.7895
| |
| |''740-745'' | |
| |- | | |- |
| |8 | | | 7 |
| |''755.102-760.8163'' | | | 702.0 |
| |787.3016
| | | exact 3/2 |
| |794.0753
| | | G |
| |795.4286
| |
| |802.2343
| |
| |804.1555
| |
| |806.6919
| |
| |809.1429
| |
| |810.3598 | |
| |818.0451 | |
| |''845.7143-851.4286''
| |
| |- | | |- |
| |9 | | | 8 |
| |''849.4898-855.9184'' | | | 802.2 |
| |885.7143
| | | 100/63 |
| |893.3347
| | | G#, Ab |
| |894.8571
| |
| |902.5136
| |
| |904.6749
| |
| |907.5284
| |
| |910.2857
| |
| |911.6547 | |
| |920.30075 | |
| |''951.4286-957.8571''
| |
| |- | | |- |
| |10 | | | 9 |
| |''943.8776-951.0204'' | | | 902.5 |
| |984.127
| | | 27/16 |
| |992.5941
| | | A |
| |994.2857
| |
| |1002.7929
| |
| |1005.1943
| |
| |1008.3649
| |
| |1011.4286
| |
| |1012.9497 | |
| |1022.5564 | |
| |''1057.1429-1064.2857''
| |
| |- | | |- |
| |11 | | | 10 |
| |''1038.2653-1046.12245'' | | | 1002.8 |
| |1082.5397
| | | 16/9 |
| |1091.8535
| | | A#, Bb |
| |1093.7143
| |
| |1103.0721
| |
| |1105.7138
| |
| |1109.2014
| |
| |1112.5714
| |
| |1114.2447 | |
| |1124.812 | |
| |''1162.8571-1170.7143''
| |
| |- | | |- |
| |12 | | | 11 |
| |''1038.2653-1046.12245'' | | | 1103.1 |
| |1180.9524
| | | 17/9 |
| |1191.1129
| | | B |
| |1193.1429
| |
| |1203.3514
| |
| |1206.2332
| |
| |1210.0379
| |
| |1213.7143
| |
| |1215.5397 | |
| |1227.0677 | |
| |''1268.5714-1277.5714''
| |
| |- | | |- |
| |13 | | | 12 |
| |''1229.8265-1236.3265'' | | | 1203.4 |
| |1279.3651
| | | 2/1 |
| |1290.37235
| | | C |
| |1292.5714
| |
| |1303.6307
| |
| |1306.7526
| |
| |1310.8744
| |
| |1314.8571
| |
| |1316.8346 | |
| |1329.3233 | |
| |''1374.2857-1383.5714''
| |
| |- | | |- |
| |14 | | | 13 |
| |''1321.4286-1331.4286'' | | | 1303.6 |
| |1377.7778 | | | 17/8 |
| |1389.6318 | | | C#, Db |
| |1392 | | |- |
| |1403.91 | | | 14 |
| |1407.2721 | | | 1403.9 |
| |1411.7109
| | | exact 9/4 |
| |1416
| | | D |
| |1418.1296
| |
| |1431.57895 | |
| |''1480-1490'' | |
| |} | | |} |
| [[Category:Edf]] | | |
| [[Category:Edonoi]] | | == See also == |
| [[Category:todo:improve synopsis]] | | * [[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]] |