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| {{Infobox ET}} | | {{Infobox ET}} |
| '''[[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.
| | {{ED intro}} |
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| Lookalikes: [[12edo]], [[19ED3|19ed3]], [[31ed6]]
| | == 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]]. |
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| == Intervals == | | == Intervals == |
| {| class="wikitable" | | {| class="wikitable center-1 right-2 center-3" |
| |+
| | |- |
| ! rowspan="2" | Scale<br>Degree
| | ! # |
| ! rowspan="2" | ''ed233\420-5¢''
| | ! Cents |
| ! rowspan="2" | ed31\54 | | ! Approximate ratios |
| ! rowspan="2" | ed121/81 (~ed11\19) | | ! 12edo notation |
| ! rowspan="2" | ed696¢
| |
| ! rowspan="2" | ed32\55 | |
| ! rowspan="2" | [[12edo]]=''r¢'' | |
| ! rowspan="2" | ed3/2
| |
| ! colspan="2" | Pyrite
| |
| ! rowspan="2" | ed708¢
| |
| ! rowspan="2" | ed122/81 (~ed13\22)
| |
| ! rowspan="2" | ed34\57
| |
| ! rowspan="2" | ''ed37\60+5¢''
| |
| |- | | |- |
| ! (~ed17\29)
| | | 0 |
| ! (~ed10\17)
| | | 0 |
| | | exact 1/1 |
| | | C |
| |- | | |- |
| | 1 | | | 1 |
| | ''94.3878-95.102''
| | | 100.3 |
| | 98.4127
| | | 18/17, 17/16 |
| | 99.2594
| | | C#, Db |
| | 99.4286
| |
| | 99.7403
| |
| | ''100''
| |
| | 100.2793
| |
| | 100.5194
| |
| | 100.8365 | |
| | 101.1429 | |
| | 101.295 | |
| | 102.2556
| |
| | ''105.7143-106.4286''
| |
| |- | | |- |
| | 2 | | | 2 |
| | ''188.7755-190.2041''
| | | 200.6 |
| | 196.8254
| | | 9/8 |
| | 198.5188
| | | D |
| | 198.8571
| |
| | 199.4805
| |
| | ''200''
| |
| | 200.5586 | |
| | 201.0389 | |
| | 201.673 | |
| | 202.2857
| |
| | 202.5899
| |
| | 204.5113
| |
| | ''211.4286-212.8571''
| |
| |- | | |- |
| | 3 | | | 3 |
| | ''283.1633-285.3061''
| | | 300.8 |
| | 295.238
| | | 19/16, 44/37 |
| | 297.7782
| | | D#, Eb |
| | 298.2857
| |
| | 299.2208
| |
| | ''300''
| |
| | 300.8379 | |
| | 301.5583 | |
| | 302.5095 | |
| | 303.4286
| |
| | 303.8849
| |
| | 306.7669
| |
| | ''317.1429-319.2857''
| |
| |- | | |- |
| | 4 | | | 4 |
| | ''377.551-380.4082''
| | | 401.1 |
| | 393.6508
| | | 63/50 |
| | 397.03765
| | | E |
| | 397.7143
| |
| | 398.961
| |
| | ''400''
| |
| | 401.1171 | |
| | 402.0777
| |
| | 403.346
| |
| | 404.5714
| |
| | 405.1799
| |
| | 409.0226 | |
| | ''422.8571-425.7143'' | |
| |- | | |- |
| | 5 | | | 5 |
| | ''471.9388-475.5102''
| | | 501.4 |
| | 492.0635
| | |4/3 |
| | 496.2971
| | | F |
| | 497.1429
| |
| | 498.7013
| |
| | ''500''
| |
| | 501.3964 | |
| | 502.5972
| |
| | 504.1825
| |
| | 505.7143
| |
| | 506.4749
| |
| | 511.2781 | |
| | ''528.5714-532.1429'' | |
| |- | | |- |
| | 6 | | | 6 |
| | ''566.3265-570.6122''
| | | 601.7 |
| | 590.476
| | | 64/45 |
| | 595.5565
| | | F#, Gb |
| | 596.5714
| |
| | 598.4416
| |
| | ''600''
| |
| | 601.6757 | |
| | 603.1166
| |
| | 605.019
| |
| | 606.8571
| |
| | 607.7698
| |
| | 613.5338 | |
| | ''634.2857-638.5714'' | |
| |- | | |- |
| | 7 | | | 7 |
| | ''660.7143-665.714''3 | | | 702.0 |
| | 688.8889 | | | exact 3/2 |
| | 694.8158
| | | G |
| | 696
| |
| | 698.1818
| |
| | ''700''
| |
| | 701.955
| |
| | 703.636
| |
| | 705.85545
| |
| | 708
| |
| | 709.0648
| |
| | 715.7895
| |
| | ''740-745'' | |
| |- | | |- |
| | 8 | | | 8 |
| | ''755.102-760.8163''
| | | 802.2 |
| | 787.3016
| | | 100/63 |
| | 794.0753
| | | G#, Ab |
| | 795.4286
| |
| | 797.9221
| |
| | ''800''
| |
| | 802.2343 | |
| | 804.1555
| |
| | 806.6919
| |
| | 809.1429
| |
| | 810.3598
| |
| | 818.0451 | |
| | ''845.7143-851.4286'' | |
| |- | | |- |
| | 9 | | | 9 |
| | ''849.4898-855.9184''
| | | 902.5 |
| | 885.7143
| | | 27/16 |
| | 893.3347
| | | A |
| | 894.8571
| |
| | 897.6623
| |
| | ''900''
| |
| | 902.5136 | |
| | 904.6749
| |
| | 907.5284
| |
| | 910.2857
| |
| | 911.6547
| |
| | 920.30075 | |
| | ''951.4286-957.8571'' | |
| |- | | |- |
| | 10 | | | 10 |
| | ''943.8776-951.0204''
| | | 1002.8 |
| | 984.127
| | | 16/9 |
| | 992.5941
| | | A#, Bb |
| | 994.2857
| |
| | 997.4126
| |
| | ''1000''
| |
| | 1002.7929 | |
| | 1005.1943
| |
| | 1008.3649
| |
| | 1011.4286
| |
| | 1012.9497
| |
| | 1022.5564 | |
| | ''1057.1429-1064.2857'' | |
| |- | | |- |
| | 11 | | | 11 |
| | ''1038.2653-1046.12245''
| | | 1103.1 |
| | 1082.5397
| | | 17/9 |
| | 1091.8535
| | | B |
| | 1093.7143
| |
| | 1097.1429
| |
| | ''1100''
| |
| | 1103.0721 | |
| | 1105.7138
| |
| | 1109.2014
| |
| | 1112.5714
| |
| | 1114.2447
| |
| | 1124.812 | |
| | ''1162.8571-1170.7143'' | |
| |- | | |- |
| | 12 | | | 12 |
| | ''1038.2653-1046.12245''
| | | 1203.4 |
| | 1180.9524
| | | 2/1 |
| | 1191.1129
| | | C |
| | 1193.1429
| |
| | 1196.8831
| |
| | ''1200''
| |
| | 1203.3514 | |
| | 1206.2332
| |
| | 1210.0379
| |
| | 1213.7143
| |
| | 1215.5397
| |
| | 1227.0677 | |
| | ''1268.5714-1277.5714'' | |
| |- | | |- |
| | 13 | | | 13 |
| | ''1229.8265-1236.3265''
| | | 1303.6 |
| | 1279.3651
| | | 17/8 |
| | 1290.37235
| | | C#, Db |
| | 1292.5714
| |
| | 1296.6234
| |
| | ''1300''
| |
| | 1303.6307 | |
| | 1306.7526
| |
| | 1310.8744
| |
| | 1314.8571
| |
| | 1316.8346
| |
| | 1329.3233 | |
| | ''1374.2857-1383.5714'' | |
| |- | | |- |
| | 14 | | | 14 |
| | ''1321.4286-1331.4286''
| | | 1403.9 |
| | 1377.7778
| | | exact 9/4 |
| | 1389.6318
| | | D |
| | 1392
| |
| | 1396.3636
| |
| | ''1400''
| |
| | 1403.91 | |
| | 1407.2721
| |
| | 1411.7109
| |
| | 1416
| |
| | 1418.1296 | |
| | 1431.57895
| |
| | ''1480-1490'' | |
| |} | | |} |
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| Different choices for the size of the fifth are listed in the top row.
| | == 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}} |
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| [[Category:Edf]] | | [[Category:12edo]] |
| [[Category:Edonoi]]
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| [[Category:todo:improve synopsis]]
| |