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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}}


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]].


== 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''
|}
|}


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}}


[[Category:Edf]]
[[Category:12edo]]
[[Category:Edonoi]]
[[Category:todo:improve synopsis]]
Retrieved from "https://en.xen.wiki/w/7edf"