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| '''[[EDF|Division of the just perfect fifth]] into 14 equal parts''' (14EDF) is related to [[24edo|24 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 50.1396 cents. The patent val has a generally sharp tendency for harmonics up to 22, with the exception for 7, 14, and 21.
| | {{Infobox ET}} |
| | {{ED intro}} |
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| Lookalikes: [[24edo]], [[38edt]]
| | == Theory == |
| ==Intervals== | | 14edf is related to [[24edo]], but with the perfect fifth rather than the [[2/1|octave]] being just, which stretches the octave by about 3.35 cents. The [[patent val]] has a generally sharp tendency for harmonics up to 22, with the exception for [[7/1|7]], [[14/1|14]], and [[21/1|21]]. |
| {| class="wikitable" | | |
| |+ | | === Harmonics === |
| ! rowspan="2" |
| | {{Harmonics in equal|14|3|2|intervals=integer|columns=11}} |
| ! rowspan="2" |''ed233\420-5¢ (~51ed4!)''
| | {{Harmonics in equal|14|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 14edf (continued)}} |
| ! rowspan="2" |ed31\54 (~49ed4!)
| | |
| ! rowspan="2" |ed121/81
| | === Subsets and supersets === |
| ! rowspan="2" |ed3/2
| | Since 14 factors into primes as {{nowrap| 2 × 7 }}, 14edf contains subset edfs [[2edf]] and [[7edf]]. |
| ! colspan="2" |Pyrite
| | |
| ! rowspan="2" |ed122/81 (~ed13\22)
| | == Intervals == |
| ! rowspan="2" |ed34\57 (~47ed4!)
| | {{todo|inline=1|complete table|text=Add column with approximated JI ratios and/or notation.}} |
| ! rowspan="2" |''ed37\60+5¢''
| | |
| | {| class="wikitable center-1 right-2" |
| |- | | |- |
| !(~ed17\29) | | ! # |
| !(~ed10\17) | | ! Cents |
| |- | | |- |
| |1 | | | 0 |
| |''47.1939-47.551'' | | | 0.0 |
| |49.20635
| |
| |49.6297
| |
| |50.1396
| |
| |50.2597
| |
| |50.41825
| |
| |50.6475
| |
| |51.1278
| |
| |''52.8571-53.2143''
| |
| |- | | |- |
| |2 | | | 1 |
| |''94.3878-95.102'' | | | 50.1 |
| |98.4127
| |
| |99.2594
| |
| |100.2793
| |
| |100.5194
| |
| |100.8365
| |
| |101.295
| |
| |102.2556
| |
| |''105.7143-106.4286''
| |
| |- | | |- |
| |3 | | | 2 |
| |''141.5816-142.653'' | | | 100.3 |
| |147.61905
| |
| |148.8891
| |
| |150.4189
| |
| |150.77915
| |
| |151.2547
| |
| |151.9425
| |
| |153.3835
| |
| |''158.5714-159.6429''
| |
| |- | | |- |
| |4 | | | 3 |
| |''188.7755-190.2041'' | | | 150.4 |
| |196.8254
| |
| |198.5188
| |
| |200.5586
| |
| |201.0389
| |
| |201.673
| |
| |202.5899
| |
| |204.5113
| |
| |''211.4286-212.8571''
| |
| |- | | |- |
| |5 | | | 4 |
| |''235.9694-237.7551'' | | | 200.6 |
| |246.03175
| |
| |248.1485
| |
| |250.6982
| |
| |251.2986
| |
| |252.0912
| |
| |253.2374
| |
| |255.6391
| |
| |''264.2857-266.0714''
| |
| |- | | |- |
| |6 | | | 5 |
| |''283.1633-285.3061'' | | | 250.7 |
| |295.2381
| |
| |297.782
| |
| |300.8379
| |
| |301.5583
| |
| |302.5095
| |
| |303.8849
| |
| |306.7669
| |
| |''317.1429-319.2857''
| |
| |- | | |- |
| |7 | | | 6 |
| |''331.3571-332.857''1 | | | 300.8 |
| |344.4444
| |
| |347.408
| |
| |350.9775
| |
| |351.818
| |
| |352.9277
| |
| |354.5324
| |
| |357.8947
| |
| |''370-372.5''
| |
| |- | | |- |
| |8 | | | 7 |
| |''377.551-380.4082'' | | | 351.0 |
| |393.6508
| |
| |397.03765
| |
| |401.1171
| |
| |402.0777
| |
| |403.346
| |
| |405.1799
| |
| |409.0226
| |
| |''422.8571-425.7143''
| |
| |- | | |- |
| |9 | | | 8 |
| |''424.7449-427.9592'' | | | 401.1 |
| |442.8571
| |
| |446.66735
| |
| |451.2568
| |
| |452.33745
| |
| |453.7642
| |
| |455.8274
| |
| |460.1504
| |
| |''475.7143-478.9286''
| |
| |- | | |- |
| |10 | | | 9 |
| |''471.9388-475.5102'' | | | 451.3 |
| |492.0635
| |
| |496.2971
| |
| |501.3964
| |
| |502.5972
| |
| |504.1825
| |
| |506.4749
| |
| |511.2781
| |
| |''528.5714-532.1429''
| |
| |- | | |- |
| |11 | | | 10 |
| |''519.13265-523.0612'' | | | 501.4 |
| |541.2698
| |
| |545.9268
| |
| |551.536
| |
| |552.8569
| |
| |554.6007
| |
| |557.1223
| |
| |562.406
| |
| |''581.4286-585.3571''
| |
| |- | | |- |
| |12 | | | 11 |
| |''566.3265-570.6122'' | | | 551.5 |
| |590.4762
| |
| |595.5565
| |
| |601.6757
| |
| |603.1166
| |
| |605.019
| |
| |607.7698
| |
| |613.5338
| |
| |''634.2857-638.5714''
| |
| |- | | |- |
| |13 | | | 12 |
| |''613.5204-618.1633'' | | | 601.7 |
| |639.6825
| |
| |645.1862
| |
| |651.8154
| |
| |653.3763
| |
| |655.4372
| |
| |658.4173
| |
| |664.66165
| |
| |''687.1429-691.7857''
| |
| |- | | |- |
| |14 | | | 13 |
| |''660.7143-665.714''3 | | | 651.8 |
| |688.8889
| |
| |694.8158
| |
| |701.955
| |
| |703.636
| |
| |705.85545
| |
| |709.0648
| |
| |715.7895
| |
| |''740-745''
| |
| |- | | |- |
| |15 | | | 14 |
| |''707.9082-713.2653'' | | | 702.0 |
| |738.0952
| |
| |744.4456
| |
| |752.0946
| |
| |753.89575
| |
| |756.2736
| |
| |759.7123
| |
| |766.9173
| |
| |''792.8571-798.2143''
| |
| |- | | |- |
| |16 | | | 15 |
| |''755.102-760.8163'' | | | 752.1 |
| |787.3016
| |
| |794.0753
| |
| |802.2343
| |
| |804.1555
| |
| |806.6919
| |
| |810.3598
| |
| |818.0451
| |
| |''845.7143-851.4286''
| |
| |- | | |- |
| |17 | | | 16 |
| |''802.2959-808.36735'' | | | 802.2 |
| |836.5079
| |
| |843.705
| |
| |852.3739
| |
| |854.4152
| |
| |857.1102
| |
| |961.0073
| |
| |869.1729
| |
| |''898.5714-904.6429''
| |
| |- | | |- |
| |18 | | | 17 |
| |''849.4898-855.9184'' | | | 852.4 |
| |885.7143
| |
| |893.3347
| |
| |902.5136
| |
| |904.6749
| |
| |907.5284
| |
| |911.6547
| |
| |920.30075
| |
| |''951.4286-957.8571''
| |
| |- | | |- |
| |19 | | | 18 |
| |''896.6387-903.4694'' | | | 902.5 |
| |934.9206
| |
| |942.9644
| |
| |952.6532
| |
| |954.9346
| |
| |957.9467
| |
| |962.3022
| |
| |971.4286
| |
| |''1004.2857-1011.0714''
| |
| |- | | |- |
| |20 | | | 19 |
| |''943.8776-951.0204'' | | | 952.7 |
| |984.127
| |
| |992.5941
| |
| |1002.7929
| |
| |1005.1943
| |
| |1008.3649
| |
| |1012.9497
| |
| |1022.5564
| |
| |''1057.1429-1064.2857''
| |
| |- | | |- |
| |21 | | | 20 |
| |''991.0714-998.5714'' | | | 1002.8 |
| |1033.333
| |
| |1042.2238
| |
| |1052.9235
| |
| |1055.454
| |
| |1058.7832
| |
| |1063.5972
| |
| |1073.6842
| |
| |''1110-1117.5''
| |
| |- | | |- |
| |22 | | | 21 |
| |''1038.2653-1046.12245'' | | | 1052.9 |
| |1082.5397
| |
| |1091.8535
| |
| |1103.0721
| |
| |1105.7138
| |
| |1109.2014
| |
| |1114.2447
| |
| |1124.812
| |
| |''1162.8571-1170.7143''
| |
| |- | | |- |
| |23 | | | 22 |
| |''1085.4592-1093.6735'' | | | 1103.1 |
| |1131.7646
| |
| |1141.4832
| |
| |1153.2118
| |
| |1155.9735
| |
| |1159.6297
| |
| |1164.8922
| |
| |1175.93985
| |
| |''1215.7143-1223.9286''
| |
| |- | | |- |
| |24 | | | 23 |
| |''1132.6531-1141.2245'' | | | 1153.2 |
| |1180.9524
| |
| |1191.1129
| |
| |1203.3514
| |
| |1206.2332
| |
| |1210.0379
| |
| |1215.5397
| |
| |1227.0677
| |
| |''1268.5714-1277.5714''
| |
| |- | | |- |
| |25 | | | 24 |
| |''1179.8469-1188.7755'' | | | 1203.4 |
| |1230.1587
| |
| |1240.74265
| |
| |1253.4911
| |
| |1256.4929
| |
| |1260.4561
| |
| |1266.18715
| |
| |1278.1955
| |
| |''1321.4286-1330.3571''
| |
| |- | | |- |
| |26 | | | 25 |
| |''1227.0408-1236.3265'' | | | 1253.5 |
| |1279.3651
| |
| |1290.37235
| |
| |1303.6307
| |
| |1306.7526
| |
| |1310.8744
| |
| |1316.8346
| |
| |1329.3233
| |
| |''1374.2857-1383.5714''
| |
| |- | | |- |
| |27 | | | 26 |
| |''1274.2347-1283.87755'' | | | 1303.6 |
| |1328.5714
| |
| |1340.0021
| |
| |1353.7704
| |
| |1357.01235
| |
| |1361.2927
| |
| |1367.4821
| |
| |1380.4511
| |
| |''1427.1429-1436.7857''
| |
| |- | | |- |
| |28 | | | 27 |
| |''1321.4286-1331.4286'' | | | 1353.8 |
| |1377.7778 | | |- |
| |1389.6318 | | | 28 |
| |1403.91 | | | 1403.9 |
| |1407.2721
| |
| |1411.7109
| |
| |1418.1296
| |
| |1431.57895
| |
| |''1480-1490''
| |
| |} | | |} |
| [[Category:Edf]] | | |
| [[Category:Edonoi]] | | == See also == |
| [[Category:todo:improve synopsis]] | | * [[24edo]] – relative edo |
| | * [[38edt]] – relative edt |
| | * [[56ed5]] – relative ed5 |
| | * [[62ed6]] – relative ed6 |
| | * [[83ed11]] – relative ed11 |
| | * [[86ed12]] – relative ed12 |
| | * [[198ed304]] – close to the zeta-optimized tuning for 24edo |
| | |
| | [[Category:24edo]] |