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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}}


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 ===
!
{{Harmonics in equal|14|3|2|intervals=integer|columns=11}}
!ed31\54
{{Harmonics in equal|14|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 14edf (continued)}}
!ed121/81
 
!ed3/2
=== Subsets and supersets ===
!Golden (~ed10\17)
Since 14 factors into primes as {{nowrap| 2 × 7 }}, 14edf contains subset edfs [[2edf]] and [[7edf]].
!ed34\57 (~47ed4!)
 
|Approximate Ratios*
== Intervals ==
{{todo|inline=1|complete table|text=Add column with approximated JI ratios and/or notation.}}
 
{| class="wikitable center-1 right-2"
|-
! #
! Cents
|-
| 0
| 0.0
|-
| 1
| 50.1
|-
| 2
| 100.3
|-
| 3
| 150.4
|-
| 4
| 200.6
|-
|-
|1
| 5
|49.20635
| 250.7
|49.6297
|50.1396
|50.41825
|51.1278
|33/32, 34/33
|-
|-
|2
| 6
|98.4127
| 300.8
|99.2594
|100.2793
|100.8365
|102.2556
|17/16, 18/17
|-
|-
|3
| 7
|147.61905
| 351.0
|148.8891
|150.4189
|151.2547
|153.3835
|12/11
|-
|-
|4
| 8
|196.8254
| 401.1
|198.5188
|200.5586
|201.673
|204.5113
|9/8
|-
|-
|5
| 9
|246.03175
| 451.3
|248.1485
|250.6982
|252.0912
|255.6391
|22/19
|-
|-
|6
| 10
|295.2381
| 501.4
|297.782
|300.8379
|302.5095
|306.7669
|19/16
|-
|-
|7
| 11
|344.4444
| 551.5
|347.408
|350.9775
|352.9277
|357.8947
|11/9
|-
|-
|8
| 12
|393.6508
| 601.7
|397.03765
|401.1171
|403.346
|409.0226
|24/19
|-
|-
|9
| 13
|442.8571
| 651.8
|446.66735
|451.2568
|453.7642
|460.1504
|22/17
|-
|-
|10
| 14
|492.0635
| 702.0
|496.2971
|501.3964
|504.1825
|511.2781
|4/3
|-
|-
|11
| 15
|541.2698
| 752.1
|545.9268
|551.536
|554.6007
|562.406
|11/8
|-
|-
|12
| 16
|590.4762
| 802.2
|595.5565
|601.6757
|605.019
|613.5338
|17/12
|-
|-
|13
| 17
|639.6825
| 852.4
|645.1862
|651.8154
|655.4372
|664.66165
|16/11
|-
|-
|14
| 18
|688.8889
| 902.5
|694.8158
|701.955
|705.85545
|715.7895
|3/2
|-
|-
|15
| 19
|738.0952
| 952.7
|744.4456
|752.0946
|756.2736
|766.9173
|17/11
|-
|-
|16
| 20
|787.3016
| 1002.8
|794.0753
|802.2343
|806.6919
|818.0451
|19/12
|-
|-
|17
| 21
|836.5079
| 1052.9
|843.705
|852.3739
|857.1102
|869.1729
|18/11
|-
|-
|18
| 22
|885.7143
| 1103.1
|893.3347
|902.5136
|907.5284
|920.30075
|32/19
|-
|-
|19
| 23
|934.9206
| 1153.2
|942.9644
|952.6532
|957.9467
|971.4286
|19/11
|-
|-
|20
| 24
|984.127
| 1203.4
|992.5941
|1002.7929
|1008.3649
|1022.5564
|16/9
|-
|-
|21
| 25
|1033.333
| 1253.5
|1042.2238
|1052.9235
|1058.7832
|1073.6842
|11/6
|-
|-
|22
| 26
|1082.5397
| 1303.6
|1091.8535
|1103.0721
|1109.2014
|1124.812
|17/9, 32/17
|-
|-
|23
| 27
|1131.7646
| 1353.8
|1141.4832
|1153.2118
|1159.6297
|1175.93985
|33/17, 64/33
|-
|-
|24
| 28
|1180.9524
| 1403.9
|1191.1129
|1203.3514
|1210.0379
|1227.0677
|2/1
|}
|}
[[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]]
Retrieved from "https://en.xen.wiki/w/14edf"