14edf: Difference between revisions

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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 exception for 7, 14, and 21.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Edf]]
+== Theory ==
-[[Category:Edonoi]]
+edf 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]].
-[[Category:todo:improve synopsis]]
+=== Harmonics ===
+{{Harmonics in equal|14|3|2|intervals=integer|columns=11}}
+{{Harmonics in equal|14|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 14edf (continued)}}
+=== Subsets and supersets ===
+Since 14 factors into primes as {{nowrap| 2 × 7 }}, 14edf contains subset edfs [[2edf]] and [[7edf]].
+== 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
+|-
+| 5
+| 250.7
+|-
+| 6
+| 300.8
+|-
+| 7
+| 351.0
+|-
+| 8
+| 401.1
+|-
+| 9
+| 451.3
+|-
+| 10
+| 501.4
+|-
+| 11
+| 551.5
+|-
+| 12
+| 601.7
+|-
+| 13
+| 651.8
+|-
+| 14
+| 702.0
+|-
+| 15
+| 752.1
+|-
+| 16
+| 802.2
+|-
+| 17
+| 852.4
+|-
+| 18
+| 902.5
+|-
+| 19
+| 952.7
+|-
+| 20
+| 1002.8
+|-
+| 21
+| 1052.9
+|-
+| 22
+| 1103.1
+|-
+| 23
+| 1153.2
+|-
+| 24
+| 1203.4
+|-
+| 25
+| 1253.5
+|-
+| 26
+| 1303.6
+|-
+| 27
+| 1353.8
+|-
+| 28
+| 1403.9
+|}
+== See also ==
+* [[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]]