38edf: Difference between revisions
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'''[[EDF|Division of the just perfect fifth]] into 38 equal parts''' (38EDF) is related to [[65edo | {{Infobox ET}} | ||
'''[[EDF|Division of the just perfect fifth]] into 38 equal parts''' (38EDF) is related to [[65edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The [[octave]] is [[Octave stretch|stretched]] by about 0.7125 [[cents]] and the step size is about 18.4725 cents. | |||
Lookalikes: [[65edo]], [[103edt]] | Lookalikes: [[65edo]], [[103edt]] | ||
== Harmonics == | |||
[[ | {{Harmonics in equal|38|3|2|intervals=prime}} | ||
== Intervals == | |||
{| class="wikitable mw-collapsible" | |||
|+ Intervals of 38edf | |||
|- | |||
! Step number | |||
! Cents value | |||
|- | |||
| style="text-align:center;" |1 | |||
| style="text-align:right;" |18.4725 | |||
|- | |||
| style="text-align:center;" |2 | |||
| style="text-align:right;" |36.945 | |||
|- | |||
| style="text-align:center;" |3 | |||
| style="text-align:right;" |55.4175 | |||
|- | |||
| style="text-align:center;" |4 | |||
| style="text-align:right;" |73.89 | |||
|- | |||
| style="text-align:center;" |5 | |||
| style="text-align:right;" |92.3625 | |||
|- | |||
| style="text-align:center;" |6 | |||
| style="text-align:right;" |110.835 | |||
|- | |||
| style="text-align:center;" |7 | |||
| style="text-align:right;" |129.3075 | |||
|- | |||
| style="text-align:center;" |8 | |||
| style="text-align:right;" |147.78 | |||
|- | |||
| style="text-align:center;" |9 | |||
| style="text-align:right;" |166.2525 | |||
|- | |||
| style="text-align:center;" |10 | |||
| style="text-align:right;" |184.725 | |||
|- | |||
| style="text-align:center;" |11 | |||
| style="text-align:right;" |203.1975 | |||
|- | |||
| style="text-align:center;" |12 | |||
| style="text-align:right;" |221.67 | |||
|- | |||
| style="text-align:center;" |13 | |||
| style="text-align:right;" |240.1425 | |||
|- | |||
| style="text-align:center;" |14 | |||
| style="text-align:right;" |258.615 | |||
|- | |||
| style="text-align:center;" |15 | |||
| style="text-align:right;" |277.0875 | |||
|- | |||
| style="text-align:center;" |16 | |||
| style="text-align:right;" |295.56 | |||
|- | |||
| style="text-align:center;" |17 | |||
| style="text-align:right;" |314.0325 | |||
|- | |||
| style="text-align:center;" |18 | |||
| style="text-align:right;" |332.505 | |||
|- | |||
| style="text-align:center;" |19 | |||
| style="text-align:right;" |350.9775 | |||
|- | |||
| style="text-align:center;" |20 | |||
| style="text-align:right;" |369.45 | |||
|- | |||
| style="text-align:center;" |21 | |||
| style="text-align:right;" |387.9225 | |||
|- | |||
| style="text-align:center;" |22 | |||
| style="text-align:right;" |406.395 | |||
|- | |||
| style="text-align:center;" |23 | |||
| style="text-align:right;" |424.8675 | |||
|- | |||
| style="text-align:center;" |24 | |||
| style="text-align:right;" |443.34 | |||
|- | |||
| style="text-align:center;" |25 | |||
| style="text-align:right;" |461.8125 | |||
|- | |||
| style="text-align:center;" |26 | |||
| style="text-align:right;" |480.285 | |||
|- | |||
| style="text-align:center;" |27 | |||
| style="text-align:right;" |498.7575 | |||
|- | |||
| style="text-align:center;" |28 | |||
| style="text-align:right;" |517.23 | |||
|- | |||
| style="text-align:center;" |29 | |||
| style="text-align:right;" |535.7025 | |||
|- | |||
| style="text-align:center;" |30 | |||
| style="text-align:right;" |553.175 | |||
|- | |||
| style="text-align:center;" |31 | |||
| style="text-align:right;" |572.6475 | |||
|- | |||
| style="text-align:center;" |32 | |||
| style="text-align:right;" |591.12 | |||
|- | |||
| style="text-align:center;" |33 | |||
| style="text-align:right;" |609.5925 | |||
|- | |||
| style="text-align:center;" |34 | |||
| style="text-align:right;" |628.065 | |||
|- | |||
| style="text-align:center;" |35 | |||
| style="text-align:right;" |646.5375 | |||
|- | |||
| style="text-align:center;" |36 | |||
| style="text-align:right;" |664.01 | |||
|- | |||
| style="text-align:center;" |37 | |||
| style="text-align:right;" |683.4825 | |||
|- | |||
| style="text-align:center;" |38 | |||
| style="text-align:right;" |701.955 | |||
|- | |||
| style="text-align:center;" |39 | |||
| style="text-align:right;" |720.4275 | |||
|- | |||
| style="text-align:center;" |40 | |||
| style="text-align:right;" |738.9 | |||
|- | |||
| style="text-align:center;" |41 | |||
| style="text-align:right;" |757.3725 | |||
|- | |||
| style="text-align:center;" |42 | |||
| style="text-align:right;" |775.845 | |||
|- | |||
| style="text-align:center;" |43 | |||
| style="text-align:right;" |794.3175 | |||
|- | |||
| style="text-align:center;" |44 | |||
| style="text-align:right;" |812.79 | |||
|- | |||
| style="text-align:center;" |45 | |||
| style="text-align:right;" |831.2625 | |||
|- | |||
| style="text-align:center;" |46 | |||
| style="text-align:right;" |849.735 | |||
|- | |||
| style="text-align:center;" |47 | |||
| style="text-align:right;" |868.2075 | |||
|- | |||
| style="text-align:center;" |48 | |||
| style="text-align:right;" |886.605 | |||
|- | |||
| style="text-align:center;" |49 | |||
| style="text-align:right;" |905.1525 | |||
|- | |||
| style="text-align:center;" |50 | |||
| style="text-align:right;" |923.625 | |||
|- | |||
| style="text-align:center;" |51 | |||
| style="text-align:right;" |942.0975 | |||
|- | |||
| style="text-align:center;" |52 | |||
| style="text-align:right;" |960.57 | |||
|- | |||
| style="text-align:center;" |53 | |||
| style="text-align:right;" |979.0425 | |||
|- | |||
| style="text-align:center;" |54 | |||
| style="text-align:right;" |997.515 | |||
|- | |||
| style="text-align:center;" |55 | |||
| style="text-align:right;" |1015.9875 | |||
|- | |||
| style="text-align:center;" |56 | |||
| style="text-align:right;" |1034.46 | |||
|- | |||
| style="text-align:center;" |57 | |||
| style="text-align:right;" |1052.9235 | |||
|- | |||
| style="text-align:center;" |58 | |||
| style="text-align:right;" |1071.405 | |||
|- | |||
| style="text-align:center;" |59 | |||
| style="text-align:right;" |1089.8775 | |||
|- | |||
| style="text-align:center;" |60 | |||
| style="text-align:right;" |1108.35 | |||
|- | |||
| style="text-align:center;" |61 | |||
| style="text-align:right;" |1126.8225 | |||
|- | |||
| style="text-align:center;" |62 | |||
| style="text-align:right;" |1145.295 | |||
|- | |||
| style="text-align:center;" |63 | |||
| style="text-align:right;" |1163.7675 | |||
|- | |||
| style="text-align:center;" |64 | |||
| style="text-align:right;" |1182.24 | |||
|- | |||
| style="text-align:center;" |65 | |||
| style="text-align:right;" |1200.7125 | |||
|- | |||
| style="text-align:center;" | 66 | |||
| style="text-align:right;" | 1219.185 | |||
|- | |||
| style="text-align:center;" | 67 | |||
| style="text-align:right;" | 1237.6575 | |||
|- | |||
| style="text-align:center;" | 68 | |||
| style="text-align:right;" | 1256.13 | |||
|- | |||
| style="text-align:center;" | 69 | |||
| style="text-align:right;" | 1274.6025 | |||
|- | |||
| style="text-align:center;" | 70 | |||
| style="text-align:right;" | 1293.075 | |||
|- | |||
| style="text-align:center;" | 71 | |||
| style="text-align:right;" | 1311.5775 | |||
|- | |||
| style="text-align:center;" | 72 | |||
| style="text-align:right;" | 1330.02 | |||
|- | |||
| style="text-align:center;" | 73 | |||
| style="text-align:right;" | 1348.4925 | |||
|- | |||
| style="text-align:center;" | 74 | |||
| style="text-align:right;" | 1366.965 | |||
|- | |||
| style="text-align:center;" | 75 | |||
| style="text-align:right;" | 1385.4375 | |||
|- | |||
| style="text-align:center;" | 76 | |||
| style="text-align:right;" | 1403.91 | |||
|} | |||
{{todo|inline=1|complete table|text=Add a third column that comments on the intervals, either what [[JI]] they approximate, what they are named, or how they can be used musically.}} | |||
{{todo|expand}} | |||