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:center;" |1 | ||
| style="text-align:right;" |18.4725 | | style="text-align:right;" |18.4725 | ||
|- | |- | ||
| style="text-align:center;" |2 | | style="text-align:center;" |2 | ||
| style="text-align:right;" |36.945 | | style="text-align:right;" |36.945 | ||
|- | |- | ||
| style="text-align:center;" |3 | | style="text-align:center;" |3 | ||
| style="text-align:right;" |55.4175 | | style="text-align:right;" |55.4175 | ||
|- | |- | ||
| style="text-align:center;" |4 | | style="text-align:center;" |4 | ||
| style="text-align:right;" |73.89 | | style="text-align:right;" |73.89 | ||
|- | |- | ||
| style="text-align:center;" |5 | | style="text-align:center;" |5 | ||
| style="text-align:right;" |92.3625 | | style="text-align:right;" |92.3625 | ||
|- | |- | ||
| style="text-align:center;" |6 | | style="text-align:center;" |6 | ||
| style="text-align:right;" |110.835 | | style="text-align:right;" |110.835 | ||
|- | |- | ||
| style="text-align:center;" |7 | | style="text-align:center;" |7 | ||
| style="text-align:right;" |129.3075 | | style="text-align:right;" |129.3075 | ||
|- | |- | ||
| style="text-align:center;" |8 | | style="text-align:center;" |8 | ||
| style="text-align:right;" |147.78 | | style="text-align:right;" |147.78 | ||
|- | |- | ||
| style="text-align:center;" |9 | | style="text-align:center;" |9 | ||
| style="text-align:right;" |166.2525 | | style="text-align:right;" |166.2525 | ||
|- | |- | ||
| style="text-align:center;" |10 | | style="text-align:center;" |10 | ||
| style="text-align:right;" |184.725 | | style="text-align:right;" |184.725 | ||
|- | |- | ||
| style="text-align:center;" |11 | | style="text-align:center;" |11 | ||
| style="text-align:right;" |203.1975 | | style="text-align:right;" |203.1975 | ||
|- | |- | ||
| style="text-align:center;" |12 | | style="text-align:center;" |12 | ||
| style="text-align:right;" |221.67 | | style="text-align:right;" |221.67 | ||
|- | |- | ||
| style="text-align:center;" |13 | | style="text-align:center;" |13 | ||
| style="text-align:right;" |240.1425 | | style="text-align:right;" |240.1425 | ||
|- | |- | ||
| style="text-align:center;" |14 | | style="text-align:center;" |14 | ||
| style="text-align:right;" |258.615 | | style="text-align:right;" |258.615 | ||
|- | |- | ||
| style="text-align:center;" |15 | | style="text-align:center;" |15 | ||
| style="text-align:right;" |277.0875 | | style="text-align:right;" |277.0875 | ||
|- | |- | ||
| style="text-align:center;" |16 | | style="text-align:center;" |16 | ||
| style="text-align:right;" |295.56 | | style="text-align:right;" |295.56 | ||
|- | |- | ||
| style="text-align:center;" |17 | | style="text-align:center;" |17 | ||
| style="text-align:right;" |314.0325 | | style="text-align:right;" |314.0325 | ||
|- | |- | ||
| style="text-align:center;" |18 | | style="text-align:center;" |18 | ||
| style="text-align:right;" |332.505 | | style="text-align:right;" |332.505 | ||
|- | |- | ||
| style="text-align:center;" |19 | | style="text-align:center;" |19 | ||
| style="text-align:right;" |350.9775 | | style="text-align:right;" |350.9775 | ||
|- | |- | ||
| style="text-align:center;" |20 | | style="text-align:center;" |20 | ||
| style="text-align:right;" |369.45 | | style="text-align:right;" |369.45 | ||
|- | |- | ||
| style="text-align:center;" |21 | | style="text-align:center;" |21 | ||
| style="text-align:right;" |387.9225 | | style="text-align:right;" |387.9225 | ||
|- | |- | ||
| style="text-align:center;" |22 | | style="text-align:center;" |22 | ||
| style="text-align:right;" |406.395 | | style="text-align:right;" |406.395 | ||
|- | |- | ||
| style="text-align:center;" |23 | | style="text-align:center;" |23 | ||
| style="text-align:right;" |424.8675 | | style="text-align:right;" |424.8675 | ||
|- | |- | ||
| style="text-align:center;" |24 | | style="text-align:center;" |24 | ||
| style="text-align:right;" |443.34 | | style="text-align:right;" |443.34 | ||
|- | |- | ||
| style="text-align:center;" |25 | | style="text-align:center;" |25 | ||
| style="text-align:right;" |461.8125 | | style="text-align:right;" |461.8125 | ||
|- | |- | ||
| style="text-align:center;" |26 | | style="text-align:center;" |26 | ||
| style="text-align:right;" |480.285 | | style="text-align:right;" |480.285 | ||
|- | |- | ||
| style="text-align:center;" |27 | | style="text-align:center;" |27 | ||
| style="text-align:right;" |498.7575 | | style="text-align:right;" |498.7575 | ||
|- | |- | ||
| style="text-align:center;" |28 | | style="text-align:center;" |28 | ||
| style="text-align:right;" |517.23 | | style="text-align:right;" |517.23 | ||
|- | |- | ||
| style="text-align:center;" |29 | | style="text-align:center;" |29 | ||
| style="text-align:right;" |535.7025 | | style="text-align:right;" |535.7025 | ||
|- | |- | ||
| style="text-align:center;" |30 | | style="text-align:center;" |30 | ||
| style="text-align:right;" |553.175 | | style="text-align:right;" |553.175 | ||
|- | |- | ||
| style="text-align:center;" |31 | | style="text-align:center;" |31 | ||
| style="text-align:right;" |572.6475 | | style="text-align:right;" |572.6475 | ||
|- | |- | ||
| style="text-align:center;" |32 | | style="text-align:center;" |32 | ||
| style="text-align:right;" |591.12 | | style="text-align:right;" |591.12 | ||
|- | |- | ||
| style="text-align:center;" |33 | | style="text-align:center;" |33 | ||
| style="text-align:right;" |609.5925 | | style="text-align:right;" |609.5925 | ||
|- | |- | ||
| style="text-align:center;" |34 | | style="text-align:center;" |34 | ||
| style="text-align:right;" |628.065 | | style="text-align:right;" |628.065 | ||
|- | |- | ||
| style="text-align:center;" |35 | | style="text-align:center;" |35 | ||
| style="text-align:right;" |646.5375 | | style="text-align:right;" |646.5375 | ||
|- | |- | ||
| style="text-align:center;" |36 | | style="text-align:center;" |36 | ||
| style="text-align:right;" |664.01 | | style="text-align:right;" |664.01 | ||
|- | |- | ||
| style="text-align:center;" |37 | | style="text-align:center;" |37 | ||
| style="text-align:right;" |683.4825 | | style="text-align:right;" |683.4825 | ||
|- | |- | ||
| style="text-align:center;" |38 | | style="text-align:center;" |38 | ||
| style="text-align:right;" |701.955 | | style="text-align:right;" |701.955 | ||
|- | |- | ||
| style="text-align:center;" |39 | | style="text-align:center;" |39 | ||
| style="text-align:right;" |720.4275 | | style="text-align:right;" |720.4275 | ||
|- | |- | ||
| style="text-align:center;" |40 | | style="text-align:center;" |40 | ||
| style="text-align:right;" |738.9 | | style="text-align:right;" |738.9 | ||
|- | |- | ||
| style="text-align:center;" |41 | | style="text-align:center;" |41 | ||
| style="text-align:right;" |757.3725 | | style="text-align:right;" |757.3725 | ||
|- | |- | ||
| style="text-align:center;" |42 | | style="text-align:center;" |42 | ||
| style="text-align:right;" |775.845 | | style="text-align:right;" |775.845 | ||
|- | |- | ||
| style="text-align:center;" |43 | | style="text-align:center;" |43 | ||
| style="text-align:right;" |794.3175 | | style="text-align:right;" |794.3175 | ||
|- | |- | ||
| style="text-align:center;" |44 | | style="text-align:center;" |44 | ||
| style="text-align:right;" |812.79 | | style="text-align:right;" |812.79 | ||
|- | |- | ||
| style="text-align:center;" |45 | | style="text-align:center;" |45 | ||
| style="text-align:right;" |831.2625 | | style="text-align:right;" |831.2625 | ||
|- | |- | ||
| style="text-align:center;" |46 | | style="text-align:center;" |46 | ||
| style="text-align:right;" |849.735 | | style="text-align:right;" |849.735 | ||
|- | |- | ||
| style="text-align:center;" |47 | | style="text-align:center;" |47 | ||
| style="text-align:right;" |868.2075 | | style="text-align:right;" |868.2075 | ||
|- | |- | ||
| style="text-align:center;" |48 | | style="text-align:center;" |48 | ||
| style="text-align:right;" |886.605 | | style="text-align:right;" |886.605 | ||
|- | |- | ||
| style="text-align:center;" |49 | | style="text-align:center;" |49 | ||
| style="text-align:right;" |905.1525 | | style="text-align:right;" |905.1525 | ||
|- | |- | ||
| style="text-align:center;" |50 | | style="text-align:center;" |50 | ||
| style="text-align:right;" |923.625 | | style="text-align:right;" |923.625 | ||
|- | |- | ||
| style="text-align:center;" |51 | | style="text-align:center;" |51 | ||
| style="text-align:right;" |942.0975 | | style="text-align:right;" |942.0975 | ||
|- | |- | ||
| style="text-align:center;" |52 | | style="text-align:center;" |52 | ||
| style="text-align:right;" |960.57 | | style="text-align:right;" |960.57 | ||
|- | |- | ||
| style="text-align:center;" |53 | | style="text-align:center;" |53 | ||
| style="text-align:right;" |979.0425 | | style="text-align:right;" |979.0425 | ||
|- | |- | ||
| style="text-align:center;" |54 | | style="text-align:center;" |54 | ||
| style="text-align:right;" |997.515 | | style="text-align:right;" |997.515 | ||
|- | |- | ||
| style="text-align:center;" |55 | | style="text-align:center;" |55 | ||
| style="text-align:right;" |1015.9875 | | style="text-align:right;" |1015.9875 | ||
|- | |- | ||
| style="text-align:center;" |56 | | style="text-align:center;" |56 | ||
| style="text-align:right;" |1034.46 | | style="text-align:right;" |1034.46 | ||
|- | |- | ||
| style="text-align:center;" |57 | | style="text-align:center;" |57 | ||
| style="text-align:right;" |1052.9235 | | style="text-align:right;" |1052.9235 | ||
|- | |- | ||
| style="text-align:center;" |58 | | style="text-align:center;" |58 | ||
| style="text-align:right;" |1071.405 | | style="text-align:right;" |1071.405 | ||
|- | |- | ||
| style="text-align:center;" |59 | | style="text-align:center;" |59 | ||
| style="text-align:right;" |1089.8775 | | style="text-align:right;" |1089.8775 | ||
|- | |- | ||
| style="text-align:center;" |60 | | style="text-align:center;" |60 | ||
| style="text-align:right;" |1108.35 | | style="text-align:right;" |1108.35 | ||
|- | |- | ||
| style="text-align:center;" |61 | | style="text-align:center;" |61 | ||
| style="text-align:right;" |1126.8225 | | style="text-align:right;" |1126.8225 | ||
|- | |- | ||
| style="text-align:center;" |62 | | style="text-align:center;" |62 | ||
| style="text-align:right;" |1145.295 | | style="text-align:right;" |1145.295 | ||
|- | |- | ||
| style="text-align:center;" |63 | | style="text-align:center;" |63 | ||
| style="text-align:right;" |1163.7675 | | style="text-align:right;" |1163.7675 | ||
|- | |- | ||
| style="text-align:center;" |64 | | style="text-align:center;" |64 | ||
| style="text-align:right;" |1182.24 | | style="text-align:right;" |1182.24 | ||
|- | |- | ||
| style="text-align:center;" |65 | | style="text-align:center;" |65 | ||
| style="text-align:right;" |1200.7125 | | style="text-align:right;" |1200.7125 | ||
|- | |- | ||
|66 | | style="text-align:center;" | 66 | ||
| | | style="text-align:right;" | 1219.185 | ||
|1219.185 | |||
|- | |- | ||
|67 | | style="text-align:center;" | 67 | ||
| | | style="text-align:right;" | 1237.6575 | ||
|1237.6575 | |||
|- | |- | ||
|68 | | style="text-align:center;" | 68 | ||
| | | style="text-align:right;" | 1256.13 | ||
|1256.13 | |||
|- | |- | ||
|69 | | style="text-align:center;" | 69 | ||
| | | style="text-align:right;" | 1274.6025 | ||
|1274.6025 | |||
|- | |- | ||
|70 | | style="text-align:center;" | 70 | ||
| | | style="text-align:right;" | 1293.075 | ||
|1293.075 | |||
|- | |- | ||
|71 | | style="text-align:center;" | 71 | ||
| | | style="text-align:right;" | 1311.5775 | ||
|1311.5775 | |||
|- | |- | ||
|72 | | style="text-align:center;" | 72 | ||
| | | style="text-align:right;" | 1330.02 | ||
|1330.02 | |||
|- | |- | ||
|73 | | style="text-align:center;" | 73 | ||
| | | style="text-align:right;" | 1348.4925 | ||
|1348.4925 | |||
|- | |- | ||
|74 | | style="text-align:center;" | 74 | ||
| | | style="text-align:right;" | 1366.965 | ||
|1366.965 | |||
|- | |- | ||
|75 | | style="text-align:center;" | 75 | ||
| | | style="text-align:right;" | 1385.4375 | ||
|1385.4375 | |||
|- | |- | ||
|76 | | style="text-align:center;" | 76 | ||
| | | style="text-align:right;" | 1403.91 | ||
|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}} | |||