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| '''3EDF''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio. It corresponds to 5.1285 [[edo]]. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]]. | | '''3edf''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)<sup>1/3</sup> as a frequency ratio. It corresponds to 5.1285 [[edo]]. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]]. |
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| ==Factoids about 3EDF== | | == Factoids about 3edf == |
| 3EDF is related to the [[Gamelismic clan|gamelismic temperaments]], which temper out 1029/1024 in the 7-limit.
| | 3edf's step size is close to the [[slendric]] temperament, which tempers out 1029/1024 in the 2.3.7 subgroup. |
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| == Intervals == | | == Intervals == |
| {| class="wikitable" | | {| class="wikitable center-all" |
| |+
| | ! # |
| ! rowspan="2" |
| | ! Cents |
| ! rowspan="2" |''ed233\420-5¢''
| |
| ! rowspan="2" |ed31\54
| |
| ! rowspan="2" |ed121/81 (~ed11\19) | |
| ! rowspan="2" |ed696¢
| |
| ! rowspan="2" |ed32\55
| |
| ! rowspan="2" |ed700¢=''r¢'' | |
| ! rowspan="2" |ed3/2
| |
| ! colspan="2" |Pyrite
| |
| ! rowspan="2" |ed708¢
| |
| ! rowspan="2" |ed122/81 (~ed13\22)
| |
| ! rowspan="2" |ed34\57
| |
| ! rowspan="2" |''ed37\60+5¢''
| |
| |- | | |- |
| !(~ed17\29)
| | | 1 |
| !(~ed10\17)
| | | 233.99 |
| |- | | |- |
| |1 | | | 2 |
| |''220.238-221.905'' | | | 467.97 |
| |229.63
| |
| |231.605
| |
| |232
| |
| |232.727
| |
| |''233.333''
| |
| |233.985
| |
| |234.545
| |
| |235.285
| |
| |236
| |
| |236.355
| |
| |238.597
| |
| |''246.667-248.333''
| |
| |- | | |- |
| |2
| | | 3 |
| |''440.476-443.8095''
| | | 701.96 |
| |259.259
| |
| |463.211
| |
| |464
| |
| |465.4545
| |
| |''466.667''
| |
| |467.97
| |
| |469.091
| |
| |470.57
| |
| |472
| |
| |472.71
| |
| |477.193
| |
| |''493.333-496.667''
| |
| |-
| |
| |3 | |
| |''660.714-665.714''
| |
| |688.888
| |
| |694.816
| |
| |696
| |
| |698.182
| |
| |''700''
| |
| |701.955 | |
| |703.636
| |
| |705.8885
| |
| |708
| |
| |709.065
| |
| |715.7895
| |
| |''740-745''
| |
| |-
| |
| |4
| |
| |''880.952-887.619''
| |
| |918.5185
| |
| |926.421
| |
| |928
| |
| |930.909
| |
| |''933.333''
| |
| |935.94
| |
| |938.181
| |
| |941.141
| |
| |944
| |
| |945.42
| |
| |954.386
| |
| |''986.667-993.333''
| |
| |-
| |
| |5
| |
| |''1101.1905-1109.524''
| |
| |1148.148
| |
| |1158.0265
| |
| |1160
| |
| |1163.636
| |
| |''1166.667''
| |
| |1169.925
| |
| |1172.727
| |
| |1176.426
| |
| |1180
| |
| |1181.775
| |
| |1192.9825
| |
| |''1233.333-1241.667''
| |
| |-
| |
| |6
| |
| |''1321.429-1331.429''
| |
| |1377.778
| |
| |1389.632
| |
| |1392
| |
| |1396.364
| |
| |''1400''
| |
| |1403.91
| |
| |1407.272
| |
| |1411.711
| |
| |1416
| |
| |1418.13
| |
| |1431.579
| |
| |''1480-1490''
| |
| |} | | |} |
| | |
| [[Category:Edf]] | | [[Category:Edf]] |
| [[Category:Edonoi]] | | [[Category:Edonoi]] |