28edf: Difference between revisions
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'''[[EDF|Division of the just perfect fifth]] into 28 equal parts''' (28EDF) is related to [[48edo|48 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 25.0698 cents (corresponding to 47.8663 [[edo]]). It is related to the regular temperament which tempers out |187 -159 28> in the 5-limit; 6656/6655, 256000/255879, and 38671875/38614472 in the 13-limit (2.3.5.11.13 subgroup), which is supported by 335, [[383edo|383]], 718, [[1053edo|1053]], and 1101 EDOs. | '''[[EDF|Division of the just perfect fifth]] into 28 equal parts''' (28EDF) is related to [[48edo|48 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 25.0698 cents (corresponding to 47.8663 [[edo]]). It is related to the regular temperament which tempers out |187 -159 28> in the 5-limit; 6656/6655, 256000/255879, and 38671875/38614472 in the 13-limit (2.3.5.11.13 subgroup), which is supported by 335, [[383edo|383]], 718, [[1053edo|1053]], and 1101 EDOs. | ||
== Intervals == | |||
{| class="wikitable" | |||
! | |||
!ed31\54 (~49edo!) | |||
!ed121/81 | |||
!ed3/2 | |||
!Golden (~ed10\17) | |||
!ed34\57 (~47edo!) | |||
|- | |||
|1 | |||
|24.6032 | |||
|24.81485 | |||
|25.0698 | |||
|25.2091 | |||
|25.5639 | |||
|- | |||
|2 | |||
|49.20635 | |||
|49.6297 | |||
|50.1396 | |||
|50.41825 | |||
|51.1278 | |||
|- | |||
|3 | |||
|73.8095 | |||
|74.4446 | |||
|75.2095 | |||
|75.6274 | |||
|76.6917 | |||
|- | |||
|4 | |||
|98.4127 | |||
|99.2594 | |||
|100.2793 | |||
|100.8365 | |||
|102.2556 | |||
|- | |||
|5 | |||
|123.0159 | |||
|124.0743 | |||
|125.3491 | |||
|10\26.0456 | |||
|127.81955 | |||
|- | |||
|6 | |||
|147.61905 | |||
|148.8891 | |||
|150.4189 | |||
|151.2547 | |||
|153.3835 | |||
|- | |||
|7 | |||
|172.2222 | |||
|173.704 | |||
|175.48875 | |||
|176.4639 | |||
|178.947 | |||
|- | |||
|8 | |||
|196.8254 | |||
|198.5188 | |||
|200.5586 | |||
|201.673 | |||
|204.5113 | |||
|- | |||
|9 | |||
|221.4286 | |||
|223.3337 | |||
|225.6284 | |||
|226.8821 | |||
|230.0752 | |||
|- | |||
|10 | |||
|246.03175 | |||
|248.1485 | |||
|250.6982 | |||
|252.0912 | |||
|255.6391 | |||
|- | |||
|11 | |||
|270.6349 | |||
|272.9634 | |||
|275.768 | |||
|277.3004 | |||
|281.203 | |||
|- | |||
|12 | |||
|295.2381 | |||
|297.782 | |||
|300.8379 | |||
|302.5095 | |||
|306.7669 | |||
|- | |||
|13 | |||
|319.8413 | |||
|322.5931 | |||
|325.9077 | |||
|327.7186 | |||
|332.3308 | |||
|- | |||
|14 | |||
|344.4444 | |||
|347.408 | |||
|350.9775 | |||
|352.9277 | |||
|357.8947 | |||
|- | |||
|15 | |||
|369.0476 | |||
|372.2228 | |||
|376.0473 | |||
|378.13685 | |||
|383.45865 | |||
|- | |||
|16 | |||
|393.6508 | |||
|397.03765 | |||
|401.1171 | |||
|403.346 | |||
|409.0226 | |||
|- | |||
|17 | |||
|418.254 | |||
|421.8525 | |||
|426.187 | |||
|428.5551 | |||
|434.5865 | |||
|- | |||
|18 | |||
|442.8571 | |||
|446.66735 | |||
|451.2568 | |||
|453.7642 | |||
|460.1504 | |||
|- | |||
|19 | |||
|467.460 | |||
|471.4822 | |||
|476.3266 | |||
|478.97333 | |||
|485.7143 | |||
|- | |||
|20 | |||
|492.0635 | |||
|496.2971 | |||
|501.3964 | |||
|504.1825 | |||
|511.2781 | |||
|- | |||
|21 | |||
|516.6667 | |||
|521.1119 | |||
|526.46625 | |||
|529.3916 | |||
|536.8421 | |||
|- | |||
|22 | |||
|541.2698 | |||
|545.9268 | |||
|551.536 | |||
|554.6007 | |||
|562.406 | |||
|- | |||
|23 | |||
|565.873 | |||
|570.7416 | |||
|576.6059 | |||
|579.8098 | |||
|587.9699 | |||
|- | |||
|24 | |||
|590.4762 | |||
|595.5565 | |||
|601.6757 | |||
|605.019 | |||
|613.5338 | |||
|- | |||
|25 | |||
|615.0794 | |||
|620.3713 | |||
|626.7455 | |||
|630.2281 | |||
|639.0977 | |||
|- | |||
|26 | |||
|639.6825 | |||
|645.1862 | |||
|651.8154 | |||
|655.4372 | |||
|664.66165 | |||
|- | |||
|27 | |||
|664.2857 | |||
|670.001 | |||
|676.8852 | |||
|680.6463 | |||
|690.2256 | |||
|- | |||
|28 | |||
|688.8889 | |||
|694.8158 | |||
|701.955 | |||
|705.85545 | |||
|715.7895 | |||
|- | |||
|29 | |||
|713.4921 | |||
|719.6307 | |||
|727.0248 | |||
|731.0646 | |||
|741.3534 | |||
|- | |||
|30 | |||
|738.0952 | |||
|744.4456 | |||
|752.0946 | |||
|756.2736 | |||
|766.9173 | |||
|- | |||
|31 | |||
|762.6984 | |||
|769.2604 | |||
|777.1645 | |||
|781.4828 | |||
|792.4812 | |||
|- | |||
|32 | |||
|787.3016 | |||
|794.0753 | |||
|802.2343 | |||
|806.6919 | |||
|818.0451 | |||
|- | |||
|33 | |||
|811.9048 | |||
|818.89015 | |||
|827.3041 | |||
|831.9011 | |||
|843.609 | |||
|- | |||
|34 | |||
|836.5079 | |||
|843.705 | |||
|852.3739 | |||
|857.1102 | |||
|869.1729 | |||
|- | |||
|35 | |||
|861.1111 | |||
|868.51985 | |||
|877.44375 | |||
|882.3193 | |||
|894.7368 | |||
|- | |||
|36 | |||
|885.7143 | |||
|893.3347 | |||
|902.5136 | |||
|907.5284 | |||
|920.30075 | |||
|- | |||
|37 | |||
|910.3175 | |||
|918.1496 | |||
|927.5834 | |||
|932.3767 | |||
|945.8647 | |||
|- | |||
|38 | |||
|934.9206 | |||
|942.9644 | |||
|952.6532 | |||
|957.9467 | |||
|971.4286 | |||
|- | |||
|39 | |||
|959.5238 | |||
|967.7793 | |||
|977.723 | |||
|983.1558 | |||
|996.9925 | |||
|- | |||
|40 | |||
|984.127 | |||
|992.5941 | |||
|1002.7929 | |||
|1008.3649 | |||
|1022.5564 | |||
|- | |||
|41 | |||
|1008.7302 | |||
|1017.409 | |||
|1027.8627 | |||
|1033.57405 | |||
|1048.1203 | |||
|- | |||
|42 | |||
|1033.333 | |||
|1042.2238 | |||
|1052.9325 | |||
|1058.7832 | |||
|1073.6842 | |||
|- | |||
|43 | |||
|1057.9365 | |||
|1067.0386 | |||
|1078.0023 | |||
|1083.9923 | |||
|1099.2481 | |||
|- | |||
|44 | |||
|1082.5397 | |||
|1091.8535 | |||
|1103.0721 | |||
|1109.2014 | |||
|1124.812 | |||
|- | |||
|45 | |||
|1107.1429 | |||
|1116.6684 | |||
|1128.142 | |||
|1137.41055 | |||
|1150.3759 | |||
|- | |||
|46 | |||
|1131.7646 | |||
|1141.4832 | |||
|1153.2118 | |||
|1159.6297 | |||
|1175.93985 | |||
|- | |||
|47 | |||
|1156.3492 | |||
|1166.2981 | |||
|1178.2816 | |||
|1184.8288 | |||
|1201.5038 | |||
|- | |||
|48 | |||
|1180.9524 | |||
|1191.1129 | |||
|1203.3514 | |||
|1210.0379 | |||
|1227.0677 | |||
|} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||