28edf: Difference between revisions

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Line 4: Line 4:
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |
! rowspan="2" |
! rowspan="2" |''ed233\420-3.5¢ (51edo!)''
! rowspan="2" |ed31\54 (~49edo!)
! rowspan="2" |ed31\54 (~49edo!)
! rowspan="2" |ed121/81 (~ed11\19)
! rowspan="2" |ed121/81 (~ed11\19)
Line 10: Line 11:
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed34\57 (~47edo!)
! rowspan="2" |ed34\57 (~47edo!)
! rowspan="2" |''ed37\60+3.5¢ (~91ed4!)''
|-
|-
!(~ed17\29)
!(~ed17\29)
Line 15: Line 17:
|-
|-
|1
|1
|''23.6505-23.7755''
|24.6032
|24.6032
|24.81485
|24.81485
Line 22: Line 25:
|25.3234
|25.3234
|25.5639
|25.5639
|''26.4286-26.5536''
|-
|-
|2
|2
|''47.301-47.551''
|49.20635
|49.20635
|49.6297
|49.6297
Line 31: Line 36:
|50.6475
|50.6475
|51.1278
|51.1278
|''52.8571-53.1071''
|-
|-
|3
|3
|''70.9515-71.3625''
|73.8095
|73.8095
|74.4446
|74.4446
Line 40: Line 47:
|75.9712
|75.9712
|76.6917
|76.6917
|''79.2857-79.6607''
|-
|-
|4
|4
|''94.602-95.102''
|98.4127
|98.4127
|99.2594
|99.2594
Line 49: Line 58:
|101.295
|101.295
|102.2556
|102.2556
|''105.7143-106.2143''
|-
|-
|5
|5
|''118.25255-118.87755''
|123.0159
|123.0159
|124.0743
|124.0743
Line 58: Line 69:
|126.6187
|126.6187
|127.81955
|127.81955
|''132.1429-132.7679''
|-
|-
|6
|6
|''141.903-142.653''
|147.61905
|147.61905
|148.8891
|148.8891
Line 67: Line 80:
|151.9425
|151.9425
|153.3835
|153.3835
|''158.5714-159.3214''
|-
|-
|7
|7
|''165.5536-166.4285''
|172.2222
|172.2222
|173.704
|173.704
Line 76: Line 91:
|177.2662
|177.2662
|178.947
|178.947
|''185-185.875''
|-
|-
|8
|8
|''189.2041-190.2041''
|196.8254
|196.8254
|198.5188
|198.5188
Line 85: Line 102:
|202.5899
|202.5899
|204.5113
|204.5113
|''211.4286-212.4286''
|-
|-
|9
|9
|''212.8576-213.9796''
|221.4286
|221.4286
|223.3337
|223.3337
Line 94: Line 113:
|227.9137
|227.9137
|230.0752
|230.0752
|''237.8571-238.9791''
|-
|-
|10
|10
|''236.5051-237.7551''
|246.03175
|246.03175
|248.1485
|248.1485
Line 103: Line 124:
|253.2374
|253.2374
|255.6391
|255.6391
|''264.2857-265.5357''
|-
|-
|11
|11
|''260.1556-261.5306''
|270.6349
|270.6349
|272.9634
|272.9634
Line 112: Line 135:
|278.5612
|278.5612
|281.203
|281.203
|''290.7143-292.0693''
|-
|-
|12
|12
|''283.8061-285.3061''
|295.2381
|295.2381
|297.782
|297.782
Line 121: Line 146:
|303.8849
|303.8849
|306.7669
|306.7669
|''317.1429-318.6429''
|-
|-
|13
|13
|''307.4566-309.0816''
|319.8413
|319.8413
|322.5931
|322.5931
Line 130: Line 157:
|329.2087
|329.2087
|332.3308
|332.3308
|''343.5714-345.2664''
|-
|-
|14
|14
|''331.1071-332.857''1
|344.4444
|344.4444
|347.408
|347.408
Line 139: Line 168:
|354.5324
|354.5324
|357.8947
|357.8947
|''370-371.75''
|-
|-
|15
|15
|''354.75765-356.63265''
|369.0476
|369.0476
|372.2228
|372.2228
Line 146: Line 177:
|376.9479
|376.9479
|378.13685
|378.13685
|279.8561
|379.8561
|383.45865
|383.45865
|''396.4286-398.3036''
|-
|-
|16
|16
|''378.4082-380.4082''
|393.6508
|393.6508
|397.03765
|397.03765
Line 157: Line 190:
|405.1799
|405.1799
|409.0226
|409.0226
|''422.8571-424.8571''
|-
|-
|17
|17
|''402.0587-404.1837''
|418.254
|418.254
|421.8525
|421.8525
Line 166: Line 201:
|430.5036
|430.5036
|434.5865
|434.5865
|''449.2857-451.4107''
|-
|-
|18
|18
|''425.7092-427.9592''
|442.8571
|442.8571
|446.66735
|446.66735
Line 175: Line 212:
|455.8274
|455.8274
|460.1504
|460.1504
|''475.7143-477.9643''
|-
|-
|19
|19
|''449.3597-451.7347''
|467.460
|467.460
|471.4822
|471.4822
Line 184: Line 223:
|481.1511
|481.1511
|485.7143
|485.7143
|''502.1429-504.5179''
|-
|-
|20
|20
|''473.0102-475.5102''
|492.0635
|492.0635
|496.2971
|496.2971
Line 193: Line 234:
|506.4749
|506.4749
|511.2781
|511.2781
|''528.5714-531.0714''
|-
|-
|21
|21
|''496.6507-499.2857''
|516.6667
|516.6667
|521.1119
|521.1119
Line 202: Line 245:
|531.7986
|531.7986
|536.8421
|536.8421
|''555-557.625''
|-
|-
|22
|22
|''520.3112-523.0612''
|541.2698
|541.2698
|545.9268
|545.9268
Line 211: Line 256:
|557.1223
|557.1223
|562.406
|562.406
|''581.4286-584.1786''
|-
|-
|23
|23
|''543.6917-546.8367''
|565.873
|565.873
|570.7416
|570.7416
Line 220: Line 267:
|582.4461
|582.4461
|587.9699
|587.9699
|''607.8571-610.7321''
|-
|-
|24
|24
|''567.6122-570.6122''
|590.4762
|590.4762
|595.5565
|595.5565
Line 229: Line 278:
|607.7698
|607.7698
|613.5338
|613.5338
|''634.2857-637.2857''
|-
|-
|25
|25
|''591.2628-594.3878''
|615.0794
|615.0794
|620.3713
|620.3713
Line 238: Line 289:
|633.0936
|633.0936
|639.0977
|639.0977
|''660.7143-663.8393''
|-
|-
|26
|26
|''614.9133-618.1633''
|639.6825
|639.6825
|645.1862
|645.1862
Line 247: Line 300:
|658.4173
|658.4173
|664.66165
|664.66165
|''687.1429-690.3929''
|-
|-
|27
|27
|''638.5638-641.9388''
|664.2857
|664.2857
|670.001
|670.001
Line 256: Line 311:
|983.7411
|983.7411
|690.2256
|690.2256
|''713.5714-716.9264''
|-
|-
|28
|28
|''662.2143-665.714''3
|688.8889
|688.8889
|694.8158
|694.8158
Line 265: Line 322:
|709.0648
|709.0648
|715.7895
|715.7895
|''740-743.5''
|-
|-
|29
|29
|''685.8648-689.4898''
|713.4921
|713.4921
|719.6307
|719.6307
Line 274: Line 333:
|734.3885
|734.3885
|741.3534
|741.3534
|''766.4286-770.0536''
|-
|-
|30
|30
|''709.5153-713.2653''
|738.0952
|738.0952
|744.4456
|744.4456
Line 283: Line 344:
|759.7123
|759.7123
|766.9173
|766.9173
|''792.8571-796.6071''
|-
|-
|31
|31
|''733.1658-737.0408''
|762.6984
|762.6984
|769.2604
|769.2604
Line 292: Line 355:
|785.036
|785.036
|792.4812
|792.4812
|''819.2857-823.1607''
|-
|-
|32
|32
|''756.8163-760.8163''
|787.3016
|787.3016
|794.0753
|794.0753
Line 301: Line 366:
|810.3598
|810.3598
|818.0451
|818.0451
|''845.7143-849.7143''
|-
|-
|33
|33
|''780.4668-784.5918''
|811.9048
|811.9048
|818.89015
|818.89015
Line 310: Line 377:
|835.6835
|835.6835
|843.609
|843.609
|''872.1429-876.2679''
|-
|-
|34
|34
|''804.11735-808.36735''
|836.5079
|836.5079
|843.705
|843.705
Line 319: Line 388:
|961.0073
|961.0073
|869.1729
|869.1729
|''898.5714-902.8214''
|-
|-
|35
|35
|''827.7679-832.1429''
|861.1111
|861.1111
|868.51985
|868.51985
Line 328: Line 399:
|886.331
|886.331
|894.7368
|894.7368
|''925-929.375''
|-
|-
|36
|36
|''851.4184-855.9184''
|885.7143
|885.7143
|893.3347
|893.3347
Line 337: Line 410:
|911.6547
|911.6547
|920.30075
|920.30075
|''951.4286-955.9286''
|-
|-
|37
|37
|''875.0689-879.6939''
|910.3175
|910.3175
|918.1496
|918.1496
Line 346: Line 421:
|936.9785
|936.9785
|945.8647
|945.8647
|''977.8571-982.4821''
|-
|-
|38
|38
|''898.7194-903.4694''
|934.9206
|934.9206
|942.9644
|942.9644
Line 355: Line 432:
|962.3022
|962.3022
|971.4286
|971.4286
|''1004.2857-1009.0357''
|-
|-
|39
|39
|''922.3699-927.2449''
|959.5238
|959.5238
|967.7793
|967.7793
Line 364: Line 443:
|987.626
|987.626
|996.9925
|996.9925
|''1030.7143-1035.5893''
|-
|-
|40
|40
|''946.0204-951.0204''
|984.127
|984.127
|992.5941
|992.5941
Line 373: Line 454:
|1012.9497
|1012.9497
|1022.5564
|1022.5564
|''1057.1429-1062.1429''
|-
|-
|41
|41
|''696.6709-974.7959''
|1008.7302
|1008.7302
|1017.409
|1017.409
Line 382: Line 465:
|1038.2735
|1038.2735
|1048.1203
|1048.1203
|''1083.5714-1088.6964''
|-
|-
|42
|42
|''993.3214-998.5714''
|1033.333
|1033.333
|1042.2238
|1042.2238
Line 391: Line 476:
|1063.5972
|1063.5972
|1073.6842
|1073.6842
|''1110-1115.25''
|-
|-
|43
|43
|''1013.9719-1022.3469''
|1057.9365
|1057.9365
|1067.0386
|1067.0386
Line 400: Line 487:
|1088.92095
|1088.92095
|1099.2481
|1099.2481
|''1136.4286-1141.8036''
|-
|-
|44
|44
|''1040.62245-1046.12245''
|1082.5397
|1082.5397
|1091.8535
|1091.8535
Line 409: Line 498:
|1114.2447
|1114.2447
|1124.812
|1124.812
|''1162.8571-1167.3571''
|-
|-
|45
|45
|''1064.273-1069.898''
|1107.1429
|1107.1429
|1116.6684
|1116.6684
Line 418: Line 509:
|1139.5684
|1139.5684
|1150.3759
|1150.3759
|''1189.2857-1194.9107''
|-
|-
|46
|46
|''1088.9235-1093.6735''
|1131.7646
|1131.7646
|1141.4832
|1141.4832
Line 427: Line 520:
|1164.8922
|1164.8922
|1175.93985
|1175.93985
|''1215.7143-1221.4643''
|-
|-
|47
|47
|''1111.574-1117.449''
|1156.3492
|1156.3492
|1166.2981
|1166.2981
Line 436: Line 531:
|1190.2159
|1190.2159
|1201.5038
|1201.5038
|''1242.1429-1248.0179''
|-
|-
|48
|48
|''1135.2245-1141.2245''
|1180.9524
|1180.9524
|1191.1129
|1191.1129
Line 445: Line 542:
|1215.5397
|1215.5397
|1227.0677
|1227.0677
|''1268.5714-1274.5714''
|-
|-
|49
|49
|''1158.875-1165''
|1205.5556
|1205.5556
|1215.9278
|1215.9278
Line 454: Line 553:
|1240.8634
|1240.8634
|1252.6316
|1252.6316
|''1295-1301.125''
|-
|-
|50
|50
|''1182.5255-1188.7755''
|1230.1587
|1230.1587
|1240.74265
|1240.74265
Line 463: Line 564:
|1266.18715
|1266.18715
|1278.1955
|1278.1955
|''1321.4286-1327.6786''
|-
|-
|51
|51
|''1206.176-1212.551''
|1254.7619
|1254.7619
|1265.5575
|1265.5575
Line 472: Line 575:
|1291.5109
|1291.5109
|1303.7594
|1303.7594
|''1347.8571-1354.2321''
|-
|-
|52
|52
|''1229.8265-1236.3265''
|1279.3651
|1279.3651
|1290.37235
|1290.37235
Line 481: Line 586:
|1316.8346
|1316.8346
|1329.3233
|1329.3233
|''1374.2857-1380.7857''
|-
|-
|53
|53
|''1253.477-1260.102''
|1303.96825
|1303.96825
|1315.1872
|1315.1872
Line 490: Line 597:
|1342.1584
|1342.1584
|1354.8872
|1354.8872
|''1400.7143-1407.3393''
|-
|-
|54
|54
|''1277.12755-1283.87755''
|1328.5714
|1328.5714
|1340.0021
|1340.0021
Line 499: Line 608:
|1367.4821
|1367.4821
|1380.4511
|1380.4511
|''1427.1429-1433.8929''
|-
|-
|55
|55
|''1300.7781-1307.6531''
|1353.1746
|1353.1746
|1364.8169
|1364.8169
Line 508: Line 619:
|1392.8059
|1392.8059
|1406.015
|1406.015
|''1453.5714-1460.4464''
|-
|-
|56
|56
|''1324.4286-1331.4286''
|1377.7778
|1377.7778
|1389.6318
|1389.6318
Line 517: Line 630:
|1418.1296
|1418.1296
|1431.57895
|1431.57895
|''1480-1487''
|}
|}
[[Category:Edf]]
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 21:30, 25 June 2019

Division of the just perfect fifth into 28 equal parts (28EDF) is related to 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, 383, 718, 1053, and 1101 EDOs.

Intervals

ed233\420-3.5¢ (51edo!) ed31\54 (~49edo!) ed121/81 (~ed11\19) ed3/2 Pyrite ed122/81 (~ed13\22) ed34\57 (~47edo!) ed37\60+3.5¢ (~91ed4!)
(~ed17\29) (~ed10\17)
1 23.6505-23.7755 24.6032 24.81485 25.0698 25.1299 25.2091 25.3234 25.5639 26.4286-26.5536
2 47.301-47.551 49.20635 49.6297 50.1396 50.2597 50.41825 50.6475 51.1278 52.8571-53.1071
3 70.9515-71.3625 73.8095 74.4446 75.2095 75.3896 75.6274 75.9712 76.6917 79.2857-79.6607
4 94.602-95.102 98.4127 99.2594 100.2793 100.5194 100.8365 101.295 102.2556 105.7143-106.2143
5 118.25255-118.87755 123.0159 124.0743 125.3491 125.6493 10\26.0456 126.6187 127.81955 132.1429-132.7679
6 141.903-142.653 147.61905 148.8891 150.4189 150.77915 151.2547 151.9425 153.3835 158.5714-159.3214
7 165.5536-166.4285 172.2222 173.704 175.48875 175.909 176.4639 177.2662 178.947 185-185.875
8 189.2041-190.2041 196.8254 198.5188 200.5586 201.0389 201.673 202.5899 204.5113 211.4286-212.4286
9 212.8576-213.9796 221.4286 223.3337 225.6284 226.1687 226.8821 227.9137 230.0752 237.8571-238.9791
10 236.5051-237.7551 246.03175 248.1485 250.6982 251.2986 252.0912 253.2374 255.6391 264.2857-265.5357
11 260.1556-261.5306 270.6349 272.9634 275.768 276.4284 277.3004 278.5612 281.203 290.7143-292.0693
12 283.8061-285.3061 295.2381 297.782 300.8379 301.5583 302.5095 303.8849 306.7669 317.1429-318.6429
13 307.4566-309.0816 319.8413 322.5931 325.9077 326.6682 327.7186 329.2087 332.3308 343.5714-345.2664
14 331.1071-332.8571 344.4444 347.408 350.9775 351.818 352.9277 354.5324 357.8947 370-371.75
15 354.75765-356.63265 369.0476 372.2228 376.0473 376.9479 378.13685 379.8561 383.45865 396.4286-398.3036
16 378.4082-380.4082 393.6508 397.03765 401.1171 402.0777 403.346 405.1799 409.0226 422.8571-424.8571
17 402.0587-404.1837 418.254 421.8525 426.187 427.2076 428.5551 430.5036 434.5865 449.2857-451.4107
18 425.7092-427.9592 442.8571 446.66735 451.2568 452.33745 453.7642 455.8274 460.1504 475.7143-477.9643
19 449.3597-451.7347 467.460 471.4822 476.3266 477.4673 478.97333 481.1511 485.7143 502.1429-504.5179
20 473.0102-475.5102 492.0635 496.2971 501.3964 502.5972 504.1825 506.4749 511.2781 528.5714-531.0714
21 496.6507-499.2857 516.6667 521.1119 526.46625 527.727 529.3916 531.7986 536.8421 555-557.625
22 520.3112-523.0612 541.2698 545.9268 551.536 552.8569 554.6007 557.1223 562.406 581.4286-584.1786
23 543.6917-546.8367 565.873 570.7416 576.6059 577.9867 579.8098 582.4461 587.9699 607.8571-610.7321
24 567.6122-570.6122 590.4762 595.5565 601.6757 603.1166 605.019 607.7698 613.5338 634.2857-637.2857
25 591.2628-594.3878 615.0794 620.3713 626.7455 628.2465 630.2281 633.0936 639.0977 660.7143-663.8393
26 614.9133-618.1633 639.6825 645.1862 651.8154 653.3763 655.4372 658.4173 664.66165 687.1429-690.3929
27 638.5638-641.9388 664.2857 670.001 676.8852 678.5062 680.6463 983.7411 690.2256 713.5714-716.9264
28 662.2143-665.7143 688.8889 694.8158 701.955 703.636 705.85545 709.0648 715.7895 740-743.5
29 685.8648-689.4898 713.4921 719.6307 727.0248 728.7659 731.0646 734.3885 741.3534 766.4286-770.0536
30 709.5153-713.2653 738.0952 744.4456 752.0946 753.89575 756.2736 759.7123 766.9173 792.8571-796.6071
31 733.1658-737.0408 762.6984 769.2604 777.1645 779.0256 781.4828 785.036 792.4812 819.2857-823.1607
32 756.8163-760.8163 787.3016 794.0753 802.2343 804.1555 806.6919 810.3598 818.0451 845.7143-849.7143
33 780.4668-784.5918 811.9048 818.89015 827.3041 829.2853 831.9011 835.6835 843.609 872.1429-876.2679
34 804.11735-808.36735 836.5079 843.705 852.3739 854.4152 857.1102 961.0073 869.1729 898.5714-902.8214
35 827.7679-832.1429 861.1111 868.51985 877.44375 879.545 882.3193 886.331 894.7368 925-929.375
36 851.4184-855.9184 885.7143 893.3347 902.5136 904.6749 907.5284 911.6547 920.30075 951.4286-955.9286
37 875.0689-879.6939 910.3175 918.1496 927.5834 929.8048 932.3767 936.9785 945.8647 977.8571-982.4821
38 898.7194-903.4694 934.9206 942.9644 952.6532 954.9346 957.9467 962.3022 971.4286 1004.2857-1009.0357
39 922.3699-927.2449 959.5238 967.7793 977.723 980.0645 983.1558 987.626 996.9925 1030.7143-1035.5893
40 946.0204-951.0204 984.127 992.5941 1002.7929 1005.1943 1008.3649 1012.9497 1022.5564 1057.1429-1062.1429
41 696.6709-974.7959 1008.7302 1017.409 1027.8627 1030.3242 1033.57405 1038.2735 1048.1203 1083.5714-1088.6964
42 993.3214-998.5714 1033.333 1042.2238 1052.9325 1055.454 1058.7832 1063.5972 1073.6842 1110-1115.25
43 1013.9719-1022.3469 1057.9365 1067.0386 1078.0023 1080.5839 1083.9923 1088.92095 1099.2481 1136.4286-1141.8036
44 1040.62245-1046.12245 1082.5397 1091.8535 1103.0721 1105.7138 1109.2014 1114.2447 1124.812 1162.8571-1167.3571
45 1064.273-1069.898 1107.1429 1116.6684 1128.142 1130.8436 1137.41055 1139.5684 1150.3759 1189.2857-1194.9107
46 1088.9235-1093.6735 1131.7646 1141.4832 1153.2118 1155.9735 1159.6297 1164.8922 1175.93985 1215.7143-1221.4643
47 1111.574-1117.449 1156.3492 1166.2981 1178.2816 1181.1033 1184.8288 1190.2159 1201.5038 1242.1429-1248.0179
48 1135.2245-1141.2245 1180.9524 1191.1129 1203.3514 1206.2332 1210.0379 1215.5397 1227.0677 1268.5714-1274.5714
49 1158.875-1165 1205.5556 1215.9278 1228.42125 1231.6306 1235.247 1240.8634 1252.6316 1295-1301.125
50 1182.5255-1188.7755 1230.1587 1240.74265 1253.4911 1256.4929 1260.4561 1266.18715 1278.1955 1321.4286-1327.6786
51 1206.176-1212.551 1254.7619 1265.5575 1278.5609 1281.6228 128.6653 1291.5109 1303.7594 1347.8571-1354.2321
52 1229.8265-1236.3265 1279.3651 1290.37235 1303.6307 1306.7526 1310.8744 1316.8346 1329.3233 1374.2857-1380.7857
53 1253.477-1260.102 1303.96825 1315.1872 1328.7005 1331.8825 1336.0835 1342.1584 1354.8872 1400.7143-1407.3393
54 1277.12755-1283.87755 1328.5714 1340.0021 1353.7704 1357.01235 1361.2927 1367.4821 1380.4511 1427.1429-1433.8929
55 1300.7781-1307.6531 1353.1746 1364.8169 1378.8418 1382.1422 1386.5018 1392.8059 1406.015 1453.5714-1460.4464
56 1324.4286-1331.4286 1377.7778 1389.6318 1403.91 1407.2721 1411.7109 1418.1296 1431.57895 1480-1487
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