8ed16/15: Difference between revisions

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Line 1: Line 1:
'''Delta scale''' is the equal division of the classic diatonic semitone ([[16/15]]) into eight parts of 13.9664 cents each, corresponding to 85.9204 [[edo]].
'''Delta scale''' is the equal division of the classic diatonic semitone ([[16/15]]) into eight parts of 13.9664 cents each, corresponding to 85.9204 [[edo]]. It is inconsistent to the 5-limit and higher limit, as 3/2, 5/4, and 6/5 fall on the 50th, 28th, and 23rd steps in the best direct mapping, respectively.


Lookalikes: [[86edo]], [[136ed3]], [[50edf]]
Lookalikes: [[86edo]], [[136ed3]], [[50edf]]
Line 15: Line 15:
! | 222ED6
! | 222ED6
! | [[136edt|136ED3]]
! | [[136edt|136ED3]]
! | [[50edf|50ED3/2]]
! | 75ED11/6
|-
|-
| | 0
| | 0
Line 32: Line 32:
| | 13.973
| | 13.973
| | 13.985
| | 13.985
| | 14.039
| | 13.992
| |  
| |  
|-
|-
Line 41: Line 41:
| | 27.946
| | 27.946
| | 27.970
| | 27.970
| | 28.078
| | 27.983
| |  
| |  
|-
|-
Line 50: Line 50:
| | 41.918
| | 41.918
| | 41.955
| | 41.955
| | 42.117
| | 41.975
| |  
| |  
|-
|-
Line 59: Line 59:
| | 55.891
| | 55.891
| | 55.940
| | 55.940
| | 56.156
| | 55.966
| |  
| |  
|-
|-
Line 68: Line 68:
| | 69.864
| | 69.864
| | 69.925
| | 69.925
| | 70.196
| | 69.958
| |  
| |  
|-
|-
Line 77: Line 77:
| | 83.837
| | 83.837
| | 83.910
| | 83.910
| | 84.235
| | 83.949
| |  
| |  
|-
|-
Line 86: Line 86:
| | 97.809
| | 97.809
| | 97.895
| | 97.895
| | 98.274
| | 97.941
| |  
| |  
|-
|-
Line 95: Line 95:
| | 111.782
| | 111.782
| | 111.880
| | 111.880
| | 112.313
| | 111.932
| | [[16/15]]
| | [[16/15]]
|-
|-
Line 104: Line 104:
| | 125.755
| | 125.755
| | 125.865
| | 125.865
| | 126.352
| | 125.924
| |  
| |  
|-
|-
Line 113: Line 113:
| | 139.728
| | 139.728
| | 139.850
| | 139.850
| | 140.391
| | 139.915
| |  
| |  
|-
|-
Line 122: Line 122:
| | 153.700
| | 153.700
| | 153.835
| | 153.835
| | 154.430
| | 153.907
| |  
| |  
|-
|-
Line 131: Line 131:
| | 167.673
| | 167.673
| | 167.820
| | 167.820
| | 168.469
| | 167.898
| |  
| |  
|-
|-
Line 140: Line 140:
| | 181.646
| | 181.646
| | 181.805
| | 181.805
| | 182.508
| | 181.890
| | [[10/9]]
| | [[10/9]]
|-
|-
Line 149: Line 149:
| | 195.619
| | 195.619
| | 195.789
| | 195.789
| | 196.547
| | 195.881
| |  
| |  
|-
|-
Line 158: Line 158:
| | 209.592
| | 209.592
| | 209.774
| | 209.774
| | 210.587
| | 209.873
| |  
| |  
|-
|-
Line 167: Line 167:
| | 223.564
| | 223.564
| | 223.759
| | 223.759
| | 224.626
| | 223.864
| | 33/29
| |  
|-
|-
| | 17
| | 17
Line 176: Line 176:
| | 237.537
| | 237.537
| | 237.744
| | 237.744
| | 238.665
| | 237.856
| |  
| |  
|-
|-
Line 185: Line 185:
| | 251.510
| | 251.510
| | 251.729
| | 251.729
| | 252.704
| | 251.847
| | [[22/19]]
| | [[22/19]]
|-
|-
Line 194: Line 194:
| | 265.483
| | 265.483
| | 265.714
| | 265.714
| | 266.743
| | 265.839
| | [[7/6]]
| | [[7/6]]
|-
|-
Line 203: Line 203:
| | 279.455
| | 279.455
| | 279.699
| | 279.699
| | 280.782
| | 279.830
| |  
| |  
|-
|-
Line 212: Line 212:
| | 293.428
| | 293.428
| | 293.684
| | 293.684
| | 294.821
| | 293.822
| |  
| |  
|-
|-
Line 221: Line 221:
| | 307.401
| | 307.401
| | 307.669
| | 307.669
| | 308.860
| | 307.813
| |  
| |  
|-
|-
Line 230: Line 230:
| | 321.374
| | 321.374
| | 321.654
| | 321.654
| | 322.899
| | 321.805
| | [[6/5]]
| | [[6/5]]
|-
|-
Line 239: Line 239:
| | 335.346
| | 335.346
| | 335.639
| | 335.639
| | 336.938
| | 335.796
| |  
| |  
|-
|-
Line 248: Line 248:
| | 349.319
| | 349.319
| | 349.624
| | 349.624
| | 350.978
| | 349.788
| | [[11/9]]
| | [[11/9]]
|-
|-
Line 257: Line 257:
| | 363.292
| | 363.292
| | 363.609
| | 363.609
| | 365.017
| | 363.779
| |  
| |  
|-
|-
Line 266: Line 266:
| | 377.265
| | 377.265
| | 377.594
| | 377.594
| | 379.056
| | 377.771
| |  
| |  
|-
|-
Line 275: Line 275:
| | 391.238
| | 391.238
| | 391.579
| | 391.579
| | 393.095
| | 391.762
| | [[5/4]]
| | [[5/4]]
|-
|-
Line 284: Line 284:
| | 405.210
| | 405.210
| | 405.564
| | 405.564
| | 407.134
| | 405.754
| |  
| |  
|-
|-
Line 293: Line 293:
| | 419.183
| | 419.183
| | 419.549
| | 419.549
| | 421.173
| | 419.745
| |  
| |  
|-
|-
Line 302: Line 302:
| | 433.156
| | 433.156
| | 433.534
| | 433.534
| | 435.212
| | 433.737
| | [[9/7]]
| | [[9/7]]
|-
|-
Line 311: Line 311:
| | 447.129
| | 447.129
| | 447.519
| | 447.519
| | 449.251
| | 447.728
| |  
| |  
|-
|-
Line 320: Line 320:
| | 461.101
| | 461.101
| | 461.504
| | 461.504
| | 463.290
| | 461.720
| | [[17/13]]
| | [[17/13]]
|-
|-
Line 329: Line 329:
| | 475.074
| | 475.074
| | 475.489
| | 475.489
| | 477.329
| | 475.711
| |  
| |  
|-
|-
Line 338: Line 338:
| | 489.047
| | 489.047
| | 489.474
| | 489.474
| | 491.369
| | 489.703
| |  
| |  
|-
|-
Line 347: Line 347:
| | 503.020
| | 503.020
| | 503.459
| | 503.459
| | 505.408
| | 503.694
| |  
| |  
|-
|-
Line 356: Line 356:
| | 516.993
| | 516.993
| | 517.444
| | 517.444
| | 519.447
| | 517.686
| |  
| |  
|-
|-
Line 365: Line 365:
| | 530.965
| | 530.965
| | 531.429
| | 531.429
| | 533.486
| | 531.677
| |  
| |  
|-
|-
Line 374: Line 374:
| | 544.938
| | 544.938
| | 545.414
| | 545.414
| | 547.525
| | 545.669
| |  
| |  
|-
|-
Line 383: Line 383:
| | 558.911
| | 558.911
| | 559.399
| | 559.399
| | 561.564
| | 559.660
| |  
| |  
|-
|-
Line 392: Line 392:
| | 572.884
| | 572.884
| | 573.383
| | 573.383
| | 575.603
| | 573.652
| |  
| |  
|-
|-
Line 401: Line 401:
| | 586.856
| | 586.856
| | 587.368
| | 587.368
| | 589.642
| | 587.643
| | [[7/5]]
| | [[7/5]]
|-
|-
Line 410: Line 410:
| | 600.829
| | 600.829
| | 601.353
| | 601.353
| | 603.681
| | 601.635
| | [[17/12]]
| | [[17/12]]
|-
|-
Line 419: Line 419:
| | 614.802
| | 614.802
| | 615.338
| | 615.338
| | 617.720
| | 615.626
| |  
| |  
|-
|-
Line 428: Line 428:
| | 628.775
| | 628.775
| | 629.323
| | 629.323
| | 631.760
| | 629.618
| |  
| |  
|-
|-
Line 437: Line 437:
| | 642.747
| | 642.747
| | 643.308
| | 643.308
| | 645.799
| | 643.609
| |  
| |  
|-
|-
Line 446: Line 446:
| | 656.720
| | 656.720
| | 657.293
| | 657.293
| | 659.838
| | 657.601
| |  
| |  
|-
|-
Line 455: Line 455:
| | 670.693
| | 670.693
| | 671.278
| | 671.278
| | 673.877
| | 671.592
| |  
| |  
|-
|-
Line 464: Line 464:
| | 684.666
| | 684.666
| | 685.263
| | 685.263
| | 687.916
| | 685.584
| |  
| |  
|-
|-
Line 473: Line 473:
| | 698.639
| | 698.639
| | 699.248
| | 699.248
| | 701.955
| | 699.575
| | [[3/2]]
| | [[3/2]]
|-
|-
Line 482: Line 482:
| | 712.611
| | 712.611
| | 713.233
| | 713.233
| | 715.994
| | 713.567
| |  
| |  
|-
|-
Line 491: Line 491:
| | 726.584
| | 726.584
| | 727.218
| | 727.218
| | 730.033
| | 727.558
| |  
| |  
|-
|-
Line 500: Line 500:
| | 740.557
| | 740.557
| | 741.203
| | 741.203
| | 744.072
| | 741.550
| |  
| |  
|-
|-
Line 509: Line 509:
| | 754.530
| | 754.530
| | 755.188
| | 755.188
| | 758.111
| | 755.541
| |  
| |  
|-
|-
Line 518: Line 518:
| | 768.502
| | 768.502
| | 769.173
| | 769.173
| | 772.151
| | 769.533
| |  
| |  
|-
|-
Line 527: Line 527:
| | 782.475
| | 782.475
| | 783.158
| | 783.158
| | 786.190
| | 783.524
| |  
| |  
|-
|-
Line 536: Line 536:
| | 796.448
| | 796.448
| | 797.143
| | 797.143
| | 800.229
| | 797.516
| |  
| |  
|-
|-
Line 545: Line 545:
| | 810.421
| | 810.421
| | 811.128
| | 811.128
| | 814.268
| | 811.507
| | [[8/5]]
| | [[8/5]]
|-
|-
Line 554: Line 554:
| | 824.393
| | 824.393
| | 825.113
| | 825.113
| | 828.307
| | 825.499
| |  
| |  
|-
|-
Line 563: Line 563:
| | 838.366
| | 838.366
| | 839.098
| | 839.098
| | 842.346
| | 839.490
| | [[13/8]]
| | [[13/8]]
|-
|-
Line 572: Line 572:
| | 852.339
| | 852.339
| | 853.083
| | 853.083
| | 856.385
| | 853.482
| |  
| |  
|-
|-
Line 581: Line 581:
| | 866.312
| | 866.312
| | 867.068
| | 867.068
| | 870.424
| | 867.473
| |  
| |  
|-
|-
Line 590: Line 590:
| | 880.285
| | 880.285
| | 881.053
| | 881.053
| | 884.463
| | 881.465
| | [[5/3]]
| | [[5/3]]
|-
|-
Line 599: Line 599:
| | 894.257
| | 894.257
| | 895.038
| | 895.038
| | 898.502
| | 895.456
| |  
| |  
|-
|-
Line 608: Line 608:
| | 908.230
| | 908.230
| | 909.023
| | 909.023
| | 912.542
| | 909.448
| |  
| |  
|-
|-
Line 617: Line 617:
| | 922.203
| | 922.203
| | 923.008
| | 923.008
| | 926.581
| | 923.439
| |  
| |  
|-
|-
Line 626: Line 626:
| | 936.176
| | 936.176
| | 936.993
| | 936.993
| | 940.620
| | 937.431
| |  
| |  
|-
|-
Line 635: Line 635:
| | 950.148
| | 950.148
| | 950.978
| | 950.978
| | 954.659
| | 951.422
| |  
| |  
|-
|-
Line 644: Line 644:
| | 964.121
| | 964.121
| | 964.962
| | 964.962
| | 968.698
| | 965.414
| | [[7/4]]
| | [[7/4]]
|-
|-
Line 653: Line 653:
| | 978.094
| | 978.094
| | 978.947
| | 978.947
| | 982.737
| | 979.405
| |  
| |  
|-
|-
Line 662: Line 662:
| | 992.067
| | 992.067
| | 992.932
| | 992.932
| | 996.776
| | 993.397
| | [[16/9]]
| | [[16/9]]
|-
|-
Line 671: Line 671:
| | 1006.039
| | 1006.039
| | 1006.917
| | 1006.917
| | 1010.815
| | 1007.388
| | [[25/14]]
| | [[25/14]]
|-
|-
Line 680: Line 680:
| | 1020.012
| | 1020.012
| | 1020.902
| | 1020.902
| | 1024.854
| | 1021.380
| | [[9/5]]
| | [[9/5]]
|-
|-
Line 689: Line 689:
| | 1033.985
| | 1033.985
| | 1034.887
| | 1034.887
| | 1038.893
| | 1035.371
| |  
| |  
|-
|-
Line 698: Line 698:
| | 1047.958
| | 1047.958
| | 1048.872
| | 1048.872
| | 1052.933
| | 1049.363
| | [[11/6]]
| | [[11/6]]
|-
|-
Line 707: Line 707:
| | 1061.931
| | 1061.931
| | 1062.857
| | 1062.857
| | 1066.972
| | 1063.354
| |  
| |  
|-
|-
Line 716: Line 716:
| | 1075.903
| | 1075.903
| | 1076.842
| | 1076.842
| | 1081.011
| | 1077.346
| | [[28/15]]
| | [[28/15]]
|-
|-
Line 725: Line 725:
| | 1089.876
| | 1089.876
| | 1090.827
| | 1090.827
| | 1095.050
| | 1091.337
| | [[15/8]]
| | [[15/8]]
|-
|-
Line 734: Line 734:
| | 1103.849
| | 1103.849
| | 1104.812
| | 1104.812
| | 1109.089
| | 1105.329
| |  
| |  
|-
|-
Line 743: Line 743:
| | 1117.822
| | 1117.822
| | 1118.797
| | 1118.797
| | 1123.128
| | 1119.320
| |  
| |  
|-
|-
Line 752: Line 752:
| | 1131.794
| | 1131.794
| | 1132.782
| | 1132.782
| | 1137.167
| | 1133.312
| |  
| |  
|-
|-
Line 761: Line 761:
| | 1145.767
| | 1145.767
| | 1146.767
| | 1146.767
| | 1151.206
| | 1147.303
| |  
| |  
|-
|-
Line 770: Line 770:
| | 1159.740
| | 1159.740
| | 1160.752
| | 1160.752
| | 1165.245
| | 1161.295
| |  
| |  
|-
|-
Line 779: Line 779:
| | 1173.713
| | 1173.713
| | 1174.737
| | 1174.737
| | 1179.284
| | 1175.286
| |  
| |  
|-
|-
Line 788: Line 788:
| | 1187.685
| | 1187.685
| | 1188.722
| | 1188.722
| | 1193.324
| | 1189.278
| |  
| |  
|-
|-
Line 797: Line 797:
| | 1201.658
| | 1201.658
| | 1202.707
| | 1202.707
| | 1207.363
| | 1203.270
| | [[Octave|2/1]]
| | [[Octave|2/1]]
|}
|}

Revision as of 07:54, 13 February 2019

Delta scale is the equal division of the classic diatonic semitone (16/15) into eight parts of 13.9664 cents each, corresponding to 85.9204 edo. It is inconsistent to the 5-limit and higher limit, as 3/2, 5/4, and 6/5 fall on the 50th, 28th, and 23rd steps in the best direct mapping, respectively.

Lookalikes: 86edo, 136ed3, 50edf

Intervals

degree cents value corresponding
JI intervals
72ED25/14 86EDO 8ED16/15 222ED6 136ED3 75ED11/6
0 0.000 0.000 0.000 0.000 0.000 0.000 exact 1/1
1 13.942 13.953 13.966 13.973 13.985 13.992
2 27.883 27.907 27.933 27.946 27.970 27.983
3 41.825 41.860 41.899 41.918 41.955 41.975
4 55.767 55.814 55.866 55.891 55.940 55.966
5 69.708 69.767 69.832 69.864 69.925 69.958
6 83.650 83.721 83.798 83.837 83.910 83.949
7 97.592 97.674 97.765 97.809 97.895 97.941
8 111.534 111.628 111.731 111.782 111.880 111.932 16/15
9 125.475 125.581 125.698 125.755 125.865 125.924
10 139.417 139.535 139.664 139.728 139.850 139.915
11 153.359 153.488 153.631 153.700 153.835 153.907
12 167.300 167.442 167.597 167.673 167.820 167.898
13 181.242 181.395 181.563 181.646 181.805 181.890 10/9
14 195.184 195.349 195.530 195.619 195.789 195.881
15 209.125 209.302 209.496 209.592 209.774 209.873
16 223.067 223.256 223.463 223.564 223.759 223.864
17 237.009 237.209 237.429 237.537 237.744 237.856
18 250.950 251.163 251.395 251.510 251.729 251.847 22/19
19 264.892 265.116 265.362 265.483 265.714 265.839 7/6
20 278.834 279.070 279.328 279.455 279.699 279.830
21 292.775 293.023 293.295 293.428 293.684 293.822
22 306.717 306.977 307.261 307.401 307.669 307.813
23 320.659 320.930 321.227 321.374 321.654 321.805 6/5
24 334.601 334.884 335.194 335.346 335.639 335.796
25 348.542 348.837 349.160 349.319 349.624 349.788 11/9
26 362.484 362.791 363.127 363.292 363.609 363.779
27 376.426 376.744 377.093 377.265 377.594 377.771
28 390.367 390.698 391.059 391.238 391.579 391.762 5/4
29 404.309 404.651 405.026 405.210 405.564 405.754
30 418.251 418.605 418.992 419.183 419.549 419.745
31 432.192 432.558 432.959 433.156 433.534 433.737 9/7
32 446.134 446.512 446.925 447.129 447.519 447.728
33 460.076 460.465 460.892 461.101 461.504 461.720 17/13
34 474.017 474.419 474.858 475.074 475.489 475.711
35 487.959 488.372 488.824 489.047 489.474 489.703
36 501.901 502.326 502.791 503.020 503.459 503.694
37 515.842 516.279 516.757 516.993 517.444 517.686
38 529.784 530.233 530.724 530.965 531.429 531.677
39 543.726 544.186 544.690 544.938 545.414 545.669
40 557.668 558.140 558.656 558.911 559.399 559.660
41 571.609 572.093 572.623 572.884 573.383 573.652
42 585.551 586.047 586.589 586.856 587.368 587.643 7/5
43 599.493 600.000 600.556 600.829 601.353 601.635 17/12
44 613.434 613.953 614.522 614.802 615.338 615.626
45 627.376 627.907 628.488 628.775 629.323 629.618
46 641.318 641.860 642.455 642.747 643.308 643.609
47 655.259 655.814 656.421 656.720 657.293 657.601
48 669.201 669.767 670.388 670.693 671.278 671.592
49 683.143 683.721 684.354 684.666 685.263 685.584
50 697.084 697.674 698.321 698.639 699.248 699.575 3/2
51 711.026 711.628 712.287 712.611 713.233 713.567
52 724.968 725.581 726.253 726.584 727.218 727.558
53 738.909 739.535 740.220 740.557 741.203 741.550
54 752.851 753.488 754.186 754.530 755.188 755.541
55 766.793 767.442 768.153 768.502 769.173 769.533
56 780.735 781.395 782.119 782.475 783.158 783.524
57 794.676 795.349 796.085 796.448 797.143 797.516
58 808.618 809.302 810.052 810.421 811.128 811.507 8/5
59 822.560 823.256 824.018 824.393 825.113 825.499
60 836.501 837.209 837.985 838.366 839.098 839.490 13/8
61 850.443 851.163 851.951 852.339 853.083 853.482
62 864.385 865.116 865.917 866.312 867.068 867.473
63 878.326 879.070 879.884 880.285 881.053 881.465 5/3
64 892.268 893.023 893.850 894.257 895.038 895.456
65 906.210 906.977 907.817 908.230 909.023 909.448
66 920.151 920.930 921.783 922.203 923.008 923.439
67 934.093 934.884 935.750 936.176 936.993 937.431
68 948.035 948.837 949.716 950.148 950.978 951.422
69 961.976 962.791 963.682 964.121 964.962 965.414 7/4
70 975.918 976.744 977.649 978.094 978.947 979.405
71 989.860 990.698 991.615 992.067 992.932 993.397 16/9
72 1003.802 1004.651 1005.582 1006.039 1006.917 1007.388 25/14
73 1017.743 1018.605 1019.548 1020.012 1020.902 1021.380 9/5
74 1031.685 1032.558 1033.514 1033.985 1034.887 1035.371
75 1045.627 1046.512 1047.481 1047.958 1048.872 1049.363 11/6
76 1059.568 1060.465 1061.447 1061.931 1062.857 1063.354
77 1073.510 1074.419 1075.414 1075.903 1076.842 1077.346 28/15
78 1087.452 1088.372 1089.380 1089.876 1090.827 1091.337 15/8
79 1101.393 1102.326 1103.346 1103.849 1104.812 1105.329
80 1115.335 1116.279 1117.313 1117.822 1118.797 1119.320
81 1129.277 1130.233 1131.279 1131.794 1132.782 1133.312
82 1143.218 1144.186 1145.246 1145.767 1146.767 1147.303
83 1157.160 1158.140 1159.212 1159.740 1160.752 1161.295
84 1171.102 1172.093 1173.178 1173.713 1174.737 1175.286
85 1185.043 1186.047 1187.145 1187.685 1188.722 1189.278
86 1198.985 1200.000 1201.111 1201.658 1202.707 1203.270 2/1

See also

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