8ed16/15

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The 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, as the direct approximations of 3/2, 5/4, and 6/5 are the 50th, 28th, and 23rd steps, respectively (and 28 + 23 ≠ 50).

Lookalikes: 86edo, 136edt, 50edf

← 7ed16/15 8ed16/15 9ed16/15 →
Prime factorization 23
Step size 13.9664 ¢ 
Octave 86\8ed16/15 (1201.11 ¢) (→ 43\4ed16/15)
Twelfth 136\8ed16/15 (1899.43 ¢) (→ 17\1ed16/15)
Consistency limit 4
Distinct consistency limit 4

Harmonics

Approximation of harmonics in 8ed16/15
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.11 -2.52 +2.22 +6.97 -1.41 -2.92 +3.33 -5.05 -5.89 -3.29 -0.30
Relative (%) +8.0 -18.1 +15.9 +49.9 -10.1 -20.9 +23.9 -36.1 -42.1 -23.6 -2.2
Steps
(reduced) 		86
(6) 		136
(0) 		172
(4) 		200
(0) 		222
(6) 		241
(1) 		258
(2) 		272
(0) 		285
(5) 		297
(1) 		308
(4)

Intervals

Intervals of the delta scale
degree cents value corresponding
JI intervals
86EDO 8ED16/15 222ED6 136EDT golden 85—86EDO 171ED4 50EDF 85EDO
0 exact 1/1
1 13.9535 13.966 13.973 13.985 14.016 14.035 14.039 14.118 126/125
2 27.907 27.933 27.946 27.970 28.0315 28.07 28.078 28.235 64/63
3 41.8605 41.899 41.918 41.955 42.047 42.105 42.117 42.353 128/125, 169/165, 165/161
4 55.814 55.866 55.891 55.940 56.063 56.14 56.156 56.471 95/92
5 69.767 69.832 69.864 69.925 70.079 70.175 70.1955 70.588 51/49, 25/24
6 83.721 83.798 83.837 83.910 84.094 84.2105 84.235 84.706 85/81, 21/20
7 97.674 97.765 97.809 97.895 98.11 98.246 98.274 98.8235 55/52, 128/121, 91/86
8 111.628 111.731 111.782 111.880 112.126 112.281 112.313 112.941 16/15
9 125.581 125.698 125.755 125.865 126.124 126.316 126.352 127.059 14/13
10 139.535 139.664 139.728 139.850 140.157 140.351 140.391 141.1765 13/12
11 153.488 153.631 153.700 153.835 154.173 154.386 154.43 155.294 59/54, 47/43, 35/32
12 167.442 167.597 167.673 167.820 168.189 168.421 168.469 169.412 76/69, 65/59
13 181.395 181.563 181.646 181.805 182.205 182.456 182.508 183.529 10/9
14 195.349 195.530 195.619 195.789 196.22 196.491 196.547 197.647 28/25
15 209.302 209.496 209.592 209.774 210.236 210.526 210.5865 211.765 44/39, 35/31
16 223.256 223.463 223.564 223.759 224.252 224.561 224.626 225.882 33/29
17 237.209 237.429 237.537 237.744 238.268 238.5965 238.665 240 39/34 (pseudo-8/7)
18 251.163 251.395 251.51 251.729 252.283 252.632 252.704 254.118 37/32, 22/19
19 265.116 265.362 265.483 265.714 266.299 266.667 266.743 268.235 7/6
20 279.07 279.328 279.455 279.699 280.315 280.702 280.78 282.353 27/23, 47/40, 20/17
21 293.023 293.295 293.428 293.684 294.3305 294.737 294.821 296.353 45/38, 77/65, 32/27
22 306.977 307.261 307.401 307.669 308.346 308.772 308.86 310.588 80/67, 43/36
23 320.93 321.227 321.374 321.654 322.362 322.807 322.899 324.706 65/54
(pseudo-6/5)
24 334.884 335.194 335.346 335.639 336.378 336.842 336.938 338.8235 17/14
25 348.837 349.160 349.319 349.624 350.3935 350.877 350.9775 352.941 11/9, 104/85, 60/49
26 362.791 363.127 363.292 363.609 364.409 364.912 365.017 367.059 37/30
27 376.744 377.093 377.265 377.594 378.425 378.947 379.056 381.1765 46/37, 97/78
28 390.698 391.059 391.238 391.579 392.441 392.9825 393.095 395.294 94/75, 89/71 (pseudo-5/4)
29 404.651 405.026 405.210 405.564 406.456 407.0175 407.134 409.412 24/19, 91/72
30 418.605 418.992 419.183 419.549 420.472 421.053 421.173 423.529 14/11, 65/51, 51/40
31 432.558 432.959 433.156 433.534 434.488 435.088 435.212 437.647 104/81, 113/88, 122/95, 9/7
32 446.512 446.925 447.129 447.519 445.503 449.123 449.251 451.765 22/17
33 460.465 460.892 461.101 461.504 462.519 463.158 463.29 465.882 17/13
34 474.419 474.858 475.074 475.489 476.535 477.193 477.329 480
35 488.372 488.824 489.047 489.474 490.551 491.228 491.3685 494.118
36 502.326 502.791 503.02 503.459 504.567 505.263 505.408 508.235
37 516.279 516.757 516.993 517.444 518.582 519.298 519.448 522.353
38 530.233 530.724 530.965 531.429 532.598 533.333 533.486 536.471
39 544.186 544.69 544.938 545.414 546.614 547.368 547.525 550.558
40 558.14 558.656 558.911 559.399 560.63 561.4035 561.564 564.706
41 572.093 572.623 572.884 573.383 574.645 575.439 575.603 578.8235
42 586.047 586.589 586.856 587.368 588.661 589.474 589.642 592.941 7/5
43 600 600.556 600.829 601.353 602.677 603.509 603.681 606.059 17/12
44 613.953 614.522 614.802 615.338 616.6925 617.544 617.72 620.1765
45 627.907 628.488 628.775 629.323 630.708 631.578 631.7595 635.294
46 641.860 642.455 642.747 643.308 644.724 645.614 645.799 649.412
47 655.814 656.421 656.720 657.293 658.74 659.649 659.838 663.519
48 669.767 670.388 670.693 671.278 672.7555 673.684 673.877 677.647
49 683.721 684.354 684.666 685.263 686.771 687.719 687.916 691.765
50 697.674 698.321 698.639 699.248 700.787 701.754 701.955 705.882 3/2
51 711.628 712.287 712.611 713.233 714.803 715.7895 715.994 720
52 725.581 726.253 726.584 727.218 728.8185 729.825 730.033 734.118
53 739.535 740.220 740.557 741.203 742.824 743.86 744.072 748.235
54 753.488 754.186 754.530 755.188 756.85 757.895 758.111 762.353
55 767.442 768.153 768.502 769.173 770.866 771.93 772.1505 776.471
56 781.395 782.119 782.475 783.158 784.881 785.965 786.19 790.588
57 795.349 796.085 796.448 797.143 798.897 800 800.229 804.706
58 809.302 810.052 810.421 811.128 812.913 814.035 814.268 818.8235 8/5
59 823.256 824.018 824.393 825.113 826.929 828.07 828.307 832.941
60 837.209 837.985 838.366 839.098 840.944 842.105 842.346 847.059 13/8
61 851.163 851.951 852.339 853.083 854.96 856.14 856.385 861.1765
62 865.116 865.917 866.312 867.068 868.976 870.175 870.424 875.294
63 879.070 879.884 880.285 881.053 882.9915 884.2105 884.463 889.412 5/3
64 893.023 893.850 894.257 895.038 897.007 898.246 898.502 903.529
65 906.977 907.817 908.230 909.023 911.023 912.281 912.5415 917.647
66 920.930 921.783 922.203 923.008 925.039 926.316 926.581 931.1765
67 934.884 935.750 936.176 936.993 939.0555 940.351 940.692 945.882
68 948.837 949.716 950.148 950.978 953.07 954.386 954.659 960
69 962.791 963.682 964.121 964.962 967.086 968.421 968.698 974.118 7/4
70 976.744 977.649 978.094 978.947 981.102 982.456 982.737 988.235
71 990.698 991.615 992.067 992.932 995.1175 996.491 996.776 1002.353 16/9
72 1004.651 1005.582 1006.039 1006.917 1009.133 1010.526 1010.815 1016.471 25/14
73 1018.605 1019.548 1020.012 1020.902 1023.149 1024.561 1024.854 1030.588 9/5
74 1032.558 1033.514 1033.985 1034.887 1037.165 1038.5965 1038.893 1044.706
75 1046.512 1047.481 1047.958 1048.872 1051.18 1052.632 1052.9325 1058.8235 11/6
76 1060.465 1061.447 1061.931 1062.857 1065.196 1066.667 1066.972 1072.941
77 1074.419 1075.414 1075.903 1076.842 1079.212 1080.702 1081.011 1087.059 28/15
78 1088.372 1089.380 1089.876 1090.827 1093.228 1094.737 1095.05 1101.1765 15/8
79 1102.326 1103.346 1103.849 1104.812 1107.243 1108.772 1109.089 1115.294
80 1116.279 1117.313 1117.822 1118.797 1121.259 1122.807 1123.128 1129.412
81 1130.233 1131.279 1131.794 1132.782 1135.275 1136.842 1137.167 1143.529
82 1144.186 1145.246 1145.767 1146.767 1149.291 1150.877 1151.206 1157.647
83 1158.14 1159.212 1159.74 1160.752 1163.306 1164.912 1165.245 1171.765
84 1172.093 1173.178 1173.713 1174.737 1177.322 1178.947 1179.284 1185.882
85 1186.047 1187.145 1187.685 1188.722 1191.338 1192.9825 1193.3235 1200
86 1200 1201.111 1201.658 1202.707 1205.3535 1207.0175 1207.363 1214.118 2/1
87 1213.9535 1215.078 1215.631 1216.692 1219.369 1221.053 1221.402 1228.235
88 1227.907 1229.044 1229.604 1230.677 1233.385 1235.088 1235.441 1242.353
89 1241.8605 1243.0105 1243.577 1244.662 1247.401 1249.123 1249.48 1256.471
90 1255.814 1256.698 1257.549 1258.647 1261.4165 1263.158 1263.519 1270.588
91 1269.767 1270.943 1271.522 1272.632 1275.432 1277.193 1277.558 1284.706
92 1283.721 1284.91 1285.495 1286.617 1289.448 1291.228 1291.597 1298.8235
93 1297.674 1298.876 1299.468 1300.602 1303.464 1305.263 1305.636 1312.941
94 1311.628 1312.426 1314.404 1314.5865 1317.479 1319.298 1319.675 1327.059
95 1325.581 1326.809 1327.413 1328.5715 1331.495 1333.333 1333.7145 1341.1765
96 1339.535 1340.775 1341.386 1342.5565 1345.511 1347.368 1347.754 1355.294
97 1353.488 1354.742 1355.358 1356.414 1359.527 1361.4035 1361.793 1369.412
98 1367.442 1368.708 1369.3315 1370.526 1373.542 1375.439 1375.832 1383.529
99 1381.395 1382.675 1383.304 1384.511 1387.558 1389.474 1389.871 1397.647 20/9
100 1395.349 1396.641 1397.277 1398.496 1401.574 1403.509 1403.91 1411.765 9/4


Todo: rework

simplify or split table somehow so it works better on phone displays and vertical monitors; expand the introduction to talk about who developed the scale and why, what they were trying to achieve; add multimedia, either links to music written with the scale, or diagrams of the scale’s properties, or both

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