Jinn

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The jinn is a unit of interval size which is defined as 1/16808 of an octave, the step size of 16808edo. 16808edo is consistent and distinct though the 35 limit, and is a very strong system for intervals less than the 37 prime limit, which includes most of what people find of interest.

Below the intervals of the 35-limit tonality diamond are tabulated, with the sizes listed in both cents and jinns. The worst error occurs for 33/25 and 50/33, which is less than 1/4 of a jinn off.

interval size in cents size in jinns
36/35 48.7700 683.110
35/34 50.1840 702.914
34/33 51.6820 723.899
33/32 53.273 746.176
32/31 54.964 769.868
31/30 56.767 795.114
30/29 58.692 822.073
29/28 60.751 850.923
28/27 62.961 881.872
27/26 65.337 915.158
26/25 67.900 951.056
25/24 70.672 989.885
24/23 73.681 1032.020
23/22 76.956 1077.903
22/21 80.537 1128.055
21/20 84.467 1183.104
20/19 88.801 1243.802
19/18 93.603 1311.066
18/17 98.955 1386.024
35/33 101.867 1426.813
17/16 104.955 1470.075
33/31 108.237 1516.045
16/15 111.731 1564.983
31/29 115.458 1617.187
15/14 119.443 1672.996
29/27 123.712 1732.795
14/13 128.298 1797.031
27/25 133.238 1866.214
13/12 138.573 1940.941
38/35 142.373 1994.177
25/23 144.353 2021.905
12/11 150.637 2109.923
35/32 155.140 2172.989
23/21 157.493 2205.958
34/31 159.920 2239.944
11/10 165.004 2311.159
32/29 170.423 2387.055
21/19 173.268 2426.906
31/28 176.210 2468.110
10/9 182.404 2554.868
29/26 189.050 2647.954
19/17 192.558 2697.090
28/25 196.198 2748.087
9/8 203.910 2856.099
35/31 210.104 2942.857
26/23 212.253 2972.961
17/15 216.687 3035.058
25/22 221.309 3099.808
33/29 223.696 3133.232
8/7 231.174 3237.978
31/27 239.171 3349.982
23/20 241.961 3389.062
38/33 244.240 3420.989
15/13 247.741 3470.026
22/19 253.805 3554.961
29/25 256.950 3599.010
36/31 258.874 3625.968
7/6 266.871 3737.972
34/29 275.378 3857.131
27/23 277.591 3888.120
20/17 281.358 3940.892
33/28 284.447 3984.155
13/11 289.210 4050.864
32/27 294.135 4119.851
19/16 297.513 4167.166
25/21 301.847 4227.864
31/26 304.508 4265.141
6/5 315.641 4421.082
35/29 325.562 4560.044
29/24 327.622 4588.895
23/19 330.761 4632.864
40/33 333.041 4664.791
17/14 336.130 4708.054
28/23 340.552 4769.992
11/9 347.408 4866.027
38/31 352.477 4937.034
27/22 354.547 4966.022
16/13 359.472 5035.009
21/17 365.825 5123.996
26/21 369.747 5178.920
31/25 372.408 5216.197
36/29 374.333 5243.155
5/4 386.314 5410.967
44/35 396.178 5549.138
34/27 399.090 5589.926
29/23 401.303 5620.915
24/19 404.442 5664.884
19/15 409.244 5732.149
33/26 412.745 5781.186
14/11 417.508 5847.895
23/18 424.364 5943.930
32/25 427.373 5986.065
9/7 435.084 6094.078
40/31 441.278 6180.836
31/24 443.081 6206.082
22/17 446.363 6252.051
35/27 449.275 6292.840
13/10 454.214 6362.023
30/23 459.994 6442.988
17/13 464.428 6505.085
38/29 467.936 6554.221
21/16 470.781 6594.071
46/35 473.135 6627.040
25/19 475.114 6654.769
29/22 478.259 6698.818
33/25 480.646 6732.242
4/3 498.045 6975.950
35/26 514.612 7207.998
31/23 516.761 7238.102
27/20 519.551 7277.182
23/17 523.319 7329.954
42/31 525.745 7363.940
19/14 528.687 7405.144
34/25 532.328 7456.141
15/11 536.951 7520.890
26/19 543.015 7605.825
48/35 546.815 7659.061
11/8 551.318 7722.127
40/29 556.737 7798.023
29/21 558.796 7826.873
18/13 563.382 7891.109
25/18 568.717 7965.835
32/23 571.726 8007.971
46/33 575.001 8053.853
7/5 582.512 8159.054
38/27 591.648 8287.017
31/22 593.718 8316.005
24/17 597.000 8361.974
17/12 603.000 8446.026
44/31 606.282 8491.995
27/19 608.352 8520.983
10/7 617.488 8648.946
33/23 624.999 8754.147
23/16 628.274 8800.029
36/25 631.283 8842.165
13/9 636.618 8916.891
42/29 641.204 8981.127
29/20 643.263 9009.977
16/11 648.682 9085.873
35/24 653.185 9148.939
19/13 656.985 9202.175
22/15 663.049 9287.110
25/17 667.672 9351.859
28/19 671.313 9402.856
31/21 674.255 9444.060
34/23 676.681 9478.046
40/27 680.449 9530.818
46/31 683.239 9569.898
52/35 685.388 9600.002
3/2 701.955 9832.050
50/33 719.354 10075.758
44/29 721.741 10109.182
38/25 724.886 10153.231
35/23 726.865 10180.96
32/21 729.219 10213.929
29/19 732.064 10253.779
26/17 735.572 10302.915
23/15 740.006 10365.012
20/13 745.786 10445.977
54/35 750.725 10515.160
17/11 753.637 10555.949
48/31 756.919 10601.918
31/20 758.722 10627.164
14/9 764.916 10713.922
25/16 772.627 10821.935
36/23 775.636 10864.070
11/7 782.492 10960.105
52/33 787.255 11026.814
30/19 790.756 11075.851
19/12 795.558 11143.116
46/29 798.697 11187.085
27/17 800.910 11218.074
35/22 803.822 11258.862
8/5 813.686 11397.033
29/18 825.667 11564.845
50/31 827.592 11591.803
21/13 830.253 11629.080
34/21 834.175 11684.004
13/8 840.528 11772.991
44/27 845.453 11841.978
31/19 847.523 11870.966
18/11 852.592 11941.973
23/14 859.448 12038.008
28/17 863.870 12099.946
33/20 866.959 12143.209
38/23 869.239 12175.136
48/29 872.378 12219.105
58/35 874.438 12247.956
5/3 884.359 12386.918
52/31 895.492 12542.859
42/25 898.153 12580.136
32/19 902.487 12640.834
27/16 905.865 12688.149
22/13 910.790 12757.136
56/33 915.553 12823.845
17/10 918.642 12867.108
46/27 922.409 12919.880
29/17 924.622 12950.869
12/7 933.129 13070.028
31/18 941.126 13182.032
50/29 943.050 13208.990
19/11 946.195 13253.039
26/15 952.259 13337.974
33/19 955.760 13387.011
40/23 958.039 13418.938
54/31 960.829 13458.018
7/4 968.826 13570.022
58/33 976.304 13674.768
44/25 978.691 13708.192
30/17 983.313 13772.942
23/13 987.747 13835.039
62/35 989.896 13865.143
16/9 996.090 13951.901
25/14 1003.802 14059.913
34/19 1007.442 14110.910
52/29 1010.950 14160.046
9/5 1017.596 14253.132
56/31 1023.790 14339.890
38/21 1026.732 14381.094
29/16 1029.577 14420.945
20/11 1034.996 14496.841
31/17 1040.080 14568.056
42/23 1042.507 14602.042
64/35 1044.860 14635.011
11/6 1049.363 14698.077
46/25 1055.647 14786.095
35/19 1057.627 14813.823
24/13 1061.427 14867.059
50/27 1066.762 14941.786
13/7 1071.702 15010.969
54/29 1076.288 15075.205
28/15 1080.557 15135.004
58/31 1084.542 15190.813
15/8 1088.269 15243.017
62/33 1091.763 15291.955
32/17 1095.045 15337.925
66/35 1098.133 15381.187
17/9 1101.045 15421.976
36/19 1106.397 15496.934
19/10 1111.199 15564.198
40/21 1115.533 15624.896
21/11 1119.463 15679.945
44/23 1123.044 15730.097
23/12 1126.319 15775.980
48/25 1129.328 15818.115
25/13 1132.100 15856.944
52/27 1134.663 15892.842
27/14 1137.039 15926.128
56/29 1139.249 15957.077
29/15 1141.308 15985.927
60/31 1143.233 16012.886
31/16 1145.036 16038.132
64/33 1146.727 16061.824
33/17 1148.318 16084.101
68/35 1149.816 16105.086
35/18 1151.230 16124.890
2 1200.000 16808.000