Jinn

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

Below the intervals of the 35-odd-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	10180.960
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