Harmonic entropy of just intervals

This is a procedurally generated table of several hundred just intonation intervals between 1/1 and 8/1: roughly evenly spaced with about one interval every 4-5 cents.

The table shows how wide each interval is in cents, as well as showing its harmonic entropy.

For a more general-purpose list of intervals, see Gallery of just intervals.

Methodology

This table was made with Scale Workshop. It was made by starting with 810ed8 (270edo but treating 8/1 as the period), then using "convert interval values>fraction" with a tolerance of 4.4 cents to convert all the intervals into the nearest simple just interval (according to Scale Workshop's default settings). Then Scale Workshop's built-in harmonic entropy table was used to get the cents and the harmonic entropy (again, everything left on its default settings).

The table

Harmonic entropy of just intervals

Ratio	Size (cents)	Harmonic entropy (%)	Comments
1/1	0.000	0.000
390/389	4.445	3.760
195/194	8.901	14.289
130/129	13.369	29.536
97/96	17.940	47.113
78/77	22.339	63.285
65/64	26.841	77.192
56/55	31.194	87.233
49/48	35.697	94.083
43/42	40.737	98.235
39/38	44.970	99.690
35/34	50.184	99.958
32/31	54.964	99.447
30/29	58.692	98.855
28/27	62.961	98.131
26/25	67.900	97.339
24/23	73.681	96.526
23/22	76.956	96.119
22/21	80.537	95.722
21/20	84.467	95.323
20/19	88.801	94.928
19/18	93.603	94.534
18/17	98.955	94.138
17/16	104.955	93.748
16/15	111.731	93.375
15/14	119.443	93.016
14/13	128.298	92.675
27/25	133.238	92.514
13/12	138.573	92.347
12/11	150.637	92.045
23/21	157.493	91.881
34/31	159.920	91.829
11/10	165.004	91.727
21/19	173.268	91.551
41/37	177.718	91.462
10/9	182.404	91.367
19/17	192.558	91.175
9/8	203.910	91.000
35/31	210.104	90.909
17/15	216.687	90.809
25/22	221.310	90.746
49/43	226.134	90.706
8/7	231.174	90.701
23/20	241.961	90.726
15/13	247.741	90.623
22/19	253.805	90.413
29/25	256.950	90.286
57/49	261.816	90.135
7/6	266.871	90.099
27/23	277.591	90.529
20/17	281.358	90.732
13/11	289.210	90.867
19/16	297.513	90.317
25/21	301.847	89.806
37/31	306.309	89.268
73/61	310.905	88.838
6/5	315.641	88.670
35/29	325.562	89.348
23/19	330.761	90.058
17/14	336.130	90.813
28/23	340.552	91.327
11/9	347.408	91.786
16/13	359.472	91.181
21/17	365.826	90.053
31/25	372.408	88.498
46/37	376.930	87.477
5/4	386.314	86.433
89/71	391.184	86.736
44/35	396.178	87.574
29/23	401.303	88.739
24/19	404.442	89.458
19/15	409.244	90.412
14/11	417.508	91.306
23/18	424.364	91.415
9/7	435.084	91.284
49/38	440.139	91.361
22/17	446.363	91.641
13/10	454.214	92.079
17/13	464.428	91.930
21/16	470.781	90.841
25/19	475.114	89.528
29/22	478.259	88.318
41/31	484.027	85.801
61/46	488.611	83.904
121/91	493.282	82.505
4/3	498.045	81.976
67/50	506.680	83.591
43/32	511.518	85.531
31/23	516.761	87.848
23/17	523.319	90.284
19/14	528.687	91.567
15/11	536.951	92.317
26/19	543.015	92.254
37/27	545.479	92.154
11/8	551.318	91.819
18/13	563.382	90.784
25/18	568.717	90.231
32/23	571.726	89.927
67/48	577.352	89.498
7/5	582.512	89.352
38/27	591.648	89.727
24/17	597.000	90.174
17/12	603.000	90.642
27/19	608.352	90.950
10/7	617.488	91.230
43/30	623.249	91.380
23/16	628.274	91.555
13/9	636.618	92.012
16/11	648.682	92.948
19/13	656.985	93.440
22/15	663.049	93.268
25/17	667.672	92.484
31/21	674.255	89.925
37/25	678.717	87.087
49/33	684.379	82.440
64/43	688.482	78.794
100/67	693.320	74.956
3/2	701.955	71.779
182/121	706.718	72.810
92/61	711.390	75.553
62/41	715.973	79.322
47/31	720.471	83.329
38/25	724.886	86.938
32/21	729.219	89.774
26/17	735.572	92.399
23/15	740.006	93.257
20/13	745.786	93.525
17/11	753.638	93.117
31/20	758.722	92.691
14/9	764.916	92.202
25/16	772.627	91.717
47/30	777.238	91.493
11/7	782.492	91.272
30/19	790.756	90.881
19/12	795.558	90.588
27/17	800.910	90.222
35/22	803.822	90.033
67/42	808.526	89.806
8/5	813.686	89.732
37/23	823.070	90.195
21/13	830.253	90.896
34/21	834.175	91.296
13/8	840.528	91.817
18/11	852.592	91.703
23/14	859.448	90.557
28/17	863.871	89.342
43/26	870.990	86.943
63/38	875.223	85.597
5/3	884.359	84.167
127/76	888.909	84.530
62/37	893.692	85.623
42/25	898.154	87.045
32/19	902.487	88.529
22/13	910.790	90.839
17/10	918.642	91.911
29/17	924.622	92.114
12/7	933.129	91.936
43/25	938.890	91.611
19/11	946.195	90.913
26/15	952.259	90.085
47/27	959.642	89.027
7/4	968.826	88.381
93/53	973.486	88.539
44/25	978.691	89.061
30/17	983.313	89.680
23/13	987.747	90.241
16/9	996.090	90.836
25/14	1003.802	90.734
34/19	1007.442	90.562
9/5	1017.596	90.182
74/41	1022.282	90.185
38/21	1026.732	90.292
20/11	1034.996	90.598
31/17	1040.080	90.750
53/29	1043.927	90.833
11/6	1049.363	90.918
24/13	1061.427	91.130
37/20	1065.030	91.211
13/7	1071.702	91.394
28/15	1080.557	91.657
15/8	1088.269	91.912
32/17	1095.045	92.173
17/9	1101.045	92.438
36/19	1106.397	92.704
19/10	1111.199	92.968
21/11	1119.463	93.512
23/12	1126.319	94.067
25/13	1132.100	94.649
27/14	1137.039	95.215
29/15	1141.309	95.749
31/16	1145.036	96.208
33/17	1148.318	96.553
37/19	1153.831	96.788
41/21	1158.282	96.316
47/24	1163.552	94.342
55/28	1168.806	90.065
63/32	1172.736	84.977
77/39	1177.661	76.268
95/48	1181.872	67.226
129/65	1186.631	56.465
193/97	1191.053	47.543
389/195	1195.555	41.234
2/1	1200.000	39.006
389/194	1204.456	41.246
195/97	1208.901	47.467
129/64	1213.473	56.700
97/48	1217.940	66.810
77/38	1222.631	76.861
65/32	1226.841	84.341
55/27	1231.767	90.672
49/24	1235.697	93.888
43/21	1240.737	96.081
39/19	1244.970	96.733
35/17	1250.184	96.662
31/15	1256.767	95.974
29/14	1260.751	95.470
27/13	1265.337	94.913
25/12	1270.672	94.335
23/11	1276.956	93.767
21/10	1284.467	93.226
40/19	1288.801	92.971
19/9	1293.603	92.713
17/8	1304.955	92.212
32/15	1311.731	91.962
15/7	1319.443	91.713
43/20	1325.204	91.549
28/13	1328.298	91.468
54/25	1333.238	91.338
13/6	1338.573	91.201
24/11	1350.637	90.891
35/16	1355.140	90.798
68/31	1359.920	90.737
11/5	1365.004	90.741
31/14	1376.210	90.799
20/9	1382.404	90.645
29/13	1389.050	90.242
47/21	1394.726	89.813
9/4	1403.910	89.442
79/35	1409.397	89.622
43/19	1414.005	89.985
25/11	1421.310	90.755
41/18	1425.152	91.119
16/7	1431.174	91.447
23/10	1441.961	90.803
30/13	1447.741	89.775
37/16	1451.344	88.987
58/25	1456.950	87.767
121/52	1462.108	86.960
7/3	1466.871	86.699
61/26	1476.357	87.725
40/17	1481.358	88.788
33/14	1484.447	89.469
26/11	1489.210	90.374
19/8	1497.513	91.263
31/13	1504.508	91.358
67/28	1510.481	91.232
12/5	1515.641	91.162
29/12	1527.622	91.519
17/7	1536.130	92.120
39/16	1542.483	92.492
22/9	1547.408	92.527
27/11	1554.547	91.809
32/13	1559.472	90.533
37/15	1563.075	89.159
47/19	1567.994	86.769
62/25	1572.408	84.387
97/39	1577.413	81.915
5/2	1586.314	79.831
178/71	1591.184	80.481
93/37	1595.647	82.086
63/25	1600.109	84.302
43/17	1606.562	87.719
38/15	1609.244	88.973
28/11	1617.508	91.634
23/9	1624.364	92.434
18/7	1635.084	92.172
49/19	1640.139	91.840
31/12	1643.081	91.658
57/22	1648.150	91.431
13/5	1654.214	91.300
34/13	1664.428	91.237
21/8	1670.781	90.960
29/11	1678.259	90.106
37/14	1682.518	89.391
61/23	1688.611	88.342
117/44	1693.120	87.764
8/3	1698.045	87.525
67/25	1706.680	88.237
43/16	1711.518	89.069
27/10	1719.551	90.435
19/7	1728.687	91.142
49/18	1733.742	91.064
30/11	1736.951	90.897
41/15	1740.794	90.654
85/31	1746.234	90.327
11/4	1751.318	90.168
47/17	1760.551	90.312
25/9	1768.717	90.677
39/14	1773.657	90.867
67/24	1777.352	90.985
14/5	1782.512	91.109
31/11	1793.718	91.367
17/6	1803.000	91.650
37/13	1810.816	91.957
20/7	1817.488	92.272
43/15	1823.249	92.602
23/8	1828.274	92.938
26/9	1836.618	93.633
29/10	1843.264	94.306
32/11	1848.682	94.862
35/12	1853.185	95.221
38/13	1856.985	95.305
41/14	1860.237	95.088
47/16	1865.507	93.821
53/18	1869.595	91.704
65/22	1875.523	86.386
77/26	1879.616	81.103
98/33	1884.379	73.722
131/44	1888.790	66.544
200/67	1893.320	60.026
3/1	1901.955	54.245
367/122	1906.679	56.071
187/62	1911.238	60.881
127/42	1915.641	67.404
94/31	1920.471	75.286
76/25	1924.886	81.991
64/21	1929.219	87.364
55/18	1933.722	91.364
46/15	1940.006	94.439
43/14	1942.692	95.041
37/12	1949.389	95.375
34/11	1953.638	95.100
31/10	1958.722	94.593
28/9	1964.916	93.929
25/8	1972.627	93.206
47/15	1977.238	92.840
22/7	1982.492	92.487
60/19	1990.756	92.024
19/6	1995.558	91.813
54/17	2000.910	91.606
35/11	2003.822	91.516
67/21	2008.526	91.378
16/5	2013.686	91.231
29/9	2025.667	90.874
42/13	2030.253	90.752
81/25	2035.193	90.679
13/4	2040.528	90.693
49/15	2049.383	90.886
36/11	2052.592	90.938
23/7	2059.448	90.832
33/10	2066.959	90.254
43/13	2070.990	89.797
63/19	2075.223	89.312
10/3	2084.359	88.773
127/38	2088.909	88.907
57/17	2094.513	89.429
37/11	2100.026	90.130
27/8	2105.865	90.864
44/13	2110.790	91.364
17/5	2118.642	91.902
58/17	2124.622	92.131
24/7	2133.129	92.030
31/9	2141.126	91.024
38/11	2146.195	89.734
45/13	2149.696	88.572
59/17	2154.216	86.904
94/27	2159.642	85.001
7/2	2168.826	83.459
186/53	2173.486	83.881
95/27	2177.962	84.993
60/17	2183.313	86.860
46/13	2187.747	88.508
39/11	2191.165	89.654
32/9	2196.090	90.939
25/7	2203.802	91.985
43/12	2209.563	92.143
18/5	2217.596	91.868
65/18	2222.931	91.484
29/8	2229.577	90.831
40/11	2234.996	90.215
51/14	2238.085	89.874
117/32	2244.438	89.346
11/3	2249.363	89.211
59/16	2259.172	89.729
37/10	2265.030	90.282
26/7	2271.702	90.802
41/11	2277.745	91.024
15/4	2288.269	91.072
79/21	2293.756	91.101
34/9	2301.045	91.261
72/19	2306.397	91.442
19/5	2311.199	91.637
42/11	2319.463	92.015
23/6	2326.319	92.389
27/7	2337.039	93.165
31/8	2345.036	93.896
35/9	2351.230	94.391
39/10	2356.169	94.508
47/12	2363.552	93.521
55/14	2368.806	91.325
63/16	2372.736	88.598
75/19	2377.069	84.455
95/24	2381.872	78.764
127/32	2386.422	72.968
191/48	2390.960	67.739
387/97	2395.532	64.080
4/1	2400.000	62.798
389/97	2404.456	64.076
193/48	2408.993	67.714
129/32	2413.473	72.852
97/24	2417.940	78.558
77/19	2422.631	84.164
65/16	2426.841	88.282
53/13	2432.977	92.286
49/12	2435.697	93.337
41/10	2442.749	94.509
37/9	2447.434	94.478
33/8	2453.273	94.049
29/7	2460.751	93.336
25/6	2470.672	92.507
46/11	2476.956	92.096
67/16	2479.307	91.958
21/5	2484.467	91.696
59/14	2490.346	91.443
38/9	2493.603	91.333
55/13	2497.104	91.229
17/4	2504.955	91.063
64/15	2511.731	90.911
30/7	2519.443	90.589
43/10	2525.204	90.237
56/13	2528.298	90.045
108/25	2533.238	89.798
13/3	2538.573	89.729
61/14	2548.059	90.228
35/8	2555.140	90.942
57/13	2558.940	91.316
22/5	2565.004	91.732
31/7	2576.210	91.266
40/9	2582.404	90.118
49/11	2586.334	89.120
67/15	2591.038	87.824
103/23	2595.526	86.696
9/2	2603.910	85.700
167/37	2609.101	86.069
86/19	2614.005	87.026
59/13	2618.644	88.237
41/9	2625.152	89.931
32/7	2631.174	91.047
23/5	2641.961	91.557
37/8	2651.344	90.918
51/11	2655.593	90.538
121/26	2662.108	90.078
14/3	2666.871	89.943
61/13	2676.357	90.178
47/10	2679.193	90.338
33/7	2684.447	90.654
52/11	2689.210	90.913
19/4	2697.513	91.250
81/17	2702.865	91.441
43/9	2707.608	91.620
67/14	2710.481	91.756
24/5	2715.641	92.033
29/6	2727.622	92.932
34/7	2736.130	93.640
39/8	2742.483	93.885
44/9	2747.408	93.589
54/11	2754.547	91.677
64/13	2759.472	88.918
74/15	2763.075	86.111
94/19	2767.994	81.362
129/26	2772.945	76.173
199/40	2777.636	71.787
5/1	2786.314	68.009
361/72	2791.116	69.236
186/37	2795.647	72.363
126/25	2800.109	76.655
91/18	2805.444	82.237
76/15	2809.244	85.883
61/12	2814.930	90.123
51/10	2820.597	92.661
46/9	2824.364	93.525
41/8	2829.062	93.937
36/7	2835.084	93.804
31/6	2843.081	93.178
57/11	2848.150	92.750
26/5	2854.214	92.307
47/9	2861.597	91.870
21/4	2870.781	91.425
79/15	2876.268	91.152
37/7	2882.518	90.820
53/10	2887.191	90.579
117/22	2893.120	90.378
16/3	2898.045	90.360
59/11	2907.854	90.739
43/8	2911.518	90.933
27/5	2919.551	91.115
65/12	2924.886	90.826
38/7	2928.687	90.366
49/9	2933.742	89.479
60/11	2936.951	88.814
93/17	2942.035	87.822
181/33	2946.542	87.184
11/2	2951.318	86.954
94/17	2960.551	87.918
61/11	2965.567	88.943
50/9	2968.717	89.611
39/7	2973.657	90.516
67/12	2977.352	91.004
28/5	2982.512	91.342
45/8	2990.224	91.271
62/11	2993.718	91.121
17/3	3003.000	90.796
91/16	3009.354	90.823
40/7	3017.488	91.140
63/11	3021.418	91.351
23/4	3028.274	91.759
52/9	3036.618	92.295
29/5	3043.264	92.782
35/6	3053.185	93.524
41/7	3060.237	93.677
47/8	3065.507	93.159
53/9	3069.595	92.138
65/11	3075.523	89.379
77/13	3079.616	86.553
95/16	3083.827	83.035
131/22	3088.790	78.596
197/33	3093.189	75.071
6/1	3101.955	71.731
367/61	3106.679	72.714
187/31	3111.238	75.340
127/21	3115.641	78.905
91/15	3121.085	83.711
73/12	3125.835	87.463
61/10	3130.571	90.313
55/9	3133.722	91.647
49/8	3137.652	92.720
43/7	3142.692	93.315
37/6	3149.389	93.281
31/5	3158.722	92.634
56/9	3164.916	92.175
25/4	3172.627	91.679
69/11	3178.911	91.336
44/7	3182.492	91.164
63/10	3186.422	91.034
120/19	3190.756	90.949
19/3	3195.558	90.954
127/20	3200.108	91.016
51/8	3206.910	91.113
32/5	3213.686	90.949
45/7	3221.398	90.200
58/9	3225.667	89.582
84/13	3230.253	88.880
162/25	3235.193	88.287
13/2	3240.528	88.036
98/15	3249.383	88.679
59/9	3255.262	89.542
46/7	3259.448	90.160
33/5	3266.959	90.915
53/8	3273.505	91.119
20/3	3284.359	91.038
127/19	3288.909	91.050
47/7	3296.681	91.284
27/4	3305.865	91.845
61/9	3312.975	92.403
34/5	3318.642	92.846
41/6	3327.107	93.164
48/7	3333.129	92.684
55/8	3337.632	91.625
62/9	3341.126	90.272
76/11	3346.195	87.464
97/14	3351.070	83.990
125/18	3355.031	80.945
195/28	3359.971	77.500
7/1	3368.826	74.586
379/54	3373.400	75.394
190/27	3377.962	77.639
127/18	3382.512	80.826
92/13	3387.747	84.821
78/11	3391.165	87.227
64/9	3396.090	90.022
50/7	3403.802	92.504
43/6	3409.563	93.087
36/5	3417.596	92.889
65/9	3422.931	92.505
29/4	3429.577	91.982
51/7	3438.085	91.477
117/16	3444.438	91.266
22/3	3449.363	91.188
59/8	3459.172	91.036
37/5	3465.030	90.729
52/7	3471.702	90.110
67/9	3475.397	89.685
97/13	3479.368	89.251
15/2	3488.269	88.748
158/21	3493.756	88.946
83/11	3498.729	89.408
53/7	3504.679	90.087
38/5	3511.199	90.725
84/11	3519.463	91.165
23/3	3526.319	91.334
77/10	3533.830	91.570
54/7	3537.039	91.735
31/4	3545.036	92.279
70/9	3551.230	92.737
39/5	3556.169	92.976
47/6	3563.552	92.726
55/7	3568.806	91.736
63/8	3572.736	90.390
71/9	3575.787	88.962
95/12	3581.872	85.279
127/16	3586.422	82.182
191/24	3590.960	79.377
383/48	3595.486	77.393
8/1	3600.000	76.672