Harmonic entropy of just intervals: Difference between revisions

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Add a column based on a Discord conversation. Will fill in the column soon, for now it’s a placeholder. (If someone else wants to fill it in first though, I’m happy for that :) But otherwise I will in the coming days)
Eufalesio (talk | contribs)
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m dumb wording
 
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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]].
This is a procedurally generated table of several hundred [[just intonation]] intervals between [[1/1]] and [[16/1]]: 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]].
The table shows how wide each interval is in cents, as well as showing its [[harmonic entropy]].
Line 6: Line 6:


== Methodology ==
== 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).
This table was made with [[Scale Workshop]]. It was made by starting with [[270edo]] across four octaves, then using "convert interval values > fraction" with a tolerance of 4.4{{c}} 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, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).


== Table of intervals ==
== Table of intervals ==
 
=== 1/1 to 2/1 ===
=== 1/1 to 3/2 ===
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 0 to 1200{{c}}
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
|-
!Entropy <br>(%, Rényi order 7.0) !! Comments
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
|-
| [[1/1]] || 0.000 || 0.000 || 0.000
|-
| [[390/389]] || 4.445 || 3.760 || 0.907
|-
| [[195/194]] || 8.901 || 14.289 || 3.681
|-
| [[130/129]] || 13.369 || 29.536 || 8.458
|-
| [[97/96]] || 17.940 || 47.113 || 15.574
|-
| [[78/77]] || 22.339 || 63.285 || 24.669
|-
| [[65/64]] || 26.841 || 77.192 || 36.309
|-
| [[56/55]] || 31.194 || 87.233 || 49.779
|-
| [[49/48]] || 35.697 || 94.083 || 65.929
|-
| [[43/42]] || 40.737 || 98.235 || 86.459
|-
| [[39/38]] || 44.970 || 99.690 || 99.596
|-
| [[35/34]] || 50.184 || 99.958 || 98.660
|-
| [[32/31]] || 54.964 || 99.447 || 96.764
|-
| [[30/29]] || 58.692 || 98.855 || 95.355
|-
| [[28/27]] || 62.961 || 98.131 || 93.820
|-
| [[26/25]] || 67.900 || 97.339 || 92.155
|-
| [[24/23]] || 73.681 || 96.526 || 90.360
|-
| [[23/22]] || 76.956 || 96.119 || 89.411
|-
| [[22/21]] || 80.537 || 95.722 || 88.427
|-
| [[21/20]] || 84.467 || 95.323 || 87.402
|-
| [[20/19]] || 88.801 || 94.928 || 86.324
|-
| [[19/18]] || 93.603 || 94.534 || 85.175
|-
| [[18/17]] || 98.955 || 94.138 || 83.939
|-
| [[17/16]] || 104.955 || 93.748 || 82.606
|-
| [[16/15]] || 111.731 || 93.375 || 81.182
|-
| [[15/14]] || 119.443 || 93.016 || 79.687
|-
| [[14/13]] || 128.298 || 92.675 || 78.137
|-
| [[27/25]] || 133.238 || 92.514 || 77.302
|-
| [[13/12]] || 138.573 || 92.347 || 76.478
|-
| [[12/11]] || 150.637 || 92.045 || 74.569
|-
| [[23/21]] || 157.493 || 91.881 || 73.578
|-
| [[34/31]] || 159.920 || 91.829 || 72.985
|-
| [[11/10]] || 165.004 || 91.727 || 72.187
|-
| [[21/19]] || 173.268 || 91.551 || 71.706
|-
| [[41/37]] || 177.718 || 91.462 || 70.122
|-
| [[10/9]] || 182.404 || 91.367 || 69.257
|-
| [[19/17]] || 192.558 || 91.175 || 70.455
|-
| [[9/8]] || 203.910 || 91.000 || 65.852
|-
| [[35/31]] || 210.104 || 90.909 || 67.768
|-
| [[17/15]] || 216.687 || 90.809 || 70.456
|-
| [[25/22]] || 221.309 || 90.746 || 66.917
|-
| [[49/43]] || 226.134 || 90.706 || 63.360
|-
| [[8/7]] || 231.174 || 90.701 || 62.087
|-
| [[23/20]] || 241.961 || 90.726 || 68.150
|-
| [[15/13]] || 247.741 || 90.623 || 72.999
|-
| [[22/19]] || 253.805 || 90.413 || 66.529
|-
| [[29/25]] || 256.950 || 90.286 || 62.777
|-
| [[57/49]] || 261.816 || 90.135 || 58.880
|-
| [[7/6]] || 266.871 || 90.099 || 57.449
|-
| [[27/23]] || 277.591 || 90.529 || 63.339
|-
| [[20/17]] || 281.358 || 90.732 || 68.028
|-
| [[13/11]] || 289.210 || 90.867 || 75.314
|-
| [[19/16]] || 297.513 || 90.317 || 69.059
|-
| [[25/21]] || 301.847 || 89.806 || 62.212
|-
| [[37/31]] || 306.308 || 89.268 || 56.838
|-
| [[73/61]] || 310.905 || 88.838 || 53.461
|-
| [[6/5]] || 315.641 || 88.670 || 52.311
|-
| [[35/29]] || 325.562 || 89.348 || 57.574
|-
| [[23/19]] || 330.761 || 90.058 || 64.423
|-
| [[17/14]] || 336.130 || 90.813 || 72.542
|-
| [[28/23]] || 340.552 || 91.327 || 73.081
|-
| [[11/9]] || 347.408 || 91.786 || 71.098
|-
| [[16/13]] || 359.472 || 91.181 || 76.294
|-
| [[21/17]] || 365.825 || 90.053 || 68.023
|-
| [[31/25]] || 372.408 || 88.498 || 56.195
|-
| [[46/37]] || 376.930 || 87.477 || 50.618
|-
| [[5/4]] || 386.314 || 86.433 || 45.966
|-
| [[89/71]] || 391.184 || 86.736 || 47.224
|-
| [[44/35]] || 396.178 || 87.574 || 51.114
|-
| [[29/23]] || 401.303 || 88.739 || 57.835
|-
| [[24/19]] || 404.442 || 89.458 || 63.288
|-
| [[19/15]] || 409.244 || 90.412 || 72.808
|-
| [[14/11]] || 417.508 || 91.306 || 75.636
|-
| [[23/18]] || 424.364 || 91.415 || 69.571
|-
| [[9/7]] || 435.084 || 91.284 || 63.938
|-
| [[49/38]] || 440.139 || 91.361 || 65.252
|-
|-
| [[1/1]] || 0.000 || 0.000
| [[22/17]] || 446.363 || 91.641 || 69.925
| ||  
|-
|-
| [[390/389]] || 4.445 || 3.760
| [[13/10]] || 454.214 || 92.079 || 74.367
| ||  
|-
|-
| [[195/194]] || 8.901 || 14.289
| [[17/13]] || 464.428 || 91.930 || 78.493
| ||  
|-
|-
| [[130/129]] || 13.369 || 29.536
| [[21/16]] || 470.781 || 90.841 || 75.987
| ||  
|-
|-
| [[97/96]] || 17.940 || 47.113
| [[25/19]] || 475.114 || 89.528 || 65.532
| ||  
|-
|-
| [[78/77]] || 22.339 || 63.285
| [[29/22]] || 478.259 || 88.318 || 58.453
| ||  
|-
|-
| [[65/64]] || 26.841 || 77.192
| [[41/31]] || 484.027 || 85.801 || 48.135
| ||  
|-
|-
| [[56/55]] || 31.194 || 87.233
| [[61/46]] || 488.610 || 83.904 || 42.464
| ||  
|-
|-
| [[49/48]] || 35.697 || 94.083
| [[121/91]] || 493.282 || 82.505 || 38.981
| ||  
|-
|-
| [[43/42]] || 40.737 || 98.235
| [[4/3]] || 498.045 || 81.976 || 37.808
| ||  
|-
|-
| [[39/38]] || 44.970 || 99.690
| [[67/50]] || 506.680 || 83.591 || 41.793
| ||  
|-
|-
| [[35/34]] || 50.184 || 99.958
| [[43/32]] || 511.518 || 85.531 || 47.459
| ||  
|-
|-
| [[32/31]] || 54.964 || 99.447
| [[31/23]] || 516.761 || 87.848 || 56.398
| ||  
|-
|-
| [[30/29]] || 58.692 || 98.855
| [[23/17]] || 523.319 || 90.284 || 71.419
| ||  
|-
|-
| [[28/27]] || 62.961 || 98.131
| [[19/14]] || 528.687 || 91.567 || 79.786
| ||  
|-
|-
| [[26/25]] || 67.900 || 97.339
| [[15/11]] || 536.951 || 92.317 || 76.271
| ||  
|-
|-
| [[24/23]] || 73.681 || 96.526
| [[26/19]] || 543.015 || 92.254 || 72.269
| ||  
|-
|-
| [[23/22]] || 76.956 || 96.119
| [[37/27]] || 545.479 || 92.154 || 70.833
| ||  
|-
|-
| [[22/21]] || 80.537 || 95.722
| [[11/8]] || 551.318 || 91.819 || 69.323
| ||  
|-
|-
| [[21/20]] || 84.467 || 95.323
| [[18/13]] || 563.382 || 90.784 || 72.045
| ||  
|-
|-
| [[20/19]] || 88.801 || 94.928
| [[25/18]] || 568.717 || 90.231 || 64.851
| ||  
|-
|-
| [[19/18]] || 93.603 || 94.534
| [[32/23]] || 571.726 || 89.927 || 60.988
| ||  
|-
|-
| [[18/17]] || 98.955 || 94.138
| [[67/48]] || 577.352 || 89.498 || 56.217
| ||  
|-
|-
| [[17/16]] || 104.955 || 93.748
| [[7/5]] || 582.512 || 89.352 || 54.788
| ||  
|-
|-
| [[16/15]] || 111.731 || 93.375
| [[38/27]] || 591.648 || 89.727 || 59.203
| ||  
|-
|-
| [[15/14]] || 119.443 || 93.016
| [[24/17]] || 597.000 || 90.174 || 65.794
| ||  
|-
|-
| [[14/13]] || 128.298 || 92.675
| [[17/12]] || 603.000 || 90.642 || 73.141
| ||  
|-
|-
| [[27/25]] || 133.238 || 92.514
| [[27/19]] || 608.352 || 90.950 || 69.816
| ||  
|-
|-
| [[13/12]] || 138.573 || 92.347
| [[10/7]] || 617.488 || 91.230 || 65.567
| ||  
|-
|-
| [[12/11]] || 150.637 || 92.045
| [[43/30]] || 623.249 || 91.380 || 67.163
| ||  
|-
|-
| [[23/21]] || 157.493 || 91.881
| [[23/16]] || 628.274 || 91.555 || 70.507
| ||  
|-
|-
| [[34/31]] || 159.920 || 91.829
| [[13/9]] || 636.618 || 92.012 || 73.029
| ||  
|-
|-
| [[11/10]] || 165.004 || 91.727
| [[16/11]] || 648.682 || 92.948 || 77.137
| ||  
|-
|-
| [[21/19]] || 173.268 || 91.551
| [[19/13]] || 656.985 || 93.440 || 80.684
| ||  
|-
|-
| [[41/37]] || 177.718 || 91.462
| [[22/15]] || 663.049 || 93.268 || 83.656
| ||  
|-
|-
| [[10/9]] || 182.404 || 91.367
| [[25/17]] || 667.672 || 92.484 || 84.338
| ||  
|-
|-
| [[19/17]] || 192.558 || 91.175
| [[31/21]] || 674.255 || 89.925 || 67.557
| ||  
|-
|-
| [[9/8]] || 203.910 || 91.000
| [[37/25]] || 678.717 || 87.087 || 55.540
| ||  
|-
|-
| [[35/31]] || 210.104 || 90.909
| [[49/33]] || 684.379 || 82.440 || 43.304
| ||  
|-
|-
| [[17/15]] || 216.687 || 90.809
| [[64/43]] || 688.482 || 78.794 || 36.567
| ||  
|-
|-
| [[25/22]] || 221.310 || 90.746
| [[100/67]] || 693.320 || 74.956 || 30.926
| ||  
|-
|-
| [[49/43]] || 226.134 || 90.706
| [[3/2]] || 701.955 || 71.779 || 27.000
| ||  
|-
|-
| [[8/7]] || 231.174 || 90.701
| [[182/121]] || 706.718 || 72.810 || 28.196
| ||  
|-
|-
| [[23/20]] || 241.961 || 90.726
| [[92/61]] || 711.390 || 75.553 || 31.686
| ||  
|-
|-
| [[15/13]] || 247.741 || 90.623
| [[62/41]] || 715.973 || 79.322 || 37.349
| ||  
|-
|-
| [[22/19]] || 253.805 || 90.413
| [[47/31]] || 720.471 || 83.329 || 45.071
| ||  
|-
|-
| [[29/25]] || 256.950 || 90.286
| [[38/25]] || 724.886 || 86.938 || 54.740
| ||  
|-
|-
| [[57/49]] || 261.816 || 90.135
| [[32/21]] || 729.219 || 89.774 || 66.231
| ||  
|-
|-
| [[7/6]] || 266.871 || 90.099
| [[26/17]] || 735.572 || 92.399 || 83.502
| ||  
|-
|-
| [[27/23]] || 277.591 || 90.529
| [[23/15]] || 740.006 || 93.257 || 83.983
| ||  
|-
|-
| [[20/17]] || 281.358 || 90.732
| [[20/13]] || 745.786 || 93.525 || 81.149
| ||  
|-
|-
| [[13/11]] || 289.210 || 90.867
| [[17/11]] || 753.637 || 93.117 || 77.675
| ||  
|-
|-
| [[19/16]] || 297.513 || 90.317
| [[31/20]] || 758.722 || 92.691 || 75.497
| ||  
|-
|-
| [[25/21]] || 301.847 || 89.806
| [[14/9]] || 764.916 || 92.202 || 73.877
| ||  
|-
|-
| [[37/31]] || 306.309 || 89.268
| [[25/16]] || 772.627 || 91.717 || 71.040
| ||  
|-
|-
| [[73/61]] || 310.905 || 88.838
| [[47/30]] || 777.238 || 91.493 || 68.327
| ||  
|-
|-
| [[6/5]] || 315.641 || 88.670
| [[11/7]] || 782.492 || 91.272 || 67.068
| ||  
|-
|-
| [[35/29]] || 325.562 || 89.348
| [[30/19]] || 790.756 || 90.881 || 70.442
| ||  
|-
|-
| [[23/19]] || 330.761 || 90.058
| [[19/12]] || 795.558 || 90.588 || 71.776
| ||  
|-
|-
| [[17/14]] || 336.130 || 90.813
| [[27/17]] || 800.910 || 90.222 || 65.504
| ||  
|-
|-
| [[28/23]] || 340.552 || 91.327
| [[35/22]] || 803.822 || 90.033 || 62.109
| ||  
|-
|-
| [[11/9]] || 347.408 || 91.786
| [[67/42]] || 808.526 || 89.806 || 58.378
| ||  
|-
|-
| [[16/13]] || 359.472 || 91.181
| [[8/5]] || 813.686 || 89.732 || 56.944
| ||  
|-
|-
| [[21/17]] || 365.826 || 90.053
| [[37/23]] || 823.070 || 90.195 || 61.505
| ||  
|-
|-
| [[31/25]] || 372.408 || 88.498
| [[21/13]] || 830.253 || 90.896 || 70.181
| ||  
|-
|-
| [[46/37]] || 376.930 || 87.477
| [[34/21]] || 834.175 || 91.296 || 72.501
| ||  
|-
|-
| [[5/4]] || 386.314 || 86.433
| [[13/8]] || 840.528 || 91.817 || 71.613
| ||  
|-
|-
| [[89/71]] || 391.184 || 86.736
| [[18/11]] || 852.592 || 91.703 || 77.070
| ||  
|-
|-
| [[44/35]] || 396.178 || 87.574
| [[23/14]] || 859.448 || 90.557 || 73.426
| ||  
|-
|-
| [[29/23]] || 401.303 || 88.739
| [[28/17]] || 863.870 || 89.342 || 63.482
| ||  
|-
|-
| [[24/19]] || 404.442 || 89.458
| [[43/26]] || 870.990 || 86.943 || 50.773
| ||  
|-
|-
| [[19/15]] || 409.244 || 90.412
| [[63/38]] || 875.223 || 85.597 || 45.746
| ||  
|-
|-
| [[14/11]] || 417.508 || 91.306
| [[5/3]] || 884.359 || 84.167 || 41.331
| ||  
|-
|-
| [[23/18]] || 424.364 || 91.415
| [[127/76]] || 888.909 || 84.530 || 42.413
| ||  
|-
|-
| [[9/7]] || 435.084 || 91.284
| [[62/37]] || 893.692 || 85.623 || 45.908
| ||  
|-
|-
| [[49/38]] || 440.139 || 91.361
| [[42/25]] || 898.153 || 87.045 || 51.349
| ||  
|-
|-
| [[22/17]] || 446.363 || 91.641
| [[32/19]] || 902.487 || 88.529 || 58.647
| ||  
|-
|-
| [[13/10]] || 454.214 || 92.079
| [[22/13]] || 910.790 || 90.839 || 76.249
| ||  
|-
|-
| [[17/13]] || 464.428 || 91.930
| [[17/10]] || 918.642 || 91.911 || 76.123
| ||  
|-
|-
| [[21/16]] || 470.781 || 90.841
| [[29/17]] || 924.622 || 92.114 || 71.669
| ||  
|-
|-
| [[25/19]] || 475.114 || 89.528
| [[12/7]] || 933.129 || 91.936 || 68.444
| ||  
|-
|-
| [[29/22]] || 478.259 || 88.318
| [[43/25]] || 938.890 || 91.611 || 70.144
| ||  
|-
|-
| [[41/31]] || 484.027 || 85.801
| [[19/11]] || 946.195 || 90.913 || 74.112
| ||  
|-
|-
| [[61/46]] || 488.611 || 83.904
| [[26/15]] || 952.259 || 90.085 || 65.732
| ||  
|-
|-
| [[121/91]] || 493.282 || 82.505
| [[47/27]] || 959.642 || 89.027 || 55.751
| ||  
|-
|-
| [[4/3]] || 498.045 || 81.976
| [[7/4]] || 968.826 || 88.381 || 51.230
| ||  
|-
|-
| [[67/50]] || 506.680 || 83.591
| [[93/53]] || 973.486 || 88.539 || 52.340
| ||  
|-
|-
| [[43/32]] || 511.518 || 85.531
| [[44/25]] || 978.691 || 89.061 || 56.297
| ||  
|-
|-
| [[31/23]] || 516.761 || 87.848
| [[30/17]] || 983.313 || 89.680 || 62.180
| ||  
|-
|-
| [[23/17]] || 523.319 || 90.284
| [[23/13]] || 987.747 || 90.241 || 69.519
| ||  
|-
|-
| [[19/14]] || 528.687 || 91.567
| [[16/9]] || 996.090 || 90.836 || 75.386
| ||  
|-
|-
| [[15/11]] || 536.951 || 92.317
| [[25/14]] || 1003.802 || 90.734 || 68.192
| ||  
|-
|-
| [[26/19]] || 543.015 || 92.254
| [[34/19]] || 1007.442 || 90.562 || 63.920
| ||  
|-
|-
| [[37/27]] || 545.479 || 92.154
| [[9/5]] || 1017.596 || 90.182 || 58.686
| ||  
|-
|-
| [[11/8]] || 551.318 || 91.819
| [[74/41]] || 1022.282 || 90.185 || 59.936
| ||  
|-
|-
| [[18/13]] || 563.382 || 90.784
| [[38/21]] || 1026.732 || 90.292 || 63.244
| ||  
|-
|-
| [[25/18]] || 568.717 || 90.231
| [[20/11]] || 1034.996 || 90.598 || 71.948
| ||  
|-
|-
| [[32/23]] || 571.726 || 89.927
| [[31/17]] || 1040.080 || 90.750 || 69.295
| ||  
|-
|-
| [[67/48]] || 577.352 || 89.498
| [[53/29]] || 1043.927 || 90.833 || 66.508
| ||  
|-
|-
| [[7/5]] || 582.512 || 89.352
| [[11/6]] || 1049.363 || 90.918 || 64.951
| ||  
|-
|-
| [[38/27]] || 591.648 || 89.727
| [[24/13]] || 1061.427 || 91.130 || 70.596
| ||  
|-
|-
| [[24/17]] || 597.000 || 90.174
| [[37/20]] || 1065.030 || 91.211 || 71.005
| ||  
|-
|-
| [[17/12]] || 603.000 || 90.642
| [[13/7]] || 1071.702 || 91.394 || 69.664
| ||  
|-
|-
| [[27/19]] || 608.352 || 90.950
| [[28/15]] || 1080.557 || 91.657 || 72.058
| ||  
|-
|-
| [[10/7]] || 617.488 || 91.230
| [[15/8]] || 1088.269 || 91.912 || 73.260
| ||  
|-
|-
| [[43/30]] || 623.249 || 91.380
| [[32/17]] || 1095.045 || 92.173 || 74.505
| ||  
|-
|-
| [[23/16]] || 628.274 || 91.555
| [[17/9]] || 1101.045 || 92.438 || 75.914
| ||  
|-
|-
| [[13/9]] || 636.618 || 92.012
| [[36/19]] || 1106.397 || 92.704 || 77.039
| ||  
|-
|-
| [[16/11]] || 648.682 || 92.948
| [[19/10]] || 1111.199 || 92.968 || 78.213
| ||  
|-
|-
| [[19/13]] || 656.985 || 93.440
| [[21/11]] || 1119.463 || 93.512 || 80.351
| ||  
|-
|-
| [[22/15]] || 663.049 || 93.268
| [[23/12]] || 1126.319 || 94.067 || 82.319
| ||  
|-
|-
| [[25/17]] || 667.672 || 92.484
| [[25/13]] || 1132.100 || 94.649 || 84.128
| ||  
|-
|-
| [[31/21]] || 674.255 || 89.925
| [[27/14]] || 1137.039 || 95.215 || 85.797
| ||  
|-
|-
| [[37/25]] || 678.717 || 87.087
| [[29/15]] || 1141.308 || 95.749 || 87.342
| ||  
|-
|-
| [[49/33]] || 684.379 || 82.440
| [[31/16]] || 1145.036 || 96.208 || 88.775
| ||  
|-
|-
| [[64/43]] || 688.482 || 78.794
| [[33/17]] || 1148.318 || 96.553 || 90.106
| ||  
|-
|-
| [[100/67]] || 693.320 || 74.956
| [[37/19]] || 1153.831 || 96.788 || 92.494
| ||  
|-
|-
| [[3/2]] || 701.955 || 71.779
| [[41/21]] || 1158.281 || 96.316 || 93.767
| ||  
|-
| [[47/24]] || 1163.552 || 94.342 || 79.933
|-
| [[55/28]] || 1168.806 || 90.065 || 61.125
|-
| [[63/32]] || 1172.736 || 84.977 || 48.910
|-
| [[77/39]] || 1177.661 || 76.268 || 35.956
|-
| [[95/48]] || 1181.872 || 67.226 || 26.975
|-
| [[129/65]] || 1186.631 || 56.465 || 19.139
|-
| [[193/97]] || 1191.053 || 47.543 || 14.030
|-
| [[389/195]] || 1195.555 || 41.234 || 10.933
|-
| [[2/1]] || 1200.000 || 39.006 || 9.915
|}
|}


=== 3/2 to 2/1 ===
=== 2/1 to 4/1 ===
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 1200 to 2400{{c}}
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
|-
!Entropy <br>(%, Rényi order 7.0) !! Comments
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
|-
| [[2/1]] || 1200.000 || 39.006 || 9.915
|-
| [[389/194]] || 1204.456 || 41.246 || 10.916
|-
| [[195/97]] || 1208.901 || 47.467 || 13.941
|-
| [[129/64]] || 1213.473 || 56.700 || 19.201
|-
|-
| [[3/2]] || 701.955 || 71.779
| [[97/48]] || 1217.940 || 66.810 || 26.498
| ||  
|-
|-
| [[182/121]] || 706.718 || 72.810
| [[77/38]] || 1222.631 || 76.861 || 36.491
| ||  
|-
|-
| [[92/61]] || 711.390 || 75.553
| [[65/32]] || 1226.841 || 84.341 || 47.508
| ||  
|-
|-
| [[62/41]] || 715.973 || 79.322
| [[55/27]] || 1231.767 || 90.672 || 62.844
| ||  
|-
|-
| [[47/31]] || 720.471 || 83.329
| [[49/24]] || 1235.697 || 93.888 || 76.914
| ||  
|-
|-
| [[38/25]] || 724.886 || 86.938
| [[43/21]] || 1240.737 || 96.081 || 92.874
| ||  
|-
|-
| [[32/21]] || 729.219 || 89.774
| [[39/19]] || 1244.970 || 96.733 || 92.933
| ||  
|-
|-
| [[26/17]] || 735.572 || 92.399
| [[35/17]] || 1250.184 || 96.662 || 90.721
| ||  
|-
|-
| [[23/15]] || 740.006 || 93.257
| [[31/15]] || 1256.767 || 95.974 || 88.150
| ||  
|-
|-
| [[20/13]] || 745.786 || 93.525
| [[29/14]] || 1260.751 || 95.470 || 86.704
| ||  
|-
|-
| [[17/11]] || 753.638 || 93.117
| [[27/13]] || 1265.337 || 94.913 || 85.129
| ||  
|-
|-
| [[31/20]] || 758.722 || 92.691
| [[25/12]] || 1270.672 || 94.335 || 83.403
| ||  
|-
|-
| [[14/9]] || 764.916 || 92.202
| [[23/11]] || 1276.956 || 93.767 || 81.510
| ||  
|-
|-
| [[25/16]] || 772.627 || 91.717
| [[21/10]] || 1284.467 || 93.226 || 79.440
| ||  
|-
|-
| [[47/30]] || 777.238 || 91.493
| [[40/19]] || 1288.801 || 92.971 || 78.339
| ||  
|-
|-
| [[11/7]] || 782.492 || 91.272
| [[19/9]] || 1293.603 || 92.713 || 77.210
| ||  
|-
|-
| [[30/19]] || 790.756 || 90.881
| [[17/8]] || 1304.955 || 92.212 || 74.752
| ||  
|-
|-
| [[19/12]] || 795.558 || 90.588
| [[32/15]] || 1311.731 || 91.962 || 73.263
| ||  
|-
|-
| [[27/17]] || 800.910 || 90.222
| [[15/7]] || 1319.443 || 91.713 || 71.565
| ||  
|-
|-
| [[35/22]] || 803.822 || 90.033
| [[43/20]] || 1325.204 || 91.549 || 71.747
| ||  
|-
|-
| [[67/42]] || 808.526 || 89.806
| [[28/13]] || 1328.298 || 91.468 || 70.997
| ||  
|-
|-
| [[8/5]] || 813.686 || 89.732
| [[54/25]] || 1333.238 || 91.338 || 68.520
| ||  
|-
|-
| [[37/23]] || 823.070 || 90.195
| [[13/6]] || 1338.573 || 91.201 || 67.254
| ||  
|-
|-
| [[21/13]] || 830.253 || 90.896
| [[24/11]] || 1350.637 || 90.891 || 70.532
| ||  
|-
|-
| [[34/21]] || 834.175 || 91.296
| [[35/16]] || 1355.140 || 90.798 || 66.822
| ||  
|-
|-
| [[13/8]] || 840.528 || 91.817
| [[68/31]] || 1359.920 || 90.737 || 63.227
| ||  
|-
|-
| [[18/11]] || 852.592 || 91.703
| [[11/5]] || 1365.004 || 90.741 || 61.857
| ||  
|-
|-
| [[23/14]] || 859.448 || 90.557
| [[31/14]] || 1376.210 || 90.799 || 68.226
| ||  
|-
|-
| [[28/17]] || 863.871 || 89.342
| [[20/9]] || 1382.404 || 90.645 || 74.073
| ||  
|-
|-
| [[43/26]] || 870.990 || 86.943
| [[29/13]] || 1389.050 || 90.242 || 66.560
| ||  
|-
|-
| [[63/38]] || 875.223 || 85.597
| [[47/21]] || 1394.726 || 89.813 || 59.470
| ||  
|-
|-
| [[5/3]] || 884.359 || 84.167
| [[9/4]] || 1403.910 || 89.442 || 55.051
| ||  
|-
|-
| [[127/76]] || 888.909 || 84.530
| [[79/35]] || 1409.397 || 89.622 || 56.694
| ||  
|-
|-
| [[62/37]] || 893.692 || 85.623
| [[43/19]] || 1414.005 || 89.985 || 60.526
| ||  
|-
|-
| [[42/25]] || 898.154 || 87.045
| [[25/11]] || 1421.309 || 90.755 || 70.259
| ||  
|-
|-
| [[32/19]] || 902.487 || 88.529
| [[41/18]] || 1425.152 || 91.119 || 73.291
| ||  
|-
|-
| [[22/13]] || 910.790 || 90.839
| [[16/7]] || 1431.174 || 91.447 || 72.927
| ||  
|-
|-
| [[17/10]] || 918.642 || 91.911
| [[23/10]] || 1441.961 || 90.803 || 75.583
| ||  
|-
|-
| [[29/17]] || 924.622 || 92.114
| [[30/13]] || 1447.741 || 89.775 || 66.083
| ||  
|-
|-
| [[12/7]] || 933.129 || 91.936
| [[37/16]] || 1451.344 || 88.987 || 59.558
| ||  
|-
|-
| [[43/25]] || 938.890 || 91.611
| [[58/25]] || 1456.950 || 87.767 || 52.003
| ||  
|-
|-
| [[19/11]] || 946.195 || 90.913
| [[121/52]] || 1462.108 || 86.960 || 47.981
| ||  
|-
|-
| [[26/15]] || 952.259 || 90.085
| [[7/3]] || 1466.871 || 86.699 || 46.764
| ||  
|-
|-
| [[47/27]] || 959.642 || 89.027
| [[61/26]] || 1476.357 || 87.725 || 51.478
| ||  
|-
|-
| [[7/4]] || 968.826 || 88.381
| [[40/17]] || 1481.358 || 88.788 || 57.784
| ||  
|-
|-
| [[93/53]] || 973.486 || 88.539
| [[33/14]] || 1484.447 || 89.469 || 62.970
| ||  
|-
|-
| [[44/25]] || 978.691 || 89.061
| [[26/11]] || 1489.210 || 90.374 || 72.202
| ||  
|-
|-
| [[30/17]] || 983.313 || 89.680
| [[19/8]] || 1497.513 || 91.263 || 75.523
| ||  
|-
|-
| [[23/13]] || 987.747 || 90.241
| [[31/13]] || 1504.508 || 91.358 || 69.217
| ||  
|-
|-
| [[16/9]] || 996.090 || 90.836
| [[67/28]] || 1510.481 || 91.232 || 64.457
| ||  
|-
|-
| [[25/14]] || 1003.802 || 90.734
| [[12/5]] || 1515.641 || 91.162 || 63.074
| ||  
|-
|-
| [[34/19]] || 1007.442 || 90.562
| [[29/12]] || 1527.622 || 91.519 || 69.720
| ||  
|-
|-
| [[9/5]] || 1017.596 || 90.182
| [[17/7]] || 1536.130 || 92.120 || 73.203
| ||  
|-
|-
| [[74/41]] || 1022.282 || 90.185
| [[39/16]] || 1542.483 || 92.492 || 74.937
| ||  
|-
|-
| [[38/21]] || 1026.732 || 90.292
| [[22/9]] || 1547.408 || 92.527 || 77.617
| ||  
|-
|-
| [[20/11]] || 1034.996 || 90.598
| [[27/11]] || 1554.547 || 91.809 || 80.862
| ||  
|-
|-
| [[31/17]] || 1040.080 || 90.750
| [[32/13]] || 1559.472 || 90.533 || 72.653
| ||  
|-
|-
| [[53/29]] || 1043.927 || 90.833
| [[37/15]] || 1563.075 || 89.159 || 63.401
| ||  
|-
|-
| [[11/6]] || 1049.363 || 90.918
| [[47/19]] || 1567.994 || 86.769 || 52.637
| ||  
|-
|-
| [[24/13]] || 1061.427 || 91.130
| [[62/25]] || 1572.408 || 84.387 || 45.145
| ||  
|-
|-
| [[37/20]] || 1065.030 || 91.211
| [[97/39]] || 1577.413 || 81.915 || 39.142
| ||  
|-
|-
| [[13/7]] || 1071.702 || 91.394
| [[5/2]] || 1586.314 || 79.831 || 34.998
| ||  
|-
|-
| [[28/15]] || 1080.557 || 91.657
| [[178/71]] || 1591.184 || 80.481 || 36.263
| ||  
|-
|-
| [[15/8]] || 1088.269 || 91.912
| [[93/37]] || 1595.647 || 82.086 || 39.618
| ||  
|-
|-
| [[32/17]] || 1095.045 || 92.173
| [[63/25]] || 1600.108 || 84.302 || 45.074
| ||  
|-
|-
| [[17/9]] || 1101.045 || 92.438
| [[43/17]] || 1606.562 || 87.719 || 56.694
| ||  
|-
|-
| [[36/19]] || 1106.397 || 92.704
| [[38/15]] || 1609.244 || 88.973 || 62.811
| ||  
|-
|-
| [[19/10]] || 1111.199 || 92.968
| [[28/11]] || 1617.508 || 91.634 || 80.890
| ||  
|-
|-
| [[21/11]] || 1119.463 || 93.512
| [[23/9]] || 1624.364 || 92.434 || 78.292
| ||  
|-
|-
| [[23/12]] || 1126.319 || 94.067
| [[18/7]] || 1635.084 || 92.172 || 74.096
| ||  
|-
|-
| [[25/13]] || 1132.100 || 94.649
| [[49/19]] || 1640.139 || 91.840 || 72.388
| ||  
|-
|-
| [[27/14]] || 1137.039 || 95.215
| [[31/12]] || 1643.081 || 91.658 || 70.218
| ||  
|-
|-
| [[29/15]] || 1141.309 || 95.749
| [[57/22]] || 1648.150 || 91.431 || 66.376
| ||  
|-
|-
| [[31/16]] || 1145.036 || 96.208
| [[13/5]] || 1654.214 || 91.300 || 64.521
| ||  
|-
|-
| [[33/17]] || 1148.318 || 96.553
| [[34/13]] || 1664.428 || 91.237 || 69.666
| ||  
|-
|-
| [[37/19]] || 1153.831 || 96.788
| [[21/8]] || 1670.781 || 90.960 || 75.611
| ||  
|-
|-
| [[41/21]] || 1158.282 || 96.316
| [[29/11]] || 1678.259 || 90.106 || 69.169
| ||  
|-
|-
| [[47/24]] || 1163.552 || 94.342
| [[37/14]] || 1682.518 || 89.391 || 61.489
| ||  
|-
|-
| [[55/28]] || 1168.806 || 90.065
| [[61/23]] || 1688.610 || 88.342 || 53.451
| ||  
|-
|-
| [[63/32]] || 1172.736 || 84.977
| [[117/44]] || 1693.120 || 87.764 || 50.019
| ||  
|-
|-
| [[77/39]] || 1177.661 || 76.268
| [[8/3]] || 1698.045 || 87.525 || 48.727
| ||  
|-
|-
| [[95/48]] || 1181.872 || 67.226
| [[67/25]] || 1706.680 || 88.237 || 52.642
| ||  
|-
|-
| [[129/65]] || 1186.631 || 56.465
| [[43/16]] || 1711.518 || 89.069 || 58.264
| ||  
|-
|-
| [[193/97]] || 1191.053 || 47.543
| [[27/10]] || 1719.551 || 90.435 || 71.995
| ||  
|-
|-
| [[389/195]] || 1195.555 || 41.234
| [[19/7]] || 1728.687 || 91.142 || 74.726
| ||  
|-
|-
| [[2/1]] || 1200.000 || 39.006
| [[49/18]] || 1733.742 || 91.064 || 72.204
| ||  
|-
| [[30/11]] || 1736.951 || 90.897 || 68.468
|-
| [[41/15]] || 1740.794 || 90.654 || 63.845
|-
| [[85/31]] || 1746.234 || 90.327 || 59.456
|-
| [[11/4]] || 1751.318 || 90.168 || 58.141
|-
| [[47/17]] || 1760.551 || 90.312 || 62.711
|-
| [[25/9]] || 1768.717 || 90.677 || 71.476
|-
| [[39/14]] || 1773.657 || 90.867 || 69.426
|-
| [[67/24]] || 1777.352 || 90.985 || 66.929
|-
| [[14/5]] || 1782.512 || 91.109 || 65.552
|-
| [[31/11]] || 1793.718 || 91.367 || 70.604
|-
| [[17/6]] || 1803.000 || 91.650 || 71.316
|-
| [[37/13]] || 1810.816 || 91.957 || 73.275
|-
| [[20/7]] || 1817.488 || 92.272 || 75.172
|-
| [[43/15]] || 1823.249 || 92.602 || 76.461
|-
| [[23/8]] || 1828.274 || 92.938 || 77.918
|-
| [[26/9]] || 1836.618 || 93.633 || 80.434
|-
| [[29/10]] || 1843.263 || 94.306 || 82.719
|-
| [[32/11]] || 1848.682 || 94.862 || 84.787
|-
| [[35/12]] || 1853.185 || 95.221 || 86.662
|-
| [[38/13]] || 1856.985 || 95.305 || 88.363
|-
| [[41/14]] || 1860.236 || 95.088 || 89.839
|-
| [[47/16]] || 1865.507 || 93.821 || 85.308
|-
| [[53/18]] || 1869.595 || 91.704 || 71.338
|-
| [[65/22]] || 1875.523 || 86.386 || 52.868
|-
| [[77/26]] || 1879.616 || 81.103 || 42.296
|-
| [[98/33]] || 1884.379 || 73.722 || 32.257
|-
| [[131/44]] || 1888.790 || 66.544 || 25.130
|-
| [[200/67]] || 1893.320 || 60.026 || 19.966
|-
| [[3/1]] || 1901.955 || 54.245 || 16.105
|-
| [[367/122]] || 1906.679 || 56.071 || 17.287
|-
| [[187/62]] || 1911.238 || 60.881 || 20.636
|-
| [[127/42]] || 1915.641 || 67.404 || 25.947
|-
| [[94/31]] || 1920.471 || 75.286 || 34.142
|-
| [[76/25]] || 1924.886 || 81.991 || 43.816
|-
| [[64/21]] || 1929.219 || 87.364 || 55.340
|-
| [[55/18]] || 1933.722 || 91.364 || 69.421
|-
| [[46/15]] || 1940.006 || 94.439 || 89.145
|-
| [[43/14]] || 1942.692 || 95.041 || 90.247
|-
| [[37/12]] || 1949.389 || 95.375 || 87.295
|-
| [[34/11]] || 1953.637 || 95.100 || 85.466
|-
| [[31/10]] || 1958.722 || 94.593 || 83.442
|-
| [[28/9]] || 1964.916 || 93.929 || 81.197
|-
| [[25/8]] || 1972.627 || 93.206 || 78.683
|-
| [[47/15]] || 1977.238 || 92.840 || 77.296
|-
| [[22/7]] || 1982.492 || 92.487 || 75.938
|-
| [[60/19]] || 1990.756 || 92.024 || 73.400
|-
| [[19/6]] || 1995.558 || 91.813 || 72.533
|-
| [[54/17]] || 2000.910 || 91.606 || 72.088
|-
| [[35/11]] || 2003.822 || 91.516 || 71.041
|-
| [[67/21]] || 2008.526 || 91.378 || 68.628
|-
| [[16/5]] || 2013.686 || 91.231 || 67.453
|-
| [[29/9]] || 2025.667 || 90.874 || 70.384
|-
| [[42/13]] || 2030.253 || 90.752 || 66.250
|-
| [[81/25]] || 2035.193 || 90.679 || 62.336
|-
| [[13/4]] || 2040.528 || 90.693 || 60.820
|-
| [[49/15]] || 2049.383 || 90.886 || 64.842
|-
| [[36/11]] || 2052.592 || 90.938 || 68.153
|-
| [[23/7]] || 2059.448 || 90.832 || 75.166
|-
| [[33/10]] || 2066.959 || 90.254 || 67.768
|-
| [[43/13]] || 2070.990 || 89.797 || 61.448
|-
| [[63/19]] || 2075.223 || 89.312 || 56.456
|-
| [[10/3]] || 2084.359 || 88.773 || 52.134
|-
| [[127/38]] || 2088.909 || 88.907 || 53.292
|-
| [[57/17]] || 2094.513 || 89.429 || 57.727
|-
| [[37/11]] || 2100.026 || 90.130 || 65.241
|-
| [[27/8]] || 2105.865 || 90.864 || 73.447
|-
| [[44/13]] || 2110.790 || 91.364 || 71.705
|-
| [[17/5]] || 2118.642 || 91.902 || 68.767
|-
| [[58/17]] || 2124.622 || 92.131 || 70.441
|-
| [[24/7]] || 2133.129 || 92.030 || 76.367
|-
| [[31/9]] || 2141.126 || 91.024 || 77.921
|-
| [[38/11]] || 2146.195 || 89.734 || 67.441
|-
| [[45/13]] || 2149.696 || 88.572 || 59.791
|-
| [[59/17]] || 2154.216 || 86.904 || 51.732
|-
| [[94/27]] || 2159.642 || 85.001 || 44.911
|-
| [[7/2]] || 2168.826 || 83.459 || 40.465
|-
| [[186/53]] || 2173.486 || 83.881 || 41.609
|-
| [[95/27]] || 2177.962 || 84.993 || 44.862
|-
| [[60/17]] || 2183.313 || 86.860 || 51.519
|-
| [[46/13]] || 2187.747 || 88.508 || 59.311
|-
| [[39/11]] || 2191.165 || 89.654 || 66.669
|-
| [[32/9]] || 2196.090 || 90.939 || 77.237
|-
| [[25/7]] || 2203.802 || 91.985 || 76.398
|-
| [[43/12]] || 2209.563 || 92.143 || 72.270
|-
| [[18/5]] || 2217.596 || 91.868 || 69.428
|-
| [[65/18]] || 2222.931 || 91.484 || 70.834
|-
| [[29/8]] || 2229.577 || 90.831 || 72.163
|-
| [[40/11]] || 2234.996 || 90.215 || 64.579
|-
| [[51/14]] || 2238.085 || 89.874 || 60.435
|-
| [[117/32]] || 2244.438 || 89.346 || 54.932
|-
| [[11/3]] || 2249.363 || 89.211 || 53.592
|-
| [[59/16]] || 2259.172 || 89.729 || 58.601
|-
| [[37/10]] || 2265.030 || 90.282 || 66.350
|-
| [[26/7]] || 2271.702 || 90.802 || 74.045
|-
| [[41/11]] || 2277.744 || 91.024 || 68.631
|-
| [[15/4]] || 2288.269 || 91.072 || 63.118
|-
| [[79/21]] || 2293.756 || 91.101 || 64.721
|-
| [[34/9]] || 2301.045 || 91.261 || 70.248
|-
| [[72/19]] || 2306.397 || 91.442 || 71.037
|-
| [[19/5]] || 2311.199 || 91.637 || 70.331
|-
| [[42/11]] || 2319.463 || 92.015 || 72.701
|-
| [[23/6]] || 2326.319 || 92.389 || 74.967
|-
| [[27/7]] || 2337.039 || 93.165 || 78.060
|-
| [[31/8]] || 2345.036 || 93.896 || 80.913
|-
| [[35/9]] || 2351.230 || 94.391 || 83.420
|-
| [[39/10]] || 2356.169 || 94.508 || 85.644
|-
| [[47/12]] || 2363.552 || 93.521 || 86.956
|-
| [[55/14]] || 2368.806 || 91.325 || 71.979
|-
| [[63/16]] || 2372.736 || 88.598 || 59.863
|-
| [[75/19]] || 2377.069 || 84.455 || 48.359
|-
| [[95/24]] || 2381.872 || 78.764 || 37.948
|-
| [[127/32]] || 2386.422 || 72.968 || 30.343
|-
| [[191/48]] || 2390.960 || 67.739 || 24.940
|-
| [[387/97]] || 2395.532 || 64.080 || 21.690
|-
| [[4/1]] || 2400.000 || 62.798 || 20.634
|}
|}


=== 2/1 to 3/1 ===
=== 4/1 to 8/1 ===
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 2400 to 3600{{c}}
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
|-
!Entropy <br>(%, Rényi order 7.0) !! Comments
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
|-
|-
| [[2/1]] || 1200.000 || 39.006
| [[4/1]] || 2400.000 || 62.798 || 20.634
| ||  
|-
|-
| [[389/194]] || 1204.456 || 41.246
| [[389/97]] || 2404.456 || 64.076 || 21.670
| ||  
|-
|-
| [[195/97]] || 1208.901 || 47.467
| [[193/48]] || 2408.993 || 67.714 || 24.873
| ||  
|-
|-
| [[129/64]] || 1213.473 || 56.700
| [[129/32]] || 2413.473 || 72.852 || 30.181
| ||  
|-
|-
| [[97/48]] || 1217.940 || 66.810
| [[97/24]] || 2417.940 || 78.558 || 37.612
| ||  
|-
|-
| [[77/38]] || 1222.631 || 76.861
| [[77/19]] || 2422.631 || 84.164 || 47.718
| ||  
|-
|-
| [[65/32]] || 1226.841 || 84.341
| [[65/16]] || 2426.841 || 88.282 || 58.797
| ||  
|-
|-
| [[55/27]] || 1231.767 || 90.672
| [[53/13]] || 2432.977 || 92.286 || 78.103
| ||  
|-
|-
| [[49/24]] || 1235.697 || 93.888
| [[49/12]] || 2435.697 || 93.337 || 85.959
| ||  
|-
|-
| [[43/21]] || 1240.737 || 96.081
| [[41/10]] || 2442.749 || 94.509 || 86.517
| ||  
|-
|-
| [[39/19]] || 1244.970 || 96.733
| [[37/9]] || 2447.434 || 94.478 || 84.366
| ||  
|-
|-
| [[35/17]] || 1250.184 || 96.662
| [[33/8]] || 2453.273 || 94.049 || 81.900
| ||  
|-
|-
| [[31/15]] || 1256.767 || 95.974
| [[29/7]] || 2460.751 || 93.336 || 78.995
| ||  
|-
|-
| [[29/14]] || 1260.751 || 95.470
| [[25/6]] || 2470.672 || 92.507 || 75.746
| ||  
|-
|-
| [[27/13]] || 1265.337 || 94.913
| [[46/11]] || 2476.956 || 92.096 || 73.420
| ||  
|-
|-
| [[25/12]] || 1270.672 || 94.335
| [[67/16]] || 2479.307 || 91.958 || 72.499
| ||  
|-
|-
| [[23/11]] || 1276.956 || 93.767
| [[21/5]] || 2484.467 || 91.696 || 71.456
| ||  
|-
|-
| [[21/10]] || 1284.467 || 93.226
| [[59/14]] || 2490.346 || 91.443 || 71.514
| ||  
|-
|-
| [[40/19]] || 1288.801 || 92.971
| [[38/9]] || 2493.603 || 91.333 || 70.272
| ||  
|-
|-
| [[19/9]] || 1293.603 || 92.713
| [[55/13]] || 2497.104 || 91.229 || 67.898
| ||  
|-
|-
| [[17/8]] || 1304.955 || 92.212
| [[17/4]] || 2504.955 || 91.063 || 65.043
| ||  
|-
|-
| [[32/15]] || 1311.731 || 91.962
| [[64/15]] || 2511.731 || 90.911 || 67.501
| ||  
|-
|-
| [[15/7]] || 1319.443 || 91.713
| [[30/7]] || 2519.443 || 90.589 || 72.480
| ||  
|-
|-
| [[43/20]] || 1325.204 || 91.549
| [[43/10]] || 2525.204 || 90.237 || 65.850
| ||  
|-
|-
| [[28/13]] || 1328.298 || 91.468
| [[56/13]] || 2528.298 || 90.045 || 62.065
| ||  
|-
|-
| [[54/25]] || 1333.238 || 91.338
| [[108/25]] || 2533.238 || 89.798 || 57.981
| ||  
|-
|-
| [[13/6]] || 1338.573 || 91.201
| [[13/3]] || 2538.573 || 89.729 || 56.445
| ||  
|-
|-
| [[24/11]] || 1350.637 || 90.891
| [[61/14]] || 2548.059 || 90.228 || 61.167
| ||  
|-
|-
| [[35/16]] || 1355.140 || 90.798
| [[35/8]] || 2555.140 || 90.942 || 69.998
| ||  
|-
|-
| [[68/31]] || 1359.920 || 90.737
| [[57/13]] || 2558.940 || 91.316 || 72.908
| ||  
|-
|-
| [[11/5]] || 1365.004 || 90.741
| [[22/5]] || 2565.004 || 91.732 || 72.619
| ||  
|-
|-
| [[31/14]] || 1376.210 || 90.799
| [[31/7]] || 2576.210 || 91.266 || 76.993
| ||  
|-
|-
| [[20/9]] || 1382.404 || 90.645
| [[40/9]] || 2582.404 || 90.118 || 68.724
| ||  
|-
|-
| [[29/13]] || 1389.050 || 90.242
| [[49/11]] || 2586.334 || 89.120 || 60.757
| ||  
|-
|-
| [[47/21]] || 1394.726 || 89.813
| [[67/15]] || 2591.038 || 87.824 || 53.151
| ||  
|-
|-
| [[9/4]] || 1403.910 || 89.442
| [[103/23]] || 2595.526 || 86.696 || 48.055
| ||  
|-
|-
| [[79/35]] || 1409.397 || 89.622
| [[9/2]] || 2603.910 || 85.700 || 44.227
| ||  
|-
|-
| [[43/19]] || 1414.005 || 89.985
| [[167/37]] || 2609.101 || 86.069 || 45.583
| ||  
|-
|-
| [[25/11]] || 1421.310 || 90.755
| [[86/19]] || 2614.005 || 87.026 || 49.488
| ||  
|-
|-
| [[41/18]] || 1425.152 || 91.119
| [[59/13]] || 2618.644 || 88.237 || 55.541
| ||  
|-
|-
| [[16/7]] || 1431.174 || 91.447
| [[41/9]] || 2625.152 || 89.931 || 67.735
| ||  
|-
|-
| [[23/10]] || 1441.961 || 90.803
| [[32/7]] || 2631.174 || 91.047 || 76.544
| ||  
|-
|-
| [[30/13]] || 1447.741 || 89.775
| [[23/5]] || 2641.961 || 91.557 || 72.891
| ||  
|-
|-
| [[37/16]] || 1451.344 || 88.987
| [[37/8]] || 2651.344 || 90.918 || 69.333
| ||  
|-
|-
| [[58/25]] || 1456.950 || 87.767
| [[51/11]] || 2655.592 || 90.538 || 64.082
| ||  
|-
|-
| [[121/52]] || 1462.108 || 86.960
| [[121/26]] || 2662.108 || 90.078 || 58.707
| ||  
|-
|-
| [[7/3]] || 1466.871 || 86.699
| [[14/3]] || 2666.871 || 89.943 || 57.563
| ||  
|-
|-
| [[61/26]] || 1476.357 || 87.725
| [[61/13]] || 2676.357 || 90.178 || 62.362
| ||  
|-
|-
| [[40/17]] || 1481.358 || 88.788
| [[47/10]] || 2679.193 || 90.338 || 65.540
| ||  
|-
|-
| [[33/14]] || 1484.447 || 89.469
| [[33/7]] || 2684.447 || 90.654 || 71.433
| ||  
|-
|-
| [[26/11]] || 1489.210 || 90.374
| [[52/11]] || 2689.210 || 90.913 || 70.124
| ||  
|-
|-
| [[19/8]] || 1497.513 || 91.263
| [[19/4]] || 2697.513 || 91.250 || 66.691
| ||  
|-
|-
| [[31/13]] || 1504.508 || 91.358
| [[81/17]] || 2702.865 || 91.441 || 67.985
| ||  
|-
|-
| [[67/28]] || 1510.481 || 91.232
| [[43/9]] || 2707.608 || 91.620 || 70.764
| ||  
|-
|-
| [[12/5]] || 1515.641 || 91.162
| [[67/14]] || 2710.481 || 91.756 || 72.192
| ||  
|-
|-
| [[29/12]] || 1527.622 || 91.519
| [[24/5]] || 2715.641 || 92.033 || 73.157
| ||  
|-
|-
| [[17/7]] || 1536.130 || 92.120
| [[29/6]] || 2727.622 || 92.932 || 77.031
| ||  
|-
|-
| [[39/16]] || 1542.483 || 92.492
| [[34/7]] || 2736.130 || 93.640 || 80.373
| ||  
|-
|-
| [[22/9]] || 1547.408 || 92.527
| [[39/8]] || 2742.483 || 93.885 || 83.233
| ||  
|-
|-
| [[27/11]] || 1554.547 || 91.809
| [[44/9]] || 2747.408 || 93.589 || 85.604
| ||  
|-
|-
| [[32/13]] || 1559.472 || 90.533
| [[54/11]] || 2754.547 || 91.677 || 77.116
| ||  
|-
|-
| [[37/15]] || 1563.075 || 89.159
| [[64/13]] || 2759.472 || 88.918 || 62.079
| ||  
|-
|-
| [[47/19]] || 1567.994 || 86.769
| [[74/15]] || 2763.075 || 86.111 || 52.510
| ||  
|-
|-
| [[62/25]] || 1572.408 || 84.387
| [[94/19]] || 2767.994 || 81.362 || 41.670
| ||  
|-
|-
| [[97/39]] || 1577.413 || 81.915
| [[129/26]] || 2772.945 || 76.173 || 33.364
| ||  
|-
|-
| [[5/2]] || 1586.314 || 79.831
| [[199/40]] || 2777.636 || 71.787 || 27.906
| ||  
|-
|-
| [[178/71]] || 1591.184 || 80.481
| [[5/1]] || 2786.314 || 68.009 || 23.962
| ||  
|-
|-
| [[93/37]] || 1595.647 || 82.086
| [[361/72]] || 2791.116 || 69.236 || 25.203
| ||  
|-
|-
| [[63/25]] || 1600.109 || 84.302
| [[186/37]] || 2795.647 || 72.363 || 28.611
| ||  
|-
|-
| [[43/17]] || 1606.562 || 87.719
| [[126/25]] || 2800.108 || 76.655 || 34.095
| ||  
|-
|-
| [[38/15]] || 1609.244 || 88.973
| [[91/18]] || 2805.444 || 82.237 || 43.431
| ||  
|-
|-
| [[28/11]] || 1617.508 || 91.634
| [[76/15]] || 2809.244 || 85.883 || 51.934
| ||  
|-
|-
| [[23/9]] || 1624.364 || 92.434
| [[61/12]] || 2814.930 || 90.123 || 67.494
| ||  
|-
|-
| [[18/7]] || 1635.084 || 92.172
| [[51/10]] || 2820.597 || 92.661 || 84.199
| ||  
|-
|-
| [[49/19]] || 1640.139 || 91.840
| [[46/9]] || 2824.364 || 93.525 || 86.193
| ||  
|-
|-
| [[31/12]] || 1643.081 || 91.658
| [[41/8]] || 2829.062 || 93.937 || 84.008
| ||  
|-
|-
| [[57/22]] || 1648.150 || 91.431
| [[36/7]] || 2835.084 || 93.804 || 81.270
| ||  
|-
|-
| [[13/5]] || 1654.214 || 91.300
| [[31/6]] || 2843.081 || 93.178 || 78.031
| ||  
|-
|-
| [[34/13]] || 1664.428 || 91.237
| [[57/11]] || 2848.150 || 92.750 || 76.045
| ||  
|-
|-
| [[21/8]] || 1670.781 || 90.960
| [[26/5]] || 2854.214 || 92.307 || 74.485
| ||  
|-
|-
| [[29/11]] || 1678.259 || 90.106
| [[47/9]] || 2861.597 || 91.870 || 71.896
| ||  
|-
|-
| [[37/14]] || 1682.518 || 89.391
| [[21/4]] || 2870.781 || 91.425 || 68.672
| ||  
|-
|-
| [[61/23]] || 1688.611 || 88.342
| [[79/15]] || 2876.268 || 91.152 || 70.103
| ||  
|-
|-
| [[117/44]] || 1693.120 || 87.764
| [[37/7]] || 2882.518 || 90.820 || 70.829
| ||  
|-
|-
| [[8/3]] || 1698.045 || 87.525
| [[53/10]] || 2887.191 || 90.579 || 66.050
| ||  
|-
|-
| [[67/25]] || 1706.680 || 88.237
| [[117/22]] || 2893.120 || 90.378 || 61.195
| ||  
|-
|-
| [[43/16]] || 1711.518 || 89.069
| [[16/3]] || 2898.045 || 90.360 || 59.869
| ||  
|-
|-
| [[27/10]] || 1719.551 || 90.435
| [[59/11]] || 2907.854 || 90.739 || 64.773
| ||  
|-
|-
| [[19/7]] || 1728.687 || 91.142
| [[43/8]] || 2911.518 || 90.933 || 68.839
| ||  
|-
|-
| [[49/18]] || 1733.742 || 91.064
| [[27/5]] || 2919.551 || 91.115 || 74.991
| ||  
|-
|-
| [[30/11]] || 1736.951 || 90.897
| [[65/12]] || 2924.886 || 90.826 || 75.969
| ||  
|-
|-
| [[41/15]] || 1740.794 || 90.654
| [[38/7]] || 2928.687 || 90.366 || 72.997
| ||  
|-
|-
| [[85/31]] || 1746.234 || 90.327
| [[49/9]] || 2933.742 || 89.479 || 63.506
| ||  
|-
|-
| [[11/4]] || 1751.318 || 90.168
| [[60/11]] || 2936.951 || 88.814 || 58.100
| ||  
|-
|-
| [[47/17]] || 1760.551 || 90.312
| [[93/17]] || 2942.035 || 87.822 || 51.716
| ||  
|-
|-
| [[25/9]] || 1768.717 || 90.677
| [[181/33]] || 2946.542 || 87.184 || 48.353
| ||  
|-
|-
| [[39/14]] || 1773.657 || 90.867
| [[11/2]] || 2951.318 || 86.954 || 47.153
| ||  
|-
|-
| [[67/24]] || 1777.352 || 90.985
| [[94/17]] || 2960.551 || 87.918 || 51.700
| ||  
|-
|-
| [[14/5]] || 1782.512 || 91.109
| [[61/11]] || 2965.567 || 88.943 || 57.950
| ||  
|-
|-
| [[31/11]] || 1793.718 || 91.367
| [[50/9]] || 2968.717 || 89.611 || 63.197
| ||  
|-
|-
| [[17/6]] || 1803.000 || 91.650
| [[39/7]] || 2973.657 || 90.516 || 72.515
| ||  
|-
|-
| [[37/13]] || 1810.816 || 91.957
| [[67/12]] || 2977.352 || 91.004 || 76.031
| ||  
|-
|-
| [[20/7]] || 1817.488 || 92.272
| [[28/5]] || 2982.512 || 91.342 || 75.084
| ||  
|-
|-
| [[43/15]] || 1823.249 || 92.602
| [[45/8]] || 2990.224 || 91.271 || 68.577
| ||  
|-
|-
| [[23/8]] || 1828.274 || 92.938
| [[62/11]] || 2993.718 || 91.121 || 64.852
| ||  
|-
|-
| [[26/9]] || 1836.618 || 93.633
| [[17/3]] || 3003.000 || 90.796 || 60.390
| ||  
|-
|-
| [[29/10]] || 1843.264 || 94.306
| [[91/16]] || 3009.354 || 90.823 || 62.564
| ||  
|-
|-
| [[32/11]] || 1848.682 || 94.862
| [[40/7]] || 3017.488 || 91.140 || 70.111
| ||  
|-
|-
| [[35/12]] || 1853.185 || 95.221
| [[63/11]] || 3021.418 || 91.351 || 71.253
| ||  
|-
|-
| [[38/13]] || 1856.985 || 95.305
| [[23/4]] || 3028.274 || 91.759 || 69.888
| ||  
|-
|-
| [[41/14]] || 1860.237 || 95.088
| [[52/9]] || 3036.618 || 92.295 || 72.655
| ||  
|-
|-
| [[47/16]] || 1865.507 || 93.821
| [[29/5]] || 3043.263 || 92.782 || 75.650
| ||  
|-
|-
| [[53/18]] || 1869.595 || 91.704
| [[35/6]] || 3053.185 || 93.524 || 79.261
| ||  
|-
|-
| [[65/22]] || 1875.523 || 86.386
| [[41/7]] || 3060.236 || 93.677 || 82.545
| ||  
|-
|-
| [[77/26]] || 1879.616 || 81.103
| [[47/8]] || 3065.507 || 93.159 || 84.962
| ||  
|-
|-
| [[98/33]] || 1884.379 || 73.722
| [[53/9]] || 3069.595 || 92.138 || 81.317
| ||  
|-
|-
| [[131/44]] || 1888.790 || 66.544
| [[65/11]] || 3075.523 || 89.379 || 64.058
| ||  
|-
|-
| [[200/67]] || 1893.320 || 60.026
| [[77/13]] || 3079.616 || 86.553 || 53.435
| ||  
|-
|-
| [[3/1]] || 1901.955 || 54.245
| [[95/16]] || 3083.827 || 83.035 || 44.350
| ||  
|-
|}
| [[131/22]] || 3088.790 || 78.596 || 36.061
 
|-
=== 3/1 to 4/1 ===
| [[197/33]] || 3093.189 || 75.071 || 30.903
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[3/1]] || 1901.955 || 54.245
| [[6/1]] || 3101.955 || 71.731 || 26.753
| ||  
|-
|-
| [[367/122]] || 1906.679 || 56.071
| [[367/61]] || 3106.679 || 72.714 || 27.900
| ||  
|-
|-
| [[187/62]] || 1911.238 || 60.881
| [[187/31]] || 3111.238 || 75.340 || 31.250
| ||  
|-
|-
| [[127/42]] || 1915.641 || 67.404
| [[127/21]] || 3115.641 || 78.905 || 36.582
| ||  
|-
|-
| [[94/31]] || 1920.471 || 75.286
| [[91/15]] || 3121.085 || 83.711 || 46.033
| ||  
|-
|-
| [[76/25]] || 1924.886 || 81.991
| [[73/12]] || 3125.834 || 87.463 || 56.863
| ||  
|-
|-
| [[64/21]] || 1929.219 || 87.364
| [[61/10]] || 3130.571 || 90.313 || 70.005
| ||  
|-
|-
| [[55/18]] || 1933.722 || 91.364
| [[55/9]] || 3133.722 || 91.647 || 79.353
| ||  
|-
|-
| [[46/15]] || 1940.006 || 94.439
| [[49/8]] || 3137.652 || 92.720 || 84.646
| ||  
|-
|-
| [[43/14]] || 1942.692 || 95.041
| [[43/7]] || 3142.692 || 93.315 || 82.594
| ||  
|-
|-
| [[37/12]] || 1949.389 || 95.375
| [[37/6]] || 3149.389 || 93.281 || 79.454
| ||  
|-
|-
| [[34/11]] || 1953.638 || 95.100
| [[31/5]] || 3158.722 || 92.634 || 75.931
| ||  
|-
|-
| [[31/10]] || 1958.722 || 94.593
| [[56/9]] || 3164.916 || 92.175 || 73.112
| ||  
|-
|-
| [[28/9]] || 1964.916 || 93.929
| [[25/4]] || 3172.627 || 91.679 || 70.854
| ||  
|-
|-
| [[25/8]] || 1972.627 || 93.206
| [[69/11]] || 3178.911 || 91.336 || 71.355
| ||  
|-
|-
| [[47/15]] || 1977.238 || 92.840
| [[44/7]] || 3182.492 || 91.164 || 69.795
| ||  
|-
|-
| [[22/7]] || 1982.492 || 92.487
| [[63/10]] || 3186.422 || 91.034 || 66.313
| ||  
|-
|-
| [[60/19]] || 1990.756 || 92.024
| [[120/19]] || 3190.756 || 90.949 || 63.284
| ||  
|-
|-
| [[19/6]] || 1995.558 || 91.813
| [[19/3]] || 3195.558 || 90.954 || 62.086
| ||  
|-
|-
| [[54/17]] || 2000.910 || 91.606
| [[127/20]] || 3200.108 || 91.016 || 63.188
| ||  
|-
|-
| [[35/11]] || 2003.822 || 91.516
| [[51/8]] || 3206.910 || 91.113 || 68.646
| ||  
|-
|-
| [[67/21]] || 2008.526 || 91.378
| [[32/5]] || 3213.686 || 90.949 || 75.401
| ||  
|-
|-
| [[16/5]] || 2013.686 || 91.231
| [[45/7]] || 3221.398 || 90.200 || 68.953
| ||  
|-
|-
| [[29/9]] || 2025.667 || 90.874
| [[58/9]] || 3225.667 || 89.582 || 61.610
| ||  
|-
|-
| [[42/13]] || 2030.253 || 90.752
| [[84/13]] || 3230.253 || 88.880 || 55.552
| ||  
|-
|-
| [[81/25]] || 2035.193 || 90.679
| [[162/25]] || 3235.193 || 88.287 || 51.486
| ||  
|-
|-
| [[13/4]] || 2040.528 || 90.693
| [[13/2]] || 3240.528 || 88.036 || 49.983
| ||  
|-
|-
| [[49/15]] || 2049.383 || 90.886
| [[98/15]] || 3249.383 || 88.679 || 54.121
| ||  
|-
|-
| [[36/11]] || 2052.592 || 90.938
| [[59/9]] || 3255.262 || 89.542 || 61.420
| ||  
|-
|-
| [[23/7]] || 2059.448 || 90.832
| [[46/7]] || 3259.448 || 90.160 || 68.593
| ||  
|-
|-
| [[33/10]] || 2066.959 || 90.254
| [[33/5]] || 3266.959 || 90.915 || 75.373
| ||  
|-
|-
| [[43/13]] || 2070.990 || 89.797
| [[53/8]] || 3273.505 || 91.119 || 68.956
| ||  
|-
|-
| [[63/19]] || 2075.223 || 89.312
| [[20/3]] || 3284.359 || 91.038 || 63.048
| ||  
|-
|-
| [[10/3]] || 2084.359 || 88.773
| [[127/19]] || 3288.909 || 91.050 || 64.127
| ||  
|-
|-
| [[127/38]] || 2088.909 || 88.907
| [[47/7]] || 3296.681 || 91.284 || 69.942
| ||  
|-
|-
| [[57/17]] || 2094.513 || 89.429
| [[27/4]] || 3305.865 || 91.845 || 72.072
| ||  
|-
|-
| [[37/11]] || 2100.026 || 90.130
| [[61/9]] || 3312.975 || 92.403 || 74.047
| ||  
|-
|-
| [[27/8]] || 2105.865 || 90.864
| [[34/5]] || 3318.642 || 92.846 || 76.869
| ||  
|-
|-
| [[44/13]] || 2110.790 || 91.364
| [[41/6]] || 3327.107 || 93.164 || 80.690
| ||  
|-
|-
| [[17/5]] || 2118.642 || 91.902
| [[48/7]] || 3333.129 || 92.684 || 83.653
| ||  
|-
|-
| [[58/17]] || 2124.622 || 92.131
| [[55/8]] || 3337.632 || 91.625 || 79.909
| ||  
|-
|-
| [[24/7]] || 2133.129 || 92.030
| [[62/9]] || 3341.126 || 90.272 || 70.109
| ||  
|-
|-
| [[31/9]] || 2141.126 || 91.024
| [[76/11]] || 3346.195 || 87.464 || 56.641
| ||  
|-
|-
| [[38/11]] || 2146.195 || 89.734
| [[97/14]] || 3351.070 || 83.990 || 46.182
| ||  
|-
|-
| [[45/13]] || 2149.696 || 88.572
| [[125/18]] || 3355.031 || 80.945 || 39.535
| ||  
|-
|-
| [[59/17]] || 2154.216 || 86.904
| [[195/28]] || 3359.970 || 77.500 || 33.579
| ||  
|-
|-
| [[94/27]] || 2159.642 || 85.001
| [[7/1]] || 3368.826 || 74.586 || 29.390
| ||  
|-
|-
| [[7/2]] || 2168.826 || 83.459
| [[379/54]] || 3373.400 || 75.394 || 30.489
| ||  
|-
|-
| [[186/53]] || 2173.486 || 83.881
| [[190/27]] || 3377.962 || 77.639 || 33.801
| ||  
|-
|-
| [[95/27]] || 2177.962 || 84.993
| [[127/18]] || 3382.512 || 80.826 || 39.313
| ||  
|-
|-
| [[60/17]] || 2183.313 || 86.860
| [[92/13]] || 3387.747 || 84.821 || 48.386
| ||  
|-
|-
| [[46/13]] || 2187.747 || 88.508
| [[78/11]] || 3391.165 || 87.227 || 55.880
| ||  
|-
|-
| [[39/11]] || 2191.165 || 89.654
| [[64/9]] || 3396.090 || 90.022 || 68.814
| ||  
|-
|-
| [[32/9]] || 2196.090 || 90.939
| [[50/7]] || 3403.802 || 92.504 || 83.841
| ||  
|-
|-
| [[25/7]] || 2203.802 || 91.985
| [[43/6]] || 3409.563 || 93.087 || 81.264
| ||  
|-
|-
| [[43/12]] || 2209.563 || 92.143
| [[36/5]] || 3417.596 || 92.889 || 77.539
| ||  
|-
|-
| [[18/5]] || 2217.596 || 91.868
| [[65/9]] || 3422.931 || 92.505 || 74.973
| ||  
|-
|-
| [[65/18]] || 2222.931 || 91.484
| [[29/4]] || 3429.577 || 91.982 || 73.165
| ||  
|-
|-
| [[29/8]] || 2229.577 || 90.831
| [[51/7]] || 3438.085 || 91.477 || 70.297
| ||  
|-
|-
| [[40/11]] || 2234.996 || 90.215
| [[117/16]] || 3444.438 || 91.266 || 65.747
| ||  
|-
|-
| [[51/14]] || 2238.085 || 89.874
| [[22/3]] || 3449.363 || 91.188 || 64.411
| ||  
|-
|-
| [[117/32]] || 2244.438 || 89.346
| [[59/8]] || 3459.172 || 91.036 || 69.063
| ||  
|-
|-
| [[11/3]] || 2249.363 || 89.211
| [[37/5]] || 3465.030 || 90.729 || 74.001
| ||  
|-
|-
| [[59/16]] || 2259.172 || 89.729
| [[52/7]] || 3471.702 || 90.110 || 66.126
| ||  
|-
|-
| [[37/10]] || 2265.030 || 90.282
| [[67/9]] || 3475.397 || 89.685 || 60.509
| ||  
|-
|-
| [[26/7]] || 2271.702 || 90.802
| [[97/13]] || 3479.368 || 89.251 || 55.971
| ||  
|-
|-
| [[41/11]] || 2277.745 || 91.024
| [[15/2]] || 3488.269 || 88.748 || 51.847
| ||  
|-
|-
| [[15/4]] || 2288.269 || 91.072
| [[158/21]] || 3493.756 || 88.946 || 53.484
| ||  
|-
|-
| [[79/21]] || 2293.756 || 91.101
| [[83/11]] || 3498.729 || 89.408 || 57.716
| ||  
|-
|-
| [[34/9]] || 2301.045 || 91.261
| [[53/7]] || 3504.679 || 90.087 || 66.089
| ||  
|-
|-
| [[72/19]] || 2306.397 || 91.442
| [[38/5]] || 3511.199 || 90.725 || 74.056
| ||  
|-
|-
| [[19/5]] || 2311.199 || 91.637
| [[84/11]] || 3519.463 || 91.165 || 67.580
| ||  
|-
|-
| [[42/11]] || 2319.463 || 92.015
| [[23/3]] || 3526.319 || 91.334 || 65.218
| ||  
|-
|-
| [[23/6]] || 2326.319 || 92.389
| [[77/10]] || 3533.830 || 91.570 || 67.961
| ||  
|-
|-
| [[27/7]] || 2337.039 || 93.165
| [[54/7]] || 3537.039 || 91.735 || 70.328
| ||  
|-
|-
| [[31/8]] || 2345.036 || 93.896
| [[31/4]] || 3545.036 || 92.279 || 73.654
| ||  
|-
|-
| [[35/9]] || 2351.230 || 94.391
| [[70/9]] || 3551.230 || 92.737 || 75.346
| ||  
|-
|-
| [[39/10]] || 2356.169 || 94.508
| [[39/5]] || 3556.169 || 92.976 || 77.758
| ||  
|-
|-
| [[47/12]] || 2363.552 || 93.521
| [[47/6]] || 3563.552 || 92.726 || 81.598
| ||  
|-
|-
| [[55/14]] || 2368.806 || 91.325
| [[55/7]] || 3568.806 || 91.736 || 80.615
| ||  
|-
|-
| [[63/16]] || 2372.736 || 88.598
| [[63/8]] || 3572.736 || 90.390 || 70.693
| ||  
|-
|-
| [[75/19]] || 2377.069 || 84.455
| [[71/9]] || 3575.787 || 88.962 || 62.507
| ||  
|-
|-
| [[95/24]] || 2381.872 || 78.764
| [[95/12]] || 3581.872 || 85.279 || 48.938
| ||  
|-
|-
| [[127/32]] || 2386.422 || 72.968
| [[127/16]] || 3586.422 || 82.182 || 41.351
| ||  
|-
|-
| [[191/48]] || 2390.960 || 67.739
| [[191/24]] || 3590.960 || 79.377 || 35.966
| ||  
|-
|-
| [[387/97]] || 2395.532 || 64.080
| [[383/48]] || 3595.486 || 77.393 || 32.761
| ||  
|-
|-
| [[4/1]] || 2400.000 || 62.798
| [[8/1]] || 3600.000 || 76.672 || 31.713
| ||  
|}
|}


=== 4/1 to 6/1 ===
=== 8/1 to 16/1 ===
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 3600 to 4800{{c}}
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[4/1]] || 2400.000 || 62.798
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
| ||
|-
|-
| [[389/97]] || 2404.456 || 64.076
| [[8/1]] || 3600.000 || 76.672 || 31.713
| ||  
|-
|-
| [[193/48]] || 2408.993 || 67.714
| [[385/48]] || 3604.503 || 77.364 || 32.804
| ||  
|-
|-
| [[129/32]] || 2413.473 || 72.852
| [[193/24]] || 3608.993 || 79.306 || 36.012
| ||  
|-
|-
| [[97/24]] || 2417.940 || 78.558
| [[129/16]] || 3613.473 || 82.060 || 41.323
| ||  
|-
|-
| [[77/19]] || 2422.631 || 84.164
| [[97/12]] || 3617.940 || 85.094 || 48.721
| ||  
|-
|-
| [[65/16]] || 2426.841 || 88.282
| [[73/9]] || 3623.879 || 88.737 || 61.801
| ||  
|-
|-
| [[53/13]] || 2432.977 || 92.286
| [[65/8]] || 3626.841 || 90.169 || 69.646
| ||  
|-
|-
| [[49/12]] || 2435.697 || 93.337
| [[57/7]] || 3630.642 || 91.549 || 79.669
| ||  
|-
|-
| [[41/10]] || 2442.749 || 94.509
| [[49/6]] || 3635.697 || 92.628 || 82.024
| ||  
|-
|-
| [[37/9]] || 2447.434 || 94.478
| [[41/5]] || 3642.749 || 93.023 || 78.239
| ||  
|-
|-
| [[33/8]] || 2453.273 || 94.049
| [[33/4]] || 3653.273 || 92.507 || 74.177
| ||  
|-
|-
| [[29/7]] || 2460.751 || 93.336
| [[91/11]] || 3658.036 || 92.181 || 72.380
| ||  
|-
|-
| [[25/6]] || 2470.672 || 92.507
| [[58/7]] || 3660.751 || 92.011 || 70.627
| ||  
|-
|-
| [[46/11]] || 2476.956 || 92.096
| [[25/3]] || 3670.672 || 91.520 || 66.415
| ||  
|-
|-
| [[67/16]] || 2479.307 || 91.958
| [[117/14]] || 3675.612 || 91.277 || 67.716
| ||  
|-
|-
| [[21/5]] || 2484.467 || 91.696
| [[67/8]] || 3679.307 || 91.059 || 70.190
| ||  
|-
|-
| [[59/14]] || 2490.346 || 91.443
| [[42/5]] || 3684.467 || 90.661 || 72.830
| ||  
|-
|-
| [[38/9]] || 2493.603 || 91.333
| [[59/7]] || 3690.346 || 90.106 || 65.391
| ||  
|-
|-
| [[55/13]] || 2497.104 || 91.229
| [[110/13]] || 3697.104 || 89.474 || 57.492
| ||  
|-
|-
| [[17/4]] || 2504.955 || 91.063
| [[17/2]] || 3704.955 || 89.148 || 54.268
| ||  
|-
|-
| [[64/15]] || 2511.731 || 90.911
| [[128/15]] || 3711.731 || 89.402 || 56.734
| ||  
|-
|-
| [[30/7]] || 2519.443 || 90.589
| [[77/9]] || 3716.234 || 89.785 || 61.038
| ||  
|-
|-
| [[43/10]] || 2525.204 || 90.237
| [[60/7]] || 3719.443 || 90.106 || 65.332
| ||  
|-
|-
| [[56/13]] || 2528.298 || 90.045
| [[43/5]] || 3725.204 || 90.677 || 72.770
| ||  
|-
|-
| [[108/25]] || 2533.238 || 89.798
| [[95/11]] || 3732.509 || 91.255 || 69.106
| ||  
|-
|-
| [[13/3]] || 2538.573 || 89.729
| [[26/3]] || 3738.573 || 91.610 || 67.183
| ||  
|-
|-
| [[61/14]] || 2548.059 || 90.228
| [[61/7]] || 3748.059 || 92.151 || 71.040
| ||  
|-
|-
| [[35/8]] || 2555.140 || 90.942
| [[35/4]] || 3755.140 || 92.594 || 74.884
| ||  
|-
|-
| [[57/13]] || 2558.940 || 91.316
| [[79/9]] || 3760.627 || 92.837 || 76.786
| ||  
|-
|-
| [[22/5]] || 2565.004 || 91.732
| [[44/5]] || 3765.004 || 92.808 || 78.930
| ||  
|-
|-
| [[31/7]] || 2576.210 || 91.266
| [[53/6]] || 3771.550 || 92.065 || 81.714
| ||  
|-
|-
| [[40/9]] || 2582.404 || 90.118
| [[62/7]] || 3776.210 || 90.798 || 73.622
| ||  
|-
|-
| [[49/11]] || 2586.334 || 89.120
| [[71/8]] || 3779.697 || 89.397 || 64.348
| ||  
|-
|-
| [[67/15]] || 2591.038 || 87.824
| [[98/11]] || 3786.334 || 85.814 || 49.724
| ||  
|-
|-
| [[103/23]] || 2595.526 || 86.696
| [[134/15]] || 3791.038 || 82.979 || 42.173
| ||  
|-
|-
| [[9/2]] || 2603.910 || 85.700
| [[206/23]] || 3795.526 || 80.585 || 37.158
| ||  
|-
|-
| [[167/37]] || 2609.101 || 86.069
| [[9/1]] || 3803.910 || 78.487 || 33.500
| ||  
|-
|-
| [[86/19]] || 2614.005 || 87.026
| [[343/38]] || 3808.965 || 79.252 || 34.878
| ||  
|-
|-
| [[59/13]] || 2618.644 || 88.237
| [[181/20]] || 3813.501 || 81.100 || 38.408
| ||  
|-
|-
| [[41/9]] || 2625.152 || 89.931
| [[118/13]] || 3818.644 || 84.004 || 45.035
| ||  
|-
|-
| [[32/7]] || 2631.174 || 91.047
| [[91/10]] || 3823.040 || 86.618 || 52.905
| ||  
|-
|-
| [[23/5]] || 2641.961 || 91.557
| [[73/8]] || 3827.789 || 89.122 || 63.684
| ||  
|-
|-
| [[37/8]] || 2651.344 || 90.918
| [[64/7]] || 3831.174 || 90.519 || 72.620
| ||  
|-
|-
| [[51/11]] || 2655.593 || 90.538
| [[55/6]] || 3835.677 || 91.815 || 81.602
| ||  
|-
|-
| [[121/26]] || 2662.108 || 90.078
| [[46/5]] || 3841.961 || 92.648 || 79.540
| ||  
|-
|-
| [[14/3]] || 2666.871 || 89.943
| [[37/4]] || 3851.344 || 92.585 || 75.474
| ||  
|-
|-
| [[61/13]] || 2676.357 || 90.178
| [[65/7]] || 3858.015 || 92.199 || 71.715
| ||  
|-
|-
| [[47/10]] || 2679.193 || 90.338
| [[121/13]] || 3862.108 || 91.941 || 69.445
| ||  
|-
|-
| [[33/7]] || 2684.447 || 90.654
| [[28/3]] || 3866.871 || 91.644 || 68.437
| ||  
|-
|-
| [[52/11]] || 2689.210 || 90.913
| [[47/5]] || 3879.193 || 90.732 || 71.679
| ||  
|-
|-
| [[19/4]] || 2697.513 || 91.250
| [[66/7]] || 3884.447 || 90.277 || 65.124
| ||  
|-
|-
| [[81/17]] || 2702.865 || 91.441
| [[85/9]] || 3887.359 || 90.041 || 61.645
| ||  
|-
|-
| [[43/9]] || 2707.608 || 91.620
| [[19/2]] || 3897.513 || 89.594 || 56.279
| ||  
|-
|-
| [[67/14]] || 2710.481 || 91.756
| [[181/19]] || 3902.302 || 89.701 || 57.538
| ||  
|-
|-
| [[24/5]] || 2715.641 || 92.033
| [[86/9]] || 3907.608 || 90.028 || 61.747
| ||  
|-
|-
| [[29/6]] || 2727.622 || 92.932
| [[67/7]] || 3910.481 || 90.256 || 65.199
| ||  
|-
|-
| [[34/7]] || 2736.130 || 93.640
| [[48/5]] || 3915.641 || 90.728 || 71.780
| ||  
|-
|-
| [[39/8]] || 2742.483 || 93.885
| [[29/3]] || 3927.622 || 91.657 || 69.328
| ||  
|-
|-
| [[44/9]] || 2747.408 || 93.589
| [[97/10]] || 3933.582 || 92.028 || 70.853
| ||  
|-
|-
| [[54/11]] || 2754.547 || 91.677
| [[68/7]] || 3936.130 || 92.168 || 72.306
| ||  
|-
|-
| [[64/13]] || 2759.472 || 88.918
| [[39/4]] || 3942.483 || 92.425 || 76.055
| ||  
|-
|-
| [[74/15]] || 2763.075 || 86.111
| [[49/5]] || 3951.338 || 92.127 || 80.025
| ||  
|-
|-
| [[94/19]] || 2767.994 || 81.362
| [[59/6]] || 3957.217 || 91.041 || 78.171
| ||  
|-
|-
| [[129/26]] || 2772.945 || 76.173
| [[69/7]] || 3961.403 || 89.683 || 67.696
| ||  
|-
|-
| [[199/40]] || 2777.636 || 71.787
| [[89/9]] || 3966.970 || 87.167 || 54.700
| ||  
|-
|-
| [[5/1]] || 2786.314 || 68.009
| [[129/13]] || 3972.945 || 83.992 || 44.361
| ||  
|-
|-
| [[361/72]] || 2791.116 || 69.236
| [[199/20]] || 3977.636 || 81.728 || 38.911
| ||  
|-
|-
| [[186/37]] || 2795.647 || 72.363
| [[10/1]] || 3986.314 || 79.780 || 34.989
| ||  
|-
|-
| [[126/25]] || 2800.109 || 76.655
| [[361/36]] || 3991.116 || 80.437 || 36.252
| ||  
|-
|-
| [[91/18]] || 2805.444 || 82.237
| [[181/18]] || 3995.905 || 82.193 || 39.947
| ||  
|-
|-
| [[76/15]] || 2809.244 || 85.883
| [[121/12]] || 4000.681 || 84.621 || 46.056
| ||  
|-
|-
| [[61/12]] || 2814.930 || 90.123
| [[91/9]] || 4005.444 || 87.182 || 54.555
| ||  
|-
|-
| [[51/10]] || 2820.597 || 92.661
| [[71/7]] || 4010.871 || 89.704 || 67.126
| ||  
|-
|-
| [[46/9]] || 2824.364 || 93.525
| [[61/6]] || 4014.930 || 91.082 || 77.529
| ||  
|-
|-
| [[41/8]] || 2829.062 || 93.937
| [[51/5]] || 4020.597 || 92.220 || 80.758
| ||  
|-
|-
| [[36/7]] || 2835.084 || 93.804
| [[41/4]] || 4029.062 || 92.605 || 76.712
| ||  
|-
|-
| [[31/6]] || 2843.081 || 93.178
| [[72/7]] || 4035.084 || 92.356 || 73.073
| ||  
|-
|-
| [[57/11]] || 2848.150 || 92.750
| [[31/3]] || 4043.081 || 91.796 || 70.334
| ||  
|-
|-
| [[26/5]] || 2854.214 || 92.307
| [[83/8]] || 4050.047 || 91.222 || 71.949
| ||  
|-
|-
| [[47/9]] || 2861.597 || 91.870
| [[52/5]] || 4054.214 || 90.858 || 70.652
| ||  
|-
|-
| [[21/4]] || 2870.781 || 91.425
| [[94/9]] || 4061.597 || 90.262 || 61.915
| ||  
|-
|-
| [[79/15]] || 2876.268 || 91.152
| [[21/2]] || 4070.781 || 89.908 || 57.273
| ||  
|-
|-
| [[37/7]] || 2882.518 || 90.820
| [[179/17]] || 4075.624 || 89.990 || 58.448
| ||  
|-
|-
| [[53/10]] || 2887.191 || 90.579
| [[74/7]] || 4082.518 || 90.399 || 64.359
| ||  
|-
|-
| [[117/22]] || 2893.120 || 90.378
| [[53/5]] || 4087.191 || 90.789 || 69.995
| ||  
|-
|-
| [[16/3]] || 2898.045 || 90.360
| [[117/11]] || 4093.120 || 91.311 || 71.041
| ||  
|-
|-
| [[59/11]] || 2907.854 || 90.739
| [[32/3]] || 4098.045 || 91.721 || 70.066
| ||  
|-
|-
| [[43/8]] || 2911.518 || 90.933
| [[75/7]] || 4105.757 || 92.214 || 72.572
| ||  
|-
|-
| [[27/5]] || 2919.551 || 91.115
| [[43/4]] || 4111.518 || 92.328 || 76.211
| ||  
|-
|-
| [[65/12]] || 2924.886 || 90.826
| [[54/5]] || 4119.551 || 91.684 || 80.063
| ||  
|-
|-
| [[38/7]] || 2928.687 || 90.366
| [[65/6]] || 4124.886 || 90.424 || 72.814
| ||  
|-
|-
| [[49/9]] || 2933.742 || 89.479
| [[76/7]] || 4128.687 || 89.080 || 63.335
| ||  
|-
|-
| [[60/11]] || 2936.951 || 88.814
| [[87/8]] || 4131.532 || 87.858 || 56.993
| ||  
|-
|-
| [[93/17]] || 2942.035 || 87.822
| [[120/11]] || 4136.951 || 85.258 || 47.263
| ||  
|-
|-
| [[181/33]] || 2946.542 || 87.184
| [[186/17]] || 4142.035 || 82.949 || 40.960
| ||  
|-
|-
| [[11/2]] || 2951.318 || 86.954
| [[362/33]] || 4146.542 || 81.497 || 37.654
| ||  
|-
|-
| [[94/17]] || 2960.551 || 87.918
| [[11/1]] || 4151.318 || 80.923 || 36.487
| ||  
|-
|-
| [[61/11]] || 2965.567 || 88.943
| [[199/18]] || 4160.040 || 82.753 || 40.536
| ||  
|-
|-
| [[50/9]] || 2968.717 || 89.611
| [[122/11]] || 4165.567 || 85.227 || 47.248
| ||  
|-
|-
| [[39/7]] || 2973.657 || 90.516
| [[89/8]] || 4170.880 || 87.785 || 56.740
| ||  
|-
|-
| [[67/12]] || 2977.352 || 91.004
| [[78/7]] || 4173.657 || 88.990 || 62.875
| ||  
|-
|-
| [[28/5]] || 2982.512 || 91.342
| [[67/6]] || 4177.352 || 90.328 || 72.066
| ||  
|-
|-
| [[45/8]] || 2990.224 || 91.271
| [[56/5]] || 4182.512 || 91.600 || 80.389
| ||  
|-
|-
| [[62/11]] || 2993.718 || 91.121
| [[45/4]] || 4190.224 || 92.309 || 76.901
| ||  
|-
|-
| [[17/3]] || 3003.000 || 90.796
| [[79/7]] || 4195.711 || 92.234 || 73.551
| ||  
|-
|-
| [[91/16]] || 3009.354 || 90.823
| [[34/3]] || 4203.000 || 91.759 || 71.407
| ||  
|-
|-
| [[40/7]] || 3017.488 || 91.140
| [[91/8]] || 4209.354 || 91.208 || 72.159
| ||  
|-
|-
| [[63/11]] || 3021.418 || 91.351
| [[57/5]] || 4213.154 || 90.874 || 70.065
| ||  
|-
|-
| [[23/4]] || 3028.274 || 91.759
| [[80/7]] || 4217.488 || 90.537 || 65.217
| ||  
|-
|-
| [[52/9]] || 3036.618 || 92.295
| [[126/11]] || 4221.418 || 90.300 || 61.683
| ||  
|-
|-
| [[29/5]] || 3043.264 || 92.782
| [[23/2]] || 4228.274 || 90.141 || 59.271
| ||  
|-
|-
| [[35/6]] || 3053.185 || 93.524
| [[104/9]] || 4236.618 || 90.448 || 62.997
| ||  
|-
|-
| [[41/7]] || 3060.237 || 93.677
| [[58/5]] || 4243.263 || 90.982 || 70.207
| ||  
|-
|-
| [[47/8]] || 3065.507 || 93.159
| [[35/3]] || 4253.185 || 91.865 || 72.236
| ||  
|-
|-
| [[53/9]] || 3069.595 || 92.138
| [[117/10]] || 4258.124 || 92.171 || 73.294
| ||  
|-
|-
| [[65/11]] || 3075.523 || 89.379
| [[47/4]] || 4265.507 || 92.188 || 77.572
| ||  
|-
|-
| [[77/13]] || 3079.616 || 86.553
| [[59/5]] || 4272.858 || 91.253 || 79.374
| ||  
|-
|-
| [[95/16]] || 3083.827 || 83.035
| [[71/6]] || 4277.742 || 89.927 || 69.007
| ||  
|-
|-
| [[131/22]] || 3088.790 || 78.596
| [[95/8]] || 4283.827 || 87.551 || 55.324
| ||  
|-
|-
| [[197/33]] || 3093.189 || 75.071
| [[131/11]] || 4288.790 || 85.337 || 46.968
| ||  
|-
|-
| [[6/1]] || 3101.955 || 71.731
| [[191/16]] || 4292.915 || 83.658 || 42.013
| ||
|}
 
=== 6/1 to 8/1 ===
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[6/1]] || 3101.955 || 71.731
| [[12/1]] || 4301.955 || 81.853 || 37.504
| ||
|-
|-
| [[367/61]] || 3106.679 || 72.714
| [[361/30]] || 4306.757 || 82.366 || 38.662
| ||  
|-
|-
| [[187/31]] || 3111.238 || 75.340
| [[181/15]] || 4311.546 || 83.790 || 42.265
| ||  
|-
|-
| [[127/21]] || 3115.641 || 78.905
| [[121/10]] || 4316.322 || 85.773 || 48.300
| ||  
|-
|-
| [[91/15]] || 3121.085 || 83.711
| [[85/7]] || 4322.443 || 88.421 || 59.579
| ||  
|-
|-
| [[73/12]] || 3125.835 || 87.463
| [[73/6]] || 4325.834 || 89.679 || 67.466
| ||  
|-
|-
| [[61/10]] || 3130.571 || 90.313
| [[61/5]] || 4330.571 || 91.015 || 78.002
| ||  
|-
|-
| [[55/9]] || 3133.722 || 91.647
| [[49/4]] || 4337.652 || 92.004 || 77.028
| ||  
|-
|-
| [[49/8]] || 3137.652 || 92.720
| [[86/7]] || 4342.692 || 92.130 || 74.003
| ||  
|-
|-
| [[43/7]] || 3142.692 || 93.315
| [[37/3]] || 4349.389 || 91.861 || 72.160
| ||  
|-
|-
| [[37/6]] || 3149.389 || 93.281
| [[62/5]] || 4358.722 || 91.180 || 69.278
| ||  
|-
|-
| [[31/5]] || 3158.722 || 92.634
| [[87/7]] || 4362.706 || 90.922 || 65.101
| ||  
|-
|-
| [[56/9]] || 3164.916 || 92.175
| [[25/2]] || 4372.627 || 90.671 || 60.096
| ||  
|-
|-
| [[25/4]] || 3172.627 || 91.679
| [[163/13]] || 4377.946 || 90.837 || 61.619
| ||  
|-
|-
| [[69/11]] || 3178.911 || 91.336
| [[88/7]] || 4382.492 || 91.128 || 65.187
| ||  
|-
|-
| [[44/7]] || 3182.492 || 91.164
| [[63/5]] || 4386.422 || 91.450 || 69.379
| ||  
|-
|-
| [[63/10]] || 3186.422 || 91.034
| [[101/8]] || 4389.854 || 91.745 || 72.115
| ||  
|-
|-
| [[120/19]] || 3190.756 || 90.949
| [[38/3]] || 4395.558 || 92.186 || 72.796
| ||  
|-
|-
| [[19/3]] || 3195.558 || 90.954
| [[127/10]] || 4400.108 || 92.375 || 73.739
| ||  
|-
|-
| [[127/20]] || 3200.108 || 91.016
| [[51/4]] || 4406.910 || 92.143 || 77.501
| ||  
|-
|-
| [[51/8]] || 3206.910 || 91.113
| [[64/5]] || 4413.686 || 90.999 || 75.769
| ||  
|-
|-
| [[32/5]] || 3213.686 || 90.949
| [[90/7]] || 4421.398 || 88.468 || 58.207
| ||  
|-
|-
| [[45/7]] || 3221.398 || 90.200
| [[116/9]] || 4425.667 || 86.712 || 50.516
| ||  
|-
|-
| [[58/9]] || 3225.667 || 89.582
| [[181/14]] || 4430.989 || 84.615 || 43.643
| ||  
|-
|-
| [[84/13]] || 3230.253 || 88.880
| [[337/26]] || 4435.398 || 83.344 || 40.239
| ||  
|-
|-
| [[162/25]] || 3235.193 || 88.287
| [[13/1]] || 4440.528 || 82.766 || 38.877
| ||  
|-
|-
| [[13/2]] || 3240.528 || 88.036
| [[196/15]] || 4449.383 || 84.323 || 43.108
| ||  
|-
|-
| [[98/15]] || 3249.383 || 88.679
| [[131/10]] || 4453.794 || 85.956 || 48.319
| ||  
|-
|-
| [[59/9]] || 3255.262 || 89.542
| [[92/7]] || 4459.448 || 88.265 || 58.011
| ||  
|-
|-
| [[46/7]] || 3259.448 || 90.160
| [[79/6]] || 4462.582 || 89.429 || 64.808
| ||  
|-
|-
| [[33/5]] || 3266.959 || 90.915
| [[66/5]] || 4466.959 || 90.754 || 75.179
| ||  
|-
|-
| [[53/8]] || 3273.505 || 91.119
| [[53/4]] || 4473.505 || 91.921 || 78.063
| ||  
|-
|-
| [[20/3]] || 3284.359 || 91.038
| [[40/3]] || 4484.359 || 92.092 || 73.638
| ||  
|-
|-
| [[127/19]] || 3288.909 || 91.050
| [[107/8]] || 4489.760 || 91.736 || 72.281
| ||  
|-
|-
| [[47/7]] || 3296.681 || 91.284
| [[67/5]] || 4492.993 || 91.487 || 69.568
| ||  
|-
|-
| [[27/4]] || 3305.865 || 91.845
| [[94/7]] || 4496.681 || 91.231 || 65.916
| ||  
|-
|-
| [[61/9]] || 3312.975 || 92.403
| [[27/2]] || 4505.865 || 90.886 || 61.598
| ||  
|-
|-
| [[34/5]] || 3318.642 || 92.846
| [[149/11]] || 4511.684 || 90.972 || 63.372
| ||  
|-
|-
| [[41/6]] || 3327.107 || 93.164
| [[68/5]] || 4518.642 || 91.340 || 69.503
| ||  
|-
|-
| [[48/7]] || 3333.129 || 92.684
| [[41/3]] || 4527.107 || 91.810 || 73.901
| ||  
|-
|-
| [[55/8]] || 3337.632 || 91.625
| [[55/4]] || 4537.632 || 91.476 || 77.976
| ||  
|-
|-
| [[62/9]] || 3341.126 || 90.272
| [[69/5]] || 4543.916 || 90.311 || 72.427
| ||  
|-
|-
| [[76/11]] || 3346.195 || 87.464
| [[97/7]] || 4551.070 || 88.055 || 56.667
| ||  
|-
|-
| [[97/14]] || 3351.070 || 83.990
| [[125/9]] || 4555.031 || 86.605 || 50.022
| ||  
|-
|-
| [[125/18]] || 3355.031 || 80.945
| [[195/14]] || 4559.970 || 84.931 || 44.083
| ||  
|-
|-
| [[195/28]] || 3359.971 || 77.500
| [[14/1]] || 4568.826 || 83.521 || 39.954
| ||  
|-
|-
| [[7/1]] || 3368.826 || 74.586
| [[379/27]] || 4573.400 || 83.942 || 41.088
| ||  
|-
|-
| [[379/54]] || 3373.400 || 75.394
| [[183/13]] || 4578.312 || 85.179 || 44.783
| ||  
|-
|-
| [[190/27]] || 3377.962 || 77.639
| [[127/9]] || 4582.512 || 86.647 || 49.967
| ||  
|-
|-
| [[127/18]] || 3382.512 || 80.826
| [[85/6]] || 4589.314 || 89.132 || 62.314
| ||  
|-
|-
| [[92/13]] || 3387.747 || 84.821
| [[71/5]] || 4593.383 || 90.358 || 71.686
| ||  
|-
|-
| [[78/11]] || 3391.165 || 87.227
| [[57/4]] || 4599.468 || 91.555 || 78.226
| ||  
|-
|-
| [[64/9]] || 3396.090 || 90.022
| [[100/7]] || 4603.802 || 91.933 || 76.083
| ||  
|-
|-
| [[50/7]] || 3403.802 || 92.504
| [[43/3]] || 4609.563 || 91.963 || 74.300
| ||  
|-
|-
| [[43/6]] || 3409.563 || 93.087
| [[72/5]] || 4617.596 || 91.554 || 69.486
| ||  
|-
|-
| [[36/5]] || 3417.596 || 92.889
| [[101/7]] || 4621.028 || 91.360 || 66.298
| ||  
|-
|-
| [[65/9]] || 3422.931 || 92.505
| [[29/2]] || 4629.577 || 91.126 || 62.605
| ||  
|-
|-
| [[29/4]] || 3429.577 || 91.982
| [[131/9]] || 4636.198 || 91.269 || 64.909
| ||  
|-
|-
| [[51/7]] || 3438.085 || 91.477
| [[73/5]] || 4641.476 || 91.513 || 69.532
| ||  
|-
|-
| [[117/16]] || 3444.438 || 91.266
| [[117/8]] || 4644.438 || 91.650 || 72.268
| ||  
|-
|-
| [[22/3]] || 3449.363 || 91.188
| [[44/3]] || 4649.363 || 91.788 || 74.668
| ||  
|-
|-
| [[59/8]] || 3459.172 || 91.036
| [[59/4]] || 4659.172 || 91.167 || 78.067
| ||  
|-
|-
| [[37/5]] || 3465.030 || 90.729
| [[74/5]] || 4665.030 || 89.937 || 69.658
| ||  
|-
|-
| [[52/7]] || 3471.702 || 90.110
| [[89/6]] || 4668.925 || 88.775 || 61.044
| ||  
|-
|-
| [[67/9]] || 3475.397 || 89.685
| [[134/9]] || 4675.397 || 86.563 || 49.961
| ||  
|-
|-
| [[97/13]] || 3479.368 || 89.251
| [[194/13]] || 4679.368 || 85.312 || 45.361
| ||  
|-
|-
| [[15/2]] || 3488.269 || 88.748
| [[15/1]] || 4688.269 || 83.951 || 41.161
| ||  
|-
|-
| [[158/21]] || 3493.756 || 88.946
| [[331/22]] || 4693.507 || 84.433 || 42.631
| ||  
|-
|-
| [[83/11]] || 3498.729 || 89.408
| [[181/12]] || 4697.860 || 85.477 || 46.079
| ||  
|-
|-
| [[53/7]] || 3504.679 || 90.087
| [[121/8]] || 4702.636 || 87.013 || 52.174
| ||  
|-
|-
| [[38/5]] || 3511.199 || 90.725
| [[91/6]] || 4707.399 || 88.619 || 60.650
| ||  
|-
|-
| [[84/11]] || 3519.463 || 91.165
| [[76/5]] || 4711.199 || 89.736 || 68.979
| ||  
|-
|-
| [[23/3]] || 3526.319 || 91.334
| [[61/4]] || 4716.885 || 90.936 || 78.094
| ||  
|-
|-
| [[77/10]] || 3533.830 || 91.570
| [[46/3]] || 4726.319 || 91.578 || 75.085
| ||  
|-
|-
| [[54/7]] || 3537.039 || 91.735
| [[77/5]] || 4733.830 || 91.363 || 69.891
| ||  
|-
|-
| [[31/4]] || 3545.036 || 92.279
| [[108/7]] || 4737.039 || 91.235 || 67.108
| ||  
|-
|-
| [[70/9]] || 3551.230 || 92.737
| [[31/2]] || 4745.036 || 91.079 || 63.942
| ||  
|-
|-
| [[39/5]] || 3556.169 || 92.976
| [[140/9]] || 4751.230 || 91.213 || 65.968
| ||  
|-
|-
| [[47/6]] || 3563.552 || 92.726
| [[78/5]] || 4756.169 || 91.411 || 70.041
| ||  
|-
|-
| [[55/7]] || 3568.806 || 91.736
| [[47/3]] || 4763.552 || 91.583 || 75.574
| ||  
|-
|-
| [[63/8]] || 3572.736 || 90.390
| [[63/4]] || 4772.736 || 90.874 || 77.783
| ||  
|-
|-
| [[71/9]] || 3575.787 || 88.962
| [[79/5]] || 4778.223 || 89.704 || 67.807
| ||  
|-
|-
| [[95/12]] || 3581.872 || 85.279
| [[95/6]] || 4781.872 || 88.659 || 60.160
| ||  
|-
|-
| [[127/16]] || 3586.422 || 82.182
| [[127/8]] || 4786.422 || 87.219 || 52.446
| ||  
|-
|-
| [[191/24]] || 3590.960 || 79.377
| [[191/12]] || 4790.960 || 85.884 || 46.901
| ||  
|-
|-
| [[383/48]] || 3595.486 || 77.393
| [[383/24]] || 4795.486 || 84.936 || 43.524
| ||  
|-
|-
| [[8/1]] || 3600.000 || 76.672
| [[16/1]] || 4800.000 || 84.596 || 42.308
| ||  
|}
|}


Line 1,913: Line 1,691:
* [[Runoff]]
* [[Runoff]]


[[Category:Tables]][[Category:Harmonic entropy]]
[[Category:Lists of intervals]]
 
[[Category:Harmonic entropy]]
 
{{todo|inline=1|complete table|comment=Fill in the values for the Rényi order 7.0 column of each table.}}

Latest revision as of 10:06, 13 January 2026

This is a procedurally generated table of several hundred just intonation intervals between 1/1 and 16/1: 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 270edo across four octaves, then using "convert interval values > fraction" with a tolerance of 4.4 ¢ 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, with all parameters left as default for the column "%, Rényi order 1.0", and all set to default except Réyni order for the column "%, Rényi order 7.0" (which was as the name suggests).

Table of intervals

1/1 to 2/1

Harmonic entropy of just intervals size 0 to 1200 ¢
Just interval Size (cents) Entropy (Réyni 1.0) Entropy (Réyni 7.0)
1/1 0.000 0.000 0.000
390/389 4.445 3.760 0.907
195/194 8.901 14.289 3.681
130/129 13.369 29.536 8.458
97/96 17.940 47.113 15.574
78/77 22.339 63.285 24.669
65/64 26.841 77.192 36.309
56/55 31.194 87.233 49.779
49/48 35.697 94.083 65.929
43/42 40.737 98.235 86.459
39/38 44.970 99.690 99.596
35/34 50.184 99.958 98.660
32/31 54.964 99.447 96.764
30/29 58.692 98.855 95.355
28/27 62.961 98.131 93.820
26/25 67.900 97.339 92.155
24/23 73.681 96.526 90.360
23/22 76.956 96.119 89.411
22/21 80.537 95.722 88.427
21/20 84.467 95.323 87.402
20/19 88.801 94.928 86.324
19/18 93.603 94.534 85.175
18/17 98.955 94.138 83.939
17/16 104.955 93.748 82.606
16/15 111.731 93.375 81.182
15/14 119.443 93.016 79.687
14/13 128.298 92.675 78.137
27/25 133.238 92.514 77.302
13/12 138.573 92.347 76.478
12/11 150.637 92.045 74.569
23/21 157.493 91.881 73.578
34/31 159.920 91.829 72.985
11/10 165.004 91.727 72.187
21/19 173.268 91.551 71.706
41/37 177.718 91.462 70.122
10/9 182.404 91.367 69.257
19/17 192.558 91.175 70.455
9/8 203.910 91.000 65.852
35/31 210.104 90.909 67.768
17/15 216.687 90.809 70.456
25/22 221.309 90.746 66.917
49/43 226.134 90.706 63.360
8/7 231.174 90.701 62.087
23/20 241.961 90.726 68.150
15/13 247.741 90.623 72.999
22/19 253.805 90.413 66.529
29/25 256.950 90.286 62.777
57/49 261.816 90.135 58.880
7/6 266.871 90.099 57.449
27/23 277.591 90.529 63.339
20/17 281.358 90.732 68.028
13/11 289.210 90.867 75.314
19/16 297.513 90.317 69.059
25/21 301.847 89.806 62.212
37/31 306.308 89.268 56.838
73/61 310.905 88.838 53.461
6/5 315.641 88.670 52.311
35/29 325.562 89.348 57.574
23/19 330.761 90.058 64.423
17/14 336.130 90.813 72.542
28/23 340.552 91.327 73.081
11/9 347.408 91.786 71.098
16/13 359.472 91.181 76.294
21/17 365.825 90.053 68.023
31/25 372.408 88.498 56.195
46/37 376.930 87.477 50.618
5/4 386.314 86.433 45.966
89/71 391.184 86.736 47.224
44/35 396.178 87.574 51.114
29/23 401.303 88.739 57.835
24/19 404.442 89.458 63.288
19/15 409.244 90.412 72.808
14/11 417.508 91.306 75.636
23/18 424.364 91.415 69.571
9/7 435.084 91.284 63.938
49/38 440.139 91.361 65.252
22/17 446.363 91.641 69.925
13/10 454.214 92.079 74.367
17/13 464.428 91.930 78.493
21/16 470.781 90.841 75.987
25/19 475.114 89.528 65.532
29/22 478.259 88.318 58.453
41/31 484.027 85.801 48.135
61/46 488.610 83.904 42.464
121/91 493.282 82.505 38.981
4/3 498.045 81.976 37.808
67/50 506.680 83.591 41.793
43/32 511.518 85.531 47.459
31/23 516.761 87.848 56.398
23/17 523.319 90.284 71.419
19/14 528.687 91.567 79.786
15/11 536.951 92.317 76.271
26/19 543.015 92.254 72.269
37/27 545.479 92.154 70.833
11/8 551.318 91.819 69.323
18/13 563.382 90.784 72.045
25/18 568.717 90.231 64.851
32/23 571.726 89.927 60.988
67/48 577.352 89.498 56.217
7/5 582.512 89.352 54.788
38/27 591.648 89.727 59.203
24/17 597.000 90.174 65.794
17/12 603.000 90.642 73.141
27/19 608.352 90.950 69.816
10/7 617.488 91.230 65.567
43/30 623.249 91.380 67.163
23/16 628.274 91.555 70.507
13/9 636.618 92.012 73.029
16/11 648.682 92.948 77.137
19/13 656.985 93.440 80.684
22/15 663.049 93.268 83.656
25/17 667.672 92.484 84.338
31/21 674.255 89.925 67.557
37/25 678.717 87.087 55.540
49/33 684.379 82.440 43.304
64/43 688.482 78.794 36.567
100/67 693.320 74.956 30.926
3/2 701.955 71.779 27.000
182/121 706.718 72.810 28.196
92/61 711.390 75.553 31.686
62/41 715.973 79.322 37.349
47/31 720.471 83.329 45.071
38/25 724.886 86.938 54.740
32/21 729.219 89.774 66.231
26/17 735.572 92.399 83.502
23/15 740.006 93.257 83.983
20/13 745.786 93.525 81.149
17/11 753.637 93.117 77.675
31/20 758.722 92.691 75.497
14/9 764.916 92.202 73.877
25/16 772.627 91.717 71.040
47/30 777.238 91.493 68.327
11/7 782.492 91.272 67.068
30/19 790.756 90.881 70.442
19/12 795.558 90.588 71.776
27/17 800.910 90.222 65.504
35/22 803.822 90.033 62.109
67/42 808.526 89.806 58.378
8/5 813.686 89.732 56.944
37/23 823.070 90.195 61.505
21/13 830.253 90.896 70.181
34/21 834.175 91.296 72.501
13/8 840.528 91.817 71.613
18/11 852.592 91.703 77.070
23/14 859.448 90.557 73.426
28/17 863.870 89.342 63.482
43/26 870.990 86.943 50.773
63/38 875.223 85.597 45.746
5/3 884.359 84.167 41.331
127/76 888.909 84.530 42.413
62/37 893.692 85.623 45.908
42/25 898.153 87.045 51.349
32/19 902.487 88.529 58.647
22/13 910.790 90.839 76.249
17/10 918.642 91.911 76.123
29/17 924.622 92.114 71.669
12/7 933.129 91.936 68.444
43/25 938.890 91.611 70.144
19/11 946.195 90.913 74.112
26/15 952.259 90.085 65.732
47/27 959.642 89.027 55.751
7/4 968.826 88.381 51.230
93/53 973.486 88.539 52.340
44/25 978.691 89.061 56.297
30/17 983.313 89.680 62.180
23/13 987.747 90.241 69.519
16/9 996.090 90.836 75.386
25/14 1003.802 90.734 68.192
34/19 1007.442 90.562 63.920
9/5 1017.596 90.182 58.686
74/41 1022.282 90.185 59.936
38/21 1026.732 90.292 63.244
20/11 1034.996 90.598 71.948
31/17 1040.080 90.750 69.295
53/29 1043.927 90.833 66.508
11/6 1049.363 90.918 64.951
24/13 1061.427 91.130 70.596
37/20 1065.030 91.211 71.005
13/7 1071.702 91.394 69.664
28/15 1080.557 91.657 72.058
15/8 1088.269 91.912 73.260
32/17 1095.045 92.173 74.505
17/9 1101.045 92.438 75.914
36/19 1106.397 92.704 77.039
19/10 1111.199 92.968 78.213
21/11 1119.463 93.512 80.351
23/12 1126.319 94.067 82.319
25/13 1132.100 94.649 84.128
27/14 1137.039 95.215 85.797
29/15 1141.308 95.749 87.342
31/16 1145.036 96.208 88.775
33/17 1148.318 96.553 90.106
37/19 1153.831 96.788 92.494
41/21 1158.281 96.316 93.767
47/24 1163.552 94.342 79.933
55/28 1168.806 90.065 61.125
63/32 1172.736 84.977 48.910
77/39 1177.661 76.268 35.956
95/48 1181.872 67.226 26.975
129/65 1186.631 56.465 19.139
193/97 1191.053 47.543 14.030
389/195 1195.555 41.234 10.933
2/1 1200.000 39.006 9.915

2/1 to 4/1

Harmonic entropy of just intervals size 1200 to 2400 ¢
Just interval Size (cents) Entropy (Réyni 1.0) Entropy (Réyni 7.0)
2/1 1200.000 39.006 9.915
389/194 1204.456 41.246 10.916
195/97 1208.901 47.467 13.941
129/64 1213.473 56.700 19.201
97/48 1217.940 66.810 26.498
77/38 1222.631 76.861 36.491
65/32 1226.841 84.341 47.508
55/27 1231.767 90.672 62.844
49/24 1235.697 93.888 76.914
43/21 1240.737 96.081 92.874
39/19 1244.970 96.733 92.933
35/17 1250.184 96.662 90.721
31/15 1256.767 95.974 88.150
29/14 1260.751 95.470 86.704
27/13 1265.337 94.913 85.129
25/12 1270.672 94.335 83.403
23/11 1276.956 93.767 81.510
21/10 1284.467 93.226 79.440
40/19 1288.801 92.971 78.339
19/9 1293.603 92.713 77.210
17/8 1304.955 92.212 74.752
32/15 1311.731 91.962 73.263
15/7 1319.443 91.713 71.565
43/20 1325.204 91.549 71.747
28/13 1328.298 91.468 70.997
54/25 1333.238 91.338 68.520
13/6 1338.573 91.201 67.254
24/11 1350.637 90.891 70.532
35/16 1355.140 90.798 66.822
68/31 1359.920 90.737 63.227
11/5 1365.004 90.741 61.857
31/14 1376.210 90.799 68.226
20/9 1382.404 90.645 74.073
29/13 1389.050 90.242 66.560
47/21 1394.726 89.813 59.470
9/4 1403.910 89.442 55.051
79/35 1409.397 89.622 56.694
43/19 1414.005 89.985 60.526
25/11 1421.309 90.755 70.259
41/18 1425.152 91.119 73.291
16/7 1431.174 91.447 72.927
23/10 1441.961 90.803 75.583
30/13 1447.741 89.775 66.083
37/16 1451.344 88.987 59.558
58/25 1456.950 87.767 52.003
121/52 1462.108 86.960 47.981
7/3 1466.871 86.699 46.764
61/26 1476.357 87.725 51.478
40/17 1481.358 88.788 57.784
33/14 1484.447 89.469 62.970
26/11 1489.210 90.374 72.202
19/8 1497.513 91.263 75.523
31/13 1504.508 91.358 69.217
67/28 1510.481 91.232 64.457
12/5 1515.641 91.162 63.074
29/12 1527.622 91.519 69.720
17/7 1536.130 92.120 73.203
39/16 1542.483 92.492 74.937
22/9 1547.408 92.527 77.617
27/11 1554.547 91.809 80.862
32/13 1559.472 90.533 72.653
37/15 1563.075 89.159 63.401
47/19 1567.994 86.769 52.637
62/25 1572.408 84.387 45.145
97/39 1577.413 81.915 39.142
5/2 1586.314 79.831 34.998
178/71 1591.184 80.481 36.263
93/37 1595.647 82.086 39.618
63/25 1600.108 84.302 45.074
43/17 1606.562 87.719 56.694
38/15 1609.244 88.973 62.811
28/11 1617.508 91.634 80.890
23/9 1624.364 92.434 78.292
18/7 1635.084 92.172 74.096
49/19 1640.139 91.840 72.388
31/12 1643.081 91.658 70.218
57/22 1648.150 91.431 66.376
13/5 1654.214 91.300 64.521
34/13 1664.428 91.237 69.666
21/8 1670.781 90.960 75.611
29/11 1678.259 90.106 69.169
37/14 1682.518 89.391 61.489
61/23 1688.610 88.342 53.451
117/44 1693.120 87.764 50.019
8/3 1698.045 87.525 48.727
67/25 1706.680 88.237 52.642
43/16 1711.518 89.069 58.264
27/10 1719.551 90.435 71.995
19/7 1728.687 91.142 74.726
49/18 1733.742 91.064 72.204
30/11 1736.951 90.897 68.468
41/15 1740.794 90.654 63.845
85/31 1746.234 90.327 59.456
11/4 1751.318 90.168 58.141
47/17 1760.551 90.312 62.711
25/9 1768.717 90.677 71.476
39/14 1773.657 90.867 69.426
67/24 1777.352 90.985 66.929
14/5 1782.512 91.109 65.552
31/11 1793.718 91.367 70.604
17/6 1803.000 91.650 71.316
37/13 1810.816 91.957 73.275
20/7 1817.488 92.272 75.172
43/15 1823.249 92.602 76.461
23/8 1828.274 92.938 77.918
26/9 1836.618 93.633 80.434
29/10 1843.263 94.306 82.719
32/11 1848.682 94.862 84.787
35/12 1853.185 95.221 86.662
38/13 1856.985 95.305 88.363
41/14 1860.236 95.088 89.839
47/16 1865.507 93.821 85.308
53/18 1869.595 91.704 71.338
65/22 1875.523 86.386 52.868
77/26 1879.616 81.103 42.296
98/33 1884.379 73.722 32.257
131/44 1888.790 66.544 25.130
200/67 1893.320 60.026 19.966
3/1 1901.955 54.245 16.105
367/122 1906.679 56.071 17.287
187/62 1911.238 60.881 20.636
127/42 1915.641 67.404 25.947
94/31 1920.471 75.286 34.142
76/25 1924.886 81.991 43.816
64/21 1929.219 87.364 55.340
55/18 1933.722 91.364 69.421
46/15 1940.006 94.439 89.145
43/14 1942.692 95.041 90.247
37/12 1949.389 95.375 87.295
34/11 1953.637 95.100 85.466
31/10 1958.722 94.593 83.442
28/9 1964.916 93.929 81.197
25/8 1972.627 93.206 78.683
47/15 1977.238 92.840 77.296
22/7 1982.492 92.487 75.938
60/19 1990.756 92.024 73.400
19/6 1995.558 91.813 72.533
54/17 2000.910 91.606 72.088
35/11 2003.822 91.516 71.041
67/21 2008.526 91.378 68.628
16/5 2013.686 91.231 67.453
29/9 2025.667 90.874 70.384
42/13 2030.253 90.752 66.250
81/25 2035.193 90.679 62.336
13/4 2040.528 90.693 60.820
49/15 2049.383 90.886 64.842
36/11 2052.592 90.938 68.153
23/7 2059.448 90.832 75.166
33/10 2066.959 90.254 67.768
43/13 2070.990 89.797 61.448
63/19 2075.223 89.312 56.456
10/3 2084.359 88.773 52.134
127/38 2088.909 88.907 53.292
57/17 2094.513 89.429 57.727
37/11 2100.026 90.130 65.241
27/8 2105.865 90.864 73.447
44/13 2110.790 91.364 71.705
17/5 2118.642 91.902 68.767
58/17 2124.622 92.131 70.441
24/7 2133.129 92.030 76.367
31/9 2141.126 91.024 77.921
38/11 2146.195 89.734 67.441
45/13 2149.696 88.572 59.791
59/17 2154.216 86.904 51.732
94/27 2159.642 85.001 44.911
7/2 2168.826 83.459 40.465
186/53 2173.486 83.881 41.609
95/27 2177.962 84.993 44.862
60/17 2183.313 86.860 51.519
46/13 2187.747 88.508 59.311
39/11 2191.165 89.654 66.669
32/9 2196.090 90.939 77.237
25/7 2203.802 91.985 76.398
43/12 2209.563 92.143 72.270
18/5 2217.596 91.868 69.428
65/18 2222.931 91.484 70.834
29/8 2229.577 90.831 72.163
40/11 2234.996 90.215 64.579
51/14 2238.085 89.874 60.435
117/32 2244.438 89.346 54.932
11/3 2249.363 89.211 53.592
59/16 2259.172 89.729 58.601
37/10 2265.030 90.282 66.350
26/7 2271.702 90.802 74.045
41/11 2277.744 91.024 68.631
15/4 2288.269 91.072 63.118
79/21 2293.756 91.101 64.721
34/9 2301.045 91.261 70.248
72/19 2306.397 91.442 71.037
19/5 2311.199 91.637 70.331
42/11 2319.463 92.015 72.701
23/6 2326.319 92.389 74.967
27/7 2337.039 93.165 78.060
31/8 2345.036 93.896 80.913
35/9 2351.230 94.391 83.420
39/10 2356.169 94.508 85.644
47/12 2363.552 93.521 86.956
55/14 2368.806 91.325 71.979
63/16 2372.736 88.598 59.863
75/19 2377.069 84.455 48.359
95/24 2381.872 78.764 37.948
127/32 2386.422 72.968 30.343
191/48 2390.960 67.739 24.940
387/97 2395.532 64.080 21.690
4/1 2400.000 62.798 20.634

4/1 to 8/1

Harmonic entropy of just intervals size 2400 to 3600 ¢
Just interval Size (cents) Entropy (Réyni 1.0) Entropy (Réyni 7.0)
4/1 2400.000 62.798 20.634
389/97 2404.456 64.076 21.670
193/48 2408.993 67.714 24.873
129/32 2413.473 72.852 30.181
97/24 2417.940 78.558 37.612
77/19 2422.631 84.164 47.718
65/16 2426.841 88.282 58.797
53/13 2432.977 92.286 78.103
49/12 2435.697 93.337 85.959
41/10 2442.749 94.509 86.517
37/9 2447.434 94.478 84.366
33/8 2453.273 94.049 81.900
29/7 2460.751 93.336 78.995
25/6 2470.672 92.507 75.746
46/11 2476.956 92.096 73.420
67/16 2479.307 91.958 72.499
21/5 2484.467 91.696 71.456
59/14 2490.346 91.443 71.514
38/9 2493.603 91.333 70.272
55/13 2497.104 91.229 67.898
17/4 2504.955 91.063 65.043
64/15 2511.731 90.911 67.501
30/7 2519.443 90.589 72.480
43/10 2525.204 90.237 65.850
56/13 2528.298 90.045 62.065
108/25 2533.238 89.798 57.981
13/3 2538.573 89.729 56.445
61/14 2548.059 90.228 61.167
35/8 2555.140 90.942 69.998
57/13 2558.940 91.316 72.908
22/5 2565.004 91.732 72.619
31/7 2576.210 91.266 76.993
40/9 2582.404 90.118 68.724
49/11 2586.334 89.120 60.757
67/15 2591.038 87.824 53.151
103/23 2595.526 86.696 48.055
9/2 2603.910 85.700 44.227
167/37 2609.101 86.069 45.583
86/19 2614.005 87.026 49.488
59/13 2618.644 88.237 55.541
41/9 2625.152 89.931 67.735
32/7 2631.174 91.047 76.544
23/5 2641.961 91.557 72.891
37/8 2651.344 90.918 69.333
51/11 2655.592 90.538 64.082
121/26 2662.108 90.078 58.707
14/3 2666.871 89.943 57.563
61/13 2676.357 90.178 62.362
47/10 2679.193 90.338 65.540
33/7 2684.447 90.654 71.433
52/11 2689.210 90.913 70.124
19/4 2697.513 91.250 66.691
81/17 2702.865 91.441 67.985
43/9 2707.608 91.620 70.764
67/14 2710.481 91.756 72.192
24/5 2715.641 92.033 73.157
29/6 2727.622 92.932 77.031
34/7 2736.130 93.640 80.373
39/8 2742.483 93.885 83.233
44/9 2747.408 93.589 85.604
54/11 2754.547 91.677 77.116
64/13 2759.472 88.918 62.079
74/15 2763.075 86.111 52.510
94/19 2767.994 81.362 41.670
129/26 2772.945 76.173 33.364
199/40 2777.636 71.787 27.906
5/1 2786.314 68.009 23.962
361/72 2791.116 69.236 25.203
186/37 2795.647 72.363 28.611
126/25 2800.108 76.655 34.095
91/18 2805.444 82.237 43.431
76/15 2809.244 85.883 51.934
61/12 2814.930 90.123 67.494
51/10 2820.597 92.661 84.199
46/9 2824.364 93.525 86.193
41/8 2829.062 93.937 84.008
36/7 2835.084 93.804 81.270
31/6 2843.081 93.178 78.031
57/11 2848.150 92.750 76.045
26/5 2854.214 92.307 74.485
47/9 2861.597 91.870 71.896
21/4 2870.781 91.425 68.672
79/15 2876.268 91.152 70.103
37/7 2882.518 90.820 70.829
53/10 2887.191 90.579 66.050
117/22 2893.120 90.378 61.195
16/3 2898.045 90.360 59.869
59/11 2907.854 90.739 64.773
43/8 2911.518 90.933 68.839
27/5 2919.551 91.115 74.991
65/12 2924.886 90.826 75.969
38/7 2928.687 90.366 72.997
49/9 2933.742 89.479 63.506
60/11 2936.951 88.814 58.100
93/17 2942.035 87.822 51.716
181/33 2946.542 87.184 48.353
11/2 2951.318 86.954 47.153
94/17 2960.551 87.918 51.700
61/11 2965.567 88.943 57.950
50/9 2968.717 89.611 63.197
39/7 2973.657 90.516 72.515
67/12 2977.352 91.004 76.031
28/5 2982.512 91.342 75.084
45/8 2990.224 91.271 68.577
62/11 2993.718 91.121 64.852
17/3 3003.000 90.796 60.390
91/16 3009.354 90.823 62.564
40/7 3017.488 91.140 70.111
63/11 3021.418 91.351 71.253
23/4 3028.274 91.759 69.888
52/9 3036.618 92.295 72.655
29/5 3043.263 92.782 75.650
35/6 3053.185 93.524 79.261
41/7 3060.236 93.677 82.545
47/8 3065.507 93.159 84.962
53/9 3069.595 92.138 81.317
65/11 3075.523 89.379 64.058
77/13 3079.616 86.553 53.435
95/16 3083.827 83.035 44.350
131/22 3088.790 78.596 36.061
197/33 3093.189 75.071 30.903
6/1 3101.955 71.731 26.753
367/61 3106.679 72.714 27.900
187/31 3111.238 75.340 31.250
127/21 3115.641 78.905 36.582
91/15 3121.085 83.711 46.033
73/12 3125.834 87.463 56.863
61/10 3130.571 90.313 70.005
55/9 3133.722 91.647 79.353
49/8 3137.652 92.720 84.646
43/7 3142.692 93.315 82.594
37/6 3149.389 93.281 79.454
31/5 3158.722 92.634 75.931
56/9 3164.916 92.175 73.112
25/4 3172.627 91.679 70.854
69/11 3178.911 91.336 71.355
44/7 3182.492 91.164 69.795
63/10 3186.422 91.034 66.313
120/19 3190.756 90.949 63.284
19/3 3195.558 90.954 62.086
127/20 3200.108 91.016 63.188
51/8 3206.910 91.113 68.646
32/5 3213.686 90.949 75.401
45/7 3221.398 90.200 68.953
58/9 3225.667 89.582 61.610
84/13 3230.253 88.880 55.552
162/25 3235.193 88.287 51.486
13/2 3240.528 88.036 49.983
98/15 3249.383 88.679 54.121
59/9 3255.262 89.542 61.420
46/7 3259.448 90.160 68.593
33/5 3266.959 90.915 75.373
53/8 3273.505 91.119 68.956
20/3 3284.359 91.038 63.048
127/19 3288.909 91.050 64.127
47/7 3296.681 91.284 69.942
27/4 3305.865 91.845 72.072
61/9 3312.975 92.403 74.047
34/5 3318.642 92.846 76.869
41/6 3327.107 93.164 80.690
48/7 3333.129 92.684 83.653
55/8 3337.632 91.625 79.909
62/9 3341.126 90.272 70.109
76/11 3346.195 87.464 56.641
97/14 3351.070 83.990 46.182
125/18 3355.031 80.945 39.535
195/28 3359.970 77.500 33.579
7/1 3368.826 74.586 29.390
379/54 3373.400 75.394 30.489
190/27 3377.962 77.639 33.801
127/18 3382.512 80.826 39.313
92/13 3387.747 84.821 48.386
78/11 3391.165 87.227 55.880
64/9 3396.090 90.022 68.814
50/7 3403.802 92.504 83.841
43/6 3409.563 93.087 81.264
36/5 3417.596 92.889 77.539
65/9 3422.931 92.505 74.973
29/4 3429.577 91.982 73.165
51/7 3438.085 91.477 70.297
117/16 3444.438 91.266 65.747
22/3 3449.363 91.188 64.411
59/8 3459.172 91.036 69.063
37/5 3465.030 90.729 74.001
52/7 3471.702 90.110 66.126
67/9 3475.397 89.685 60.509
97/13 3479.368 89.251 55.971
15/2 3488.269 88.748 51.847
158/21 3493.756 88.946 53.484
83/11 3498.729 89.408 57.716
53/7 3504.679 90.087 66.089
38/5 3511.199 90.725 74.056
84/11 3519.463 91.165 67.580
23/3 3526.319 91.334 65.218
77/10 3533.830 91.570 67.961
54/7 3537.039 91.735 70.328
31/4 3545.036 92.279 73.654
70/9 3551.230 92.737 75.346
39/5 3556.169 92.976 77.758
47/6 3563.552 92.726 81.598
55/7 3568.806 91.736 80.615
63/8 3572.736 90.390 70.693
71/9 3575.787 88.962 62.507
95/12 3581.872 85.279 48.938
127/16 3586.422 82.182 41.351
191/24 3590.960 79.377 35.966
383/48 3595.486 77.393 32.761
8/1 3600.000 76.672 31.713

8/1 to 16/1

Harmonic entropy of just intervals size 3600 to 4800 ¢
Just interval Size (cents) Entropy (Réyni 1.0) Entropy (Réyni 7.0)
8/1 3600.000 76.672 31.713
385/48 3604.503 77.364 32.804
193/24 3608.993 79.306 36.012
129/16 3613.473 82.060 41.323
97/12 3617.940 85.094 48.721
73/9 3623.879 88.737 61.801
65/8 3626.841 90.169 69.646
57/7 3630.642 91.549 79.669
49/6 3635.697 92.628 82.024
41/5 3642.749 93.023 78.239
33/4 3653.273 92.507 74.177
91/11 3658.036 92.181 72.380
58/7 3660.751 92.011 70.627
25/3 3670.672 91.520 66.415
117/14 3675.612 91.277 67.716
67/8 3679.307 91.059 70.190
42/5 3684.467 90.661 72.830
59/7 3690.346 90.106 65.391
110/13 3697.104 89.474 57.492
17/2 3704.955 89.148 54.268
128/15 3711.731 89.402 56.734
77/9 3716.234 89.785 61.038
60/7 3719.443 90.106 65.332
43/5 3725.204 90.677 72.770
95/11 3732.509 91.255 69.106
26/3 3738.573 91.610 67.183
61/7 3748.059 92.151 71.040
35/4 3755.140 92.594 74.884
79/9 3760.627 92.837 76.786
44/5 3765.004 92.808 78.930
53/6 3771.550 92.065 81.714
62/7 3776.210 90.798 73.622
71/8 3779.697 89.397 64.348
98/11 3786.334 85.814 49.724
134/15 3791.038 82.979 42.173
206/23 3795.526 80.585 37.158
9/1 3803.910 78.487 33.500
343/38 3808.965 79.252 34.878
181/20 3813.501 81.100 38.408
118/13 3818.644 84.004 45.035
91/10 3823.040 86.618 52.905
73/8 3827.789 89.122 63.684
64/7 3831.174 90.519 72.620
55/6 3835.677 91.815 81.602
46/5 3841.961 92.648 79.540
37/4 3851.344 92.585 75.474
65/7 3858.015 92.199 71.715
121/13 3862.108 91.941 69.445
28/3 3866.871 91.644 68.437
47/5 3879.193 90.732 71.679
66/7 3884.447 90.277 65.124
85/9 3887.359 90.041 61.645
19/2 3897.513 89.594 56.279
181/19 3902.302 89.701 57.538
86/9 3907.608 90.028 61.747
67/7 3910.481 90.256 65.199
48/5 3915.641 90.728 71.780
29/3 3927.622 91.657 69.328
97/10 3933.582 92.028 70.853
68/7 3936.130 92.168 72.306
39/4 3942.483 92.425 76.055
49/5 3951.338 92.127 80.025
59/6 3957.217 91.041 78.171
69/7 3961.403 89.683 67.696
89/9 3966.970 87.167 54.700
129/13 3972.945 83.992 44.361
199/20 3977.636 81.728 38.911
10/1 3986.314 79.780 34.989
361/36 3991.116 80.437 36.252
181/18 3995.905 82.193 39.947
121/12 4000.681 84.621 46.056
91/9 4005.444 87.182 54.555
71/7 4010.871 89.704 67.126
61/6 4014.930 91.082 77.529
51/5 4020.597 92.220 80.758
41/4 4029.062 92.605 76.712
72/7 4035.084 92.356 73.073
31/3 4043.081 91.796 70.334
83/8 4050.047 91.222 71.949
52/5 4054.214 90.858 70.652
94/9 4061.597 90.262 61.915
21/2 4070.781 89.908 57.273
179/17 4075.624 89.990 58.448
74/7 4082.518 90.399 64.359
53/5 4087.191 90.789 69.995
117/11 4093.120 91.311 71.041
32/3 4098.045 91.721 70.066
75/7 4105.757 92.214 72.572
43/4 4111.518 92.328 76.211
54/5 4119.551 91.684 80.063
65/6 4124.886 90.424 72.814
76/7 4128.687 89.080 63.335
87/8 4131.532 87.858 56.993
120/11 4136.951 85.258 47.263
186/17 4142.035 82.949 40.960
362/33 4146.542 81.497 37.654
11/1 4151.318 80.923 36.487
199/18 4160.040 82.753 40.536
122/11 4165.567 85.227 47.248
89/8 4170.880 87.785 56.740
78/7 4173.657 88.990 62.875
67/6 4177.352 90.328 72.066
56/5 4182.512 91.600 80.389
45/4 4190.224 92.309 76.901
79/7 4195.711 92.234 73.551
34/3 4203.000 91.759 71.407
91/8 4209.354 91.208 72.159
57/5 4213.154 90.874 70.065
80/7 4217.488 90.537 65.217
126/11 4221.418 90.300 61.683
23/2 4228.274 90.141 59.271
104/9 4236.618 90.448 62.997
58/5 4243.263 90.982 70.207
35/3 4253.185 91.865 72.236
117/10 4258.124 92.171 73.294
47/4 4265.507 92.188 77.572
59/5 4272.858 91.253 79.374
71/6 4277.742 89.927 69.007
95/8 4283.827 87.551 55.324
131/11 4288.790 85.337 46.968
191/16 4292.915 83.658 42.013
12/1 4301.955 81.853 37.504
361/30 4306.757 82.366 38.662
181/15 4311.546 83.790 42.265
121/10 4316.322 85.773 48.300
85/7 4322.443 88.421 59.579
73/6 4325.834 89.679 67.466
61/5 4330.571 91.015 78.002
49/4 4337.652 92.004 77.028
86/7 4342.692 92.130 74.003
37/3 4349.389 91.861 72.160
62/5 4358.722 91.180 69.278
87/7 4362.706 90.922 65.101
25/2 4372.627 90.671 60.096
163/13 4377.946 90.837 61.619
88/7 4382.492 91.128 65.187
63/5 4386.422 91.450 69.379
101/8 4389.854 91.745 72.115
38/3 4395.558 92.186 72.796
127/10 4400.108 92.375 73.739
51/4 4406.910 92.143 77.501
64/5 4413.686 90.999 75.769
90/7 4421.398 88.468 58.207
116/9 4425.667 86.712 50.516
181/14 4430.989 84.615 43.643
337/26 4435.398 83.344 40.239
13/1 4440.528 82.766 38.877
196/15 4449.383 84.323 43.108
131/10 4453.794 85.956 48.319
92/7 4459.448 88.265 58.011
79/6 4462.582 89.429 64.808
66/5 4466.959 90.754 75.179
53/4 4473.505 91.921 78.063
40/3 4484.359 92.092 73.638
107/8 4489.760 91.736 72.281
67/5 4492.993 91.487 69.568
94/7 4496.681 91.231 65.916
27/2 4505.865 90.886 61.598
149/11 4511.684 90.972 63.372
68/5 4518.642 91.340 69.503
41/3 4527.107 91.810 73.901
55/4 4537.632 91.476 77.976
69/5 4543.916 90.311 72.427
97/7 4551.070 88.055 56.667
125/9 4555.031 86.605 50.022
195/14 4559.970 84.931 44.083
14/1 4568.826 83.521 39.954
379/27 4573.400 83.942 41.088
183/13 4578.312 85.179 44.783
127/9 4582.512 86.647 49.967
85/6 4589.314 89.132 62.314
71/5 4593.383 90.358 71.686
57/4 4599.468 91.555 78.226
100/7 4603.802 91.933 76.083
43/3 4609.563 91.963 74.300
72/5 4617.596 91.554 69.486
101/7 4621.028 91.360 66.298
29/2 4629.577 91.126 62.605
131/9 4636.198 91.269 64.909
73/5 4641.476 91.513 69.532
117/8 4644.438 91.650 72.268
44/3 4649.363 91.788 74.668
59/4 4659.172 91.167 78.067
74/5 4665.030 89.937 69.658
89/6 4668.925 88.775 61.044
134/9 4675.397 86.563 49.961
194/13 4679.368 85.312 45.361
15/1 4688.269 83.951 41.161
331/22 4693.507 84.433 42.631
181/12 4697.860 85.477 46.079
121/8 4702.636 87.013 52.174
91/6 4707.399 88.619 60.650
76/5 4711.199 89.736 68.979
61/4 4716.885 90.936 78.094
46/3 4726.319 91.578 75.085
77/5 4733.830 91.363 69.891
108/7 4737.039 91.235 67.108
31/2 4745.036 91.079 63.942
140/9 4751.230 91.213 65.968
78/5 4756.169 91.411 70.041
47/3 4763.552 91.583 75.574
63/4 4772.736 90.874 77.783
79/5 4778.223 89.704 67.807
95/6 4781.872 88.659 60.160
127/8 4786.422 87.219 52.446
191/12 4790.960 85.884 46.901
383/24 4795.486 84.936 43.524
16/1 4800.000 84.596 42.308

See also

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