Harmonic entropy of just intervals: Difference between revisions

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m →The table: Added subheadings for easier navigation
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
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)
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{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ Harmonic entropy of just intervals
! Ratio !! Size (cents) !! Harmonic entropy (%) !! Comments
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[1/1]] || 0.000 || 0.000 ||
| [[1/1]] || 0.000 || 0.000  
| ||  
|-
|-
| [[390/389]] || 4.445 || 3.760 ||
| [[390/389]] || 4.445 || 3.760  
| ||  
|-
|-
| [[195/194]] || 8.901 || 14.289 ||
| [[195/194]] || 8.901 || 14.289  
| ||  
|-
|-
| [[130/129]] || 13.369 || 29.536 ||
| [[130/129]] || 13.369 || 29.536  
| ||  
|-
|-
| [[97/96]] || 17.940 || 47.113 ||
| [[97/96]] || 17.940 || 47.113  
| ||  
|-
|-
| [[78/77]] || 22.339 || 63.285 ||
| [[78/77]] || 22.339 || 63.285  
| ||  
|-
|-
| [[65/64]] || 26.841 || 77.192 ||
| [[65/64]] || 26.841 || 77.192  
| ||  
|-
|-
| [[56/55]] || 31.194 || 87.233 ||
| [[56/55]] || 31.194 || 87.233  
| ||  
|-
|-
| [[49/48]] || 35.697 || 94.083 ||
| [[49/48]] || 35.697 || 94.083  
| ||  
|-
|-
| [[43/42]] || 40.737 || 98.235 ||
| [[43/42]] || 40.737 || 98.235  
| ||  
|-
|-
| [[39/38]] || 44.970 || 99.690 ||
| [[39/38]] || 44.970 || 99.690  
| ||  
|-
|-
| [[35/34]] || 50.184 || 99.958 ||
| [[35/34]] || 50.184 || 99.958  
| ||  
|-
|-
| [[32/31]] || 54.964 || 99.447 ||
| [[32/31]] || 54.964 || 99.447  
| ||  
|-
|-
| [[30/29]] || 58.692 || 98.855 ||
| [[30/29]] || 58.692 || 98.855  
| ||  
|-
|-
| [[28/27]] || 62.961 || 98.131 ||
| [[28/27]] || 62.961 || 98.131  
| ||  
|-
|-
| [[26/25]] || 67.900 || 97.339 ||
| [[26/25]] || 67.900 || 97.339  
| ||  
|-
|-
| [[24/23]] || 73.681 || 96.526 ||
| [[24/23]] || 73.681 || 96.526  
| ||  
|-
|-
| [[23/22]] || 76.956 || 96.119 ||
| [[23/22]] || 76.956 || 96.119  
| ||  
|-
|-
| [[22/21]] || 80.537 || 95.722 ||
| [[22/21]] || 80.537 || 95.722  
| ||  
|-
|-
| [[21/20]] || 84.467 || 95.323 ||
| [[21/20]] || 84.467 || 95.323  
| ||  
|-
|-
| [[20/19]] || 88.801 || 94.928 ||
| [[20/19]] || 88.801 || 94.928  
| ||  
|-
|-
| [[19/18]] || 93.603 || 94.534 ||
| [[19/18]] || 93.603 || 94.534  
| ||  
|-
|-
| [[18/17]] || 98.955 || 94.138 ||
| [[18/17]] || 98.955 || 94.138  
| ||  
|-
|-
| [[17/16]] || 104.955 || 93.748 ||
| [[17/16]] || 104.955 || 93.748  
| ||  
|-
|-
| [[16/15]] || 111.731 || 93.375 ||
| [[16/15]] || 111.731 || 93.375  
| ||  
|-
|-
| [[15/14]] || 119.443 || 93.016 ||
| [[15/14]] || 119.443 || 93.016  
| ||  
|-
|-
| [[14/13]] || 128.298 || 92.675 ||
| [[14/13]] || 128.298 || 92.675  
| ||  
|-
|-
| [[27/25]] || 133.238 || 92.514 ||
| [[27/25]] || 133.238 || 92.514  
| ||  
|-
|-
| [[13/12]] || 138.573 || 92.347 ||
| [[13/12]] || 138.573 || 92.347  
| ||  
|-
|-
| [[12/11]] || 150.637 || 92.045 ||
| [[12/11]] || 150.637 || 92.045  
| ||  
|-
|-
| [[23/21]] || 157.493 || 91.881 ||
| [[23/21]] || 157.493 || 91.881  
| ||  
|-
|-
| [[34/31]] || 159.920 || 91.829 ||
| [[34/31]] || 159.920 || 91.829  
| ||  
|-
|-
| [[11/10]] || 165.004 || 91.727 ||
| [[11/10]] || 165.004 || 91.727  
| ||  
|-
|-
| [[21/19]] || 173.268 || 91.551 ||
| [[21/19]] || 173.268 || 91.551  
| ||  
|-
|-
| [[41/37]] || 177.718 || 91.462 ||
| [[41/37]] || 177.718 || 91.462  
| ||  
|-
|-
| [[10/9]] || 182.404 || 91.367 ||
| [[10/9]] || 182.404 || 91.367  
| ||  
|-
|-
| [[19/17]] || 192.558 || 91.175 ||
| [[19/17]] || 192.558 || 91.175  
| ||  
|-
|-
| [[9/8]] || 203.910 || 91.000 ||
| [[9/8]] || 203.910 || 91.000  
| ||  
|-
|-
| [[35/31]] || 210.104 || 90.909 ||
| [[35/31]] || 210.104 || 90.909  
| ||  
|-
|-
| [[17/15]] || 216.687 || 90.809 ||
| [[17/15]] || 216.687 || 90.809  
| ||  
|-
|-
| [[25/22]] || 221.310 || 90.746 ||
| [[25/22]] || 221.310 || 90.746  
| ||  
|-
|-
| [[49/43]] || 226.134 || 90.706 ||
| [[49/43]] || 226.134 || 90.706  
| ||  
|-
|-
| [[8/7]] || 231.174 || 90.701 ||
| [[8/7]] || 231.174 || 90.701  
| ||  
|-
|-
| [[23/20]] || 241.961 || 90.726 ||
| [[23/20]] || 241.961 || 90.726  
| ||  
|-
|-
| [[15/13]] || 247.741 || 90.623 ||
| [[15/13]] || 247.741 || 90.623  
| ||  
|-
|-
| [[22/19]] || 253.805 || 90.413 ||
| [[22/19]] || 253.805 || 90.413  
| ||  
|-
|-
| [[29/25]] || 256.950 || 90.286 ||
| [[29/25]] || 256.950 || 90.286  
| ||  
|-
|-
| [[57/49]] || 261.816 || 90.135 ||
| [[57/49]] || 261.816 || 90.135  
| ||  
|-
|-
| [[7/6]] || 266.871 || 90.099 ||
| [[7/6]] || 266.871 || 90.099  
| ||  
|-
|-
| [[27/23]] || 277.591 || 90.529 ||
| [[27/23]] || 277.591 || 90.529  
| ||  
|-
|-
| [[20/17]] || 281.358 || 90.732 ||
| [[20/17]] || 281.358 || 90.732  
| ||  
|-
|-
| [[13/11]] || 289.210 || 90.867 ||
| [[13/11]] || 289.210 || 90.867  
| ||  
|-
|-
| [[19/16]] || 297.513 || 90.317 ||
| [[19/16]] || 297.513 || 90.317  
| ||  
|-
|-
| [[25/21]] || 301.847 || 89.806 ||
| [[25/21]] || 301.847 || 89.806  
| ||  
|-
|-
| [[37/31]] || 306.309 || 89.268 ||
| [[37/31]] || 306.309 || 89.268  
| ||  
|-
|-
| [[73/61]] || 310.905 || 88.838 ||
| [[73/61]] || 310.905 || 88.838  
| ||  
|-
|-
| [[6/5]] || 315.641 || 88.670 ||
| [[6/5]] || 315.641 || 88.670  
| ||  
|-
|-
| [[35/29]] || 325.562 || 89.348 ||
| [[35/29]] || 325.562 || 89.348  
| ||  
|-
|-
| [[23/19]] || 330.761 || 90.058 ||
| [[23/19]] || 330.761 || 90.058  
| ||  
|-
|-
| [[17/14]] || 336.130 || 90.813 ||
| [[17/14]] || 336.130 || 90.813  
| ||  
|-
|-
| [[28/23]] || 340.552 || 91.327 ||
| [[28/23]] || 340.552 || 91.327  
| ||  
|-
|-
| [[11/9]] || 347.408 || 91.786 ||
| [[11/9]] || 347.408 || 91.786  
| ||  
|-
|-
| [[16/13]] || 359.472 || 91.181 ||
| [[16/13]] || 359.472 || 91.181  
| ||  
|-
|-
| [[21/17]] || 365.826 || 90.053 ||
| [[21/17]] || 365.826 || 90.053  
| ||  
|-
|-
| [[31/25]] || 372.408 || 88.498 ||
| [[31/25]] || 372.408 || 88.498  
| ||  
|-
|-
| [[46/37]] || 376.930 || 87.477 ||
| [[46/37]] || 376.930 || 87.477  
| ||  
|-
|-
| [[5/4]] || 386.314 || 86.433 ||
| [[5/4]] || 386.314 || 86.433  
| ||  
|-
|-
| [[89/71]] || 391.184 || 86.736 ||
| [[89/71]] || 391.184 || 86.736  
| ||  
|-
|-
| [[44/35]] || 396.178 || 87.574 ||
| [[44/35]] || 396.178 || 87.574  
| ||  
|-
|-
| [[29/23]] || 401.303 || 88.739 ||
| [[29/23]] || 401.303 || 88.739  
| ||  
|-
|-
| [[24/19]] || 404.442 || 89.458 ||
| [[24/19]] || 404.442 || 89.458  
| ||  
|-
|-
| [[19/15]] || 409.244 || 90.412 ||
| [[19/15]] || 409.244 || 90.412  
| ||  
|-
|-
| [[14/11]] || 417.508 || 91.306 ||
| [[14/11]] || 417.508 || 91.306  
| ||  
|-
|-
| [[23/18]] || 424.364 || 91.415 ||
| [[23/18]] || 424.364 || 91.415  
| ||  
|-
|-
| [[9/7]] || 435.084 || 91.284 ||
| [[9/7]] || 435.084 || 91.284  
| ||  
|-
|-
| [[49/38]] || 440.139 || 91.361 ||
| [[49/38]] || 440.139 || 91.361  
| ||  
|-
|-
| [[22/17]] || 446.363 || 91.641 ||
| [[22/17]] || 446.363 || 91.641  
| ||  
|-
|-
| [[13/10]] || 454.214 || 92.079 ||
| [[13/10]] || 454.214 || 92.079  
| ||  
|-
|-
| [[17/13]] || 464.428 || 91.930 ||
| [[17/13]] || 464.428 || 91.930  
| ||  
|-
|-
| [[21/16]] || 470.781 || 90.841 ||
| [[21/16]] || 470.781 || 90.841  
| ||  
|-
|-
| [[25/19]] || 475.114 || 89.528 ||
| [[25/19]] || 475.114 || 89.528  
| ||  
|-
|-
| [[29/22]] || 478.259 || 88.318 ||
| [[29/22]] || 478.259 || 88.318  
| ||  
|-
|-
| [[41/31]] || 484.027 || 85.801 ||
| [[41/31]] || 484.027 || 85.801  
| ||  
|-
|-
| [[61/46]] || 488.611 || 83.904 ||
| [[61/46]] || 488.611 || 83.904  
| ||  
|-
|-
| [[121/91]] || 493.282 || 82.505 ||
| [[121/91]] || 493.282 || 82.505  
| ||  
|-
|-
| [[4/3]] || 498.045 || 81.976 ||
| [[4/3]] || 498.045 || 81.976  
| ||  
|-
|-
| [[67/50]] || 506.680 || 83.591 ||
| [[67/50]] || 506.680 || 83.591  
| ||  
|-
|-
| [[43/32]] || 511.518 || 85.531 ||
| [[43/32]] || 511.518 || 85.531  
| ||  
|-
|-
| [[31/23]] || 516.761 || 87.848 ||
| [[31/23]] || 516.761 || 87.848  
| ||  
|-
|-
| [[23/17]] || 523.319 || 90.284 ||
| [[23/17]] || 523.319 || 90.284  
| ||  
|-
|-
| [[19/14]] || 528.687 || 91.567 ||
| [[19/14]] || 528.687 || 91.567  
| ||  
|-
|-
| [[15/11]] || 536.951 || 92.317 ||
| [[15/11]] || 536.951 || 92.317  
| ||  
|-
|-
| [[26/19]] || 543.015 || 92.254 ||
| [[26/19]] || 543.015 || 92.254  
| ||  
|-
|-
| [[37/27]] || 545.479 || 92.154 ||
| [[37/27]] || 545.479 || 92.154  
| ||  
|-
|-
| [[11/8]] || 551.318 || 91.819 ||
| [[11/8]] || 551.318 || 91.819  
| ||  
|-
|-
| [[18/13]] || 563.382 || 90.784 ||
| [[18/13]] || 563.382 || 90.784  
| ||  
|-
|-
| [[25/18]] || 568.717 || 90.231 ||
| [[25/18]] || 568.717 || 90.231  
| ||  
|-
|-
| [[32/23]] || 571.726 || 89.927 ||
| [[32/23]] || 571.726 || 89.927  
| ||  
|-
|-
| [[67/48]] || 577.352 || 89.498 ||
| [[67/48]] || 577.352 || 89.498  
| ||  
|-
|-
| [[7/5]] || 582.512 || 89.352 ||
| [[7/5]] || 582.512 || 89.352  
| ||  
|-
|-
| [[38/27]] || 591.648 || 89.727 ||
| [[38/27]] || 591.648 || 89.727  
| ||  
|-
|-
| [[24/17]] || 597.000 || 90.174 ||
| [[24/17]] || 597.000 || 90.174  
| ||  
|-
|-
| [[17/12]] || 603.000 || 90.642 ||
| [[17/12]] || 603.000 || 90.642  
| ||  
|-
|-
| [[27/19]] || 608.352 || 90.950 ||
| [[27/19]] || 608.352 || 90.950  
| ||  
|-
|-
| [[10/7]] || 617.488 || 91.230 ||
| [[10/7]] || 617.488 || 91.230  
| ||  
|-
|-
| [[43/30]] || 623.249 || 91.380 ||
| [[43/30]] || 623.249 || 91.380  
| ||  
|-
|-
| [[23/16]] || 628.274 || 91.555 ||
| [[23/16]] || 628.274 || 91.555  
| ||  
|-
|-
| [[13/9]] || 636.618 || 92.012 ||
| [[13/9]] || 636.618 || 92.012  
| ||  
|-
|-
| [[16/11]] || 648.682 || 92.948 ||
| [[16/11]] || 648.682 || 92.948  
| ||  
|-
|-
| [[19/13]] || 656.985 || 93.440 ||
| [[19/13]] || 656.985 || 93.440  
| ||  
|-
|-
| [[22/15]] || 663.049 || 93.268 ||
| [[22/15]] || 663.049 || 93.268  
| ||  
|-
|-
| [[25/17]] || 667.672 || 92.484 ||
| [[25/17]] || 667.672 || 92.484  
| ||  
|-
|-
| [[31/21]] || 674.255 || 89.925 ||
| [[31/21]] || 674.255 || 89.925  
| ||  
|-
|-
| [[37/25]] || 678.717 || 87.087 ||
| [[37/25]] || 678.717 || 87.087  
| ||  
|-
|-
| [[49/33]] || 684.379 || 82.440 ||
| [[49/33]] || 684.379 || 82.440  
| ||  
|-
|-
| [[64/43]] || 688.482 || 78.794 ||
| [[64/43]] || 688.482 || 78.794  
| ||  
|-
|-
| [[100/67]] || 693.320 || 74.956 ||
| [[100/67]] || 693.320 || 74.956  
| ||  
|-
|-
| [[3/2]] || 701.955 || 71.779 ||
| [[3/2]] || 701.955 || 71.779  
| ||  
|}
|}


Line 255: Line 374:
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ Harmonic entropy of just intervals
! Ratio !! Size (cents) !! Harmonic entropy (%) !! Comments
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[3/2]] || 701.955 || 71.779 ||
| [[3/2]] || 701.955 || 71.779  
| ||  
|-
|-
| [[182/121]] || 706.718 || 72.810 ||
| [[182/121]] || 706.718 || 72.810  
| ||  
|-
|-
| [[92/61]] || 711.390 || 75.553 ||
| [[92/61]] || 711.390 || 75.553  
| ||  
|-
|-
| [[62/41]] || 715.973 || 79.322 ||
| [[62/41]] || 715.973 || 79.322  
| ||  
|-
|-
| [[47/31]] || 720.471 || 83.329 ||
| [[47/31]] || 720.471 || 83.329  
| ||  
|-
|-
| [[38/25]] || 724.886 || 86.938 ||
| [[38/25]] || 724.886 || 86.938  
| ||  
|-
|-
| [[32/21]] || 729.219 || 89.774 ||
| [[32/21]] || 729.219 || 89.774  
| ||  
|-
|-
| [[26/17]] || 735.572 || 92.399 ||
| [[26/17]] || 735.572 || 92.399  
| ||  
|-
|-
| [[23/15]] || 740.006 || 93.257 ||
| [[23/15]] || 740.006 || 93.257  
| ||  
|-
|-
| [[20/13]] || 745.786 || 93.525 ||
| [[20/13]] || 745.786 || 93.525  
| ||  
|-
|-
| [[17/11]] || 753.638 || 93.117 ||
| [[17/11]] || 753.638 || 93.117  
| ||  
|-
|-
| [[31/20]] || 758.722 || 92.691 ||
| [[31/20]] || 758.722 || 92.691  
| ||  
|-
|-
| [[14/9]] || 764.916 || 92.202 ||
| [[14/9]] || 764.916 || 92.202  
| ||  
|-
|-
| [[25/16]] || 772.627 || 91.717 ||
| [[25/16]] || 772.627 || 91.717  
| ||  
|-
|-
| [[47/30]] || 777.238 || 91.493 ||
| [[47/30]] || 777.238 || 91.493  
| ||  
|-
|-
| [[11/7]] || 782.492 || 91.272 ||
| [[11/7]] || 782.492 || 91.272  
| ||  
|-
|-
| [[30/19]] || 790.756 || 90.881 ||
| [[30/19]] || 790.756 || 90.881  
| ||  
|-
|-
| [[19/12]] || 795.558 || 90.588 ||
| [[19/12]] || 795.558 || 90.588  
| ||  
|-
|-
| [[27/17]] || 800.910 || 90.222 ||
| [[27/17]] || 800.910 || 90.222  
| ||  
|-
|-
| [[35/22]] || 803.822 || 90.033 ||
| [[35/22]] || 803.822 || 90.033  
| ||  
|-
|-
| [[67/42]] || 808.526 || 89.806 ||
| [[67/42]] || 808.526 || 89.806  
| ||  
|-
|-
| [[8/5]] || 813.686 || 89.732 ||
| [[8/5]] || 813.686 || 89.732  
| ||  
|-
|-
| [[37/23]] || 823.070 || 90.195 ||
| [[37/23]] || 823.070 || 90.195  
| ||  
|-
|-
| [[21/13]] || 830.253 || 90.896 ||
| [[21/13]] || 830.253 || 90.896  
| ||  
|-
|-
| [[34/21]] || 834.175 || 91.296 ||
| [[34/21]] || 834.175 || 91.296  
| ||  
|-
|-
| [[13/8]] || 840.528 || 91.817 ||
| [[13/8]] || 840.528 || 91.817  
| ||  
|-
|-
| [[18/11]] || 852.592 || 91.703 ||
| [[18/11]] || 852.592 || 91.703  
| ||  
|-
|-
| [[23/14]] || 859.448 || 90.557 ||
| [[23/14]] || 859.448 || 90.557  
| ||  
|-
|-
| [[28/17]] || 863.871 || 89.342 ||
| [[28/17]] || 863.871 || 89.342  
| ||  
|-
|-
| [[43/26]] || 870.990 || 86.943 ||
| [[43/26]] || 870.990 || 86.943  
| ||  
|-
|-
| [[63/38]] || 875.223 || 85.597 ||
| [[63/38]] || 875.223 || 85.597  
| ||  
|-
|-
| [[5/3]] || 884.359 || 84.167 ||
| [[5/3]] || 884.359 || 84.167  
| ||  
|-
|-
| [[127/76]] || 888.909 || 84.530 ||
| [[127/76]] || 888.909 || 84.530  
| ||  
|-
|-
| [[62/37]] || 893.692 || 85.623 ||
| [[62/37]] || 893.692 || 85.623  
| ||  
|-
|-
| [[42/25]] || 898.154 || 87.045 ||
| [[42/25]] || 898.154 || 87.045  
| ||  
|-
|-
| [[32/19]] || 902.487 || 88.529 ||
| [[32/19]] || 902.487 || 88.529  
| ||  
|-
|-
| [[22/13]] || 910.790 || 90.839 ||
| [[22/13]] || 910.790 || 90.839  
| ||  
|-
|-
| [[17/10]] || 918.642 || 91.911 ||
| [[17/10]] || 918.642 || 91.911  
| ||  
|-
|-
| [[29/17]] || 924.622 || 92.114 ||
| [[29/17]] || 924.622 || 92.114  
| ||  
|-
|-
| [[12/7]] || 933.129 || 91.936 ||
| [[12/7]] || 933.129 || 91.936  
| ||  
|-
|-
| [[43/25]] || 938.890 || 91.611 ||
| [[43/25]] || 938.890 || 91.611  
| ||  
|-
|-
| [[19/11]] || 946.195 || 90.913 ||
| [[19/11]] || 946.195 || 90.913  
| ||  
|-
|-
| [[26/15]] || 952.259 || 90.085 ||
| [[26/15]] || 952.259 || 90.085  
| ||  
|-
|-
| [[47/27]] || 959.642 || 89.027 ||
| [[47/27]] || 959.642 || 89.027  
| ||  
|-
|-
| [[7/4]] || 968.826 || 88.381 ||
| [[7/4]] || 968.826 || 88.381  
| ||  
|-
|-
| [[93/53]] || 973.486 || 88.539 ||
| [[93/53]] || 973.486 || 88.539  
| ||  
|-
|-
| [[44/25]] || 978.691 || 89.061 ||
| [[44/25]] || 978.691 || 89.061  
| ||  
|-
|-
| [[30/17]] || 983.313 || 89.680 ||
| [[30/17]] || 983.313 || 89.680  
| ||  
|-
|-
| [[23/13]] || 987.747 || 90.241 ||
| [[23/13]] || 987.747 || 90.241  
| ||  
|-
|-
| [[16/9]] || 996.090 || 90.836 ||
| [[16/9]] || 996.090 || 90.836  
| ||  
|-
|-
| [[25/14]] || 1003.802 || 90.734 ||
| [[25/14]] || 1003.802 || 90.734  
| ||  
|-
|-
| [[34/19]] || 1007.442 || 90.562 ||
| [[34/19]] || 1007.442 || 90.562  
| ||  
|-
|-
| [[9/5]] || 1017.596 || 90.182 ||
| [[9/5]] || 1017.596 || 90.182  
| ||  
|-
|-
| [[74/41]] || 1022.282 || 90.185 ||
| [[74/41]] || 1022.282 || 90.185  
| ||  
|-
|-
| [[38/21]] || 1026.732 || 90.292 ||
| [[38/21]] || 1026.732 || 90.292  
| ||  
|-
|-
| [[20/11]] || 1034.996 || 90.598 ||
| [[20/11]] || 1034.996 || 90.598  
| ||  
|-
|-
| [[31/17]] || 1040.080 || 90.750 ||
| [[31/17]] || 1040.080 || 90.750  
| ||  
|-
|-
| [[53/29]] || 1043.927 || 90.833 ||
| [[53/29]] || 1043.927 || 90.833  
| ||  
|-
|-
| [[11/6]] || 1049.363 || 90.918 ||
| [[11/6]] || 1049.363 || 90.918  
| ||  
|-
|-
| [[24/13]] || 1061.427 || 91.130 ||
| [[24/13]] || 1061.427 || 91.130  
| ||  
|-
|-
| [[37/20]] || 1065.030 || 91.211 ||
| [[37/20]] || 1065.030 || 91.211  
| ||  
|-
|-
| [[13/7]] || 1071.702 || 91.394 ||
| [[13/7]] || 1071.702 || 91.394  
| ||  
|-
|-
| [[28/15]] || 1080.557 || 91.657 ||
| [[28/15]] || 1080.557 || 91.657  
| ||  
|-
|-
| [[15/8]] || 1088.269 || 91.912 ||
| [[15/8]] || 1088.269 || 91.912  
| ||  
|-
|-
| [[32/17]] || 1095.045 || 92.173 ||
| [[32/17]] || 1095.045 || 92.173  
| ||  
|-
|-
| [[17/9]] || 1101.045 || 92.438 ||
| [[17/9]] || 1101.045 || 92.438  
| ||  
|-
|-
| [[36/19]] || 1106.397 || 92.704 ||
| [[36/19]] || 1106.397 || 92.704  
| ||  
|-
|-
| [[19/10]] || 1111.199 || 92.968 ||
| [[19/10]] || 1111.199 || 92.968  
| ||  
|-
|-
| [[21/11]] || 1119.463 || 93.512 ||
| [[21/11]] || 1119.463 || 93.512  
| ||  
|-
|-
| [[23/12]] || 1126.319 || 94.067 ||
| [[23/12]] || 1126.319 || 94.067  
| ||  
|-
|-
| [[25/13]] || 1132.100 || 94.649 ||
| [[25/13]] || 1132.100 || 94.649  
| ||  
|-
|-
| [[27/14]] || 1137.039 || 95.215 ||
| [[27/14]] || 1137.039 || 95.215  
| ||  
|-
|-
| [[29/15]] || 1141.309 || 95.749 ||
| [[29/15]] || 1141.309 || 95.749  
| ||  
|-
|-
| [[31/16]] || 1145.036 || 96.208 ||
| [[31/16]] || 1145.036 || 96.208  
| ||  
|-
|-
| [[33/17]] || 1148.318 || 96.553 ||
| [[33/17]] || 1148.318 || 96.553  
| ||  
|-
|-
| [[37/19]] || 1153.831 || 96.788 ||
| [[37/19]] || 1153.831 || 96.788  
| ||  
|-
|-
| [[41/21]] || 1158.282 || 96.316 ||
| [[41/21]] || 1158.282 || 96.316  
| ||  
|-
|-
| [[47/24]] || 1163.552 || 94.342 ||
| [[47/24]] || 1163.552 || 94.342  
| ||  
|-
|-
| [[55/28]] || 1168.806 || 90.065 ||
| [[55/28]] || 1168.806 || 90.065  
| ||  
|-
|-
| [[63/32]] || 1172.736 || 84.977 ||
| [[63/32]] || 1172.736 || 84.977  
| ||  
|-
|-
| [[77/39]] || 1177.661 || 76.268 ||
| [[77/39]] || 1177.661 || 76.268  
| ||  
|-
|-
| [[95/48]] || 1181.872 || 67.226 ||
| [[95/48]] || 1181.872 || 67.226  
| ||  
|-
|-
| [[129/65]] || 1186.631 || 56.465 ||
| [[129/65]] || 1186.631 || 56.465  
| ||  
|-
|-
| [[193/97]] || 1191.053 || 47.543 ||
| [[193/97]] || 1191.053 || 47.543  
| ||  
|-
|-
| [[389/195]] || 1195.555 || 41.234 ||
| [[389/195]] || 1195.555 || 41.234  
| ||  
|-
|-
| [[2/1]] || 1200.000 || 39.006 ||
| [[2/1]] || 1200.000 || 39.006  
| ||  
|}
|}


Line 433: Line 639:
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ Harmonic entropy of just intervals
! Ratio !! Size (cents) !! Harmonic entropy (%) !! Comments
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[2/1]] || 1200.000 || 39.006 ||
| [[2/1]] || 1200.000 || 39.006  
| ||  
|-
|-
| [[389/194]] || 1204.456 || 41.246 ||
| [[389/194]] || 1204.456 || 41.246  
| ||  
|-
|-
| [[195/97]] || 1208.901 || 47.467 ||
| [[195/97]] || 1208.901 || 47.467  
| ||  
|-
|-
| [[129/64]] || 1213.473 || 56.700 ||
| [[129/64]] || 1213.473 || 56.700  
| ||  
|-
|-
| [[97/48]] || 1217.940 || 66.810 ||
| [[97/48]] || 1217.940 || 66.810  
| ||  
|-
|-
| [[77/38]] || 1222.631 || 76.861 ||
| [[77/38]] || 1222.631 || 76.861  
| ||  
|-
|-
| [[65/32]] || 1226.841 || 84.341 ||
| [[65/32]] || 1226.841 || 84.341  
| ||  
|-
|-
| [[55/27]] || 1231.767 || 90.672 ||
| [[55/27]] || 1231.767 || 90.672  
| ||  
|-
|-
| [[49/24]] || 1235.697 || 93.888 ||
| [[49/24]] || 1235.697 || 93.888  
| ||  
|-
|-
| [[43/21]] || 1240.737 || 96.081 ||
| [[43/21]] || 1240.737 || 96.081  
| ||  
|-
|-
| [[39/19]] || 1244.970 || 96.733 ||
| [[39/19]] || 1244.970 || 96.733  
| ||  
|-
|-
| [[35/17]] || 1250.184 || 96.662 ||
| [[35/17]] || 1250.184 || 96.662  
| ||  
|-
|-
| [[31/15]] || 1256.767 || 95.974 ||
| [[31/15]] || 1256.767 || 95.974  
| ||  
|-
|-
| [[29/14]] || 1260.751 || 95.470 ||
| [[29/14]] || 1260.751 || 95.470  
| ||  
|-
|-
| [[27/13]] || 1265.337 || 94.913 ||
| [[27/13]] || 1265.337 || 94.913  
| ||  
|-
|-
| [[25/12]] || 1270.672 || 94.335 ||
| [[25/12]] || 1270.672 || 94.335  
| ||  
|-
|-
| [[23/11]] || 1276.956 || 93.767 ||
| [[23/11]] || 1276.956 || 93.767  
| ||  
|-
|-
| [[21/10]] || 1284.467 || 93.226 ||
| [[21/10]] || 1284.467 || 93.226  
| ||  
|-
|-
| [[40/19]] || 1288.801 || 92.971 ||
| [[40/19]] || 1288.801 || 92.971  
| ||  
|-
|-
| [[19/9]] || 1293.603 || 92.713 ||
| [[19/9]] || 1293.603 || 92.713  
| ||  
|-
|-
| [[17/8]] || 1304.955 || 92.212 ||
| [[17/8]] || 1304.955 || 92.212  
| ||  
|-
|-
| [[32/15]] || 1311.731 || 91.962 ||
| [[32/15]] || 1311.731 || 91.962  
| ||  
|-
|-
| [[15/7]] || 1319.443 || 91.713 ||
| [[15/7]] || 1319.443 || 91.713  
| ||  
|-
|-
| [[43/20]] || 1325.204 || 91.549 ||
| [[43/20]] || 1325.204 || 91.549  
| ||  
|-
|-
| [[28/13]] || 1328.298 || 91.468 ||
| [[28/13]] || 1328.298 || 91.468  
| ||  
|-
|-
| [[54/25]] || 1333.238 || 91.338 ||
| [[54/25]] || 1333.238 || 91.338  
| ||  
|-
|-
| [[13/6]] || 1338.573 || 91.201 ||
| [[13/6]] || 1338.573 || 91.201  
| ||  
|-
|-
| [[24/11]] || 1350.637 || 90.891 ||
| [[24/11]] || 1350.637 || 90.891  
| ||  
|-
|-
| [[35/16]] || 1355.140 || 90.798 ||
| [[35/16]] || 1355.140 || 90.798  
| ||  
|-
|-
| [[68/31]] || 1359.920 || 90.737 ||
| [[68/31]] || 1359.920 || 90.737  
| ||  
|-
|-
| [[11/5]] || 1365.004 || 90.741 ||
| [[11/5]] || 1365.004 || 90.741  
| ||  
|-
|-
| [[31/14]] || 1376.210 || 90.799 ||
| [[31/14]] || 1376.210 || 90.799  
| ||  
|-
|-
| [[20/9]] || 1382.404 || 90.645 ||
| [[20/9]] || 1382.404 || 90.645  
| ||  
|-
|-
| [[29/13]] || 1389.050 || 90.242 ||
| [[29/13]] || 1389.050 || 90.242  
| ||  
|-
|-
| [[47/21]] || 1394.726 || 89.813 ||
| [[47/21]] || 1394.726 || 89.813  
| ||  
|-
|-
| [[9/4]] || 1403.910 || 89.442 ||
| [[9/4]] || 1403.910 || 89.442  
| ||  
|-
|-
| [[79/35]] || 1409.397 || 89.622 ||
| [[79/35]] || 1409.397 || 89.622  
| ||  
|-
|-
| [[43/19]] || 1414.005 || 89.985 ||
| [[43/19]] || 1414.005 || 89.985  
| ||  
|-
|-
| [[25/11]] || 1421.310 || 90.755 ||
| [[25/11]] || 1421.310 || 90.755  
| ||  
|-
|-
| [[41/18]] || 1425.152 || 91.119 ||
| [[41/18]] || 1425.152 || 91.119  
| ||  
|-
|-
| [[16/7]] || 1431.174 || 91.447 ||
| [[16/7]] || 1431.174 || 91.447  
| ||  
|-
|-
| [[23/10]] || 1441.961 || 90.803 ||
| [[23/10]] || 1441.961 || 90.803  
| ||  
|-
|-
| [[30/13]] || 1447.741 || 89.775 ||
| [[30/13]] || 1447.741 || 89.775  
| ||  
|-
|-
| [[37/16]] || 1451.344 || 88.987 ||
| [[37/16]] || 1451.344 || 88.987  
| ||  
|-
|-
| [[58/25]] || 1456.950 || 87.767 ||
| [[58/25]] || 1456.950 || 87.767  
| ||  
|-
|-
| [[121/52]] || 1462.108 || 86.960 ||
| [[121/52]] || 1462.108 || 86.960  
| ||  
|-
|-
| [[7/3]] || 1466.871 || 86.699 ||
| [[7/3]] || 1466.871 || 86.699  
| ||  
|-
|-
| [[61/26]] || 1476.357 || 87.725 ||
| [[61/26]] || 1476.357 || 87.725  
| ||  
|-
|-
| [[40/17]] || 1481.358 || 88.788 ||
| [[40/17]] || 1481.358 || 88.788  
| ||  
|-
|-
| [[33/14]] || 1484.447 || 89.469 ||
| [[33/14]] || 1484.447 || 89.469  
| ||  
|-
|-
| [[26/11]] || 1489.210 || 90.374 ||
| [[26/11]] || 1489.210 || 90.374  
| ||  
|-
|-
| [[19/8]] || 1497.513 || 91.263 ||
| [[19/8]] || 1497.513 || 91.263  
| ||  
|-
|-
| [[31/13]] || 1504.508 || 91.358 ||
| [[31/13]] || 1504.508 || 91.358  
| ||  
|-
|-
| [[67/28]] || 1510.481 || 91.232 ||
| [[67/28]] || 1510.481 || 91.232  
| ||  
|-
|-
| [[12/5]] || 1515.641 || 91.162 ||
| [[12/5]] || 1515.641 || 91.162  
| ||  
|-
|-
| [[29/12]] || 1527.622 || 91.519 ||
| [[29/12]] || 1527.622 || 91.519  
| ||  
|-
|-
| [[17/7]] || 1536.130 || 92.120 ||
| [[17/7]] || 1536.130 || 92.120  
| ||  
|-
|-
| [[39/16]] || 1542.483 || 92.492 ||
| [[39/16]] || 1542.483 || 92.492  
| ||  
|-
|-
| [[22/9]] || 1547.408 || 92.527 ||
| [[22/9]] || 1547.408 || 92.527  
| ||  
|-
|-
| [[27/11]] || 1554.547 || 91.809 ||
| [[27/11]] || 1554.547 || 91.809  
| ||  
|-
|-
| [[32/13]] || 1559.472 || 90.533 ||
| [[32/13]] || 1559.472 || 90.533  
| ||  
|-
|-
| [[37/15]] || 1563.075 || 89.159 ||
| [[37/15]] || 1563.075 || 89.159  
| ||  
|-
|-
| [[47/19]] || 1567.994 || 86.769 ||
| [[47/19]] || 1567.994 || 86.769  
| ||  
|-
|-
| [[62/25]] || 1572.408 || 84.387 ||
| [[62/25]] || 1572.408 || 84.387  
| ||  
|-
|-
| [[97/39]] || 1577.413 || 81.915 ||
| [[97/39]] || 1577.413 || 81.915  
| ||  
|-
|-
| [[5/2]] || 1586.314 || 79.831 ||
| [[5/2]] || 1586.314 || 79.831  
| ||  
|-
|-
| [[178/71]] || 1591.184 || 80.481 ||
| [[178/71]] || 1591.184 || 80.481  
| ||  
|-
|-
| [[93/37]] || 1595.647 || 82.086 ||
| [[93/37]] || 1595.647 || 82.086  
| ||  
|-
|-
| [[63/25]] || 1600.109 || 84.302 ||
| [[63/25]] || 1600.109 || 84.302  
| ||  
|-
|-
| [[43/17]] || 1606.562 || 87.719 ||
| [[43/17]] || 1606.562 || 87.719  
| ||  
|-
|-
| [[38/15]] || 1609.244 || 88.973 ||
| [[38/15]] || 1609.244 || 88.973  
| ||  
|-
|-
| [[28/11]] || 1617.508 || 91.634 ||
| [[28/11]] || 1617.508 || 91.634  
| ||  
|-
|-
| [[23/9]] || 1624.364 || 92.434 ||
| [[23/9]] || 1624.364 || 92.434  
| ||  
|-
|-
| [[18/7]] || 1635.084 || 92.172 ||
| [[18/7]] || 1635.084 || 92.172  
| ||  
|-
|-
| [[49/19]] || 1640.139 || 91.840 ||
| [[49/19]] || 1640.139 || 91.840  
| ||  
|-
|-
| [[31/12]] || 1643.081 || 91.658 ||
| [[31/12]] || 1643.081 || 91.658  
| ||  
|-
|-
| [[57/22]] || 1648.150 || 91.431 ||
| [[57/22]] || 1648.150 || 91.431  
| ||  
|-
|-
| [[13/5]] || 1654.214 || 91.300 ||
| [[13/5]] || 1654.214 || 91.300  
| ||  
|-
|-
| [[34/13]] || 1664.428 || 91.237 ||
| [[34/13]] || 1664.428 || 91.237  
| ||  
|-
|-
| [[21/8]] || 1670.781 || 90.960 ||
| [[21/8]] || 1670.781 || 90.960  
| ||  
|-
|-
| [[29/11]] || 1678.259 || 90.106 ||
| [[29/11]] || 1678.259 || 90.106  
| ||  
|-
|-
| [[37/14]] || 1682.518 || 89.391 ||
| [[37/14]] || 1682.518 || 89.391  
| ||  
|-
|-
| [[61/23]] || 1688.611 || 88.342 ||
| [[61/23]] || 1688.611 || 88.342  
| ||  
|-
|-
| [[117/44]] || 1693.120 || 87.764 ||
| [[117/44]] || 1693.120 || 87.764  
| ||  
|-
|-
| [[8/3]] || 1698.045 || 87.525 ||
| [[8/3]] || 1698.045 || 87.525  
| ||  
|-
|-
| [[67/25]] || 1706.680 || 88.237 ||
| [[67/25]] || 1706.680 || 88.237  
| ||  
|-
|-
| [[43/16]] || 1711.518 || 89.069 ||
| [[43/16]] || 1711.518 || 89.069  
| ||  
|-
|-
| [[27/10]] || 1719.551 || 90.435 ||
| [[27/10]] || 1719.551 || 90.435  
| ||  
|-
|-
| [[19/7]] || 1728.687 || 91.142 ||
| [[19/7]] || 1728.687 || 91.142  
| ||  
|-
|-
| [[49/18]] || 1733.742 || 91.064 ||
| [[49/18]] || 1733.742 || 91.064  
| ||  
|-
|-
| [[30/11]] || 1736.951 || 90.897 ||
| [[30/11]] || 1736.951 || 90.897  
| ||  
|-
|-
| [[41/15]] || 1740.794 || 90.654 ||
| [[41/15]] || 1740.794 || 90.654  
| ||  
|-
|-
| [[85/31]] || 1746.234 || 90.327 ||
| [[85/31]] || 1746.234 || 90.327  
| ||  
|-
|-
| [[11/4]] || 1751.318 || 90.168 ||
| [[11/4]] || 1751.318 || 90.168  
| ||  
|-
|-
| [[47/17]] || 1760.551 || 90.312 ||
| [[47/17]] || 1760.551 || 90.312  
| ||  
|-
|-
| [[25/9]] || 1768.717 || 90.677 ||
| [[25/9]] || 1768.717 || 90.677  
| ||  
|-
|-
| [[39/14]] || 1773.657 || 90.867 ||
| [[39/14]] || 1773.657 || 90.867  
| ||  
|-
|-
| [[67/24]] || 1777.352 || 90.985 ||
| [[67/24]] || 1777.352 || 90.985  
| ||  
|-
|-
| [[14/5]] || 1782.512 || 91.109 ||
| [[14/5]] || 1782.512 || 91.109  
| ||  
|-
|-
| [[31/11]] || 1793.718 || 91.367 ||
| [[31/11]] || 1793.718 || 91.367  
| ||  
|-
|-
| [[17/6]] || 1803.000 || 91.650 ||
| [[17/6]] || 1803.000 || 91.650  
| ||  
|-
|-
| [[37/13]] || 1810.816 || 91.957 ||
| [[37/13]] || 1810.816 || 91.957  
| ||  
|-
|-
| [[20/7]] || 1817.488 || 92.272 ||
| [[20/7]] || 1817.488 || 92.272  
| ||  
|-
|-
| [[43/15]] || 1823.249 || 92.602 ||
| [[43/15]] || 1823.249 || 92.602  
| ||  
|-
|-
| [[23/8]] || 1828.274 || 92.938 ||
| [[23/8]] || 1828.274 || 92.938  
| ||  
|-
|-
| [[26/9]] || 1836.618 || 93.633 ||
| [[26/9]] || 1836.618 || 93.633  
| ||  
|-
|-
| [[29/10]] || 1843.264 || 94.306 ||
| [[29/10]] || 1843.264 || 94.306  
| ||  
|-
|-
| [[32/11]] || 1848.682 || 94.862 ||
| [[32/11]] || 1848.682 || 94.862  
| ||  
|-
|-
| [[35/12]] || 1853.185 || 95.221 ||
| [[35/12]] || 1853.185 || 95.221  
| ||  
|-
|-
| [[38/13]] || 1856.985 || 95.305 ||
| [[38/13]] || 1856.985 || 95.305  
| ||  
|-
|-
| [[41/14]] || 1860.237 || 95.088 ||
| [[41/14]] || 1860.237 || 95.088  
| ||  
|-
|-
| [[47/16]] || 1865.507 || 93.821 ||
| [[47/16]] || 1865.507 || 93.821  
| ||  
|-
|-
| [[53/18]] || 1869.595 || 91.704 ||
| [[53/18]] || 1869.595 || 91.704  
| ||  
|-
|-
| [[65/22]] || 1875.523 || 86.386 ||
| [[65/22]] || 1875.523 || 86.386  
| ||  
|-
|-
| [[77/26]] || 1879.616 || 81.103 ||
| [[77/26]] || 1879.616 || 81.103  
| ||  
|-
|-
| [[98/33]] || 1884.379 || 73.722 ||
| [[98/33]] || 1884.379 || 73.722  
| ||  
|-
|-
| [[131/44]] || 1888.790 || 66.544 ||
| [[131/44]] || 1888.790 || 66.544  
| ||  
|-
|-
| [[200/67]] || 1893.320 || 60.026 ||
| [[200/67]] || 1893.320 || 60.026  
| ||  
|-
|-
| [[3/1]] || 1901.955 || 54.245 ||
| [[3/1]] || 1901.955 || 54.245  
| ||  
|}
|}


Line 677: Line 1,003:
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ Harmonic entropy of just intervals
! Ratio !! Size (cents) !! Harmonic entropy (%) !! Comments
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[3/1]] || 1901.955 || 54.245 ||
| [[3/1]] || 1901.955 || 54.245  
| ||  
|-
|-
| [[367/122]] || 1906.679 || 56.071 ||
| [[367/122]] || 1906.679 || 56.071  
| ||  
|-
|-
| [[187/62]] || 1911.238 || 60.881 ||
| [[187/62]] || 1911.238 || 60.881  
| ||  
|-
|-
| [[127/42]] || 1915.641 || 67.404 ||
| [[127/42]] || 1915.641 || 67.404  
| ||  
|-
|-
| [[94/31]] || 1920.471 || 75.286 ||
| [[94/31]] || 1920.471 || 75.286  
| ||  
|-
|-
| [[76/25]] || 1924.886 || 81.991 ||
| [[76/25]] || 1924.886 || 81.991  
| ||  
|-
|-
| [[64/21]] || 1929.219 || 87.364 ||
| [[64/21]] || 1929.219 || 87.364  
| ||  
|-
|-
| [[55/18]] || 1933.722 || 91.364 ||
| [[55/18]] || 1933.722 || 91.364  
| ||  
|-
|-
| [[46/15]] || 1940.006 || 94.439 ||
| [[46/15]] || 1940.006 || 94.439  
| ||  
|-
|-
| [[43/14]] || 1942.692 || 95.041 ||
| [[43/14]] || 1942.692 || 95.041  
| ||  
|-
|-
| [[37/12]] || 1949.389 || 95.375 ||
| [[37/12]] || 1949.389 || 95.375  
| ||  
|-
|-
| [[34/11]] || 1953.638 || 95.100 ||
| [[34/11]] || 1953.638 || 95.100  
| ||  
|-
|-
| [[31/10]] || 1958.722 || 94.593 ||
| [[31/10]] || 1958.722 || 94.593  
| ||  
|-
|-
| [[28/9]] || 1964.916 || 93.929 ||
| [[28/9]] || 1964.916 || 93.929  
| ||  
|-
|-
| [[25/8]] || 1972.627 || 93.206 ||
| [[25/8]] || 1972.627 || 93.206  
| ||  
|-
|-
| [[47/15]] || 1977.238 || 92.840 ||
| [[47/15]] || 1977.238 || 92.840  
| ||  
|-
|-
| [[22/7]] || 1982.492 || 92.487 ||
| [[22/7]] || 1982.492 || 92.487  
| ||  
|-
|-
| [[60/19]] || 1990.756 || 92.024 ||
| [[60/19]] || 1990.756 || 92.024  
| ||  
|-
|-
| [[19/6]] || 1995.558 || 91.813 ||
| [[19/6]] || 1995.558 || 91.813  
| ||  
|-
|-
| [[54/17]] || 2000.910 || 91.606 ||
| [[54/17]] || 2000.910 || 91.606  
| ||  
|-
|-
| [[35/11]] || 2003.822 || 91.516 ||
| [[35/11]] || 2003.822 || 91.516  
| ||  
|-
|-
| [[67/21]] || 2008.526 || 91.378 ||
| [[67/21]] || 2008.526 || 91.378  
| ||  
|-
|-
| [[16/5]] || 2013.686 || 91.231 ||
| [[16/5]] || 2013.686 || 91.231  
| ||  
|-
|-
| [[29/9]] || 2025.667 || 90.874 ||
| [[29/9]] || 2025.667 || 90.874  
| ||  
|-
|-
| [[42/13]] || 2030.253 || 90.752 ||
| [[42/13]] || 2030.253 || 90.752  
| ||  
|-
|-
| [[81/25]] || 2035.193 || 90.679 ||
| [[81/25]] || 2035.193 || 90.679  
| ||  
|-
|-
| [[13/4]] || 2040.528 || 90.693 ||
| [[13/4]] || 2040.528 || 90.693  
| ||  
|-
|-
| [[49/15]] || 2049.383 || 90.886 ||
| [[49/15]] || 2049.383 || 90.886  
| ||  
|-
|-
| [[36/11]] || 2052.592 || 90.938 ||
| [[36/11]] || 2052.592 || 90.938  
| ||  
|-
|-
| [[23/7]] || 2059.448 || 90.832 ||
| [[23/7]] || 2059.448 || 90.832  
| ||  
|-
|-
| [[33/10]] || 2066.959 || 90.254 ||
| [[33/10]] || 2066.959 || 90.254  
| ||  
|-
|-
| [[43/13]] || 2070.990 || 89.797 ||
| [[43/13]] || 2070.990 || 89.797  
| ||  
|-
|-
| [[63/19]] || 2075.223 || 89.312 ||
| [[63/19]] || 2075.223 || 89.312  
| ||  
|-
|-
| [[10/3]] || 2084.359 || 88.773 ||
| [[10/3]] || 2084.359 || 88.773  
| ||  
|-
|-
| [[127/38]] || 2088.909 || 88.907 ||
| [[127/38]] || 2088.909 || 88.907  
| ||  
|-
|-
| [[57/17]] || 2094.513 || 89.429 ||
| [[57/17]] || 2094.513 || 89.429  
| ||  
|-
|-
| [[37/11]] || 2100.026 || 90.130 ||
| [[37/11]] || 2100.026 || 90.130  
| ||  
|-
|-
| [[27/8]] || 2105.865 || 90.864 ||
| [[27/8]] || 2105.865 || 90.864  
| ||  
|-
|-
| [[44/13]] || 2110.790 || 91.364 ||
| [[44/13]] || 2110.790 || 91.364  
| ||  
|-
|-
| [[17/5]] || 2118.642 || 91.902 ||
| [[17/5]] || 2118.642 || 91.902  
| ||  
|-
|-
| [[58/17]] || 2124.622 || 92.131 ||
| [[58/17]] || 2124.622 || 92.131  
| ||  
|-
|-
| [[24/7]] || 2133.129 || 92.030 ||
| [[24/7]] || 2133.129 || 92.030  
| ||  
|-
|-
| [[31/9]] || 2141.126 || 91.024 ||
| [[31/9]] || 2141.126 || 91.024  
| ||  
|-
|-
| [[38/11]] || 2146.195 || 89.734 ||
| [[38/11]] || 2146.195 || 89.734  
| ||  
|-
|-
| [[45/13]] || 2149.696 || 88.572 ||
| [[45/13]] || 2149.696 || 88.572  
| ||  
|-
|-
| [[59/17]] || 2154.216 || 86.904 ||
| [[59/17]] || 2154.216 || 86.904  
| ||  
|-
|-
| [[94/27]] || 2159.642 || 85.001 ||
| [[94/27]] || 2159.642 || 85.001  
| ||  
|-
|-
| [[7/2]] || 2168.826 || 83.459 ||
| [[7/2]] || 2168.826 || 83.459  
| ||  
|-
|-
| [[186/53]] || 2173.486 || 83.881 ||
| [[186/53]] || 2173.486 || 83.881  
| ||  
|-
|-
| [[95/27]] || 2177.962 || 84.993 ||
| [[95/27]] || 2177.962 || 84.993  
| ||  
|-
|-
| [[60/17]] || 2183.313 || 86.860 ||
| [[60/17]] || 2183.313 || 86.860  
| ||  
|-
|-
| [[46/13]] || 2187.747 || 88.508 ||
| [[46/13]] || 2187.747 || 88.508  
| ||  
|-
|-
| [[39/11]] || 2191.165 || 89.654 ||
| [[39/11]] || 2191.165 || 89.654  
| ||  
|-
|-
| [[32/9]] || 2196.090 || 90.939 ||
| [[32/9]] || 2196.090 || 90.939  
| ||  
|-
|-
| [[25/7]] || 2203.802 || 91.985 ||
| [[25/7]] || 2203.802 || 91.985  
| ||  
|-
|-
| [[43/12]] || 2209.563 || 92.143 ||
| [[43/12]] || 2209.563 || 92.143  
| ||  
|-
|-
| [[18/5]] || 2217.596 || 91.868 ||
| [[18/5]] || 2217.596 || 91.868  
| ||  
|-
|-
| [[65/18]] || 2222.931 || 91.484 ||
| [[65/18]] || 2222.931 || 91.484  
| ||  
|-
|-
| [[29/8]] || 2229.577 || 90.831 ||
| [[29/8]] || 2229.577 || 90.831  
| ||  
|-
|-
| [[40/11]] || 2234.996 || 90.215 ||
| [[40/11]] || 2234.996 || 90.215  
| ||  
|-
|-
| [[51/14]] || 2238.085 || 89.874 ||
| [[51/14]] || 2238.085 || 89.874  
| ||  
|-
|-
| [[117/32]] || 2244.438 || 89.346 ||
| [[117/32]] || 2244.438 || 89.346  
| ||  
|-
|-
| [[11/3]] || 2249.363 || 89.211 ||
| [[11/3]] || 2249.363 || 89.211  
| ||  
|-
|-
| [[59/16]] || 2259.172 || 89.729 ||
| [[59/16]] || 2259.172 || 89.729  
| ||  
|-
|-
| [[37/10]] || 2265.030 || 90.282 ||
| [[37/10]] || 2265.030 || 90.282  
| ||  
|-
|-
| [[26/7]] || 2271.702 || 90.802 ||
| [[26/7]] || 2271.702 || 90.802  
| ||  
|-
|-
| [[41/11]] || 2277.745 || 91.024 ||
| [[41/11]] || 2277.745 || 91.024  
| ||  
|-
|-
| [[15/4]] || 2288.269 || 91.072 ||
| [[15/4]] || 2288.269 || 91.072  
| ||  
|-
|-
| [[79/21]] || 2293.756 || 91.101 ||
| [[79/21]] || 2293.756 || 91.101  
| ||  
|-
|-
| [[34/9]] || 2301.045 || 91.261 ||
| [[34/9]] || 2301.045 || 91.261  
| ||  
|-
|-
| [[72/19]] || 2306.397 || 91.442 ||
| [[72/19]] || 2306.397 || 91.442  
| ||  
|-
|-
| [[19/5]] || 2311.199 || 91.637 ||
| [[19/5]] || 2311.199 || 91.637  
| ||  
|-
|-
| [[42/11]] || 2319.463 || 92.015 ||
| [[42/11]] || 2319.463 || 92.015  
| ||  
|-
|-
| [[23/6]] || 2326.319 || 92.389 ||
| [[23/6]] || 2326.319 || 92.389  
| ||  
|-
|-
| [[27/7]] || 2337.039 || 93.165 ||
| [[27/7]] || 2337.039 || 93.165  
| ||  
|-
|-
| [[31/8]] || 2345.036 || 93.896 ||
| [[31/8]] || 2345.036 || 93.896  
| ||  
|-
|-
| [[35/9]] || 2351.230 || 94.391 ||
| [[35/9]] || 2351.230 || 94.391  
| ||  
|-
|-
| [[39/10]] || 2356.169 || 94.508 ||
| [[39/10]] || 2356.169 || 94.508  
| ||  
|-
|-
| [[47/12]] || 2363.552 || 93.521 ||
| [[47/12]] || 2363.552 || 93.521  
| ||  
|-
|-
| [[55/14]] || 2368.806 || 91.325 ||
| [[55/14]] || 2368.806 || 91.325  
| ||  
|-
|-
| [[63/16]] || 2372.736 || 88.598 ||
| [[63/16]] || 2372.736 || 88.598  
| ||  
|-
|-
| [[75/19]] || 2377.069 || 84.455 ||
| [[75/19]] || 2377.069 || 84.455  
| ||  
|-
|-
| [[95/24]] || 2381.872 || 78.764 ||
| [[95/24]] || 2381.872 || 78.764  
| ||  
|-
|-
| [[127/32]] || 2386.422 || 72.968 ||
| [[127/32]] || 2386.422 || 72.968  
| ||  
|-
|-
| [[191/48]] || 2390.960 || 67.739 ||
| [[191/48]] || 2390.960 || 67.739  
| ||  
|-
|-
| [[387/97]] || 2395.532 || 64.080 ||
| [[387/97]] || 2395.532 || 64.080  
| ||  
|-
|-
| [[4/1]] || 2400.000 || 62.798 ||
| [[4/1]] || 2400.000 || 62.798  
| ||  
|}
|}


Line 857: Line 1,271:
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ Harmonic entropy of just intervals
! Ratio !! Size (cents) !! Harmonic entropy (%) !! Comments
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[4/1]] || 2400.000 || 62.798 ||
| [[4/1]] || 2400.000 || 62.798  
| ||  
|-
|-
| [[389/97]] || 2404.456 || 64.076 ||
| [[389/97]] || 2404.456 || 64.076  
| ||  
|-
|-
| [[193/48]] || 2408.993 || 67.714 ||
| [[193/48]] || 2408.993 || 67.714  
| ||  
|-
|-
| [[129/32]] || 2413.473 || 72.852 ||
| [[129/32]] || 2413.473 || 72.852  
| ||  
|-
|-
| [[97/24]] || 2417.940 || 78.558 ||
| [[97/24]] || 2417.940 || 78.558  
| ||  
|-
|-
| [[77/19]] || 2422.631 || 84.164 ||
| [[77/19]] || 2422.631 || 84.164  
| ||  
|-
|-
| [[65/16]] || 2426.841 || 88.282 ||
| [[65/16]] || 2426.841 || 88.282  
| ||  
|-
|-
| [[53/13]] || 2432.977 || 92.286 ||
| [[53/13]] || 2432.977 || 92.286  
| ||  
|-
|-
| [[49/12]] || 2435.697 || 93.337 ||
| [[49/12]] || 2435.697 || 93.337  
| ||  
|-
|-
| [[41/10]] || 2442.749 || 94.509 ||
| [[41/10]] || 2442.749 || 94.509  
| ||  
|-
|-
| [[37/9]] || 2447.434 || 94.478 ||
| [[37/9]] || 2447.434 || 94.478  
| ||  
|-
|-
| [[33/8]] || 2453.273 || 94.049 ||
| [[33/8]] || 2453.273 || 94.049  
| ||  
|-
|-
| [[29/7]] || 2460.751 || 93.336 ||
| [[29/7]] || 2460.751 || 93.336  
| ||  
|-
|-
| [[25/6]] || 2470.672 || 92.507 ||
| [[25/6]] || 2470.672 || 92.507  
| ||  
|-
|-
| [[46/11]] || 2476.956 || 92.096 ||
| [[46/11]] || 2476.956 || 92.096  
| ||  
|-
|-
| [[67/16]] || 2479.307 || 91.958 ||
| [[67/16]] || 2479.307 || 91.958  
| ||  
|-
|-
| [[21/5]] || 2484.467 || 91.696 ||
| [[21/5]] || 2484.467 || 91.696  
| ||  
|-
|-
| [[59/14]] || 2490.346 || 91.443 ||
| [[59/14]] || 2490.346 || 91.443  
| ||  
|-
|-
| [[38/9]] || 2493.603 || 91.333 ||
| [[38/9]] || 2493.603 || 91.333  
| ||  
|-
|-
| [[55/13]] || 2497.104 || 91.229 ||
| [[55/13]] || 2497.104 || 91.229  
| ||  
|-
|-
| [[17/4]] || 2504.955 || 91.063 ||
| [[17/4]] || 2504.955 || 91.063  
| ||  
|-
|-
| [[64/15]] || 2511.731 || 90.911 ||
| [[64/15]] || 2511.731 || 90.911  
| ||  
|-
|-
| [[30/7]] || 2519.443 || 90.589 ||
| [[30/7]] || 2519.443 || 90.589  
| ||  
|-
|-
| [[43/10]] || 2525.204 || 90.237 ||
| [[43/10]] || 2525.204 || 90.237  
| ||  
|-
|-
| [[56/13]] || 2528.298 || 90.045 ||
| [[56/13]] || 2528.298 || 90.045  
| ||  
|-
|-
| [[108/25]] || 2533.238 || 89.798 ||
| [[108/25]] || 2533.238 || 89.798  
| ||  
|-
|-
| [[13/3]] || 2538.573 || 89.729 ||
| [[13/3]] || 2538.573 || 89.729  
| ||  
|-
|-
| [[61/14]] || 2548.059 || 90.228 ||
| [[61/14]] || 2548.059 || 90.228  
| ||  
|-
|-
| [[35/8]] || 2555.140 || 90.942 ||
| [[35/8]] || 2555.140 || 90.942  
| ||  
|-
|-
| [[57/13]] || 2558.940 || 91.316 ||
| [[57/13]] || 2558.940 || 91.316  
| ||  
|-
|-
| [[22/5]] || 2565.004 || 91.732 ||
| [[22/5]] || 2565.004 || 91.732  
| ||  
|-
|-
| [[31/7]] || 2576.210 || 91.266 ||
| [[31/7]] || 2576.210 || 91.266  
| ||  
|-
|-
| [[40/9]] || 2582.404 || 90.118 ||
| [[40/9]] || 2582.404 || 90.118  
| ||  
|-
|-
| [[49/11]] || 2586.334 || 89.120 ||
| [[49/11]] || 2586.334 || 89.120  
| ||  
|-
|-
| [[67/15]] || 2591.038 || 87.824 ||
| [[67/15]] || 2591.038 || 87.824  
| ||  
|-
|-
| [[103/23]] || 2595.526 || 86.696 ||
| [[103/23]] || 2595.526 || 86.696  
| ||  
|-
|-
| [[9/2]] || 2603.910 || 85.700 ||
| [[9/2]] || 2603.910 || 85.700  
| ||  
|-
|-
| [[167/37]] || 2609.101 || 86.069 ||
| [[167/37]] || 2609.101 || 86.069  
| ||  
|-
|-
| [[86/19]] || 2614.005 || 87.026 ||
| [[86/19]] || 2614.005 || 87.026  
| ||  
|-
|-
| [[59/13]] || 2618.644 || 88.237 ||
| [[59/13]] || 2618.644 || 88.237  
| ||  
|-
|-
| [[41/9]] || 2625.152 || 89.931 ||
| [[41/9]] || 2625.152 || 89.931  
| ||  
|-
|-
| [[32/7]] || 2631.174 || 91.047 ||
| [[32/7]] || 2631.174 || 91.047  
| ||  
|-
|-
| [[23/5]] || 2641.961 || 91.557 ||
| [[23/5]] || 2641.961 || 91.557  
| ||  
|-
|-
| [[37/8]] || 2651.344 || 90.918 ||
| [[37/8]] || 2651.344 || 90.918  
| ||  
|-
|-
| [[51/11]] || 2655.593 || 90.538 ||
| [[51/11]] || 2655.593 || 90.538  
| ||  
|-
|-
| [[121/26]] || 2662.108 || 90.078 ||
| [[121/26]] || 2662.108 || 90.078  
| ||  
|-
|-
| [[14/3]] || 2666.871 || 89.943 ||
| [[14/3]] || 2666.871 || 89.943  
| ||  
|-
|-
| [[61/13]] || 2676.357 || 90.178 ||
| [[61/13]] || 2676.357 || 90.178  
| ||  
|-
|-
| [[47/10]] || 2679.193 || 90.338 ||
| [[47/10]] || 2679.193 || 90.338  
| ||  
|-
|-
| [[33/7]] || 2684.447 || 90.654 ||
| [[33/7]] || 2684.447 || 90.654  
| ||  
|-
|-
| [[52/11]] || 2689.210 || 90.913 ||
| [[52/11]] || 2689.210 || 90.913  
| ||  
|-
|-
| [[19/4]] || 2697.513 || 91.250 ||
| [[19/4]] || 2697.513 || 91.250  
| ||  
|-
|-
| [[81/17]] || 2702.865 || 91.441 ||
| [[81/17]] || 2702.865 || 91.441  
| ||  
|-
|-
| [[43/9]] || 2707.608 || 91.620 ||
| [[43/9]] || 2707.608 || 91.620  
| ||  
|-
|-
| [[67/14]] || 2710.481 || 91.756 ||
| [[67/14]] || 2710.481 || 91.756  
| ||  
|-
|-
| [[24/5]] || 2715.641 || 92.033 ||
| [[24/5]] || 2715.641 || 92.033  
| ||  
|-
|-
| [[29/6]] || 2727.622 || 92.932 ||
| [[29/6]] || 2727.622 || 92.932  
| ||  
|-
|-
| [[34/7]] || 2736.130 || 93.640 ||
| [[34/7]] || 2736.130 || 93.640  
| ||  
|-
|-
| [[39/8]] || 2742.483 || 93.885 ||
| [[39/8]] || 2742.483 || 93.885  
| ||  
|-
|-
| [[44/9]] || 2747.408 || 93.589 ||
| [[44/9]] || 2747.408 || 93.589  
| ||  
|-
|-
| [[54/11]] || 2754.547 || 91.677 ||
| [[54/11]] || 2754.547 || 91.677  
| ||  
|-
|-
| [[64/13]] || 2759.472 || 88.918 ||
| [[64/13]] || 2759.472 || 88.918  
| ||  
|-
|-
| [[74/15]] || 2763.075 || 86.111 ||
| [[74/15]] || 2763.075 || 86.111  
| ||  
|-
|-
| [[94/19]] || 2767.994 || 81.362 ||
| [[94/19]] || 2767.994 || 81.362  
| ||  
|-
|-
| [[129/26]] || 2772.945 || 76.173 ||
| [[129/26]] || 2772.945 || 76.173  
| ||  
|-
|-
| [[199/40]] || 2777.636 || 71.787 ||
| [[199/40]] || 2777.636 || 71.787  
| ||  
|-
|-
| [[5/1]] || 2786.314 || 68.009 ||
| [[5/1]] || 2786.314 || 68.009  
| ||  
|-
|-
| [[361/72]] || 2791.116 || 69.236 ||
| [[361/72]] || 2791.116 || 69.236  
| ||  
|-
|-
| [[186/37]] || 2795.647 || 72.363 ||
| [[186/37]] || 2795.647 || 72.363  
| ||  
|-
|-
| [[126/25]] || 2800.109 || 76.655 ||
| [[126/25]] || 2800.109 || 76.655  
| ||  
|-
|-
| [[91/18]] || 2805.444 || 82.237 ||
| [[91/18]] || 2805.444 || 82.237  
| ||  
|-
|-
| [[76/15]] || 2809.244 || 85.883 ||
| [[76/15]] || 2809.244 || 85.883  
| ||  
|-
|-
| [[61/12]] || 2814.930 || 90.123 ||
| [[61/12]] || 2814.930 || 90.123  
| ||  
|-
|-
| [[51/10]] || 2820.597 || 92.661 ||
| [[51/10]] || 2820.597 || 92.661  
| ||  
|-
|-
| [[46/9]] || 2824.364 || 93.525 ||
| [[46/9]] || 2824.364 || 93.525  
| ||  
|-
|-
| [[41/8]] || 2829.062 || 93.937 ||
| [[41/8]] || 2829.062 || 93.937  
| ||  
|-
|-
| [[36/7]] || 2835.084 || 93.804 ||
| [[36/7]] || 2835.084 || 93.804  
| ||  
|-
|-
| [[31/6]] || 2843.081 || 93.178 ||
| [[31/6]] || 2843.081 || 93.178  
| ||  
|-
|-
| [[57/11]] || 2848.150 || 92.750 ||
| [[57/11]] || 2848.150 || 92.750  
| ||  
|-
|-
| [[26/5]] || 2854.214 || 92.307 ||
| [[26/5]] || 2854.214 || 92.307  
| ||  
|-
|-
| [[47/9]] || 2861.597 || 91.870 ||
| [[47/9]] || 2861.597 || 91.870  
| ||  
|-
|-
| [[21/4]] || 2870.781 || 91.425 ||
| [[21/4]] || 2870.781 || 91.425  
| ||  
|-
|-
| [[79/15]] || 2876.268 || 91.152 ||
| [[79/15]] || 2876.268 || 91.152  
| ||  
|-
|-
| [[37/7]] || 2882.518 || 90.820 ||
| [[37/7]] || 2882.518 || 90.820  
| ||  
|-
|-
| [[53/10]] || 2887.191 || 90.579 ||
| [[53/10]] || 2887.191 || 90.579  
| ||  
|-
|-
| [[117/22]] || 2893.120 || 90.378 ||
| [[117/22]] || 2893.120 || 90.378  
| ||  
|-
|-
| [[16/3]] || 2898.045 || 90.360 ||
| [[16/3]] || 2898.045 || 90.360  
| ||  
|-
|-
| [[59/11]] || 2907.854 || 90.739 ||
| [[59/11]] || 2907.854 || 90.739  
| ||  
|-
|-
| [[43/8]] || 2911.518 || 90.933 ||
| [[43/8]] || 2911.518 || 90.933  
| ||  
|-
|-
| [[27/5]] || 2919.551 || 91.115 ||
| [[27/5]] || 2919.551 || 91.115  
| ||  
|-
|-
| [[65/12]] || 2924.886 || 90.826 ||
| [[65/12]] || 2924.886 || 90.826  
| ||  
|-
|-
| [[38/7]] || 2928.687 || 90.366 ||
| [[38/7]] || 2928.687 || 90.366  
| ||  
|-
|-
| [[49/9]] || 2933.742 || 89.479 ||
| [[49/9]] || 2933.742 || 89.479  
| ||  
|-
|-
| [[60/11]] || 2936.951 || 88.814 ||
| [[60/11]] || 2936.951 || 88.814  
| ||  
|-
|-
| [[93/17]] || 2942.035 || 87.822 ||
| [[93/17]] || 2942.035 || 87.822  
| ||  
|-
|-
| [[181/33]] || 2946.542 || 87.184 ||
| [[181/33]] || 2946.542 || 87.184  
| ||  
|-
|-
| [[11/2]] || 2951.318 || 86.954 ||
| [[11/2]] || 2951.318 || 86.954  
| ||  
|-
|-
| [[94/17]] || 2960.551 || 87.918 ||
| [[94/17]] || 2960.551 || 87.918  
| ||  
|-
|-
| [[61/11]] || 2965.567 || 88.943 ||
| [[61/11]] || 2965.567 || 88.943  
| ||  
|-
|-
| [[50/9]] || 2968.717 || 89.611 ||
| [[50/9]] || 2968.717 || 89.611  
| ||  
|-
|-
| [[39/7]] || 2973.657 || 90.516 ||
| [[39/7]] || 2973.657 || 90.516  
| ||  
|-
|-
| [[67/12]] || 2977.352 || 91.004 ||
| [[67/12]] || 2977.352 || 91.004  
| ||  
|-
|-
| [[28/5]] || 2982.512 || 91.342 ||
| [[28/5]] || 2982.512 || 91.342  
| ||  
|-
|-
| [[45/8]] || 2990.224 || 91.271 ||
| [[45/8]] || 2990.224 || 91.271  
| ||  
|-
|-
| [[62/11]] || 2993.718 || 91.121 ||
| [[62/11]] || 2993.718 || 91.121  
| ||  
|-
|-
| [[17/3]] || 3003.000 || 90.796 ||
| [[17/3]] || 3003.000 || 90.796  
| ||  
|-
|-
| [[91/16]] || 3009.354 || 90.823 ||
| [[91/16]] || 3009.354 || 90.823  
| ||  
|-
|-
| [[40/7]] || 3017.488 || 91.140 ||
| [[40/7]] || 3017.488 || 91.140  
| ||  
|-
|-
| [[63/11]] || 3021.418 || 91.351 ||
| [[63/11]] || 3021.418 || 91.351  
| ||  
|-
|-
| [[23/4]] || 3028.274 || 91.759 ||
| [[23/4]] || 3028.274 || 91.759  
| ||  
|-
|-
| [[52/9]] || 3036.618 || 92.295 ||
| [[52/9]] || 3036.618 || 92.295  
| ||  
|-
|-
| [[29/5]] || 3043.264 || 92.782 ||
| [[29/5]] || 3043.264 || 92.782  
| ||  
|-
|-
| [[35/6]] || 3053.185 || 93.524 ||
| [[35/6]] || 3053.185 || 93.524  
| ||  
|-
|-
| [[41/7]] || 3060.237 || 93.677 ||
| [[41/7]] || 3060.237 || 93.677  
| ||  
|-
|-
| [[47/8]] || 3065.507 || 93.159 ||
| [[47/8]] || 3065.507 || 93.159  
| ||  
|-
|-
| [[53/9]] || 3069.595 || 92.138 ||
| [[53/9]] || 3069.595 || 92.138  
| ||  
|-
|-
| [[65/11]] || 3075.523 || 89.379 ||
| [[65/11]] || 3075.523 || 89.379  
| ||  
|-
|-
| [[77/13]] || 3079.616 || 86.553 ||
| [[77/13]] || 3079.616 || 86.553  
| ||  
|-
|-
| [[95/16]] || 3083.827 || 83.035 ||
| [[95/16]] || 3083.827 || 83.035  
| ||  
|-
|-
| [[131/22]] || 3088.790 || 78.596 ||
| [[131/22]] || 3088.790 || 78.596  
| ||  
|-
|-
| [[197/33]] || 3093.189 || 75.071 ||
| [[197/33]] || 3093.189 || 75.071  
| ||  
|-
|-
| [[6/1]] || 3101.955 || 71.731 ||
| [[6/1]] || 3101.955 || 71.731  
| ||  
|}
|}


Line 1,107: Line 1,644:
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals
|+ Harmonic entropy of just intervals
! Ratio !! Size (cents) !! Harmonic entropy (%) !! Comments
! Ratio !! Size (cents) !! Entropy <br>(%, Rényi order 1.0)
!Entropy <br>(%, Rényi order 7.0) !! Comments
|-
|-
| [[6/1]] || 3101.955 || 71.731 ||
| [[6/1]] || 3101.955 || 71.731  
| ||
|-
|-
| [[367/61]] || 3106.679 || 72.714 ||
| [[367/61]] || 3106.679 || 72.714  
| ||  
|-
|-
| [[187/31]] || 3111.238 || 75.340 ||
| [[187/31]] || 3111.238 || 75.340  
| ||  
|-
|-
| [[127/21]] || 3115.641 || 78.905 ||
| [[127/21]] || 3115.641 || 78.905  
| ||  
|-
|-
| [[91/15]] || 3121.085 || 83.711 ||
| [[91/15]] || 3121.085 || 83.711  
| ||  
|-
|-
| [[73/12]] || 3125.835 || 87.463 ||
| [[73/12]] || 3125.835 || 87.463  
| ||  
|-
|-
| [[61/10]] || 3130.571 || 90.313 ||
| [[61/10]] || 3130.571 || 90.313  
| ||  
|-
|-
| [[55/9]] || 3133.722 || 91.647 ||
| [[55/9]] || 3133.722 || 91.647  
| ||  
|-
|-
| [[49/8]] || 3137.652 || 92.720 ||
| [[49/8]] || 3137.652 || 92.720  
| ||  
|-
|-
| [[43/7]] || 3142.692 || 93.315 ||
| [[43/7]] || 3142.692 || 93.315  
| ||  
|-
|-
| [[37/6]] || 3149.389 || 93.281 ||
| [[37/6]] || 3149.389 || 93.281  
| ||  
|-
|-
| [[31/5]] || 3158.722 || 92.634 ||
| [[31/5]] || 3158.722 || 92.634  
| ||  
|-
|-
| [[56/9]] || 3164.916 || 92.175 ||
| [[56/9]] || 3164.916 || 92.175  
| ||  
|-
|-
| [[25/4]] || 3172.627 || 91.679 ||
| [[25/4]] || 3172.627 || 91.679  
| ||  
|-
|-
| [[69/11]] || 3178.911 || 91.336 ||
| [[69/11]] || 3178.911 || 91.336  
| ||  
|-
|-
| [[44/7]] || 3182.492 || 91.164 ||
| [[44/7]] || 3182.492 || 91.164  
| ||  
|-
|-
| [[63/10]] || 3186.422 || 91.034 ||
| [[63/10]] || 3186.422 || 91.034  
| ||  
|-
|-
| [[120/19]] || 3190.756 || 90.949 ||
| [[120/19]] || 3190.756 || 90.949  
| ||  
|-
|-
| [[19/3]] || 3195.558 || 90.954 ||
| [[19/3]] || 3195.558 || 90.954  
| ||  
|-
|-
| [[127/20]] || 3200.108 || 91.016 ||
| [[127/20]] || 3200.108 || 91.016  
| ||  
|-
|-
| [[51/8]] || 3206.910 || 91.113 ||
| [[51/8]] || 3206.910 || 91.113  
| ||  
|-
|-
| [[32/5]] || 3213.686 || 90.949 ||
| [[32/5]] || 3213.686 || 90.949  
| ||  
|-
|-
| [[45/7]] || 3221.398 || 90.200 ||
| [[45/7]] || 3221.398 || 90.200  
| ||  
|-
|-
| [[58/9]] || 3225.667 || 89.582 ||
| [[58/9]] || 3225.667 || 89.582  
| ||  
|-
|-
| [[84/13]] || 3230.253 || 88.880 ||
| [[84/13]] || 3230.253 || 88.880  
| ||  
|-
|-
| [[162/25]] || 3235.193 || 88.287 ||
| [[162/25]] || 3235.193 || 88.287  
| ||  
|-
|-
| [[13/2]] || 3240.528 || 88.036 ||
| [[13/2]] || 3240.528 || 88.036  
| ||  
|-
|-
| [[98/15]] || 3249.383 || 88.679 ||
| [[98/15]] || 3249.383 || 88.679  
| ||  
|-
|-
| [[59/9]] || 3255.262 || 89.542 ||
| [[59/9]] || 3255.262 || 89.542  
| ||  
|-
|-
| [[46/7]] || 3259.448 || 90.160 ||
| [[46/7]] || 3259.448 || 90.160  
| ||  
|-
|-
| [[33/5]] || 3266.959 || 90.915 ||
| [[33/5]] || 3266.959 || 90.915  
| ||  
|-
|-
| [[53/8]] || 3273.505 || 91.119 ||
| [[53/8]] || 3273.505 || 91.119  
| ||  
|-
|-
| [[20/3]] || 3284.359 || 91.038 ||
| [[20/3]] || 3284.359 || 91.038  
| ||  
|-
|-
| [[127/19]] || 3288.909 || 91.050 ||
| [[127/19]] || 3288.909 || 91.050  
| ||  
|-
|-
| [[47/7]] || 3296.681 || 91.284 ||
| [[47/7]] || 3296.681 || 91.284  
| ||  
|-
|-
| [[27/4]] || 3305.865 || 91.845 ||
| [[27/4]] || 3305.865 || 91.845  
| ||  
|-
|-
| [[61/9]] || 3312.975 || 92.403 ||
| [[61/9]] || 3312.975 || 92.403  
| ||  
|-
|-
| [[34/5]] || 3318.642 || 92.846 ||
| [[34/5]] || 3318.642 || 92.846  
| ||  
|-
|-
| [[41/6]] || 3327.107 || 93.164 ||
| [[41/6]] || 3327.107 || 93.164  
| ||  
|-
|-
| [[48/7]] || 3333.129 || 92.684 ||
| [[48/7]] || 3333.129 || 92.684  
| ||  
|-
|-
| [[55/8]] || 3337.632 || 91.625 ||
| [[55/8]] || 3337.632 || 91.625  
| ||  
|-
|-
| [[62/9]] || 3341.126 || 90.272 ||
| [[62/9]] || 3341.126 || 90.272  
| ||  
|-
|-
| [[76/11]] || 3346.195 || 87.464 ||
| [[76/11]] || 3346.195 || 87.464  
| ||  
|-
|-
| [[97/14]] || 3351.070 || 83.990 ||
| [[97/14]] || 3351.070 || 83.990  
| ||  
|-
|-
| [[125/18]] || 3355.031 || 80.945 ||
| [[125/18]] || 3355.031 || 80.945  
| ||  
|-
|-
| [[195/28]] || 3359.971 || 77.500 ||
| [[195/28]] || 3359.971 || 77.500  
| ||  
|-
|-
| [[7/1]] || 3368.826 || 74.586 ||
| [[7/1]] || 3368.826 || 74.586  
| ||  
|-
|-
| [[379/54]] || 3373.400 || 75.394 ||
| [[379/54]] || 3373.400 || 75.394  
| ||  
|-
|-
| [[190/27]] || 3377.962 || 77.639 ||
| [[190/27]] || 3377.962 || 77.639  
| ||  
|-
|-
| [[127/18]] || 3382.512 || 80.826 ||
| [[127/18]] || 3382.512 || 80.826  
| ||  
|-
|-
| [[92/13]] || 3387.747 || 84.821 ||
| [[92/13]] || 3387.747 || 84.821  
| ||  
|-
|-
| [[78/11]] || 3391.165 || 87.227 ||
| [[78/11]] || 3391.165 || 87.227  
| ||  
|-
|-
| [[64/9]] || 3396.090 || 90.022 ||
| [[64/9]] || 3396.090 || 90.022  
| ||  
|-
|-
| [[50/7]] || 3403.802 || 92.504 ||
| [[50/7]] || 3403.802 || 92.504  
| ||  
|-
|-
| [[43/6]] || 3409.563 || 93.087 ||
| [[43/6]] || 3409.563 || 93.087  
| ||  
|-
|-
| [[36/5]] || 3417.596 || 92.889 ||
| [[36/5]] || 3417.596 || 92.889  
| ||  
|-
|-
| [[65/9]] || 3422.931 || 92.505 ||
| [[65/9]] || 3422.931 || 92.505  
| ||  
|-
|-
| [[29/4]] || 3429.577 || 91.982 ||
| [[29/4]] || 3429.577 || 91.982  
| ||  
|-
|-
| [[51/7]] || 3438.085 || 91.477 ||
| [[51/7]] || 3438.085 || 91.477  
| ||  
|-
|-
| [[117/16]] || 3444.438 || 91.266 ||
| [[117/16]] || 3444.438 || 91.266  
| ||  
|-
|-
| [[22/3]] || 3449.363 || 91.188 ||
| [[22/3]] || 3449.363 || 91.188  
| ||  
|-
|-
| [[59/8]] || 3459.172 || 91.036 ||
| [[59/8]] || 3459.172 || 91.036  
| ||  
|-
|-
| [[37/5]] || 3465.030 || 90.729 ||
| [[37/5]] || 3465.030 || 90.729  
| ||  
|-
|-
| [[52/7]] || 3471.702 || 90.110 ||
| [[52/7]] || 3471.702 || 90.110  
| ||  
|-
|-
| [[67/9]] || 3475.397 || 89.685 ||
| [[67/9]] || 3475.397 || 89.685  
| ||  
|-
|-
| [[97/13]] || 3479.368 || 89.251 ||
| [[97/13]] || 3479.368 || 89.251  
| ||  
|-
|-
| [[15/2]] || 3488.269 || 88.748 ||
| [[15/2]] || 3488.269 || 88.748  
| ||  
|-
|-
| [[158/21]] || 3493.756 || 88.946 ||
| [[158/21]] || 3493.756 || 88.946  
| ||  
|-
|-
| [[83/11]] || 3498.729 || 89.408 ||
| [[83/11]] || 3498.729 || 89.408  
| ||  
|-
|-
| [[53/7]] || 3504.679 || 90.087 ||
| [[53/7]] || 3504.679 || 90.087  
| ||  
|-
|-
| [[38/5]] || 3511.199 || 90.725 ||
| [[38/5]] || 3511.199 || 90.725  
| ||  
|-
|-
| [[84/11]] || 3519.463 || 91.165 ||
| [[84/11]] || 3519.463 || 91.165  
| ||  
|-
|-
| [[23/3]] || 3526.319 || 91.334 ||
| [[23/3]] || 3526.319 || 91.334  
| ||  
|-
|-
| [[77/10]] || 3533.830 || 91.570 ||
| [[77/10]] || 3533.830 || 91.570  
| ||  
|-
|-
| [[54/7]] || 3537.039 || 91.735 ||
| [[54/7]] || 3537.039 || 91.735  
| ||  
|-
|-
| [[31/4]] || 3545.036 || 92.279 ||
| [[31/4]] || 3545.036 || 92.279  
| ||  
|-
|-
| [[70/9]] || 3551.230 || 92.737 ||
| [[70/9]] || 3551.230 || 92.737  
| ||  
|-
|-
| [[39/5]] || 3556.169 || 92.976 ||
| [[39/5]] || 3556.169 || 92.976  
| ||  
|-
|-
| [[47/6]] || 3563.552 || 92.726 ||
| [[47/6]] || 3563.552 || 92.726  
| ||  
|-
|-
| [[55/7]] || 3568.806 || 91.736 ||
| [[55/7]] || 3568.806 || 91.736  
| ||  
|-
|-
| [[63/8]] || 3572.736 || 90.390 ||
| [[63/8]] || 3572.736 || 90.390  
| ||  
|-
|-
| [[71/9]] || 3575.787 || 88.962 ||
| [[71/9]] || 3575.787 || 88.962  
| ||  
|-
|-
| [[95/12]] || 3581.872 || 85.279 ||
| [[95/12]] || 3581.872 || 85.279  
| ||  
|-
|-
| [[127/16]] || 3586.422 || 82.182 ||
| [[127/16]] || 3586.422 || 82.182  
| ||  
|-
|-
| [[191/24]] || 3590.960 || 79.377 ||
| [[191/24]] || 3590.960 || 79.377  
| ||  
|-
|-
| [[383/48]] || 3595.486 || 77.393 ||
| [[383/48]] || 3595.486 || 77.393  
| ||  
|-
|-
| [[8/1]] || 3600.000 || 76.672 ||
| [[8/1]] || 3600.000 || 76.672  
| ||  
|}
|}


Line 1,289: Line 1,914:


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

Revision as of 17:16, 22 January 2025

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

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

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

Methodology

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

Table of intervals

1/1 to 3/2

Harmonic entropy of just intervals
Ratio Size (cents) Entropy
(%, Rényi order 1.0) 		Entropy
(%, Rényi order 7.0)		 Comments
1/1 0.000 0.000
390/389 4.445 3.760
195/194 8.901 14.289
130/129 13.369 29.536
97/96 17.940 47.113
78/77 22.339 63.285
65/64 26.841 77.192
56/55 31.194 87.233
49/48 35.697 94.083
43/42 40.737 98.235
39/38 44.970 99.690
35/34 50.184 99.958
32/31 54.964 99.447
30/29 58.692 98.855
28/27 62.961 98.131
26/25 67.900 97.339
24/23 73.681 96.526
23/22 76.956 96.119
22/21 80.537 95.722
21/20 84.467 95.323
20/19 88.801 94.928
19/18 93.603 94.534
18/17 98.955 94.138
17/16 104.955 93.748
16/15 111.731 93.375
15/14 119.443 93.016
14/13 128.298 92.675
27/25 133.238 92.514
13/12 138.573 92.347
12/11 150.637 92.045
23/21 157.493 91.881
34/31 159.920 91.829
11/10 165.004 91.727
21/19 173.268 91.551
41/37 177.718 91.462
10/9 182.404 91.367
19/17 192.558 91.175
9/8 203.910 91.000
35/31 210.104 90.909
17/15 216.687 90.809
25/22 221.310 90.746
49/43 226.134 90.706
8/7 231.174 90.701
23/20 241.961 90.726
15/13 247.741 90.623
22/19 253.805 90.413
29/25 256.950 90.286
57/49 261.816 90.135
7/6 266.871 90.099
27/23 277.591 90.529
20/17 281.358 90.732
13/11 289.210 90.867
19/16 297.513 90.317
25/21 301.847 89.806
37/31 306.309 89.268
73/61 310.905 88.838
6/5 315.641 88.670
35/29 325.562 89.348
23/19 330.761 90.058
17/14 336.130 90.813
28/23 340.552 91.327
11/9 347.408 91.786
16/13 359.472 91.181
21/17 365.826 90.053
31/25 372.408 88.498
46/37 376.930 87.477
5/4 386.314 86.433
89/71 391.184 86.736
44/35 396.178 87.574
29/23 401.303 88.739
24/19 404.442 89.458
19/15 409.244 90.412
14/11 417.508 91.306
23/18 424.364 91.415
9/7 435.084 91.284
49/38 440.139 91.361
22/17 446.363 91.641
13/10 454.214 92.079
17/13 464.428 91.930
21/16 470.781 90.841
25/19 475.114 89.528
29/22 478.259 88.318
41/31 484.027 85.801
61/46 488.611 83.904
121/91 493.282 82.505
4/3 498.045 81.976
67/50 506.680 83.591
43/32 511.518 85.531
31/23 516.761 87.848
23/17 523.319 90.284
19/14 528.687 91.567
15/11 536.951 92.317
26/19 543.015 92.254
37/27 545.479 92.154
11/8 551.318 91.819
18/13 563.382 90.784
25/18 568.717 90.231
32/23 571.726 89.927
67/48 577.352 89.498
7/5 582.512 89.352
38/27 591.648 89.727
24/17 597.000 90.174
17/12 603.000 90.642
27/19 608.352 90.950
10/7 617.488 91.230
43/30 623.249 91.380
23/16 628.274 91.555
13/9 636.618 92.012
16/11 648.682 92.948
19/13 656.985 93.440
22/15 663.049 93.268
25/17 667.672 92.484
31/21 674.255 89.925
37/25 678.717 87.087
49/33 684.379 82.440
64/43 688.482 78.794
100/67 693.320 74.956
3/2 701.955 71.779

3/2 to 2/1

Harmonic entropy of just intervals
Ratio Size (cents) Entropy
(%, Rényi order 1.0) 		Entropy
(%, Rényi order 7.0)		 Comments
3/2 701.955 71.779
182/121 706.718 72.810
92/61 711.390 75.553
62/41 715.973 79.322
47/31 720.471 83.329
38/25 724.886 86.938
32/21 729.219 89.774
26/17 735.572 92.399
23/15 740.006 93.257
20/13 745.786 93.525
17/11 753.638 93.117
31/20 758.722 92.691
14/9 764.916 92.202
25/16 772.627 91.717
47/30 777.238 91.493
11/7 782.492 91.272
30/19 790.756 90.881
19/12 795.558 90.588
27/17 800.910 90.222
35/22 803.822 90.033
67/42 808.526 89.806
8/5 813.686 89.732
37/23 823.070 90.195
21/13 830.253 90.896
34/21 834.175 91.296
13/8 840.528 91.817
18/11 852.592 91.703
23/14 859.448 90.557
28/17 863.871 89.342
43/26 870.990 86.943
63/38 875.223 85.597
5/3 884.359 84.167
127/76 888.909 84.530
62/37 893.692 85.623
42/25 898.154 87.045
32/19 902.487 88.529
22/13 910.790 90.839
17/10 918.642 91.911
29/17 924.622 92.114
12/7 933.129 91.936
43/25 938.890 91.611
19/11 946.195 90.913
26/15 952.259 90.085
47/27 959.642 89.027
7/4 968.826 88.381
93/53 973.486 88.539
44/25 978.691 89.061
30/17 983.313 89.680
23/13 987.747 90.241
16/9 996.090 90.836
25/14 1003.802 90.734
34/19 1007.442 90.562
9/5 1017.596 90.182
74/41 1022.282 90.185
38/21 1026.732 90.292
20/11 1034.996 90.598
31/17 1040.080 90.750
53/29 1043.927 90.833
11/6 1049.363 90.918
24/13 1061.427 91.130
37/20 1065.030 91.211
13/7 1071.702 91.394
28/15 1080.557 91.657
15/8 1088.269 91.912
32/17 1095.045 92.173
17/9 1101.045 92.438
36/19 1106.397 92.704
19/10 1111.199 92.968
21/11 1119.463 93.512
23/12 1126.319 94.067
25/13 1132.100 94.649
27/14 1137.039 95.215
29/15 1141.309 95.749
31/16 1145.036 96.208
33/17 1148.318 96.553
37/19 1153.831 96.788
41/21 1158.282 96.316
47/24 1163.552 94.342
55/28 1168.806 90.065
63/32 1172.736 84.977
77/39 1177.661 76.268
95/48 1181.872 67.226
129/65 1186.631 56.465
193/97 1191.053 47.543
389/195 1195.555 41.234
2/1 1200.000 39.006

2/1 to 3/1

Harmonic entropy of just intervals
Ratio Size (cents) Entropy
(%, Rényi order 1.0) 		Entropy
(%, Rényi order 7.0)		 Comments
2/1 1200.000 39.006
389/194 1204.456 41.246
195/97 1208.901 47.467
129/64 1213.473 56.700
97/48 1217.940 66.810
77/38 1222.631 76.861
65/32 1226.841 84.341
55/27 1231.767 90.672
49/24 1235.697 93.888
43/21 1240.737 96.081
39/19 1244.970 96.733
35/17 1250.184 96.662
31/15 1256.767 95.974
29/14 1260.751 95.470
27/13 1265.337 94.913
25/12 1270.672 94.335
23/11 1276.956 93.767
21/10 1284.467 93.226
40/19 1288.801 92.971
19/9 1293.603 92.713
17/8 1304.955 92.212
32/15 1311.731 91.962
15/7 1319.443 91.713
43/20 1325.204 91.549
28/13 1328.298 91.468
54/25 1333.238 91.338
13/6 1338.573 91.201
24/11 1350.637 90.891
35/16 1355.140 90.798
68/31 1359.920 90.737
11/5 1365.004 90.741
31/14 1376.210 90.799
20/9 1382.404 90.645
29/13 1389.050 90.242
47/21 1394.726 89.813
9/4 1403.910 89.442
79/35 1409.397 89.622
43/19 1414.005 89.985
25/11 1421.310 90.755
41/18 1425.152 91.119
16/7 1431.174 91.447
23/10 1441.961 90.803
30/13 1447.741 89.775
37/16 1451.344 88.987
58/25 1456.950 87.767
121/52 1462.108 86.960
7/3 1466.871 86.699
61/26 1476.357 87.725
40/17 1481.358 88.788
33/14 1484.447 89.469
26/11 1489.210 90.374
19/8 1497.513 91.263
31/13 1504.508 91.358
67/28 1510.481 91.232
12/5 1515.641 91.162
29/12 1527.622 91.519
17/7 1536.130 92.120
39/16 1542.483 92.492
22/9 1547.408 92.527
27/11 1554.547 91.809
32/13 1559.472 90.533
37/15 1563.075 89.159
47/19 1567.994 86.769
62/25 1572.408 84.387
97/39 1577.413 81.915
5/2 1586.314 79.831
178/71 1591.184 80.481
93/37 1595.647 82.086
63/25 1600.109 84.302
43/17 1606.562 87.719
38/15 1609.244 88.973
28/11 1617.508 91.634
23/9 1624.364 92.434
18/7 1635.084 92.172
49/19 1640.139 91.840
31/12 1643.081 91.658
57/22 1648.150 91.431
13/5 1654.214 91.300
34/13 1664.428 91.237
21/8 1670.781 90.960
29/11 1678.259 90.106
37/14 1682.518 89.391
61/23 1688.611 88.342
117/44 1693.120 87.764
8/3 1698.045 87.525
67/25 1706.680 88.237
43/16 1711.518 89.069
27/10 1719.551 90.435
19/7 1728.687 91.142
49/18 1733.742 91.064
30/11 1736.951 90.897
41/15 1740.794 90.654
85/31 1746.234 90.327
11/4 1751.318 90.168
47/17 1760.551 90.312
25/9 1768.717 90.677
39/14 1773.657 90.867
67/24 1777.352 90.985
14/5 1782.512 91.109
31/11 1793.718 91.367
17/6 1803.000 91.650
37/13 1810.816 91.957
20/7 1817.488 92.272
43/15 1823.249 92.602
23/8 1828.274 92.938
26/9 1836.618 93.633
29/10 1843.264 94.306
32/11 1848.682 94.862
35/12 1853.185 95.221
38/13 1856.985 95.305
41/14 1860.237 95.088
47/16 1865.507 93.821
53/18 1869.595 91.704
65/22 1875.523 86.386
77/26 1879.616 81.103
98/33 1884.379 73.722
131/44 1888.790 66.544
200/67 1893.320 60.026
3/1 1901.955 54.245

3/1 to 4/1

Harmonic entropy of just intervals
Ratio Size (cents) Entropy
(%, Rényi order 1.0) 		Entropy
(%, Rényi order 7.0)		 Comments
3/1 1901.955 54.245
367/122 1906.679 56.071
187/62 1911.238 60.881
127/42 1915.641 67.404
94/31 1920.471 75.286
76/25 1924.886 81.991
64/21 1929.219 87.364
55/18 1933.722 91.364
46/15 1940.006 94.439
43/14 1942.692 95.041
37/12 1949.389 95.375
34/11 1953.638 95.100
31/10 1958.722 94.593
28/9 1964.916 93.929
25/8 1972.627 93.206
47/15 1977.238 92.840
22/7 1982.492 92.487
60/19 1990.756 92.024
19/6 1995.558 91.813
54/17 2000.910 91.606
35/11 2003.822 91.516
67/21 2008.526 91.378
16/5 2013.686 91.231
29/9 2025.667 90.874
42/13 2030.253 90.752
81/25 2035.193 90.679
13/4 2040.528 90.693
49/15 2049.383 90.886
36/11 2052.592 90.938
23/7 2059.448 90.832
33/10 2066.959 90.254
43/13 2070.990 89.797
63/19 2075.223 89.312
10/3 2084.359 88.773
127/38 2088.909 88.907
57/17 2094.513 89.429
37/11 2100.026 90.130
27/8 2105.865 90.864
44/13 2110.790 91.364
17/5 2118.642 91.902
58/17 2124.622 92.131
24/7 2133.129 92.030
31/9 2141.126 91.024
38/11 2146.195 89.734
45/13 2149.696 88.572
59/17 2154.216 86.904
94/27 2159.642 85.001
7/2 2168.826 83.459
186/53 2173.486 83.881
95/27 2177.962 84.993
60/17 2183.313 86.860
46/13 2187.747 88.508
39/11 2191.165 89.654
32/9 2196.090 90.939
25/7 2203.802 91.985
43/12 2209.563 92.143
18/5 2217.596 91.868
65/18 2222.931 91.484
29/8 2229.577 90.831
40/11 2234.996 90.215
51/14 2238.085 89.874
117/32 2244.438 89.346
11/3 2249.363 89.211
59/16 2259.172 89.729
37/10 2265.030 90.282
26/7 2271.702 90.802
41/11 2277.745 91.024
15/4 2288.269 91.072
79/21 2293.756 91.101
34/9 2301.045 91.261
72/19 2306.397 91.442
19/5 2311.199 91.637
42/11 2319.463 92.015
23/6 2326.319 92.389
27/7 2337.039 93.165
31/8 2345.036 93.896
35/9 2351.230 94.391
39/10 2356.169 94.508
47/12 2363.552 93.521
55/14 2368.806 91.325
63/16 2372.736 88.598
75/19 2377.069 84.455
95/24 2381.872 78.764
127/32 2386.422 72.968
191/48 2390.960 67.739
387/97 2395.532 64.080
4/1 2400.000 62.798

4/1 to 6/1

Harmonic entropy of just intervals
Ratio Size (cents) Entropy
(%, Rényi order 1.0) 		Entropy
(%, Rényi order 7.0)		 Comments
4/1 2400.000 62.798
389/97 2404.456 64.076
193/48 2408.993 67.714
129/32 2413.473 72.852
97/24 2417.940 78.558
77/19 2422.631 84.164
65/16 2426.841 88.282
53/13 2432.977 92.286
49/12 2435.697 93.337
41/10 2442.749 94.509
37/9 2447.434 94.478
33/8 2453.273 94.049
29/7 2460.751 93.336
25/6 2470.672 92.507
46/11 2476.956 92.096
67/16 2479.307 91.958
21/5 2484.467 91.696
59/14 2490.346 91.443
38/9 2493.603 91.333
55/13 2497.104 91.229
17/4 2504.955 91.063
64/15 2511.731 90.911
30/7 2519.443 90.589
43/10 2525.204 90.237
56/13 2528.298 90.045
108/25 2533.238 89.798
13/3 2538.573 89.729
61/14 2548.059 90.228
35/8 2555.140 90.942
57/13 2558.940 91.316
22/5 2565.004 91.732
31/7 2576.210 91.266
40/9 2582.404 90.118
49/11 2586.334 89.120
67/15 2591.038 87.824
103/23 2595.526 86.696
9/2 2603.910 85.700
167/37 2609.101 86.069
86/19 2614.005 87.026
59/13 2618.644 88.237
41/9 2625.152 89.931
32/7 2631.174 91.047
23/5 2641.961 91.557
37/8 2651.344 90.918
51/11 2655.593 90.538
121/26 2662.108 90.078
14/3 2666.871 89.943
61/13 2676.357 90.178
47/10 2679.193 90.338
33/7 2684.447 90.654
52/11 2689.210 90.913
19/4 2697.513 91.250
81/17 2702.865 91.441
43/9 2707.608 91.620
67/14 2710.481 91.756
24/5 2715.641 92.033
29/6 2727.622 92.932
34/7 2736.130 93.640
39/8 2742.483 93.885
44/9 2747.408 93.589
54/11 2754.547 91.677
64/13 2759.472 88.918
74/15 2763.075 86.111
94/19 2767.994 81.362
129/26 2772.945 76.173
199/40 2777.636 71.787
5/1 2786.314 68.009
361/72 2791.116 69.236
186/37 2795.647 72.363
126/25 2800.109 76.655
91/18 2805.444 82.237
76/15 2809.244 85.883
61/12 2814.930 90.123
51/10 2820.597 92.661
46/9 2824.364 93.525
41/8 2829.062 93.937
36/7 2835.084 93.804
31/6 2843.081 93.178
57/11 2848.150 92.750
26/5 2854.214 92.307
47/9 2861.597 91.870
21/4 2870.781 91.425
79/15 2876.268 91.152
37/7 2882.518 90.820
53/10 2887.191 90.579
117/22 2893.120 90.378
16/3 2898.045 90.360
59/11 2907.854 90.739
43/8 2911.518 90.933
27/5 2919.551 91.115
65/12 2924.886 90.826
38/7 2928.687 90.366
49/9 2933.742 89.479
60/11 2936.951 88.814
93/17 2942.035 87.822
181/33 2946.542 87.184
11/2 2951.318 86.954
94/17 2960.551 87.918
61/11 2965.567 88.943
50/9 2968.717 89.611
39/7 2973.657 90.516
67/12 2977.352 91.004
28/5 2982.512 91.342
45/8 2990.224 91.271
62/11 2993.718 91.121
17/3 3003.000 90.796
91/16 3009.354 90.823
40/7 3017.488 91.140
63/11 3021.418 91.351
23/4 3028.274 91.759
52/9 3036.618 92.295
29/5 3043.264 92.782
35/6 3053.185 93.524
41/7 3060.237 93.677
47/8 3065.507 93.159
53/9 3069.595 92.138
65/11 3075.523 89.379
77/13 3079.616 86.553
95/16 3083.827 83.035
131/22 3088.790 78.596
197/33 3093.189 75.071
6/1 3101.955 71.731

6/1 to 8/1

Harmonic entropy of just intervals
Ratio Size (cents) Entropy
(%, Rényi order 1.0) 		Entropy
(%, Rényi order 7.0)		 Comments
6/1 3101.955 71.731
367/61 3106.679 72.714
187/31 3111.238 75.340
127/21 3115.641 78.905
91/15 3121.085 83.711
73/12 3125.835 87.463
61/10 3130.571 90.313
55/9 3133.722 91.647
49/8 3137.652 92.720
43/7 3142.692 93.315
37/6 3149.389 93.281
31/5 3158.722 92.634
56/9 3164.916 92.175
25/4 3172.627 91.679
69/11 3178.911 91.336
44/7 3182.492 91.164
63/10 3186.422 91.034
120/19 3190.756 90.949
19/3 3195.558 90.954
127/20 3200.108 91.016
51/8 3206.910 91.113
32/5 3213.686 90.949
45/7 3221.398 90.200
58/9 3225.667 89.582
84/13 3230.253 88.880
162/25 3235.193 88.287
13/2 3240.528 88.036
98/15 3249.383 88.679
59/9 3255.262 89.542
46/7 3259.448 90.160
33/5 3266.959 90.915
53/8 3273.505 91.119
20/3 3284.359 91.038
127/19 3288.909 91.050
47/7 3296.681 91.284
27/4 3305.865 91.845
61/9 3312.975 92.403
34/5 3318.642 92.846
41/6 3327.107 93.164
48/7 3333.129 92.684
55/8 3337.632 91.625
62/9 3341.126 90.272
76/11 3346.195 87.464
97/14 3351.070 83.990
125/18 3355.031 80.945
195/28 3359.971 77.500
7/1 3368.826 74.586
379/54 3373.400 75.394
190/27 3377.962 77.639
127/18 3382.512 80.826
92/13 3387.747 84.821
78/11 3391.165 87.227
64/9 3396.090 90.022
50/7 3403.802 92.504
43/6 3409.563 93.087
36/5 3417.596 92.889
65/9 3422.931 92.505
29/4 3429.577 91.982
51/7 3438.085 91.477
117/16 3444.438 91.266
22/3 3449.363 91.188
59/8 3459.172 91.036
37/5 3465.030 90.729
52/7 3471.702 90.110
67/9 3475.397 89.685
97/13 3479.368 89.251
15/2 3488.269 88.748
158/21 3493.756 88.946
83/11 3498.729 89.408
53/7 3504.679 90.087
38/5 3511.199 90.725
84/11 3519.463 91.165
23/3 3526.319 91.334
77/10 3533.830 91.570
54/7 3537.039 91.735
31/4 3545.036 92.279
70/9 3551.230 92.737
39/5 3556.169 92.976
47/6 3563.552 92.726
55/7 3568.806 91.736
63/8 3572.736 90.390
71/9 3575.787 88.962
95/12 3581.872 85.279
127/16 3586.422 82.182
191/24 3590.960 79.377
383/48 3595.486 77.393
8/1 3600.000 76.672

See also


Todo: complete table

Fill in the values for the Rényi order 7.0 column of each table.

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