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Harmonic entropy of just intervals: Difference between revisions

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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]].
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]].
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== Methodology ==
== Methodology ==
This table was made with [[Scale Workshop]]. It was made by starting with 1080ed16 ([[270edo]] but treating 16/1 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).  
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).
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 2/1 ===
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals size 0 to 1200¢
|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 0 to 1200{{c}}
|-
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
|-
|-
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=== 2/1 to 4/1 ===
=== 2/1 to 4/1 ===
{| class="wikitable mw-collapsible sortable"
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals size 1200 to 2400¢
|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 1200 to 2400{{c}}
|-
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
|-
|-
Line 838: Line 839:
|-
|-
| [[4/1]] || 2400.000 || 62.798 || 20.634
| [[4/1]] || 2400.000 || 62.798 || 20.634
|}
=== 4/1 to 8/1 ===
{| class="wikitable mw-collapsible sortable"
|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 2400 to 3600{{c}}
|-
|-
| [[2/1]] || 3600.000 || 76.672 || 31.713
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
|-
|-
| [[389/194]] || 3604.456 || 77.351 || 32.783
| [[4/1]] || 2400.000 || 62.798 || 20.634
|-
|-
| [[195/97]] || 3608.901 || 79.257 || 35.927
| [[389/97]] || 2404.456 || 64.076 || 21.670
|-
|-
| [[129/64]] || 3613.473 || 82.060 || 41.323
| [[193/48]] || 2408.993 || 67.714 || 24.873
|-
|-
| [[97/48]] || 3617.940 || 85.094 || 48.721
| [[129/32]] || 2413.473 || 72.852 || 30.181
|-
|-
| [[77/38]] || 3622.631 || 88.042 || 58.746
| [[97/24]] || 2417.940 || 78.558 || 37.612
|-
|-
| [[65/32]] || 3626.841 || 90.169 || 69.646
| [[77/19]] || 2422.631 || 84.164 || 47.718
|-
|-
| [[55/27]] || 3631.767 || 91.863 || 81.569
| [[65/16]] || 2426.841 || 88.282 || 58.797
|-
|-
| [[49/24]] || 3635.697 || 92.628 || 82.024
| [[53/13]] || 2432.977 || 92.286 || 78.103
|-
|-
| [[43/21]] || 3640.737 || 93.008 || 79.329
| [[49/12]] || 2435.697 || 93.337 || 85.959
|-
|-
| [[39/19]] || 3644.970 || 92.982 || 77.089
| [[41/10]] || 2442.749 || 94.509 || 86.517
|-
|-
| [[35/17]] || 3650.184 || 92.712 || 74.987
| [[37/9]] || 2447.434 || 94.478 || 84.366
|-
|-
| [[31/15]] || 3656.767 || 92.265 || 73.023
| [[33/8]] || 2453.273 || 94.049 || 81.900
|-
|-
| [[29/14]] || 3660.751 || 92.011 || 70.627
| [[29/7]] || 2460.751 || 93.336 || 78.995
|-
|-
| [[27/13]] || 3665.337 || 91.762 || 67.743
| [[25/6]] || 2470.672 || 92.507 || 75.746
|-
|-
| [[25/12]] || 3670.672 || 91.520 || 66.415
| [[46/11]] || 2476.956 || 92.096 || 73.420
|-
|-
| [[23/11]] || 3676.956 || 91.199 || 68.485
| [[67/16]] || 2479.307 || 91.958 || 72.499
|-
|-
| [[21/10]] || 3684.467 || 90.661 || 72.830
| [[21/5]] || 2484.467 || 91.696 || 71.456
|-
|-
| [[40/19]] || 3688.801 || 90.253 || 67.735
| [[59/14]] || 2490.346 || 91.443 || 71.514
|-
|-
| [[19/9]] || 3693.603 || 89.774 || 61.021
| [[38/9]] || 2493.603 || 91.333 || 70.272
|-
|-
| [[17/8]] || 3704.955 || 89.148 || 54.268
| [[55/13]] || 2497.104 || 91.229 || 67.898
|-
|-
| [[32/15]] || 3711.731 || 89.402 || 56.734
| [[17/4]] || 2504.955 || 91.063 || 65.043
|-
|-
| [[15/7]] || 3719.443 || 90.106 || 65.332
| [[64/15]] || 2511.731 || 90.911 || 67.501
|-
|-
| [[43/20]] || 3725.204 || 90.677 || 72.770
| [[30/7]] || 2519.443 || 90.589 || 72.480
|-
|-
| [[28/13]] || 3728.298 || 90.949 || 72.102
| [[43/10]] || 2525.204 || 90.237 || 65.850
|-
|-
| [[54/25]] || 3733.238 || 91.298 || 68.690
| [[56/13]] || 2528.298 || 90.045 || 62.065
|-
|-
| [[13/6]] || 3738.573 || 91.610 || 67.183
| [[108/25]] || 2533.238 || 89.798 || 57.981
|-
|-
| [[24/11]] || 3750.637 || 92.313 || 72.766
| [[13/3]] || 2538.573 || 89.729 || 56.445
|-
|-
| [[35/16]] || 3755.140 || 92.594 || 74.884
| [[61/14]] || 2548.059 || 90.228 || 61.167
|-
|-
| [[68/31]] || 3759.920 || 92.822 || 76.500
| [[35/8]] || 2555.140 || 90.942 || 69.998
|-
|-
| [[11/5]] || 3765.004 || 92.808 || 78.930
| [[57/13]] || 2558.940 || 91.316 || 72.908
|-
|-
| [[31/14]] || 3776.210 || 90.798 || 73.622
| [[22/5]] || 2565.004 || 91.732 || 72.619
|-
|-
| [[20/9]] || 3782.404 || 88.053 || 57.828
| [[31/7]] || 2576.210 || 91.266 || 76.993
|-
|-
| [[29/13]] || 3789.050 || 84.168 || 45.078
| [[40/9]] || 2582.404 || 90.118 || 68.724
|-
|-
| [[47/21]] || 3794.726 || 80.969 || 37.899
| [[49/11]] || 2586.334 || 89.120 || 60.757
|-
|-
| [[9/4]] || 3803.910 || 78.487 || 33.500
| [[67/15]] || 2591.038 || 87.824 || 53.151
|-
|-
| [[79/35]] || 3809.397 || 79.386 || 35.123
| [[103/23]] || 2595.526 || 86.696 || 48.055
|-
|-
| [[43/19]] || 3814.005 || 81.356 || 38.934
| [[9/2]] || 2603.910 || 85.700 || 44.227
|-
|-
| [[25/11]] || 3821.309 || 85.600 || 49.566
| [[167/37]] || 2609.101 || 86.069 || 45.583
|-
|-
| [[41/18]] || 3825.152 || 87.793 || 57.412
| [[86/19]] || 2614.005 || 87.026 || 49.488
|-
|-
| [[16/7]] || 3831.174 || 90.519 || 72.620
| [[59/13]] || 2618.644 || 88.237 || 55.541
|-
|-
| [[23/10]] || 3841.961 || 92.648 || 79.540
| [[41/9]] || 2625.152 || 89.931 || 67.735
|-
|-
| [[30/13]] || 3847.741 || 92.723 || 76.853
| [[32/7]] || 2631.174 || 91.047 || 76.544
|-
|-
| [[37/16]] || 3851.344 || 92.585 || 75.474
| [[23/5]] || 2641.961 || 91.557 || 72.891
|-
|-
| [[58/25]] || 3856.950 || 92.263 || 72.406
| [[37/8]] || 2651.344 || 90.918 || 69.333
|-
|-
| [[121/52]] || 3862.108 || 91.941 || 69.445
| [[51/11]] || 2655.592 || 90.538 || 64.082
|-
|-
| [[7/3]] || 3866.871 || 91.644 || 68.437
| [[121/26]] || 2662.108 || 90.078 || 58.707
|-
|-
| [[61/26]] || 3876.357 || 90.967 || 72.115
| [[14/3]] || 2666.871 || 89.943 || 57.563
|-
|-
| [[40/17]] || 3881.358 || 90.544 || 69.341
| [[61/13]] || 2676.357 || 90.178 || 62.362
|-
|-
| [[33/14]] || 3884.447 || 90.277 || 65.124
| [[47/10]] || 2679.193 || 90.338 || 65.540
|-
|-
| [[26/11]] || 3889.210 || 89.906 || 59.862
| [[33/7]] || 2684.447 || 90.654 || 71.433
|-
|-
| [[19/8]] || 3897.513 || 89.594 || 56.279
| [[52/11]] || 2689.210 || 90.913 || 70.124
|-
|-
| [[31/13]] || 3904.508 || 89.812 || 58.928
| [[19/4]] || 2697.513 || 91.250 || 66.691
|-
|-
| [[67/28]] || 3910.481 || 90.256 || 65.199
| [[81/17]] || 2702.865 || 91.441 || 67.985
|-
|-
| [[12/5]] || 3915.641 || 90.728 || 71.780
| [[43/9]] || 2707.608 || 91.620 || 70.764
|-
|-
| [[29/12]] || 3927.622 || 91.657 || 69.328
| [[67/14]] || 2710.481 || 91.756 || 72.192
|-
|-
| [[17/7]] || 3936.130 || 92.168 || 72.306
| [[24/5]] || 2715.641 || 92.033 || 73.157
|-
|-
| [[39/16]] || 3942.483 || 92.425 || 76.055
| [[29/6]] || 2727.622 || 92.932 || 77.031
|-
|-
| [[22/9]] || 3947.408 || 92.410 || 78.163
| [[34/7]] || 2736.130 || 93.640 || 80.373
|-
|-
| [[27/11]] || 3954.547 || 91.652 || 80.985
| [[39/8]] || 2742.483 || 93.885 || 83.233
|-
|-
| [[32/13]] || 3959.472 || 90.377 || 72.773
| [[44/9]] || 2747.408 || 93.589 || 85.604
|-
|-
| [[37/15]] || 3963.075 || 89.006 || 63.473
| [[54/11]] || 2754.547 || 91.677 || 77.116
|-
|-
| [[47/19]] || 3967.994 || 86.639 || 52.658
| [[64/13]] || 2759.472 || 88.918 || 62.079
|-
|-
| [[62/25]] || 3972.408 || 84.277 || 45.136
| [[74/15]] || 2763.075 || 86.111 || 52.510
|-
|-
| [[97/39]] || 3977.413 || 81.822 || 39.116
| [[94/19]] || 2767.994 || 81.362 || 41.670
|-
|-
| [[5/2]] || 3986.314 || 79.780 || 34.989
| [[129/26]] || 2772.945 || 76.173 || 33.364
|-
|-
| [[178/71]] || 3991.184 || 80.455 || 36.288
| [[199/40]] || 2777.636 || 71.787 || 27.906
|-
|-
| [[93/37]] || 3995.647 || 82.077 || 39.686
| [[5/1]] || 2786.314 || 68.009 || 23.962
|-
|-
| [[63/25]] || 4000.108 || 84.311 || 45.196
| [[361/72]] || 2791.116 || 69.236 || 25.203
|-
|-
| [[43/17]] || 4006.562 || 87.755 || 56.900
| [[186/37]] || 2795.647 || 72.363 || 28.611
|-
|-
| [[38/15]] || 4009.244 || 89.020 || 63.054
| [[126/25]] || 2800.108 || 76.655 || 34.095
|-
|-
| [[28/11]] || 4017.508 || 91.712 || 81.175
| [[91/18]] || 2805.444 || 82.237 || 43.431
|-
|-
| [[23/9]] || 4024.364 || 92.542 || 78.968
| [[76/15]] || 2809.244 || 85.883 || 51.934
|-
|-
| [[18/7]] || 4035.084 || 92.356 || 73.073
| [[61/12]] || 2814.930 || 90.123 || 67.494
|-
|-
| [[49/19]] || 4040.139 || 92.018 || 70.753
| [[51/10]] || 2820.597 || 92.661 || 84.199
|-
|-
| [[31/12]] || 4043.081 || 91.796 || 70.334
| [[46/9]] || 2824.364 || 93.525 || 86.193
|-
|-
| [[57/22]] || 4048.150 || 91.379 || 71.349
| [[41/8]] || 2829.062 || 93.937 || 84.008
|-
|-
| [[13/5]] || 4054.214 || 90.858 || 70.652
| [[36/7]] || 2835.084 || 93.804 || 81.270
|-
|-
| [[34/13]] || 4064.428 || 90.094 || 59.533
| [[31/6]] || 2843.081 || 93.178 || 78.031
|-
|-
| [[21/8]] || 4070.781 || 89.908 || 57.273
| [[57/11]] || 2848.150 || 92.750 || 76.045
|-
|-
| [[29/11]] || 4078.259 || 90.112 || 60.140
| [[26/5]] || 2854.214 || 92.307 || 74.485
|-
|-
| [[37/14]] || 4082.518 || 90.399 || 64.359
| [[47/9]] || 2861.597 || 91.870 || 71.896
|-
|-
| [[61/23]] || 4088.610 || 90.913 || 71.121
| [[21/4]] || 2870.781 || 91.425 || 68.672
|-
|-
| [[117/44]] || 4093.120 || 91.311 || 71.041
| [[79/15]] || 2876.268 || 91.152 || 70.103
|-
|-
| [[8/3]] || 4098.045 || 91.721 || 70.066
| [[37/7]] || 2882.518 || 90.820 || 70.829
|-
|-
| [[67/25]] || 4106.680 || 92.256 || 73.134
| [[53/10]] || 2887.191 || 90.579 || 66.050
|-
|-
| [[43/16]] || 4111.518 || 92.328 || 76.211
| [[117/22]] || 2893.120 || 90.378 || 61.195
|-
|-
| [[27/10]] || 4119.551 || 91.684 || 80.063
| [[16/3]] || 2898.045 || 90.360 || 59.869
|-
|-
| [[19/7]] || 4128.687 || 89.080 || 63.335
| [[59/11]] || 2907.854 || 90.739 || 64.773
|-
|-
| [[49/18]] || 4133.742 || 86.823 || 52.653
| [[43/8]] || 2911.518 || 90.933 || 68.839
|-
|-
| [[30/11]] || 4136.951 || 85.258 || 47.263
| [[27/5]] || 2919.551 || 91.115 || 74.991
|-
|-
| [[41/15]] || 4140.794 || 83.469 || 42.249
| [[65/12]] || 2924.886 || 90.826 || 75.969
|-
|-
| [[85/31]] || 4146.234 || 81.569 || 37.815
| [[38/7]] || 2928.687 || 90.366 || 72.997
|-
|-
| [[11/4]] || 4151.318 || 80.923 || 36.487
| [[49/9]] || 2933.742 || 89.479 || 63.506
|-
|-
| [[47/17]] || 4160.551 || 82.949 || 41.022
| [[60/11]] || 2936.951 || 88.814 || 58.100
|-
|-
| [[25/9]] || 4168.717 || 86.767 || 52.518
| [[93/17]] || 2942.035 || 87.822 || 51.716
|-
|-
| [[39/14]] || 4173.657 || 88.990 || 62.875
| [[181/33]] || 2946.542 || 87.184 || 48.353
|-
|-
| [[67/24]] || 4177.352 || 90.328 || 72.066
| [[11/2]] || 2951.318 || 86.954 || 47.153
|-
|-
| [[14/5]] || 4182.512 || 91.600 || 80.389
| [[94/17]] || 2960.551 || 87.918 || 51.700
|-
|-
| [[31/11]] || 4193.718 || 92.298 || 74.719
| [[61/11]] || 2965.567 || 88.943 || 57.950
|-
|-
| [[17/6]] || 4203.000 || 91.759 || 71.407
| [[50/9]] || 2968.717 || 89.611 || 63.197
|-
|-
| [[37/13]] || 4210.816 || 91.076 || 71.801
| [[39/7]] || 2973.657 || 90.516 || 72.515
|-
|-
| [[20/7]] || 4217.488 || 90.537 || 65.217
| [[67/12]] || 2977.352 || 91.004 || 76.031
|-
|-
| [[43/15]] || 4223.249 || 90.222 || 60.558
| [[28/5]] || 2982.512 || 91.342 || 75.084
|-
|-
| [[23/8]] || 4228.274 || 90.141 || 59.271
| [[45/8]] || 2990.224 || 91.271 || 68.577
|-
|-
| [[26/9]] || 4236.618 || 90.448 || 62.997
| [[62/11]] || 2993.718 || 91.121 || 64.852
|-
|-
| [[29/10]] || 4243.263 || 90.982 || 70.207
| [[17/3]] || 3003.000 || 90.796 || 60.390
|-
|-
| [[32/11]] || 4248.682 || 91.481 || 72.653
| [[91/16]] || 3009.354 || 90.823 || 62.564
|-
|-
| [[35/12]] || 4253.185 || 91.865 || 72.236
| [[40/7]] || 3017.488 || 91.140 || 70.111
|-
|-
| [[38/13]] || 4256.985 || 92.123 || 72.874
| [[63/11]] || 3021.418 || 91.351 || 71.253
|-
|-
| [[41/14]] || 4260.236 || 92.246 || 74.305
| [[23/4]] || 3028.274 || 91.759 || 69.888
|-
|-
| [[47/16]] || 4265.507 || 92.188 || 77.572
| [[52/9]] || 3036.618 || 92.295 || 72.655
|-
|-
| [[53/18]] || 4269.595 || 91.810 || 79.881
| [[29/5]] || 3043.263 || 92.782 || 75.650
|-
|-
| [[65/22]] || 4275.523 || 90.597 || 74.512
| [[35/6]] || 3053.185 || 93.524 || 79.261
|-
|-
| [[77/26]] || 4279.616 || 89.262 || 64.429
| [[41/7]] || 3060.236 || 93.677 || 82.545
|-
|-
| [[98/33]] || 4284.379 || 87.309 || 54.265
| [[47/8]] || 3065.507 || 93.159 || 84.962
|-
|-
| [[131/44]] || 4288.790 || 85.337 || 46.968
| [[53/9]] || 3069.595 || 92.138 || 81.317
|-
|-
| [[200/67]] || 4293.320 || 83.514 || 41.625
| [[65/11]] || 3075.523 || 89.379 || 64.058
|-
|-
| [[3/1]] || 4301.955 || 81.853 || 37.504
| [[77/13]] || 3079.616 || 86.553 || 53.435
|-
|-
| [[367/122]] || 4306.679 || 82.349 || 38.623
| [[95/16]] || 3083.827 || 83.035 || 44.350
|-
|-
| [[187/62]] || 4311.238 || 83.679 || 41.961
| [[131/22]] || 3088.790 || 78.596 || 36.061
|-
|-
| [[127/42]] || 4315.641 || 85.475 || 47.290
| [[197/33]] || 3093.189 || 75.071 || 30.903
|-
|-
| [[94/31]] || 4320.471 || 87.602 || 55.511
| [[6/1]] || 3101.955 || 71.731 || 26.753
|-
|-
| [[76/25]] || 4324.886 || 89.349 || 65.159
| [[367/61]] || 3106.679 || 72.714 || 27.900
|-
|-
| [[64/21]] || 4329.219 || 90.688 || 75.611
| [[187/31]] || 3111.238 || 75.340 || 31.250
|-
|-
| [[55/18]] || 4333.722 || 91.586 || 79.198
| [[127/21]] || 3115.641 || 78.905 || 36.582
|-
|-
| [[46/15]] || 4340.006 || 92.112 || 75.532
| [[91/15]] || 3121.085 || 83.711 || 46.033
|-
|-
| [[43/14]] || 4342.692 || 92.130 || 74.003
| [[73/12]] || 3125.834 || 87.463 || 56.863
|-
|-
| [[37/12]] || 4349.389 || 91.861 || 72.160
| [[61/10]] || 3130.571 || 90.313 || 70.005
|-
|-
| [[34/11]] || 4353.637 || 91.560 || 72.177
| [[55/9]] || 3133.722 || 91.647 || 79.353
|-
|-
| [[31/10]] || 4358.722 || 91.180 || 69.278
| [[49/8]] || 3137.652 || 92.720 || 84.646
|-
|-
| [[28/9]] || 4364.916 || 90.806 || 63.142
| [[43/7]] || 3142.692 || 93.315 || 82.594
|-
|-
| [[25/8]] || 4372.627 || 90.671 || 60.096
| [[37/6]] || 3149.389 || 93.281 || 79.454
|-
|-
| [[47/15]] || 4377.238 || 90.799 || 61.247
| [[31/5]] || 3158.722 || 92.634 || 75.931
|-
|-
| [[22/7]] || 4382.492 || 91.128 || 65.187
| [[56/9]] || 3164.916 || 92.175 || 73.112
|-
|-
| [[60/19]] || 4390.756 || 91.820 || 72.448
| [[25/4]] || 3172.627 || 91.679 || 70.854
|-
|-
| [[19/6]] || 4395.558 || 92.186 || 72.796
| [[69/11]] || 3178.911 || 91.336 || 71.355
|-
|-
| [[54/17]] || 4400.910 || 92.386 || 74.060
| [[44/7]] || 3182.492 || 91.164 || 69.795
|-
|-
| [[35/11]] || 4403.822 || 92.344 || 75.563
| [[63/10]] || 3186.422 || 91.034 || 66.313
|-
|-
| [[67/21]] || 4408.526 || 91.965 || 78.458
| [[120/19]] || 3190.756 || 90.949 || 63.284
|-
|-
| [[16/5]] || 4413.686 || 90.999 || 75.769
| [[19/3]] || 3195.558 || 90.954 || 62.086
|-
|-
| [[29/9]] || 4425.667 || 86.712 || 50.516
| [[127/20]] || 3200.108 || 91.016 || 63.188
|-
|-
| [[42/13]] || 4430.253 || 84.881 || 44.416
| [[51/8]] || 3206.910 || 91.113 || 68.646
|-
|-
| [[81/25]] || 4435.193 || 83.392 || 40.352
| [[32/5]] || 3213.686 || 90.949 || 75.401
|-
|-
| [[13/4]] || 4440.528 || 82.766 || 38.877
| [[45/7]] || 3221.398 || 90.200 || 68.953
|-
|-
| [[49/15]] || 4449.383 || 84.323 || 43.108
| [[58/9]] || 3225.667 || 89.582 || 61.610
|-
|-
| [[36/11]] || 4452.592 || 85.477 || 46.694
| [[84/13]] || 3230.253 || 88.880 || 55.552
|-
|-
| [[23/7]] || 4459.448 || 88.265 || 58.011
| [[162/25]] || 3235.193 || 88.287 || 51.486
|-
|-
| [[33/10]] || 4466.959 || 90.754 || 75.179
| [[13/2]] || 3240.528 || 88.036 || 49.983
|-
|-
| [[43/13]] || 4470.990 || 91.592 || 79.204
| [[98/15]] || 3249.383 || 88.679 || 54.121
|-
|-
| [[63/19]] || 4475.223 || 92.074 || 77.012
| [[59/9]] || 3255.262 || 89.542 || 61.420
|-
|-
| [[10/3]] || 4484.359 || 92.092 || 73.638
| [[46/7]] || 3259.448 || 90.160 || 68.593
|-
|-
| [[127/38]] || 4488.909 || 91.795 || 72.728
| [[33/5]] || 3266.959 || 90.915 || 75.373
|-
|-
| [[57/17]] || 4494.513 || 91.377 || 68.019
| [[53/8]] || 3273.505 || 91.119 || 68.956
|-
|-
| [[37/11]] || 4500.026 || 91.047 || 63.368
| [[20/3]] || 3284.359 || 91.038 || 63.048
|-
|-
| [[27/8]] || 4505.865 || 90.886 || 61.598
| [[127/19]] || 3288.909 || 91.050 || 64.127
|-
|-
| [[44/13]] || 4510.790 || 90.952 || 62.873
| [[47/7]] || 3296.681 || 91.284 || 69.942
|-
|-
| [[17/5]] || 4518.642 || 91.340 || 69.503
| [[27/4]] || 3305.865 || 91.845 || 72.072
|-
|-
| [[58/17]] || 4524.622 || 91.702 || 73.497
| [[61/9]] || 3312.975 || 92.403 || 74.047
|-
|-
| [[24/7]] || 4533.129 || 91.824 || 75.579
| [[34/5]] || 3318.642 || 92.846 || 76.869
|-
|-
| [[31/9]] || 4541.126 || 90.933 || 77.552
| [[41/6]] || 3327.107 || 93.164 || 80.690
|-
|-
| [[38/11]] || 4546.195 || 89.680 || 67.053
| [[48/7]] || 3333.129 || 92.684 || 83.653
|-
|-
| [[45/13]] || 4549.696 || 88.547 || 59.359
| [[55/8]] || 3337.632 || 91.625 || 79.909
|-
|-
| [[59/17]] || 4554.216 || 86.904 || 51.255
| [[62/9]] || 3341.126 || 90.272 || 70.109
|-
|-
| [[94/27]] || 4559.642 || 85.028 || 44.400
| [[76/11]] || 3346.195 || 87.464 || 56.641
|-
|-
| [[7/2]] || 4568.826 || 83.521 || 39.954
| [[97/14]] || 3351.070 || 83.990 || 46.182
|-
|-
| [[186/53]] || 4573.486 || 83.956 || 41.129
| [[125/18]] || 3355.031 || 80.945 || 39.535
|-
|-
| [[95/27]] || 4577.962 || 85.069 || 44.432
| [[195/28]] || 3359.970 || 77.500 || 33.579
|-
|-
| [[60/17]] || 4583.313 || 86.944 || 51.172
| [[7/1]] || 3368.826 || 74.586 || 29.390
|-
|-
| [[46/13]] || 4587.747 || 88.590 || 59.045
| [[379/54]] || 3373.400 || 75.394 || 30.489
|-
|-
| [[39/11]] || 4591.165 || 89.727 || 66.467
| [[190/27]] || 3377.962 || 77.639 || 33.801
|-
|-
| [[32/9]] || 4596.090 || 90.990 || 77.049
| [[127/18]] || 3382.512 || 80.826 || 39.313
|-
|-
| [[25/7]] || 4603.802 || 91.933 || 76.083
| [[92/13]] || 3387.747 || 84.821 || 48.386
|-
|-
| [[43/12]] || 4609.563 || 91.963 || 74.300
| [[78/11]] || 3391.165 || 87.227 || 55.880
|-
|-
| [[18/5]] || 4617.596 || 91.554 || 69.486
| [[64/9]] || 3396.090 || 90.022 || 68.814
|-
|-
| [[65/18]] || 4622.931 || 91.272 || 64.859
| [[50/7]] || 3403.802 || 92.504 || 83.841
|-
|-
| [[29/8]] || 4629.577 || 91.126 || 62.605
| [[43/6]] || 3409.563 || 93.087 || 81.264
|-
|-
| [[40/11]] || 4634.996 || 91.223 || 64.158
| [[36/5]] || 3417.596 || 92.889 || 77.539
|-
|-
| [[51/14]] || 4638.085 || 91.343 || 66.347
| [[65/9]] || 3422.931 || 92.505 || 74.973
|-
|-
| [[117/32]] || 4644.438 || 91.650 || 72.268
| [[29/4]] || 3429.577 || 91.982 || 73.165
|-
|-
| [[11/3]] || 4649.363 || 91.788 || 74.668
| [[51/7]] || 3438.085 || 91.477 || 70.297
|-
|-
| [[59/16]] || 4659.172 || 91.167 || 78.067
| [[117/16]] || 3444.438 || 91.266 || 65.747
|-
|-
| [[37/10]] || 4665.030 || 89.937 || 69.658
| [[22/3]] || 3449.363 || 91.188 || 64.411
|-
|-
| [[26/7]] || 4671.702 || 87.843 || 55.751
| [[59/8]] || 3459.172 || 91.036 || 69.063
|-
|-
| [[41/11]] || 4677.744 || 85.795 || 47.040
| [[37/5]] || 3465.030 || 90.729 || 74.001
|-
|-
| [[15/4]] || 4688.269 || 83.951 || 41.161
| [[52/7]] || 3471.702 || 90.110 || 66.126
|-
|-
| [[79/21]] || 4693.756 || 84.476 || 42.777
| [[67/9]] || 3475.397 || 89.685 || 60.509
|-
|-
| [[34/9]] || 4701.045 || 86.473 || 49.874
| [[97/13]] || 3479.368 || 89.251 || 55.971
|-
|-
| [[72/19]] || 4706.397 || 88.289 || 58.672
| [[15/2]] || 3488.269 || 88.748 || 51.847
|-
|-
| [[19/5]] || 4711.199 || 89.736 || 68.979
| [[158/21]] || 3493.756 || 88.946 || 53.484
|-
|-
| [[42/11]] || 4719.463 || 91.259 || 77.587
| [[83/11]] || 3498.729 || 89.408 || 57.716
|-
|-
| [[23/6]] || 4726.319 || 91.578 || 75.085
| [[53/7]] || 3504.679 || 90.087 || 66.089
|-
|-
| [[27/7]] || 4737.039 || 91.235 || 67.108
| [[38/5]] || 3511.199 || 90.725 || 74.056
|-
|-
| [[31/8]] || 4745.036 || 91.079 || 63.942
| [[84/11]] || 3519.463 || 91.165 || 67.580
|-
|-
| [[35/9]] || 4751.230 || 91.213 || 65.968
| [[23/3]] || 3526.319 || 91.334 || 65.218
|-
|-
| [[39/10]] || 4756.169 || 91.411 || 70.041
| [[77/10]] || 3533.830 || 91.570 || 67.961
|-
|-
| [[47/12]] || 4763.552 || 91.583 || 75.574
| [[54/7]] || 3537.039 || 91.735 || 70.328
|-
|-
| [[55/14]] || 4768.806 || 91.356 || 77.552
| [[31/4]] || 3545.036 || 92.279 || 73.654
|-
|-
| [[63/16]] || 4772.736 || 90.874 || 77.783
| [[70/9]] || 3551.230 || 92.737 || 75.346
|-
|-
| [[75/19]] || 4777.069 || 89.998 || 70.399
| [[39/5]] || 3556.169 || 92.976 || 77.758
|-
|-
| [[95/24]] || 4781.872 || 88.659 || 60.160
| [[47/6]] || 3563.552 || 92.726 || 81.598
|-
|-
| [[127/32]] || 4786.422 || 87.219 || 52.446
| [[55/7]] || 3568.806 || 91.736 || 80.615
|-
|-
| [[191/48]] || 4790.960 || 85.884 || 46.901
| [[63/8]] || 3572.736 || 90.390 || 70.693
|-
|-
| [[387/97]] || 4795.532 || 84.929 || 43.501
| [[71/9]] || 3575.787 || 88.962 || 62.507
|-
|-
| [[4/1]] || 4800.000 || 84.596 || 42.308
| [[95/12]] || 3581.872 || 85.279 || 48.938
|}
 
=== 4/1 to 8/1 ===
{| class="wikitable mw-collapsible sortable"
|+ 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
| [[127/16]] || 3586.422 || 82.182 || 41.351
|-
|-
| [[389/97]] || 2404.456 || 64.076 || 21.670
| [[191/24]] || 3590.960 || 79.377 || 35.966
|-
|-
| [[193/48]] || 2408.993 || 67.714 || 24.873
| [[383/48]] || 3595.486 || 77.393 || 32.761
|-
|-
| [[129/32]] || 2413.473 || 72.852 || 30.181
| [[8/1]] || 3600.000 || 76.672 || 31.713
|}
 
=== 8/1 to 16/1 ===
{| class="wikitable mw-collapsible sortable"
|+ style="font-size: 105%;" | Harmonic entropy of just intervals size 3600 to 4800{{c}}
|-
|-
| [[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 ===
{| class="wikitable mw-collapsible sortable"
|+ Harmonic entropy of just intervals size 3600 to 4800¢
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
! Just interval !! Size (cents) !! Entropy (Réyni 1.0) !! Entropy (Réyni 7.0)
|-
|-
Line 2,098: Line 1,691:
* [[Runoff]]
* [[Runoff]]


[[Category:Tables]][[Category:Harmonic entropy]]
[[Category:Lists of intervals]]
[[Category:Harmonic entropy]]
Retrieved from "https://en.xen.wiki/w/Harmonic_entropy_of_just_intervals"