The acronym COFT stands for Calculated Optimum Fixed Tuning, was coined by John de Laubenfels (see below), and concerns adaptive-tuning and adaptive-JI.
If the tuning of a piece is fixed, then two of the three spring types disappear: horizontal motion within a pitch is gone, so the value of those springs is of no importance. Grounding becomes a non-issue, because drift is impossible with a fixed tuning, and any tuning can be moved in absolute tuning space so that average deflection is zero (or, notes are tuned only down from 12-tET, or whatever...). So the only thing left to worry about is to sum the values of all the vertical springs and then relax them to the least pain position.
[As an example:]
I now attach an actual table output for one of the pieces on my web site (http://www.adaptune.com) (a piece which works particularly well in COFT), Mozart's Andante für Orgelwalze, K.616, sequence by Hans Jakob Heldstab. The piece is in the key of F major. This is a 5-limit target tuning; COFT for 7-limit tunings is problematical.
How to read the table:
In this table 0 == C, 1 == C# and/or Db, etc. Note that the interval most strongly represented is C to E (0 to 4), the fifth degree and the leading tone, with strength 451.285. That either is or is not surprising...
A reformulation of the relationships among the columns:
Force = Strength * (Actual - Ideal) Pain = 0.5 * Strength * (Actual - Ideal)^2
Which implies,
Pain / Force = 0.5 * (Actual - Ideal)
Pain = Force * 0.5 * (Actual - Ideal)
Pain = Force * (Actual - Ideal) / 2.0
Ptch Tuning Ptch Tuning Strength Ideal Actual Force Pain
---- ------ ---- ------ -------- -------- -------- ---------- ----------
0 5.23 1 -4.94 5.832 96.923 89.831 -41.358 146.656
0 5.23 2 -2.23 46.949 200.941 192.544 -394.208 1654.979
0 5.23 3 9.09 37.199 311.141 303.866 -270.626 984.403
0 5.23 4 -7.74 451.285 386.241 387.032 356.875 141.108
0 5.23 5 5.80 226.761 498.038 500.571 574.442 727.603
0 5.23 6 -14.35 9.708 592.176 580.420 -114.132 670.889
0 5.23 7 4.54 359.893 701.937 699.319 -942.430 1233.942
0 5.23 8 15.45 41.169 813.253 810.225 -124.669 188.763
0 5.23 9 -6.33 253.599 885.373 888.445 778.823 1195.914
0 5.23 10 4.72 88.399 996.772 999.494 240.608 327.447
0 5.23 11 -9.23 9.339 1092.321 1085.540 -63.327 214.711
1 -4.94 0 5.23 5.832 1103.077 1110.169 41.358 146.656
1 -4.94 2 -2.23 3.059 99.584 102.713 9.572 14.976
1 -4.94 3 9.09 0.366 203.955 214.035 3.691 18.602
1 -4.94 4 -7.74 63.831 310.355 297.201 -839.596 5521.784
1 -4.94 5 5.80 16.209 387.663 410.740 374.065 4316.228
1 -4.94 6 -14.35 2.292 498.885 490.589 -19.014 78.867
1 -4.94 7 4.54 15.344 600.124 609.488 143.681 672.720
1 -4.94 8 15.45 0.732 701.977 720.394 13.485 124.180
1 -4.94 9 -6.33 24.272 813.326 798.614 -357.097 2626.886
1 -4.94 10 4.72 45.310 895.760 909.663 629.968 4379.358
1 -4.94 11 -9.23 0.346 996.045 995.709 -0.116 0.020
2 -2.23 0 5.23 46.949 999.059 1007.456 394.208 1654.979
2 -2.23 1 -4.94 3.059 1100.416 1097.287 -9.572 14.976
2 -2.23 3 9.09 2.323 111.876 111.322 -1.287 0.356
2 -2.23 4 -7.74 16.489 194.369 194.488 1.966 0.117
2 -2.23 5 5.80 138.697 313.790 308.027 -799.406 2303.756
2 -2.23 6 -14.35 52.589 386.459 387.876 74.502 52.773
2 -2.23 7 4.54 140.572 498.037 506.775 1228.231 5365.742
2 -2.23 8 15.45 5.110 603.257 617.681 73.711 531.601
2 -2.23 9 -6.33 159.585 701.941 695.900 -963.948 2911.292
2 -2.23 10 4.72 101.993 813.028 806.950 -619.897 1883.826
2 -2.23 11 -9.23 75.134 884.724 892.996 621.502 2570.492
3 9.09 0 5.23 37.199 888.859 896.134 270.626 984.403
3 9.09 1 -4.94 0.366 996.045 985.965 -3.691 18.602
3 9.09 2 -2.23 2.323 1088.124 1088.678 1.287 0.356
3 9.09 4 -7.74 0.566 92.079 83.166 -5.048 22.494
3 9.09 5 5.80 7.689 199.961 196.705 -25.035 40.756
3 9.09 6 -14.35 2.365 299.082 276.554 -53.284 600.189
3 9.09 7 4.54 25.943 386.837 395.453 223.525 962.928
3 9.09 8 15.45 7.423 498.023 506.359 61.878 257.914
3 9.09 9 -6.33 10.336 587.268 584.579 -27.800 37.383
3 9.09 10 4.72 10.261 701.977 695.628 -65.147 206.811
3 9.09 11 -9.23 12.282 812.395 781.674 -377.311 5795.754
4 -7.74 0 5.23 451.285 813.759 812.968 -356.875 141.108
4 -7.74 1 -4.94 63.831 889.645 902.799 839.596 5521.784
4 -7.74 2 -2.23 16.489 1005.631 1005.512 -1.966 0.117
4 -7.74 3 9.09 0.566 1107.921 1116.834 5.048 22.494
4 -7.74 5 5.80 18.108 111.736 113.539 32.642 29.421
4 -7.74 6 -14.35 1.586 202.709 193.388 -14.786 68.908
4 -7.74 7 4.54 376.137 315.014 312.287 -1025.750 1398.642
4 -7.74 8 15.45 2.173 427.706 423.193 -9.809 22.135
4 -7.74 9 -6.33 97.215 498.177 501.413 314.560 508.915
4 -7.74 10 4.72 46.695 606.077 612.462 298.140 951.786
4 -7.74 11 -9.23 23.293 701.977 698.508 -80.808 140.168
5 5.80 0 5.23 226.761 701.962 699.429 -574.442 727.603
5 5.80 1 -4.94 16.209 812.337 789.260 -374.065 4316.228
5 5.80 2 -2.23 138.697 886.210 891.973 799.406 2303.756
5 5.80 3 9.09 7.689 1000.039 1003.295 25.035 40.756
5 5.80 4 -7.74 18.108 1088.264 1086.461 -32.642 29.421
5 5.80 7 4.54 72.968 202.097 198.748 -244.348 409.120
5 5.80 8 15.45 37.645 313.133 309.654 -130.948 227.752
5 5.80 9 -6.33 335.699 386.204 387.874 560.530 467.970
5 5.80 10 4.72 63.070 498.076 498.923 53.415 22.619
5 5.80 11 -9.23 9.907 593.238 584.969 -81.922 338.712
6 -14.35 0 5.23 9.708 607.824 619.580 114.132 670.889
6 -14.35 1 -4.94 2.292 701.115 709.411 19.014 78.867
6 -14.35 2 -2.23 52.589 813.541 812.124 -74.502 52.773
6 -14.35 3 9.09 2.365 900.918 923.446 53.284 600.189
6 -14.35 4 -7.74 1.586 997.291 1006.612 14.786 68.908
6 -14.35 7 4.54 1.087 111.876 118.899 7.631 26.795
6 -14.35 9 -6.33 32.218 314.848 308.025 -219.841 750.059
6 -14.35 10 4.72 3.984 401.085 419.074 71.670 644.639
6 -14.35 11 -9.23 1.948 498.023 505.120 13.827 49.066
7 4.54 0 5.23 359.893 498.063 500.681 942.430 1233.942
7 4.54 1 -4.94 15.344 599.876 590.512 -143.681 672.720
7 4.54 2 -2.23 140.572 701.963 693.225 -1228.231 5365.742
7 4.54 3 9.09 25.943 813.163 804.547 -223.525 962.928
7 4.54 4 -7.74 376.137 884.986 887.713 1025.750 1398.642
7 4.54 5 5.80 72.968 997.903 1001.252 244.348 409.120
7 4.54 6 -14.35 1.087 1088.124 1081.101 -7.631 26.795
7 4.54 8 15.45 1.087 111.876 110.906 -1.054 0.511
7 4.54 9 -6.33 22.275 188.167 189.126 21.346 10.228
7 4.54 10 4.72 107.402 305.931 300.175 -618.188 1779.102
7 4.54 11 -9.23 99.459 386.338 386.221 -11.575 0.674
8 15.45 0 5.23 41.169 386.747 389.775 124.669 188.763
8 15.45 1 -4.94 0.732 498.023 479.606 -13.485 124.180
8 15.45 2 -2.23 5.110 596.743 582.319 -73.711 531.601
8 15.45 3 9.09 7.423 701.977 693.641 -61.878 257.914
8 15.45 4 -7.74 2.173 772.294 776.807 9.809 22.135
8 15.45 5 5.80 37.645 886.867 890.346 130.948 227.752
8 15.45 7 4.54 1.087 1088.124 1089.094 1.054 0.511
8 15.45 9 -6.33 3.005 92.079 78.220 -41.648 288.602
8 15.45 10 4.72 1.087 182.192 189.269 7.690 27.211
8 15.45 11 -9.23 6.564 288.028 275.315 -83.447 530.435
9 -6.33 0 5.23 253.599 314.627 311.555 -778.823 1195.914
9 -6.33 1 -4.94 24.272 386.674 401.386 357.097 2626.886
9 -6.33 2 -2.23 159.585 498.059 504.100 963.948 2911.292
9 -6.33 3 9.09 10.336 612.732 615.421 27.800 37.383
9 -6.33 4 -7.74 97.215 701.823 698.587 -314.560 508.915
9 -6.33 5 5.80 335.699 813.796 812.126 -560.530 467.970
9 -6.33 6 -14.35 32.218 885.152 891.975 219.841 750.059
9 -6.33 7 4.54 22.275 1011.833 1010.874 -21.346 10.228
9 -6.33 8 15.45 3.005 1107.921 1121.780 41.648 288.602
9 -6.33 10 4.72 12.072 110.641 111.050 4.930 1.007
9 -6.33 11 -9.23 10.725 191.502 197.096 59.991 167.785
10 4.72 0 5.23 88.399 203.228 200.506 -240.608 327.447
10 4.72 1 -4.94 45.310 304.240 290.337 -629.968 4379.358
10 4.72 2 -2.23 101.993 386.972 393.050 619.897 1883.826
10 4.72 3 9.09 10.261 498.023 504.372 65.147 206.811
10 4.72 4 -7.74 46.695 593.923 587.538 -298.140 951.786
10 4.72 5 5.80 63.070 701.924 701.077 -53.415 22.619
10 4.72 6 -14.35 3.984 798.915 780.926 -71.670 644.639
10 4.72 7 4.54 107.402 894.069 899.825 618.188 1779.102
10 4.72 8 15.45 1.087 1017.808 1010.731 -7.690 27.211
10 4.72 9 -6.33 12.072 1089.359 1088.950 -4.930 1.007
10 4.72 11 -9.23 3.839 85.216 86.046 3.187 1.323
11 -9.23 0 5.23 9.339 107.679 114.460 63.327 214.711
11 -9.23 1 -4.94 0.346 203.955 204.291 0.116 0.020
11 -9.23 2 -2.23 75.134 315.276 307.004 -621.502 2570.492
11 -9.23 3 9.09 12.282 387.605 418.326 377.311 5795.754
11 -9.23 4 -7.74 23.293 498.023 501.492 80.808 140.168
11 -9.23 5 5.80 9.907 606.762 615.031 81.922 338.712
11 -9.23 6 -14.35 1.948 701.977 694.880 -13.827 49.066
11 -9.23 7 4.54 99.459 813.662 813.779 11.575 0.674
11 -9.23 8 15.45 6.564 911.972 924.685 83.447 530.435
11 -9.23 9 -6.33 10.725 1008.498 1002.904 -59.991 167.785
11 -9.23 10 4.72 3.839 1114.784 1113.954 -3.187 1.323
---- ------ ---- ------ -------- -------- -------- ---------- ----------
painSum 57647.805
COFT is useful:
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