Find the best equal temperament for an instrument - from the spectrum

For percussion containing wood or metal bars with free ends, the pattern of harmonic partials is irregular. Sethares (2010) calculated the pattern of the first 6 partials as:

        f, 2.76f, 5.41f, 8.94f, 13.35f, and 18.65f

P.1

Then, I calculated and draw the dissonant curve:

The dissonant curve


After that find the frequencies with consonant intervals, the green frequencies below come from the simple ratios from the harmonic pattern (P.1) and the blue one comes from the curve. The middle column is the ratios between each consonant step.
consonant freq.ratio b/w eachlog(octave)/
log(r between)
220
259.21.1781818184.126597564
302.51.1670524694.380129661
329.62962961.0896847267.878224355
362.32902031.0992003997.154014395
432.8
avg1.1335298535.884741494

The main concept of finding the best number of equal temperaments is to capture all of the consonant steps as close as possible with limited steps within a reasonable range. (For example, 120 steps with an octave can possibly capture all the consonant intervals, but not practical for actual performance.)
To look at individual consonant frequency ratio between each and come a good number. 
If our destination is 6m away and each consonant step is 0.5 m in length, the best equal steps are 12. In this module, each step is equal-distance. However, in the interval above, as the milestones in the journey, ratios between each consonant interval are not equal. We have to find a middle ground. The log(octave)/log(ratio in between) converts the distance into how many steps. For example, the ratio of 1.178 takes 4.12 steps to the octave (1.178^4.12=1.967). The ratio between 432:362 is omitted since other intervals have been compared to 432 in order to prevent the data from duplicating.

The average number of steps is 5.88. The number has to be an integer or at least very close to it, we cannot take half step. By doubling it, splitting a step in half, 12-TET is a balance option.
12 tetdiff %
220
232.7616328
246.2635351
260.54864780.5203116609
275.6624032
291.6528685
308.57089952.006908916
326.4703018-0.9584477626
345.4080024
365.44423010.8597737309
386.6427077
409.0708544
432.8
.
By continuing splitting a step in half, 47-TET is very close to the integer steps.
steps
15.884741494
211.76948299
317.65422448
423.53896598
529.42370747
635.30844896
741.19319046
847.07793195
952.96267345
1058.84741494
1164.73215643
1270.61689793

Calculation in this google sheet. In the tab of PERCU.


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