Well, seems I guessed wrong, I guess I should have asked before writing such a long text.

so heres an example of a recurrent sequence for

mavila: 7 9 16 25 41

and heres

meantone: 5 7 12 19 31

father: 5 8 13 21 34

I first didn't find any explanation why 5 7 12 ... generates meantone EDOs. Like the sequence of fibonacci ratios 5/8, 8/13, 13/21 converges to the golden ratio, I tried 7/12, 12/19, 19/31, ... , which seems to converge to a value slightly above the perfect fifth*, which doesn't seem to have any specific relation to meantone temperament. Then I realized there are two different recurrent sequences, from which ratios can be built that seem to converge to some kind of meantone fifth at ~ 696.2 Cent:

`EDO sequence: 2 5 7 12 19 31 50 81 ...`

MT 5th sequence: 1 3 4 7 11 18 29 47 ...

Ratios: 1/2 3/5 4/7 7/12 11/19 18/31 29/50 47/81 ...

(again, ratios in octave = 1/1200 Cent)

This seems to work for any such sequence of EDO tunings, and with any pair of scale degrees (like 7th degree in 12-EDO and 11th degree in 19-EDO) as a starting point for another sequence. It has something to do with a/b < c/d being equivalent to a/b < (a+c)/(b+d) < c/d (unless certain values equal zero), for example:

11/19 < 7/12 <=> 11/19 < 18/31 < 7/12,

11/19 < 18/31 <=> 11/19 < 29/50 < 18/31, and so on ...

I still prefer the fifth from 31-EDO, I think it's almost perfect for meantone.

*19/31 can be interpreted as 19/31 octave = 1200 * 19/31 Cent = 2^(19/31) as a frequency ratio, which is slightly greater than 3/2, the ratio of the perfect fifth.