This is a bit out of topic, but actually the sequence `sounds' really good! If, on each row, we consider the sequence of numerators and denominators and we interpret them as note durations for two performers respectively, we find that these lines are mirrored as in table canons.

I'm sharing the link of a ``mathematical rhythm'' I made. You can find it here: http://www.mariamannone.com/estratti_audio/math_rhythm.mp3

or here: https://soundcloud.com/maria-mannone/mathematical-rhythm

These are the lines I considered:

$$ \frac{1}{1}, $$

$$ \frac{1}{2}, \frac{2}{1}, $$

$$ \frac{1}{3}, \frac{3}{2}, \frac{2}{3}, \frac{3}{1}, $$

$$ \frac{1}{4}, \frac{4}{3}, \frac{3}{5}, \frac{5}{2}, \frac{2}{5}, \frac{5}{3}, \frac{3}{4}, \frac{4}{1}, $$

$$ \frac{1}{5}, \frac{5}{4}, \frac{4}{7}, \frac{7}{3}, \frac{3}{8}, \frac{8}{5}, \frac{5}{7}, \frac{7}{2}, \frac{2}{7}, \frac{7}{5}, \frac{5}{8}, \frac{8}{3}, \frac{3}{7}, \frac{7}{4}, \frac{4}{5}, \frac{5}{1}, $$

I'm sharing the link of a ``mathematical rhythm'' I made. You can find it here: http://www.mariamannone.com/estratti_audio/math_rhythm.mp3

or here: https://soundcloud.com/maria-mannone/mathematical-rhythm

These are the lines I considered:

$$ \frac{1}{1}, $$

$$ \frac{1}{2}, \frac{2}{1}, $$

$$ \frac{1}{3}, \frac{3}{2}, \frac{2}{3}, \frac{3}{1}, $$

$$ \frac{1}{4}, \frac{4}{3}, \frac{3}{5}, \frac{5}{2}, \frac{2}{5}, \frac{5}{3}, \frac{3}{4}, \frac{4}{1}, $$

$$ \frac{1}{5}, \frac{5}{4}, \frac{4}{7}, \frac{7}{3}, \frac{3}{8}, \frac{8}{5}, \frac{5}{7}, \frac{7}{2}, \frac{2}{7}, \frac{7}{5}, \frac{5}{8}, \frac{8}{3}, \frac{3}{7}, \frac{7}{4}, \frac{4}{5}, \frac{5}{1}, $$