I see what you mean. Still I would argue that both tritones and minor thirds only appear to possess the symmetrical property as a result of temperament. It does

I see what you mean. Still I would argue that both tritones and minor thirds only appear to possess the symmetrical property as a result of temperament. It doesn't exist 'in nature' as such. The frequency ratios that they represent, 7/5 and 6/5, respectively, don't lend themselves to the same type of symmetry. If you have a tritone, 7/5, you would need a 10/7 ratio to make the octave, which would be a different interval (although close). With a minor third (6/5), if you were to stack the intervals starting from let's say 500 Hz, you would go to 600, 720, 864, and 1036.8, and you'd be off 36.8 Hz from the octave.