A perfect fifth at a 1.5 ratio sounds perfect because some of the partials overlap, and because our brain is wired to respond to pitch ratios that occur in harmonic series. 1.5 is the ratio between the second and third partials of a harmonic sound.
There’s a problem, though. Take a violin, and tune the open A string to 440 Hz. This means that at a 1.5 ratio, the open E string is tuned to 660 Hz. Play both string together. Beautiful. Now, tune the open D string to 293.3333 Hz. Play D and A together. Another beautiful fifth.
Now, place your finger on the A string to play a B. Play that B together with the open D string until it sounds perfect. You now have a beautiful major sixth, and your B rings at 488.8888 Hz (293.333 * 5/3). Now play that B with the open E string.
What happened? B and E, that’s a perfect fourth: 4/3. 488.8888 * 4/3 = 651.85. Not 660. If you want to play a B and an E together on a violin, you need to tune your B at 495 Hz. That’s the headache of just intonation. On a fretless instrument like the violin, the player can adjust the pitch of each note (and add vibrato to mask potential problems), but keyboard players are out of luck. Hence equal temperament.
Back to physics and the brain.
The harmonic series describes the relative frequencies present in the motion of a perfect string or column of air. A perfect string is infinitely thin and moves only in one dimension. Real strings are not perfect. If you’re talking about piano strings and vocal cords they’re really not perfect. This means that they behave more like thin plates than perfect strings, and hence their partials are not at integer ratios.
The harmonics of a ringing piano string and a bunch of other sounds are at roughly integer ratios. As far as your brain is concerned, all that matters is being able to tell if two partials were caused by the same event, and so the brain tolerates some amount of deviation from the perfect harmonic series.
So, as far as your brain is concerned, a ratio of 1.498 for a fifth is good enough, and it allows keyboard players to play in any key without risk of playing an interval that isn’t good enough for your brain, as in the violin example above.