A sine and a bright harmonic stack can share the same peak meter yet sound worlds apart, because human loudness is weighted by spectral content.
In the world
Mastering engineers talk about LUFS, not peak amplitude, because the ear averages over about 400 ms; a sharp transient can peak high yet feel quiet, while a dense drone can feel loud with modest peaks.
A pure sine at peak 1.0 and a harmonically rich patch at peak 1.0 will not sound equally loud. The rich patch wins because the ear sums energy across the critical bands of the cochlea, and the extra partials each contribute. To balance two patches by ear you must match perceived loudness, not peaks.
Two VCAs, one fed by a sine, one fed by a harmonic stack. Adjust their gains until they sound equally loud when you A/B them. The scope will show wildly different peaks.
Did you know?
Fletcher and Munson mapped human loudness perception in 1933 by asking volunteers to compare tones for hours. They discovered that at low volumes your ears are nearly deaf to bass - you need 60 dB more power at 30 Hz to match the perceived loudness of 1 kHz. This is why the "loudness" button on old stereos boosts bass.
Explore
A neon balance scale floats on the right. On the left pan sits a single sine sphere; on the right sit stacked harmonic spheres. Drag to adjust the balance. A VU meter in the center shows perceived loudness. Try to level the scale by ear - you will find the harmonic stack needs far less amplitude to feel equally loud.