With a regular note (assuming your playing right-handed), only the part of the string on the right side of your fretting finger vibrates. When you play a harmonic, both sides vibrate, essentially playing 2 notes simultaneously.
When you move your fretting hand up the fretboard, in a regular note, the vibrating length is shorter (shorter length means a higher note).
With a harmonic, moving up the fretboard lengthens the length of the vibration on the left of your fretting finger, making it deeper. BUT, the length of string on the right becomes shorter at the same time, so the harmonic goes both higher and lower simultaneously.
This is why a harmonic on fret 24 sounds about the same as a harmonic on fret 5. The 2 lengths are equal (in reversed order).
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