Originally Posted by okto

That's how harmonics work. Harmonics are basically amplification of oscillation where two or more oscillation periods coincide. They can't occur at fractional ratios, because the oscillations have to be in-phase, IE, whole-number multiples of each other.
Think about making waves in a bathtub: when you splash at a regular frequency, the waves get bigger because each new impulse coincides with the crest or trough of the existing waves.
I just realized harmonics are really difficult to explain.

Our hypothetical 12-bladed fan produces a harmonic oscillation for every balanced pair of blades. Essentially, axes of symmetry on a rotating mass create oscillations at regular intervals. Non-prime numbers of blades will result in more axes of symmetry.
So the 12-blade fan oscillates at w(rate of rotation)/1, w/2, w/3, w/4, w/6, and w/12.

A 13-bladed fan will only oscillate at w/1 and w/13, and so will seem much quieter. The two oscillation frequencies do not have any common factors, so no harmonic amplification, so less vibration, so less noise.

Clear as mud?

Originally Posted by tbomachines

Except, regardless of how many blades it has, if they are all equal in length and spaced out evenly they will amplify like crazy. That's because each one would have the same wavelength relative to the last and following blade, they would all be generating identical pulses.

Originally Posted by tbomachines

Except, regardless of how many blades it has, if they are all equal in length and spaced out evenly they will amplify like crazy. That's because each one would have the same wavelength relative to the last and following blade, they would all be generating identical pulses.