It's interesting to see what plugins adds to a signal with a frequency analyzer.
To learn more about fundamental frequency, 2nd and 3rd harmonics, please read: Analysis of a string
Try this by feeding a simple sine wave into the plugin. Put the frequency analyzer after the plugin you want to analyze. The analyser I'm using is the great (and free) MAnalyzer from Melda Productions
This is what we expect to see in the frequency analyzer with a 220 Hz test tone
Most analog equipment adds some sort of even- and/or odd harmonic distortion. Harmonic distortion usually enhances sound at reasonable levels. The best plugin I have found, so far, for adding even and/or odd harmonics is the Waves Cobolt Saphira. If you can get your head around what harmonic distortion is, then this plugin really makes sense.
With a 100 Hz sine wave test tone and only even harmonics (EDGE)
Even harmonics frequency analysis. Even harmonics added to 100 Hz results in 200 Hz, 400 Hz, 600 Hz, etc
Only odd harmonics
Odd harmonics frequency analysis. Odd harmonics added to 100 Hz results in 300 Hz, 500 Hz, 700 Hz, etc
Even and odd harmonics together
Even and odd harmonics frequency analysis