Even and Odd Transfer Function

When the transfer function is an odd function¹, the spectrum contains only odd-numbered harmonics.
When the transfer function is even², the spectrum contains only even-numbered harmonics, thereby doubling the fundamental frequency and raising the pitch of the sound by an octave.

**Figure 8:** Output Spectrum of even and odd Transfer Functions.
$\scalebox{0.7}{\includegraphics{eps/evenodd.eps}}$

``Music 270a: Waveshaping Synthesis'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).