Editing Musical acoustics (section)

== Harmonics and non-linearities ==
[[Image:Symmetric_and_asymmetric_waveforms.svg|thumb|A symmetric and asymmetric waveform. The red (upper) wave contains only the fundamental and odd harmonics; the green (lower) wave contains the fundamental and even harmonics.]]

When a periodic wave is composed of a fundamental and only odd harmonics ({{mvar|f}}, {{math|3 ''f''}}, {{math|5 ''f''}}, {{math|7 ''f''}}, ...), the summed wave is ''half-wave [[symmetric]]''; it can be inverted and phase shifted and be exactly the same. If the wave has any even harmonics ({{math|2 ''f''}}, {{math|4 ''f''}}, {{math|6 ''f''}}, ...), it is ''asymmetrical''; the top half of the plotted wave form does not mirror image the bottom.

Conversely, a system that changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics ([[harmonic distortion]]). This is called a ''[[non-linear]] system''. If it affects the wave symmetrically, the harmonics produced are all odd. If it affects the harmonics asymmetrically, at least one even harmonic is produced (and probably also odd harmonics).