Most pitched sounds can be thought of as a collection of harmonics or overtones, which are sine waves spaced equally in frequency. The first harmonic is defined to be at the fundamental frequency, the second harmonic at twice the fundamental frequency, the third harmonic at three times, etc. (Pierce [1992] contains a good explanation of this.) The even/odd harmonic balance parameter is a measure of the overall amplitude of the first, third, fifth, etc., harmonics versus the overall amplitude of the second, fourth, sixth, etc. Listening to only the odd harmonics of a tone gives a sound something like a square wave; listening to only the even harmonics sounds somewhat similar to a note played an octave higher with the same spectrum.
This may seem like a strange parameter, but it is actually quite meaningful. Many acoustic musical instruments have different balances of odd and even harmonics, and this balance can fluctuate dramatically over the time course of the note. This even/odd balance and its variation over time have potent effects on tone quality (Krimphoff, McAdams, and Winsberg 1994). For example, the timbral difference that comes from picking a guitar at different points on the string has a lot to do with this balance.
Most synthesis algorithms make it easy to manipulate this balance. In physical modeling synthesis, one can make models of open and closed tubes or strings plucked or bowed at various critical points along the string. Frequency modulation (FM) synthesis provides a natural mechanism by mixing simple FM patches with differing carrierto-modulator ratios. Waveshaping synthesis has its odd and even distortion function components, and additive synthesis affords direct control over the spectral content. Even subtractive synthesis with poles and zeros allows for tight control over the even/odd balance (Smith 1993).
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