The Gaussian (normal) distribution provides a symmetric bell-curve probability shape useful for generating clustered musical choices

The normal distribution (Gaussian, bell curve) is a symmetric probability distribution parametrised by mean and standard deviation. It arises naturally as the limit of sums of independent random variables (central limit theorem). In algorithmic composition, the normal distribution can generate clusters of notes around a central pitch or time, with tighter clusters for smaller standard deviation. For discrete musical domains (notes, rhythms), the continuous Gaussian must be rounded or mapped to the nearest discrete value. The distribution’s unbounded tails mean that extreme values are possible but rare; composers may clamp or fold these outliers back into range.

Examples

Xenakis used Gaussian distributions to sculpt pitch clouds in Metastasis and other stochastic works. In SuperCollider: LFGauss or GaussTrig can drive pitch selection.

Assessment

What two parameters define a normal distribution? How would you use a normal distribution to generate pitches that cluster around a central note with occasional large leaps?