Musical key extraction using diffusion maps

• We use nonlinear dimensionality reduction to provide a mapping for musical keys.
• We provide a Diffusion Maps based classification framework for musical keys.
• We propose a method for determining the Diffusion Maps׳ kernel׳s scale for classification tasks.
• We demonstrate the key extraction framework on The Beatles data set.

We propose a method for automatic musical key extraction using a two-stage spectral dimensionality reduction (two consecutive mappings). First we build a data set representing the 24 Western musical keys, and then we use a nonlinear dimensionality reduction method, in order to understand the true manifold on which the musical keys lie. The order of the keys along the manifold is perfectly correlated with a cognitive model for the key space. We exploit this manifold in order to extract the musical key from a musical piece. Furthermore we propose three classifiers using the extracted manifold. The Classifiers work in two stages, by first estimating the mode and then by estimating the key within the estimated mode. Finally we examine our method on The Beatles data set and demonstrate its improved performance compared to various existing methods.