Head-related transfer function individualization is a key matter in binaural synthesis. However, currently available databases are limited in size compared to the high dimensionality of the data. In this paper, the process of generating a synthetic dataset of 1000 ear shapes and matching sets of pinna-related transfer functions (PRTFs), named WiDESPREaD (wide dataset of ear shapes and pinna-related transfer functions obtained by random ear drawings), is presented and made freely available to other researchers. Contributions in this article are threefold. First, from a proprietary dataset of 119 three-dimensional left-ear scans, a matching dataset of PRTFs was built by performing fast-multipole boundary element method (FM-BEM) calculations. Second, the underlying geometry of each type of high-dimensional data was investigated using principal component analysis. It was found that this linear machine-learning technique performs better at modeling and reducing data dimensionality on ear shapes than on matching PRTF sets. Third, based on these findings, a method was devised to generate an arbitrarily large synthetic database of PRTF sets that relies on the random drawing of ear shapes and subsequent FM-BEM computations.