A metal film perforated by a regular array of subwavelength holes shows unexpectedly large transmission at particular wavelengths, a phenomenon known as the extraordinary optical transmission (EOT) of metal hole arrays(1). EOT was first attributed to surface plasmon polaritons, stimulating a renewed interest in plasmonics(2-4) and metallic surfaces with subwavelength features(5-7). Experiments soon revealed that the field diffracted at a hole or slit is not a surface plasmon polariton mode alone8. Further theoretical analysis(9) predicted that the extra contribution, from quasi-cylindrical waves(10-13), also affects EOT. Here we report the experimental demonstration of the relative importance of surface plasmon polaritons and quasi-cylindrical waves in EOT by considering hole arrays of different hole densities. From the measured transmission spectra, we determine microscopic scattering parameters which allow us to show that quasi-cylindrical waves affect EOT only for high densities, when the hole spacing is roughly one wavelength. Apart from providing a deeper understanding of EOT, the determination of microscopic scattering parameters from the measurement of macroscopic optical properties paves the way to novel design strategies.