Number theoretical means of resolving a mixture of several harmonic sounds

In this paper, a number theoretical method is developed for the purpose of analyzing the spectre of a mixture of harmonic sounds. The method is based on the properties of prime numbers and on non-linear filtering. It is shown that a number theoretical approach is of vital importance in order to detect and observe harmonic sounds in musical polyphonies. The method is verified by applying it to the automatic transcription of piano music.