This chapter is entirely devoted to Joseph Sauveur. First, the Traité de la théorie de musique is presented, which probably dates back to 1697, but was not published until the 20th century. The Traité contains a comprehensive analysis of most aspects of music theory of the time and is the basis for all the memoirs that Sauveur would publish for the Académie des sciences of Paris from 1701 to 1713. The text is fully analyzed in the first part of the chapter. Sauveur’s memoirs are then considered, including the 1700 account published in the Histoire de l’Académie. First, the 1701 memoir is presented in detail, which is certainly the most important, since it takes up in a concise but more mature way all the aspects reported in the 1697 Traité. In this memoir the division of the octave, the considerations on harmonic sounds and finally the method of determining the standard sound (fixed sound) are given. Three very interesting memoirs follow: one that applies the theory of harmonic sounds to the classification of organ stops, and two that give general systems for dividing the octave and for obtaining tempered systems. The last work, of 1713, completes the first memoir somewhat; the main result is the determination of an analytical relation of the absolute value of the frequency of a vibrating string as a function of the parameters on which it depends. In the last part of the chapter, we look at the minutes of the procès-verbaux of the Académie, in which some interesting results are given that shed light on Sauveur’s approaches and that have not yet been considered in the literature.