The work is divided into two major parts. In the first part, Fux presents a summary of the theory on "Musica Speculativa," or the analysis of intervals as proportions between numbers. This section is in a simple lecture style, and looks at music from a purely mathematical angle, in a theoretical tradition that goes back, through the works of Renaissance theoreticians, to the Ancient Greeks. Fux explains that intervals in exact mathematical proportions result in larger and smaller half tones, and he also mentions that some organists added extra keys (split halves to use smaller and bigger half tones), but that adding extra keys on a keyboard was problematic and for this reason they divided every note in "" (two equal parts), resulting in equal temperament. He continues: