Beats and the Origins of Early Modern Science

In chapter eight of his Spiegel der Orgelmacher and Organisten (1511), the German organist and builder of church organs, Arnolt Schlick, explains that when playing music, on keyboard instruments in particular, it is impossible to have all consonant intervals tuned as pure. After giving some examples of this, Schlick goes on to indicate that a variety of systems have been invented towards arriving at a scale that is at least acceptable to our hearing. The practical guidelines that follow upon his theoretical introduction begin with the following passage:
Now, beginning on gamut F fa ut in the manual, the fifth ascending from it to tenor C: do not make it high enough, or completely pure, but hovering somewhat lower, as much as the ear can stand, yet in such a way that one does not easily notice the above mentioned deficiency unless the keys or notes of this said fifth are touched and held still for a while. Then one may hear how it sounds somewhat unsteady and wavering, and resists, and desires to unite again.