Pietro Mengoli’s Theory of Perception of Musical Intervals:
A Mathematical Approach to the Sense of Hearing in the Scientific Revolution

OAI Takaharu

Pietro Mengoli, an Italian mathematician during the scientific revolution, maintained in his Speculationi di musica (1670) that the sense of hearing was the only agent for recognizing musical intervals. This assertion was revolutionary because most contemporary musical theorists in the Quadrivium tradition believed that reason judged the intervals perceived by the sense of hearing.
Mengoli’s accounts of hearing are based on mechanics. He believed air was a particulate matter and that the human soul counted each air particle transmitted from high and low sounds, abstracted the logarithm of the ratio of these numbers, and finally recognized the size of the interval. The air particles were not counted using reason, but by using the sense of hearing only. However, because the cognitive faculty of the sense of hearing is limited, the sizes and errors of intervals the sense can recognize are also limited.
When the human soul is faced with intervals with errors that the sense of hearing cannot recognize, it tends to accept them as pure intervals defined by ratios of limited integers that can be counted by the sense of hearing. This theory shows that Mengoli considered interval perception to be an active operation the soul carries out by categorizing intervals.
Mengoli’s discourse on music offers us a fresh insight into the rationalistic current of thought about the sense of hearing in early modern Europe.

Keywords: Pietro Mengoli, Music Theory, Perception, the Sense of Hearing, the Scientific Revolution