Music is the pleasure that the human soul encounters from counting without knowing that it is counting.
Source: A letter to Christian Goldbach
Thoughts on the quote: People have many ideas about what music is. It is not surprising that Leibniz, who was a mathematician, would emphasize the mathematical aspects of counting. But, as a philosopher, he throws in the idea of the soul and also of doing something without knowing one is doing it. The fact that Leibniz lived in the age when contrapuntal music (e.g. that of Johann Sebastian Bach) was at its height is not a coincidence.
About the author: Leibniz (1646-1714) was a polymathic genius who made huge contributions to mathematics (he and Newton invented calculus independently and pretty much simultaneously), philosophy (he was a radical optimist), computing (he invented several mechanical calculators), physics, probability theory, biology, medicine, geology and linguistics (he tried to invent a universal language), among other things.