Swiss mathematician and scientist Leonard Euler's residency in Russia
coincided with the grand cultural vision of Catherine the Great and her
determination to Europeanize Russia. Under Catherine's patronage science, the
arts and trade flourished. Catherine is credited with luring Euler back to St.
Petersburg during the Enlightenment. He was one of the first mathematicians to
apply calculus to physics, and is considered to be one of the most prolific
mathematicians of all time. He was the perfector of integral calculus, the
inventor of calculus using sines, and is particularly renowned for his study of
motion.
Euler presented a developed theory of consonance, based upon an explicit,
mathematical rule for determining the ‘simplicity' of a set of frequencies such
as those making up a chord. He derived his rule from ideas of the ancients,
Ptolemy in particular. It could not take account of difference tones and
summation tones, for they had not yet been reported, but it permitted Euler to
determine by routine calculations the most complete systems of scales or modes
ever published. The last chapter of this work sketches a theory of modulation.
Euler thus began to construct a mathematical theory of the consonance of a
progression of chords.
From Dr. Anderson's Collection, Given by the Alumni
