Jewels in Her Crown: Treasures of Columbia University Libraries Special Collections

Exhibition Themes > Music > 225. Leonard Euler

225.  Leonard Euler (1707-1783).  Tentamen novae theoriae musicae. St. Petersburg: Typographia Academiae Scientiarum, 1739. Gabe M. Wiener Music & Arts Library

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

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