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Explore the mathematical foundations of sound, music, and harmony in this 57-minute Christmas Lecture from 1978. Discover how music is produced through sound wave creation, learn about the workings of the human ear and brain's interpretation of nerve impulses, and witness demonstrations using the Brazilian berimbau instrument. Examine the harmonic theorem - described as "the most astonishing mathematical result in music" - which was conjectured by Bernoulli in 1753, proved mainly by Fourier in 1807, and completed by Dirichlet in 1829, showing how any wave motion on a wire equals the sum of simple harmonics. Understand how harmonics function as the "ear's natural slide-rule" and observe the construction of various musical scales, including the pentatonic scale and Bach's well-tempered clavier that divides the octave into 12 equal semitones forming the basis of Western music. Learn about the missing seventh harmonic in modern music and hear how refreshing melodies sound when this harmonic is restored, all presented through practical demonstrations that reveal the nature and beauty of mathematical theorems in musical applications.
