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    http://richannel.org/christmas-lectures/1978/1978-christopher-zeeman#/christmas-lectures-1978-christopher-zeeman–waves-and-music

    Creating mathematical harmony with music.
    In his fifth Christmas Lecture, Christopher Zeeman turns his attention to the mathematics of sound, music and harmony.
    With the Brazilian berimbau as his instrument of choice (and aided by his three children) Zeeman demonstrates how music is produced – from the creation of sound waves to the workings of the human ear and the brain’s unique interpretation of nerve impulses. 
    We are then introduced to the “most astonishing mathematical result in music”: the harmonic theorem. Conjectured by Bernoulli  in 1753, proved mainly by Fourier in 1807 and with the proof completed by Dirichlet in 1829, the theorem shows how any wave motion on a wire is the sum of simple harmonics.
    Using harmonics – the “ear’s natural slide-rule” – Zeeman demonstrates how various musical scales are constructed, including the popular pentatonic scale and Bach’s famous well-tempered clavier which divides the octave into 12 equal semitones and forms the basis of most Western music.
    He also shows us where the seventh harmonic is missing from today’s modern music and we hear how refreshing a melody can sound when it is put back.

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