After Sauveur’s death, acoustics can be seen as a evolving discipline. Musicians and mathematicians were confronted with the new results, in particular the existence of higher harmonics. Musicians include Jean Philippe RameauRameau, Jean Philippe and Giuseppe Tartini,Tartini, Giuseppe two of the most famous composers (and performers) of the 18th century, while mathematicians include Jean d’Alembert and Leonard Euler, Euler, Leonhardtwo of the most famous mathematicians of the 18th century. However, key achievements occurred in the 19th century, particularly with the work of Hermann Helmholtz,Helmholtz, Hermann considered the father of contemporary acoustics. In his masterpiece Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik of 1863, he developed an important set of arguments. In this text, HelmholtzHelmholtz, Hermann proposed a new theory of consonances based on beats, generalizing Sauveur’s ideas, a detailed analysis of Tartini’s results on the third sound and, finally, a sufficiently convincing explanation of the meaning of Ohm’s law,Ohm, George Simon according to which all the properties of sounds are explained by the presence of elementary tones described by sinusoidal waves of given frequency; the amplitudes of these tones can be determined by Fourier’s analysis.Fourier, Jean Baptiste Joseph

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Epilogue

  • Danilo Capecchi,
  • Giulia Capecchi

摘要

After Sauveur’s death, acoustics can be seen as a evolving discipline. Musicians and mathematicians were confronted with the new results, in particular the existence of higher harmonics. Musicians include Jean Philippe RameauRameau, Jean Philippe and Giuseppe Tartini,Tartini, Giuseppe two of the most famous composers (and performers) of the 18th century, while mathematicians include Jean d’Alembert and Leonard Euler, Euler, Leonhardtwo of the most famous mathematicians of the 18th century. However, key achievements occurred in the 19th century, particularly with the work of Hermann Helmholtz,Helmholtz, Hermann considered the father of contemporary acoustics. In his masterpiece Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik of 1863, he developed an important set of arguments. In this text, HelmholtzHelmholtz, Hermann proposed a new theory of consonances based on beats, generalizing Sauveur’s ideas, a detailed analysis of Tartini’s results on the third sound and, finally, a sufficiently convincing explanation of the meaning of Ohm’s law,Ohm, George Simon according to which all the properties of sounds are explained by the presence of elementary tones described by sinusoidal waves of given frequency; the amplitudes of these tones can be determined by Fourier’s analysis.Fourier, Jean Baptiste Joseph