On the sensations of tone as a physiological basis for the theory of music / by Hermann L.F. Helmholtz ; translated, thoroughly revised and corrected, rendered conformable to the 4th (and last) German edition of 1877, with numerous additional notes and a new additional appendix bringing down information to 1885, and especially adapted to the use of musical students, by Alexander J. Ellis.

  • Hermann von Helmholtz
Date:
1895
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Licence: Public Domain Mark

Credit: On the sensations of tone as a physiological basis for the theory of music / by Hermann L.F. Helmholtz ; translated, thoroughly revised and corrected, rendered conformable to the 4th (and last) German edition of 1877, with numerous additional notes and a new additional appendix bringing down information to 1885, and especially adapted to the use of musical students, by Alexander J. Ellis. Source: Wellcome Collection.

    29/604 (page 5)
    INTROD. that tliese upper partial tones are not, as was liitherto thought, isolated phenomena of small importance, but that, with very few exceptions, they determine the qualities of tone of almost all Instruments, and are of the greatest importance for tliose qualities of tone whicb are best adapted for musical purposes. The question of bow the ear is able to perceive these harmonic upper partial tones tlien leads to an hypothesis respecting the mode in whicb the auditory nerves are excited, whicb is well fitted to reduce all the facts and laws in this department to a relatively simple mechanical conception. The Second Parttreats of the disturbances produced bythe simultaneous production of two tones, namely the cowibinutioncil tones and beat>. The physiologico-physical mvestigation shows that two tones can be simul- ^ taneously heard by the ear without mutual disturbance, when and onljr when they stand to each other in the perfectly determinate and well-known relations of intervals whicb form musical consonance. We are thus imme- diately introduced into the field of music proper, and are led to discover the physiological reason for that enigmatical numerical relation announced by Pythagoras. The magnitude of the consonant intervals is independent of the qualityof tone, but the harmoniousness of the consonances, and the distinetness of their Separation from dissonances, depend on the quality of tone. The conclusions of physiological theory here agree precisely with the musical rules for the formation of chords; they even go more into par- ticulars than it was possible for the latter to do, and bave, as I believe, the autliority of the best Composers in their favour. U In these first two Parts of the book, no attention is paid to esthetic considerations. Natural phenomena obeying a blind necessity, are alone treated. The Third Part treats of the construction of musical scales and notes. Here we come at once upon esthetic ground, and the differences of national and individual tastes begin to appear. Modern music has especially developed the principle of tonality, whicb connects all the tones in a piece of music by their relationship to one chief tone, called the tonic. On admitting this principle, the results of the preceding investigations furnish a method of constructing our modern musical scales and modes, from which all arbitrary assumption is excluded. I was unwilling to separate the physiological investigation from its musical consequences, because the correctness of these consequences must U be to the physiologist a verification of the correctness of the physical and physiological views advanced, and the reader, who takes up my book for its musical conclusions alone, cannot form a perfectly clear view of the meaning and bearing of these consequences, unless he has endeavoured to get at least some conception of their foundations in natural Science. But in order to facilitate the use of the book by readers who have no special knowledge of physics and mathematics, I have transferred to appendices, at the end of the book, all special instructions for performing the more complicated experiments, and also all mathematical investigations. These appendices are therefore especially intended for the physicist, and contain the proofs of my assertions.* In this way I hope to bave consulted the interests of both classes of readers. * 'The additional Appendix XX. by the Translator is intended especially for the use of musical students.—Translator.']