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
Catalogue details

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.

    35/604 (page 11)
    PITCH AND THE SIREN. The second essential difference between different musical tones consists in their pitch. Daily expcrience shows us that musical tones of the same pitch can be produced upon most diverse instruments by means of most diverse mechanical contrivances, and with most diverse degrees of loudness. All the motions of the air thus excited must be periodic, because they would not otherwise excite in us the Sensation of a musical tone. But the sort of motion within each single period may be any whatever, and yet if the length of the periodic time of two musical tones is the same, they have the same pitch. Hence: Pitch clepends solely on the length of time in ivhich each single Vibration is executed, or, which comes to the same thing, on the number of vibrations completed in a given time. We are accustomed to take a second as the unit of time, and shall consequently mean b}r the pitch number [or frequency\ of a tone, the number of vibrations which the particles of a sounding body perform in one second of time.* It is self-evident that we find the periodic time or vibrational period, that is length of time which U is occupied in performing a single Vibration backwards and forwards, by dividing one second of time by the pitch number. Musical tones are said to be higher, the greater their pitch numbers, that is, the shorter their vibrational periods. The exact determination of the pitch number for such elastic bodies as produce audible tones, presents considerable difficulty, and physicists had to contrive many comparatively complicated processes in Order to solve this problem for each particular case. Mathematical theory and numerous experiments had to reuder mutual assistance.f It is consequently very convenient for the demonstration of the fundamental facts in this department of knowledge, to be able to apply a peculiar instrument for producing musical tones—the so-called siren—which is constructed in such a manner as to determine the pitch number of the tone produced, by a direct observation. The principal parts of the simplest form of the siren are shown in fig. 1, after Seebeck. H A is a thin disc of cardboard or tinplate, which can be set in rapid rotation about its axle b by means of a string f f, which passes over a larger wheel. On the margin of the disc there is puuched a set of holes at equal intervals : of these there are twelve in the figure; one or more similar series of holes at equal distances are introduced on concentric circles (there is one such of eight holes in the figure), c is a pipe which is directed over one of the holes. Now, on setting the disc in rotation and blow- ing tlirough the pipe c, the air will pass frecly wlienever one of the holes comes under the cnd of the pipe, but will be chccked wlienever an unpierced portion 11 of the disc comes under it. Each hole of the disc, then, that passes the end of the pipe lets a single puff of air escape. Supposing the disc to make a single revolution and the pipe to be directed to the * [The pitch number was called the ‘vibra- iipnal number ’ in the first editiop of this trans- ation. The pitch number of ahote is commonly .called the pitch of the liote. By a convenient abbreyiation we often write a! 440, nieaning thö nöte a' having the pitch number 440 ; or ■say that the pitch of a' is 440 vib. that is, 440 ,double vibrations in a second. The second ^ccmfrequency, which I have introduced into tue text, as it is rauch usod by acousticians, ■properly represents the number of : tiincs timt any perwdicaUy recurring event happens in oiic second of time, and, applied to double vibrations, it means the same as pitch number. The pitch of a musical instrument is the pitch of the note by which it is tuned. But as pit'ch is properly a Sensation, it is necessary here to distinguish from this Sensation the pitch number or frequency of Vibration by which it is measured. The larger the pitch number, the higher or sharper the pitch is said to be. The lower the pitch number the dreper or flotter the pitch. These are all metaphorical expressions which must be taken strictly in this sense.—Translator.] + [An account of the more exact modern methods is given in App. XX. sect. B.— Translator-;]