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.

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    with 33 vibrations, and the latest grand pianos even down to Ati with 27£ vibra- tions. On larger Organs, as already mentioned, there is also a deeper Octave reach- ing to C„ witb 16i vibrations. But the mnsical character of all these tones below Et is imperfect, because \ve are here near to the limit of the power of the ear to combine vibrations into mnsical tones. These lower tones cannot therefore be used musically except in Connection with their higher octaves to which they impart a character of greater depth without rendering the conception of the pitch indeterminate. Upwards, pianofortes generally reach a with 3520, or even cv with 4224 vibra- tions. The highest tone in the orchestra is probably the five-times accented d of the piccolo flute with 4752 vibrations. Appnnn and W. Preyer by rneans of small tuning-forks excited by a violin bow have even reached the eight times accented evlil with 40,960 vibrations in a second. These high tones were very painfully unplea- sant, and the pitch of those which exceed the boundaries of the musical scale was 5} very imperfectly discriminated by musical observers.* More on this in Chap. IX. The musical tones which can be used with advantage, and have clearly dis- tinguishable pitch, have therefore between 40 and 4000 vibrations in a second, extending over 7 octaves. Those which are audible at all have from 20 to 40,000 vibrations, extending over about 11 octaves. This shows what a great variety of different pitch numbers can be perceived and distinguished by the ear. In this respect the ear is far superior to the eye, which likewise distinguishes light of dif- ferent periods of Vibration by the Sensation of different colours, for the compass of the vibrations of light distinguishable by the eye but slightly exceeds an Oetave.t Force and pitch were the two first differences which we found between musical tones; the tliird was quality of tone, which we have now to investigate. W hen Octaves below the lowest tone of the Violon- cello. Au, the lowest tone of the largest pianos. Q„ commencement of the 16-foot octave, the lowest note assigned to the Double 51 Bass in Beethoven’s Pastoral Symphony. E„ the lowest tone of the German four-stringed Double Bass, the lowest tone mentioned in the text. F„ the lowest tone of the English four-stringed Double Bass. ff,, the lowest tone of the Italian three-stringed Double Bass. A„ the lowest tone of the English three-stringed Double Bass. G, commencement of the 8-foot octave, the lowest tone of the Violoncello, written on the second leger line below the hass staff. G, the tone of the third open string of the Violoncello, c, commencement of the 4-foot octave ‘ tenor ff,’ the lowest tone of the Vidla, written on the second space of the bass staff. ’ d, the tone of the second open string of the Violoncello. /, the tone signified by the bass or F-clef. g, the lowest tone of the Violin. a, the tone of the highest open string of the Violoncello, c', commencement of the 51 2-foot octave, ‘ middle ff,’ written on the leger line between the bass and treble staves, the tone signified by the tenor or ff-clef. d’, the tone of the third open string of the Violin. cf, the tone signified by the treble or ff-clef. a't the tone of the second open string of the Violin, the ‘tuning note ’ for orchestras. c, commencement of the 1-foot octave, theusual ‘ tuning note’ for pianos. the tone of the first or highest open string of the Violin. c', commencement of the $-foot octave. f, the usual highest tone of the Flute, civ, commencement of the J-foot octave. Av, the highest tone on the Violin, boing the double Octave liarmonic of the tone of the highest open string. a>v, the usual highest tone of large pianos. dy, the highest tone of the piccolo flute. cvllt, the highest tone reached by Appunn’s forks, sec nexfc note.—-'1 raiislalor.] * [Copies of these forks, described in Prof. Preyer’s essay ‘ On the Limits of the Perception of Tone,’ (über die Grenzen der Tonwahrneh- mung, 1876, p. 20), are in the South Kensing- ton Museum, Scientific Collection. I have several times tried them. I did not myself find the tones painful or cutting, probably because there was no beating of inbarmonic upper partials. It is best to sound them with two violin bows, one giving the octave of the other. The tones can be easily heard at a distance of more than 100 feet in the gallery of the Museum.—Translator.'] f [Assuming the undulatory theory, which attributes the Sensation of light to the vibra- tions of a supposed luminous ‘ etlier,’ resern- bling air but more delicate and mobile, then the phenomena of ‘ interference ’ cnables us to calculate the lengths of waves of light in empty space, &c., hence the numbers of vibra- tions in a second, and consecpiently the ratios of these numbers, which will then clearly resemble the ratios of the pitch numbers that measure musical intervals. Assuming, then, that the yellow of the spectrum answers to the tenor c in music, and Fraunhofer’s 1 line A ’ corresponds to the G below it, Prof. Helm- holtz, in his Fhysiological Optics, (Hand- buch der physiologischen Optik, 1867, p. 237), gives the following analogies between the notes of the piano and the colours of the spectrum:— F 2, end of the Red. ff. Red. ff i Red. A, Red. A ö, Orange-red. lifOrange. c, Yellow. c i, Green. d, [Greenish-blue. d fi, Cyanogen-bluo. c, ”lndigo-blue. /, Violet. / jj, Violet. g( Ultra-violet. 'ü a S, >. b, end of the solar spectrum. The scale there- fore extends to about a Fourtli boyond the oc- tave. — Transla- tor.]