HANDBOOK OF ACOUSTICS - online book

A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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ON THE VIBRATIONS OF STRINGS.               95
point, will be absent. Thus if the string be struck at the middle point, only the odd partials will be present in the compound tone produced: if the string be struck at a point, one third of its length from the end, the 3rd, 6th, and 9th partials will be absent. Again, if a string be struck at a point, one seventh, one eighth, or one ninth of its length from the end, the 7th, 8th, or 9th partials respectively, will be absent. Now, these are the first three dissonant partials of a compound tone, so that it improves the quality of tone to have them absent; and it is a curious fact, as Helmholtz observes, that pianoforte makers, guided only by their ears, have been led to place their hammers, so as to strike the strings at about this spot.
With regard to the quality of tone in the pianoforte, it will be found, that in the middle and lower region of these instruments, the tones are chiefly composed of the first six or seven partials, the first three being usually very prominent; in fact, the second and third are not unfrequently louder than the fundamental. As the first six partials form the tonic chord, the tones that have them well balanced, sound peculiarly rich. The result of pressing down the loud pedal should be noted. The idea usually entertained is, that by keeping the dampers raised from the wires, the tones are prolonged after the fingers are taken off the notes. This is true, but not the whole truth. For as the dampers are raised from all the wires, all the latter which are capable of vibrating in unison with the already vibrating wires, will do so. For example, if the loud pedal be depressed, and the F, in the Bass clef be struck, the F2 wires an octave lower will be set vibrating in two halves ; the B^3 a fifth below that, in three parts; the F3, two octaves below the note struck, in four parts; and so on, each section sounding forth the F|. Again, the wires which were struck will not only vibrate as a whole, giving F)( but in halves giving F, which will start the wires of the F digital, and will also set the Bb2 wires vibrating in three sections. Further, the original wires will vibrate in three segments producing the partial C1, and this will start the wires cor­responding to C1 and C, and so on. It is easy to see, therefore, that when the loud pedal is held down, and a low note struck, the number of wires set vibrating is very great, giving an effect of in­creased richness. At the same time, the necessity of raising the pedal at every change of chord is very clearly seen. The result of pressing down the soft pedal is to slide the whole of the hammers along transversely, through a short distance, so that they strike only one of the two or three wires that are allotted to each note.