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96                      HAND-BOOK OF ACOUSTICS.
A great number of partials are usually present in the tones pro­duced by the violin, at least the first eight being nearly always present. The peculiar incisiveness of tone is probably due to the presence of partials above the eighth, which, as will be seen from the table on page 72, hie very closely together. The violin has four strings tuned in fifths, the highest being tuned to E1; the lower limit is therefore G(. The viola or tenor violin, which is slightly larger than the above, has also four strings tuned in fifths, the highest being A; the lower limit is consequently 0|. The violoncello has also four strings, each of which is tuned an octave lower than the corresponding one in the viola. The lower limit is therefore C2. The double bass usually has only three strings, tuned in fourths, the highest being Gg! its deepest tone is thus A3, only two notes below the violoncello, but its larger body of tone makes it seem of a deeper pitch than it actually is.
The three essentials of a stringed instrument are : (1), the string (2), the means of exciting it; (3), a sound-board or resonator. The vibration number of a stretched string varies Directly as the square root of the tension, Inversely ,, ,, ,,         ,, density,
,,          „ length,
          „ diameter.
Stringed instruments flatten with rise of temperature, and vice versa.
Points of rest, or rather of least motion, in a vibrating string are termed nodes. The vibrating part of the string between two consecutive nodes is called a ventral segment. The middle of a ventral segment is sometimes referred to as an antinode.
The occurrence of partials in the tone of a stretched string, is due to the fact, that it vibrates, not only as a whole, but simul­taneously also in halves, thirds, quarters, &c.; each segment producing a simple tone or partial, of a pitch and intensity corresponding to its length and amplitude respectively.
The occurrence and intensities of these partials depend upon (1). The nature of the string. (2). The nature of the excitation. (3). The position of the point where the string is excited.