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V. §55.]
LENGTHS AND INTERVALS. 111relations which, connect the vibration-numbers of sounds forming given intervals with each other, hold equally for the lengths of the strings by which those sounds are produced. To verify this by experiment we have only to stretch a wire between two fixed points
A and B, Fig. 36 bis, and divide it into two segments by applying a bridge to it at some intermediate point C. If A C bears to CB any one of the simple numerical ratios exhibited in the table onp. 69, we obtain the corresponding interval there given by alternately exciting the vibrations of the two segments at any pair of points in A C and CB respectively. Thus, if CB is twice as long as AC, the sound produced by the former will be one Octave lower than that produced by the latter. If A C is to CB in the proportion of 2 to 3, A Cs sound will be a Fifth above CB's ; and similarly in other cases. It was by experiments of this kind that the ancient Greek philosopher, Pythagoras, is said to have made out the existence of a connexion between certain musical intervals and the ratios of certain small integers. Thus an Octave was produced by a wire divided into two parts in the proportion of 2 to 1 ; a Fifth was obtained by division in the proportion |
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