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70 CALCULATION OF VIBRATIONNUMBERS. [II. § 36. 



In order to extend the scale an Octave upwards we have only to multiply each vibrationnumber by 2. A second multiplication by 2 will raise it by another Octave, and so on. Conversely, in order to pass to the Octave below we divide each vibrationnumber by 2. To descend a second Octave we repeat the operation, and so on.
Thus the pitch of the tonic absolutely fixes the pitch of every note in the scale of which it is the startingpoint.
Before proceeding to investigate the mechanical equivalent of the third element [§ 24] of a musical sound, its quality, we will briefly examine, in the next chapter, a subject possessing an important bearing on that enquiry. 
