DEFINITION OF THE CONSONANT INTERVALS. 179 

Fourth. Let the vibration numbers of two Compound Tones at this interval be 3ft and 4ft respectively. Then, the 4th partial of the former will exactly coincide with the 3rd partial of the latter, thus, 



or in musical language, calling the Fundamentals d and f _{(} 



Thus a Fourth, between Compound Tones, is defined by the coincidence of 3rd and 4th partials, and for exact coincidence, it is obvious that the vibration numbers of the Fundamentals must be in the ratio 4:3. If they are not exactly in this ratio the inaccuracy will manifest itself in the form of beats. Let them be 400 and 301 for example: then 
