One of his bridges accidentally not having been brought into full and hard contact with the string, and consequently only imperfectly impeding the vibrations, Sauveur discovered the harmonic overtones of the string, at first by the unaided ear, and concluded from this fact that the string was divided into aliquot parts. The string when plucked, and when the bridge stood at the third division for example, yielded the twelfth of its fundamental note. At the suggestion of some academician[138] probably, variously colored paper riders were placed at the nodes (_noeuds_) and ventral segments (_ventres_), and the division of the string due to the excitation of the overtones (_sons harmoniques_) belonging to its fundamental note (_son fondamental_) thus rendered visible. For the clumsy bridge the more convenient feather or brush was soon substituted. . While engaged in these investigations Sauveur also observed the sympathetic vibration of a string induced by the excitation of a second one in unison with it. He also discovered that the overtone of a string can respond to another string tuned to its note. He even went further and discovered that on exciting one string the overtone which it has in common with another, differently pitched string can be produced on that other; for example, on strings having for their vibrational ratio 3:4, the fourth of the lower and the third of the higher may be made to respond. It follows indisputably from this that the excited string yields overtones simultaneously with its fundamental tone. Previously to this Sauveur's attention had been drawn by other observers to the fact that the overtones of musical instruments can be picked out by attentive listening, particularly in the night.[139] He himself mentions the simultaneous sounding of the overtones and the fundamental tone.[140] That he did not give the proper consideration to this circumstance was, as will afterwards be seen, fatal to his theory. While studying beats Sauveur makes the remark that they are _displeasing_ to the ear. He held the beats were distinctly audible only when less than six occurred in a second. Larger numbers were not distinctly perceptible and gave rise accordingly to no disturbance. He then attempts to reduce the difference between consonance and dissonance to a question of beats. Let us hear his own words.[141] "Beats are unpleasing to the ear because of the unevenness of the sound, and it may be held with much plausibility that the reason why octaves are so pleasing is that we never hear their beats.[142]