MUSICAL HARMONY. 201 (more conspicuous in approaching to unison than in approaching to the other concords), which finally disap¬ pears, leaving a most agreeable and animating concord. The sound which then reaches the ear is not like a simple note, but it gives no idea of two sounds; although when compared with either of the original notes, as sounded on a third string, it seems to be related to them. 89. Mechanical explanation of Concords of Har¬ mony, With our knowledge that every musical note implies a series of vibrations of air, following with similarity of character and at equal intervals of time (Article 71), the explanation of all these observed facts is simple. For instance, to explain the harmony in the coexistence of two sounds separated by an octave. Geometrically, we may represent the disturbance of the air produced by the lower sound as a series of waves of a certain length travelling with sound-velocity ; and the disturb¬ ance produced by the upper sound as a series of waves of half the length travelling with the same sound-velocity, and therefore always holding the same relation to the series of longer waves. The union of these produces a wave more complex than either separately. If the long wave be much the larger, (in the amplitude of vibrations of its particles,) the result will be a modi¬ fied long wave, or (musically) a modified low note; if the short wave be much the larger, the result will be