This explains the relative uniformity in the character of a given compound clang even when the clang-colors of its components vary. A compound clang may pass through all possible intermediate stages into a third form of intensive auditory ideas, that of noises. When two tones are no longer included within a series of harmonious tones and when at the same time the difference between the number of their vibrations does not exceed certain limits, for higher tones about sixty vibrations and for lower thirty or even fewer, there arise disturbances in the compound clang, which correspond in number to the difference between the number of vibrations in the primary tones, and are due to the alternating coincidence of like and opposite phases of vibration. If the differences in the number of vibrations exceed the numbers mentioned, the tones at first sound continuous, for the interruptions disappear, but they are harsh. Later the harshness disappears and we have pure dissonance.
Ordinary dissonance is made up of a mixture of beats or harshness and pure dissonance.
The first two are due to perceptible or just disappearing interruptions of the sensation, the latter to the entire absence of the unity of the clang, that is, of the consonance that would have arisen if a complete or partial fusion had taken place. This lack of accord in tones, due to the relation of their pure qualities, may be designated bissonance . If through the simultaneous sounding of a great number of non-accordant tones the various conditions for an ordinary dissonance, beats, tonal beats, harshness, and bissonance, are all added together, a noise is the result. On the psychological side this means that the predominating tonal elements disappear entirely or become mere modifying elements in the total idea. For our apprehension of noises, in the case of those which last a short interval only, the general pitch of the most intense elements is determinative, in the case of those which last longer, the form of the disturbance resulting from the rapidity of the beats, from the accompanying tonal beats, etc., also has an influence.