§ 5. Harmonic Intervals.—When, of two notes simultaneously produced, the vibration period of one is exactly twice as rapid as that of the other, the two sensations show a strong tendency to blend into one. It is hard to distinguish them as two. The result of their union is a richer and fuller sensation, peculiarly agreeable to the ear. There is also a tendency to confuse the two sensations even when they do not occur simultaneously. When even a practised musician is called upon to imitate on the piano a tone whistled by the mouth, he frequently produces the tone which corresponds to half or double the number of vibrations per second, or in other words, the upper or lower octave of the note which he has to imitate. What is peculiarly interesting is that the tendency to confuse a note with its octave in memory, and to hear them as a single musical sound when they are simultaneously produced, does not depend on similarity in pitch. Notes much nearer in pitch are easily and clearly distinguished. What has been said of the octave holds also of other musical intervals, the double octave, the fifth, and the twelfth.

§ 6. Combination of Musical Sounds from different sources.— When musical sounds occur together, it usually requires attention to discriminate them. It is, as we have seen, peculiarly difficult to do so when the one is the octave, the fifth, or the twelfth of the other. The greater the relative intensity of one of the notes as compared with the others, the more easy it is to discern it as a separate tone. It is harder to distinguish in proportion to its relative faintness. The combination of tones yields a specific experience, which cannot be regarded as merely the sum of the separate experiences of the separate notes. Even when the constituent tones are discriminated, they are still apprehended as integral parts of a whole. This whole has its own characteristic pitch and its own characteristic intensity. Its pitch is approximately that of the lowest of its constituent tones, even when this is not the most intense. The intensity of the total experience is not equal to the sum of the intensities of its constituents. It is approximately equal to the intensity of the loudest among them.