HAKMONY 46? sical sound. If the body, instead of making 40 vibrations, made 8,000 per second (which cor- responds to the highest note used in music), the wave length would amount to only 1 T <^ inch; yet this very short wave and the long ne of 27 ft. travel with the same velocity of 090 ft. per second. The sounds produced by ese vibrations are either simple or composite, simple sound is a sound having only one sh, while a composite sound is one com- sed of two or more definite and separable sounds having pitches generally in the ratio 1 : 2 : 3 : 4 : 5, &c. This series of sounds called the harmonic series. Thus, the sound a tuning fork when mounted on its resonant or that of a gently blown closed organ , is simple, for the ear can distinguish but one pitch in these sounds ; while the sounds of piano or violin strings, or of reed organ pipes, are highly composite, and the ear can separate them into simple sounds whose num- bers of vibration are to each other as 1 : 2 : 3 : 4: 5, &c. For example, if we take a reed pipe giving C below the middle of the piano (which note we will designate as C 2 ), we can separate the sound of this pipe into the fol- lowing simple sounds : Oa, Cs, G 3 , C 4 , E 4 , G 4 , Bb, 8 , D 6 , E 5 , ; or, expressed in musical Nation : These simple sounds all coexist in the sound of the reed pipe, but their relative intensities diminish as they ascend in pitch ; that is, the lowest in pitch is the loudest, and serves to designate the position of the pipe in the musi- cal scale. Now it has for a long time been known that those musical sounds which were best adapted to render the etfects of musical composition, and which we distinguish for their brilliant or plaintive qualities, are always com- posite, and contain besides the fundamental sound the harmonic series ; and indeed the timbre of a sound depends entirely on the num- ber and relative intensities of its harmonics. On minute examination it has been found that a simple sound is produced only when the air near the ear oscillates forward and backward with the same kind of motion as exists in a freely swinging pendulum. If, however, the ear experiences the sensation of a composite sound, the air near it has a reciprocating motion, which is the resultant of as many pendulum vibra- tions as there are harmonics in the sound. Yet the ear is a powerful and subtle instrument for decomposing such complex motions into their simple vibratory components ; for the ear, properly aided, can separate the composite sound of a reed pipe or of a vibrating string into 12 and more distinct simple harmonic vi- brations. Those who are interested in this subject of the analysis and synthesis of sound will find a full description of various experi- mental methods in a paper by Prof. A. M. Mayer "On an Experimental Confirmation of Fourier's Theorem, as applied to the decompo- sition of the vibrations of a composite sonorous wave into its elementary pendulum vibrations," &c., in the "American Journal of Science" (1874). According to Helmholtz, the ear ac- complishes this analysis of sound by means of 3,000 little rods or cords, existing in the ductus cochlearis of the inner ear, and known as the rods of Corti. These rods are of gradu- ated lengths and thicknesses like the strings in a piano, and appear to be tuned to 3,000 simple notes, equally distributed throughout the range of the seven octaves of musical sounds. Each rod is connected with a fila- ment of the auditory nerve. The mode of ac- tion of this highly organized part of the audi- tory apparatus is as follows : the vibrations of a composite sound reaching the rods of Corti, each rod, being in tune with a simple sound or harmonic existing in the composite sound, enters into vibration and shakes its attached nerve filament, and thus the ear receives a sensation formed of as many simple sounds as really existed in the composite vibration. In- deed, it appears that the rods of Corti are set in vibration exactly as the strings of a piano vibrate to the elements of a note when we sing over the strings of the instrument. We may now consider the manner of production of beats, and the effects they produce on the ear ; and then we shall be in possession of the main facts necessary to explain the fundamental prin- ples of musical harmony. When two sounds nearly in unison fall upon the ear, they pro- duce alternate risings and fallings in the inten- sity of their resultant effect on the ear. These alternations of intensity are called beats, and are caused in the following manner : Suppose two sounds, produced by two bodies, one giv- ing 2,000 vibrations in a second, the other 2,001. It is evident that if both bodies vibrate together at the beginning of a second, they will again vibrate together at the end of the second ; therefore at these two instants the action of one of them on the air conspires with the action of the other, and thus we have an impression given to the air which is the sum of the two vibrations ; but at the half seconds the motions of the two bodies are opposed, and therefore at these instants they will neutralize each other's action if their intensities of vibra- tion are equal, and at the instant of the half seconds we shall have entire silence. Hence it follows that the number of beats per second given by any two vibrations will equal the difference in the number of vibrations these bodies separately give in one second. Their beats produce on the ear an intermittent action similar to that experienced by the eye when successive flashes of light fall upon it. These intermittent actions on the sensorium are al- ways unpleasant, and even irritating. The
