ON THE CONNECTION BETWEEN QUALITY AND MODE OF VIBRATION. Composition of vibrations, § 70-Superposition of small motions Composition of vibrations of equal periods, § 74-Two sounds producing silence, § 75-Beats of simple tones, § 76-Graphic representation of beats, § 77-Experimental study of beats, § 78. Helmholtz's discovery of the nature of dissonance; conditions under which it may arise between two simple tones, § 79-Mode of determining the whole dissonance produced by two composite sounds, § 80-Classification of the tonic intervals of the scale, according to their freedom from dissonance, SS 81-86-Picture of amount of dissonance for all intervals not wider than one octave, § 87-Consonance dependent on quality, § 88-Apparent objection to Helmholtz's theory of quality, § 89-Combination- tones, § 90-Their use in defining certain consonant intervals for simple tones, § 91-Divergence from the views of musical theorists, § 92-Dissonance due to combination-tones produced between the ON CONSONANT TRIADS. Rules for the employment of vibration-fractions, $$ 94-96-Inver- sion of intervals, § 97--Definition of a consonant triad, § 98— Determination of all the consonant tonic triads within one octave, § 99--Major and Minor groups, § 100-Mutual relation between the members of each group, § 101-Notation of Thorough Bass, Successive intervals of the Major scale, § 105-Requisites for pure SOUND AND MUSIC. CHAPTER I. ON SOUND IN GENERAL, AND THE MODE OF ITS TRANSMISSION. 1. IN listening to a Sound, all that we are immediately conscious of is a peculiar sensation. This sensation obviously depends on the action of our organs of hearing; for, if we close our ears the sensation is greatly weakened, or, if originally but feeble, altogether extinguished. Persons whose auditory apparatus is malformed, or has been destroyed by disease, may be totally unconscious of any sound, even during a thunder-storm, or the discharge of artillery. These simple considerations should prepare us to expect that what we feel as Sound may be represented, externally to ourselves, by a state of things very different to the sensation we experience. Indeed this would only be in accordance with the modes of action of our other senses; for instance, the sensation of warmth, and its cause, a coal fire,-of fragrance, and its cause, a rose,—of pain, and its cause, a blow, are quite unlike each other. Analogy, then, indicates that some purely mechanical phenomena external to the ear will prove to be turned into the sensation we call Sound by a process carried on within that organ, and the brain with which it is in direct communication. This mechanical agency, whatever may be its nature, is usually set going at a distance from the ear, and, to reach it, must traverse the intervening space. In doing so, it can pass through solid and liquid as well as gaseous bodies. If one end of a felled tree is gently scratched with the point of a penknife, the sound is distinctly audible to a listener whose ear is pressed against the other end of the tree. When a couple of pebbles are knocked together under water, the sound of the blow reaches the ear after first passing through the intervening liquid. That Sound travels through the air is a matter of universal experience, and needs no illustration. In every case, accessible to common observation, where Sound passes from one point of space to another, it necessarily traverses matter, either in a solid, liquid, or gaseous form. We may hence conjecture that the presence of a material medium of some kind is indispensable to the transmis sion of Sound. This important point can be readily brought to the test of experiment, as follows. Let a bell, kept ringing by clockwork, be placed under the receiver of an air-pump, and the air gradually exhausted. Provided that suitable precautions are taken to prevent the communication of Sound through the base of the receiver itself, the bell will appear to ring more and more feebly as the exhaustion proceeds, until, at last, it altogether ceases to be heard. On re-admitting the air, the sound of the bell will gradually recover its original loudness. It results from this experiment that Sound cannot travel in vacuo, but requires for its transmission a material medium of some kind. The air of the atmosphere is, in the vast majority of cases, the medium which conveys to the ear the mechanical impulse which that wonderful organ translates, as it were, into the language of Sound. 2. Having ascertained that a material medium, in every case, acts as the carrier of Sound, we have next to examine in what manner it performs this function. The roughest observations suffice to put us on the right track, in this enquiry, by pointing to a connection between Sound and Motion. The passage, through the air, of sounds of very great intensity is accompanied by effects which prove the atmosphere to be in a state of violent commotion. The |