Resonating pianoforte wires and tuning-forks; cause phenomenon, $$ 37, 38-Resonance of a column of air; laws of its production, § 39-Relation between the length of an air- column and the pitch of its note of maximum resonance, § 40— CHAPTER IV. ON QUALITY. Composite nature of musical sounds in general; series of con- stituent tones, and law which connects them, § 43-Experimental analysis of musical sounds, §§ 44, 45-Nomenclature of the sub- ject, § 46-Helmholtz's theory of musical quality, as depending on the number, orders, and relative intensities of the partial-tones ON THE ESSENTIAL MECHANISM OF THE PRINCIPAL MUSICAL INSTRU- Sounds of tuning-forks, § 48-Modes of vibration of an elastic tube, § 49-Meeting of equal and opposite pulses; formation of nodes, § 50-Number of nodes formed, § 51-Nature and rate of segmental vibration, $$ 52, 53-Motion of a sounding string ; quality and pitch of its note, $ 54, 55-The pianoforte, § 56- Meeting of equal and opposite systems of longitudinal waves, § 57-Reflection of Sound at a closed and at an open orifice, § 58-Modes of segmental vibration in stopped and open pipes, $59, 60-Deepest note obtainable from a pipe, § 61-Relation between length of pipe and pitch of note, § 62-Theory of re- sonance-boxes, § 63-Flue-pipes and reed-pipes, § 64-Construc- tion of flue-pipes and quality of their sounds, § 65-Mechanism of a reed; timbre of an independent reed, and of a reed associated with a pipe, § 66-Orchestral wind-instruments, § 67-Mechan- ism of the human voice, § 68-Synthetic confirmation of Helm- ON THE CONNECTION BETWEEN QUALITY AND MODE OF VIBRATION. Composition of vibrations, § 70-Superposition of small motions § 71-Phase of a vibration; non-dependence of quality on differ- ences of phase among partial-tones, § 72-Simple and resultant Composition of vibrations of equal periods, § 74-Two sounds 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, $$ 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, SS 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 · T. 1 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 |