The present text-book is concerned mainly with the instrumental appliances which minister to sound. The physical aspect of Acoustics has been lucidly mapped out by ClerkMaxwell in the following manner :—

VIBRATIONS AND WAVES.

Physical Aspect of Acoustics.

1. Sources-Vibrations of various bodies :

3. Pugging of floors, Dampers of Pianofortes.

4. Reservoirs, Resonators, Organ Pipes, Sounding-boards.

5. Regulators

6. Detectors

Organ Swell.

S The Ear, Sensitive Flames,
Membranes, Phonautographs, &c.

7. Tuning-forks, Pitch-Pipes, Musical Scales.

To bridge over the gap between this science and the art of music, slightly more extended treatment is needed :

1. MODES OF PRODUCTION. VIBRATION OF SONOROUS BODIES. 2. MODES OF PROPAGATION. REFLECTION. REFRACTION.

3. INTENSITY. CONSONANCE.

VELOCITY. WAVE-MOTION.

INTERFERENCE.

4. PITCH. MODES OF DETERMINATION AND MEASUREMENT. STANDARDS OF PITCH.

5. NATURE OF MUSICAL TONE. QUALITY. RESULTANT TONES.

6. EFFECTS OF HEAT. ATMOSPHERIC PRESSURE. MOISTURE. DENSITY.

7. SCALES. TEMPERAMENT. TUNING.

8. THE EAR AND VOICE. SPECIAL APPLICATIONS TO MUSIC.

The whole subject naturally and more concisely divides itself into-1. Mechanical; 2. Theoretical considerations: 3. Practical applications. It is, however, to be noted that these different aspects of the facts cannot be separated one from the other; the respective influences of the art of music and of scientific research having been reciprocal, gradual, and intimately combined. At the very outset of history we meet with the Monochord, nained after Pythagoras, a machine not intended for artistic performance, but which at once yielded immense practical results to music. We then enter into a long period during which instrumental appliances grew, without design and without theory. The discoveries of new or improved instruments were purely technical, often fortuitous; although every instrument added was a piece of mechanism open to scientific analysis. During the present century a return has been made to apparatus essentially scientific, for the explanation of what had been musically invented; we find soon the reciprocal influence of instruments on apparatus-no better instance of which can be given than the discovery of Tartini's "Terzo Suono," or third sound; originally taught by the great violinist to his pupils as a means of accurate tuning, but now shown by Helmholtz to involve a new and important acoustic principle.

In many cases instruments of music actually stand in the place of apparatus. Strictly considered, a musical note is of itself a mathematical fact, quite independent of its power of exciting emotion and pleasure by its artistic production. On the other hand, tuning and intonation, originally left entirely to the accurate and cultivated ear of a skilled performer, have become a branch of science, with definite laws and practical rules; insomuch that the unconscious departures from a fixed tuning, which older musicians made by a kind of instinct, are now explained; and even the disposition of various instruments, with different qualities of tone, in an orchestra is shown to be correct, or the contrary, according as the harmonics of each peculiar quality are consonant or dissonant.

CHAPTER I.

MODES OF PRODUCTION OF SOUND.

VIBRATION OF

SONOROUS BODIES.

Sound may be generated in various ways; some of these have been utilized for the production of musical or regular vibrations, others remain in the category of mere noise.

The shock of two bodies against one another is perhaps the commonest of all sources, varying, however, materially according to the nature of the sounding masses and the mode of conveyance to the ear. The simple unmusical tap of a drumstick on a membrane is of musical value in the side-drum, to preserve time and indicate rhythm, while in the Morse telegraph the click caused by the collision of magnet and keeper is, by a suitable code, made to furnish an intelligible alphabet.

Irregular Vibration.

Friction in many forms furnishes a source of sound; the irregular vibrations, which in its rougher kinds it emits, passing imperceptibly into more regular and musical tones. This gradation may often be noticed in the sharpening of a saw, and still more notably in the action of railway brakes upon a train in motion. In its more refined adaptation to instruments friction originates the tender tones of the violin and its congeners; while in the musical glasses, a wetted finger moving with friction along the edge of a consonant bell, produces a quality of sound almost painful and cloying from its excessive sweetness. The friction of air against solid bodies originates the melancholy moaning of the wind, the sharp hiss of a cane, and the loud genial crack of a carter's whip.

Explosion as of gunpowder and of explosive gases, gives rise to loud noises; in the pyrophone of Wheatstone and others it has been made to serve, though as yet rather imperfectly, the function of a musical instrument. Of a kindred nature are the various kinds of singing and sensitive flames.

Electricity, whether in its disruptive discharge at high tension, causing the rolling of thunder, or in the less awful manifestations of frictional and inductive machines, is a source of sound. In the form of a dynamic current, it has also the power of producing such an alteration in the molecules of soft iron as to be accompanied by audible musical vibration. Latterly this has been adopted into the service of music in the various forms of telephone.

Regular Vibration.

These being some of the commoner and more physical sources of vibration appreciable by the ear, there remains a larger and more distinct class, which, from its special adaptation to the production of regular waves, furnishes the bulk of the instruments and contrivances used for eliciting pleasant tones, and for building up the æsthetical art of music. They will have next to be considered at some length, and may be enumerated as follows:

IV. Of Bells.

V. Of Membranes

(1. Transverse

2. Longitudinal with (3. Torsional

(1. Radial
12. Circular

a. Nature of stroke.

b. Place struck.

c. Rigidity of string.

(A. Both ends fixed (approach to those

of strings).

B. One end fixed (nail fiddle, musical box).

c. Centre fixed (tuning-fork).

D. Both ends free, nodal points sup ported (harmonicon).

As in Chladni's experiments (gong, cymbal).

(A. Excited by blows (clock chimes).

1. Spherical B. By tangential or radial friction (musical glasses).

2. Of complex figure (give compound notes with irrelevant harmonics).

1. Independent (tambourines, zambomba).

2. With associated air-chamber (kettle drum, resonators)

1. Free (as in harmoniums).

VI. Of Reeds

2. Beating

JA. Single (clarinet, organ reed).

B. Double (bassoon, oboe).

3. Membranous 4. The lips in brass instruments.

B. The larynx (human voice).

VII. Of columns, of air

A. Open pipes.
B. Stopped pipes.

1. Organ pipes c. Half-stopped pipes.
D. Pipes with reeds.

E. Mixtures and mutation stops.

2. Consonance boxes and vessels.

(1. Trevelyan's rocker.

VIII. Vibration) 2. Sondhaus's experiment.

caused by heat) 3. Of flames 1. Chemical harmonicon, pyrophone. 12. Sensitive and singing flames.

IX. Caused by (1. Current in iron bar, Reiss's Telephonic receiver. electricity 12. Telephone, Microphone.

Strings.-Among the commonest and earliest modes of eliciting musical sounds may be named strings. They have contributed the largest share to instruments of all times and all countries, and were early employed for more accurate determinations. Their theory is simple comparatively to that of other sound-producers.

The string itself is supposed to be a perfectly uniform and flexible thread of solid matter, stretched between two fixed points. Although this ideal is not actually attained in practice, the deviations from it are not so great as to prevent necessary corrections being made. Its vibrations may be divided into transverse, longitudinal, and torsional, the former being the form more usually studied; in which, if the stretching due to lateral displacement be small in comparison with that to which the string is already subjected, it may be neglected.

Transverse Vibrations of Strings.

The laws are as follows:

1. For a given string and a given tension, the time of a vibration varies directly, the vibration number inversely, as the length.

2. When the length of the string is given, the vibration number varies directly, the time of vibration inversely, as the square root of the tension.

3. Strings of the same length and tension vibrate in times which are proportional to the square root of the linear density, the vibration number being in inverse ratio to this.

The motions of a string thus fixed at its end and excited at some intermediate point, radiate from that point to the fixed