CHAPTER IV.

EPITOMIZED ACOUSTICS.

The science of sound, including its cause and effect and the manner, velocity, and intensity of its conveyance through different media, is called -acoustics-.

The medium through which sound is most commonly propagated is air. Through this medium, at a temperature of 32° Fahrenheit, sound travels at a rate of 1090 feet per second. The quality and intensity of sound do not alter the rate of speed. If this were not true, ensemble music would be impossible. Intensity of sound is greater in condensed air; velocity of sound is greater in a warm temperature.

Many experiments have been made to determine the velocity of sound, the most reliable of which vary not over seven feet per second. The average of six of the best experiments, made in the early part of the nineteenth century, is 1089.7 feet per second at 32° Fahrenheit. Ten hundred and ninety feet per second is the rate now generally adopted.

Wind and temperature are the only circumstances affecting the velocity of sound in the air to any extent. Sound travels about four times faster through water than through air, and about ten times faster through solids such as metals and wood than through air. A sudden displacement of the molecules of a medium produces sound which travels in waves at an equal velocity in all directions. An idea of the manner in which sound waves travel may be obtained by throwing a stone in water; small waves are propagated from the point of impact which, if the water be still, spread equally in all directions, but if it be running water, the waves extend a greater distance down stream than up stream. The effect of wind on sound waves may be compared to the effect of running water on the waves propagated by the impact of the stone.

Musical tone is produced by regular vibrations; noise by irregular vibrations. The tones of the tempered chromatic scale have the following number of vibrations per second:--

Middle c 258.6 c♯ or d♭ 274.0 d 290.3 d♯ or e♭ 307.6 e 325.9 f 345.2 f♯ or g♭ 365.8 g 387.5 g♯ or a♭ 410.5 a 435.0 a♯ or b♭ 460.8 b 488.2

The preceding figures represent the vibrations of the "International Pitch" which was adopted by the Piano Manufacturers' meeting in 1891. A is the standard pitch having 435 double vibrations per second at a temperature of 68° Fahrenheit. Many pitches have prevailed in different countries at different times. At the time of Handel and Mozart, the pitch was lower (422.5 and 421.6). England has had the pitch run as high 454.7 and the United States as high as 460.8.

Sounds vibrating below a certain number lose the character of musical tones as do those vibrating above a certain number. Great discrepancies of opinion exist among theorists on this subject. Savart claims the lowest audible sound has eight vibrations per second; Helmholtz claims that there is no definite pitch of sounds having less than forty vibrations per second; Herr Appum claims to hear fifteen vibrations by the use of specially loaded tongues in reed pipes. He claims the character of tone commences at twenty vibrations, but the musical character of bass tones does not exist until frequencies exceed twenty-four vibrations per second. On the subject of the audibility of acute sounds, opinions are advanced ranging from 6,400 to 36,000 vibrations per second.

The limits of the human voices are tabulated below:--

Bass E 81.5 D 290.3 Baritone F 86.3 F♯ 365.8 Tenor A 108.7 A 435.0 Contralto E 163.0 F 690.5 Mezzo Soprano F 172.6 A 870.0 Soprano A 217.5 C 1034.6

Occasionally there are exceptional voices having a wider range than the above scale indicates.

Ratio of Intervals:--

Octave 1-- 2 Perfect fifth 2-- 3 Perfect fourth 3-- 4 Major third 4-- 5 Minor third 5-- 6 Major sixth 3-- 5 Minor sixth 5-- 8 Major second 8-- 9 Minor second 15--16 Major seventh 8--15 Minor seventh 9--16

Each tone generates "over tones" called -harmonics-. These -harmonics- are the octave, the twelfth (perfect fifth), the seventeenth (major third), the twenty-first (minor seventh) and the twenty-third (minor ninth). Other -harmonics- than the above exist but are not used at the present time in chord construction. The old theorists treated chords of the eleventh and thirteenth, but modern theorists treat these intervals as suspensions, anticipations, etc.[D] The origin of chord construction may be seen from these -harmonics-. These over tones, generated from a fundamental, are the pure (untempered) intervals. The tempered intervals, with the exception of the octave, are slightly out of tune but not enough so to shock the ear.

[Footnote D: Composers of the present day often use these intervals as chord factors.]

The pure (untempered) scale of C has the following number of vibrations per second:--

Middle c 261.0 d 293.6 e 326.2 f 348.0 g 391.5 a 435.0 b 489.3

An entire volume would be necessary to explain completely the science of acoustics. All ambitious students should consult books on acoustics. The author recommends the books on sound by the following writers:--

Appum G. B. Airy Pietro Blaserno Helmholtz Pole Benjamin Peirce Rodolphe Radau Savart Tyndall J. August Zahn