MUSICAL ELEMENTS AND TERMS. Music is the science or art which treats of tones produced by the mathematically regular vibra tions of resonant bodies, in contradistinction to a confusion of irregular vibrations created by noise or a jumble of sounds.
Modern music, therefore, considered on its technical side depends upon a perfected sys tem of mathematics and acoustics, evolved through centuries of gradual development, an evolution sketched in the historical and de scriptive article on Music in this work, to which refer, as also to GREEK MUSIC; MODE; MODULA TION; TEMPERAMENT; WELL-TEMPERED CLAVIER, and related subjects.
By its manipulation of space and time in the process of development, the whole science of music has resolved itself into the mathematical measurement, combination and distribution of sound waves. Tones, considered simply as to their duration, are magnitudes of time, which stand in a descending geometrical progression the exponent of which is 2:1, 1/2, 1/2, IA, 1/46, 1/2a, etc. The time is expressible in fractions (1/2, 3/4, 44, %, %, %, etc., time), which indicate in numbers how many parts of time (0) are contained in each bar. In space, tones can be considered as magnitudes of sound, and their distances from each other in the scale are expressed in numbers, which have refer ence to a mathematical division of the space between two sounds, adopted as limits (the octave, the third, seventh, etc.). Similar pro portions exist between the various voices, the soprano or treble, bass, etc., and between the various keys. In instrumental music, the depth and height of the tones depend upon the pro portions of the thickness, length and lightness of the chords, the quality, diameter and dis tance of the openings in wind instruments and the like; and all these proportions are deter mined and measured according to mathematical rules. Middle C, shown in the scale farther on, has about 132 vibrations to the second, and is produced by sound waves from eight to nine feet apart. Waves at half that distance apart, produce a tone one octave higher, half that again the next higher octave, and so on. In
large organs C four octaves below middle C, with 16% vibrations per second, is reached, but the effect is imperfect. The piano reaches *4 with 3,520 vibrations per second, and sometimes e5, with 4,224 vibrations. The highest note taken in the orchestra is probably £5, on the piccolo, with 4,752 vibrations. The practical range in music is from 40 to 4.000 vibrations per second, embracing seven octaves. The human ear is, however, able to compass 11 octaves, that is, notes vibrations ranging from up to 38,000 in a single second of time.
As may be Fathered from the preceding paragraphs, the simplest form of musical sound is the Tone, distinguished by the three proper ties of length, pitch and power. These three properties constitute the elemental departments of music: RHYTHMICS, treating of the length of tones, the structure of phrases, sections and periods; MELODICS, treating of the pitch and succession of tones; and DYNAMICS, treating of the power or force of tones, and the manner or form of delivery.
Tones are represented by characters called Notes, named by some nations, including the English-speaking races, after the first letters of the alphabet, A, B, C, D, E, F, G; and, by Latin nations generally after syllables, as Do, Re, Mi, Fa, Sol. La, Si. Notes by their posi tions on the Staff of five lines give the pitch of the tones, and indicate their length by their form. The notes in common use are the the names indicating the relative length of their tones. In modern music, the Whole-note, occupying all of an allotted amount of time, is regarded as the unit, although a character representing a tone twice as long as the Whole note, and called a Breve or Double-note (IT is sometimes used.
Rests,— characters used to indicate silence,— correspond in length of time to the notes which they represent, as indicated by their names: A Dot placed after a note or rest increases the duration of either by one-half; two Dots increase by three-fourths, the second dot adding one-half the length of the first.