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either simultaneous or successive: in the first case, it constitutes harmony; in the last, melody.
The science of music is twofold; for it may respect the investigation and development of the causes of sounds, and the philosophical nature and distinction of concords and discords ; or it may be directed to the prescription of rules for composition, or for combining sounds either in melody or in harmony, or in both, so as to be agreeable to the ear. So again the art of music is twofold; for, it may relate to the invention and structure of different kinds of instruments, or it may refer to the practice of singing, and of performing upon the different kinds of musical instruments. The latter is, in a restricted sense, called the art of music.
The gravity or acuteness of a sound depends entirely upon the number of vibrations of the sonorous substance, whatever it may be, in a given time. The more rapid the vibrations the acuter the tone, and vice versu. When the vibrations occur in exactly equal times, the sounds yielded are called unisons. If the times of vibration be as one to two, the sounds generated are, at the interval, called an octare. When a male and female voice sing the same air, they proceed throughout at the interval of an octave. Between the two extremes of an octave, other notes are interposed, and to these names are given. Foreigners have usually employed the names Ut, Re, Mi, Pa, Sol, La; but the first seven letters of the alphabet are more generally employed. If one extreme of an octave be denoted by the letter C, for example, then will the other extremily be C also, and the intermediate notes, proceeding from grave to acute, will be D, E, F, G, A, B. These, however, do not constitute equal intervals, the space between E and F, and that between B and C, being only semitones, while all the other intervals are tones. The octave, then, contains twelve semitones; and the places of these are changed by means of flats and sharps, and in a manner on which depends the place of the key or fundamental note.
2. The vibrations of a musical string are easily determined mathematically, by means of the following formula. Let W represent the weight of a musical string, L its length, P the tending or stretching force, & the space described by a falling body in one second of time, then
* See the article, ACOUSTICS.
LW will T, the time of vibration of the string, be =
2 g P From this the absolute frequency of sound may be ascertained; and the real place of the note, from the relation of its number of vibrations in a second to 250 or 256, the latter of which may be assumed as a very convenient standard for the vibrations in a second when the note yielded is the C denoted by the mark of the tenor cliff.
3. In a simple composition, all the intervals are referred to a single fundamental or key note. All audible sounds are considered as repetitions of a series within the interval of an octave. One third of a chord in length, and equally stretched, would yield, on being made to vibrate, the fifth above the superior octave, one fourth of the chord the double octave, and one-fifth the third above it. Thus, we have the common chord, or harmonic triad, that is, the fundamental note with its third and fifth, constituting the most perfect harmony ; being also the foundation of the most simple and natural melodies. The intermediate steps are supplied by completing the triad of the fifth, which gives us the seventh, in the ratio of 8 to 15, and the second in the ratio of 8 to 9; and the triad in which the key note is the fifth, whence there result the fourth and sixth, in the ratio of 3 to 4 and 3 to 5. From this it follows, that if a musical string and its parts, or eight separate strings, be equally stretched, and in proportion to one another as the numbers 1, , , , }, 5, 15, , their vibrations will exhibit the natural, or diatonic series of sounds in the octave.
4. In a long piece of music the ear becomes fatigued unless the fundamental note is changed: one of the auxiliary triads, therefore, is taken for the fundamental harmony; and sometimes the modulation is continued till every note of the scale becomes a key note ; the transpositions being effected by means of flats and sharps. For still fariher variety we change the place of the middle note of the three triads, placing the minor third, or the interval of 5 to 6, below the major, or 4 to 5; and the scale thus formed is called the minor mode in contradistinction to
the major. The former is usually the characteristic of plaintive, the latter of cheerful music. A is the key note of the natural minor mode, C the key note of the natural major mode.
5. As to the names and positions of the notes, in relation to the absolute frequency of vibration, they may be determined simply. If a tone yielded by a vibration once in a second be called the lowest or first C, then two vibrations in a second will be an octave higher, or the second C; 4 vibrations, or another octave higher, the third C; and 8, 16, 32, 64, 128, 256, 512, 1024, 2048, &c. will yield the succession of C's. Of these the fifth in order, or that vibrating 16 times in a second, will be nearly the lowest audible note; and the fourteenth, the highest used in music; though, perhaps, the fifteenth or sixteenth may be distinguishable. If the notes in a chromatic or semitonic octave be turned to correspond with the tones of strings which vibrate respectively 250, 271, 287, 304, 323, 342, 362, 384, 406, 431, 456, 483, 512 times in a second, they will be tuned to correspond with what is denominated the isotonic or equal temperament, in which music may be performed having any key note, and yet free from any perceptible aberrations from just harmony. This subject of temperament is one of the most difficult in music. It is ably treated by Dr. Smith in his Harmonics, and by Dr. Robison in the article Temperament, in the Supplement to the Encyclopædia Britannica.
6. The sounds of musical instruments depend either on the vibrations of solid bodies, or of the air, or of both; and the vibrations of solids are derived either from tension or from elasticity. Vibrations from tension are employed in stringed instruments, or in sonorous membranes. The essential varieties of stringed instruments are seen in the harp, the harpsichord, the pianoforte, the guitar, the violin, the monochord, and the Æolian harp. To all these a sounding board is added, which not only increases the strength of tone by reflection, but contributes by its own elastic vibrations to the propagation of the sound. The principal membranous instruments are the drum and the tambourine. In the vibrations of the tuning fork, the gong, the cymbal, the bell, &c. elasticity is the imme
diate agent. Simple wind instruments are the syrinx, the flute, the fageolet, &c. mixed wind instruments are the trumpet, the clarionet, the serpent, &c. The construction of many of these is very curious. · But as we are obliged to consult brevity, we cannot here enter into detail : the remainder of this chapier must be devoted to a slight bistorical sketch, with a description of one or two of the more unusual and recently invented instruments.
7. Moses expressly records, that musical instruments were made before the Flood; and that Jubal, the seventh in descent from Adam, by his eldest son Cain, father (instructor) of all such as handle the harp and organ." Gen. iv. 21. Most nations have introduced music into their religious ceremonies. The art was early admitted into the rites of the Egyptians and Hebrews, and constituted a considerable part of the Grecian and Roman religious service. It soon obtained an introduction into the Christian church, as the Acts of the Apostles discover in many passages. The chanting of psalms was introduced into the western churches by St. Ambrose, about A. D. 350, and was improved by St. Gregory the Great, in the year 600. In England, music was first employed in the church service by St. Augustine, and afterwards much improved by St. Dunstan, who was himself an eminent musician, and first furnished the English churches with the organ. The first organ seen in France was sent from Constantinople, in 757, as a present to king Pepin, from the emperor Constantine V. It became frequent in Italy, Germany, and England, during the tenth century.
8. In musical compositions, for the church, England appears to have borne away the palm from every other country. Tallis and Bird, wbo flourished in the sixteenth century, are denominated the fathers of our genuine and national church music. Tallis is considered, by historians, as one of the greatest musicians, not only of this country, but of Europe ; he was the composer of the pieces and responses used in our cathedrals to the present day, and with his pupil Bird, is justly stiled the pride of our coun try and honour of his profession. The names also of Bull, Blow, Orlando, Gibbons, H. Purcell, Croft, Boyce, &c, will
be ever held in veneration by all lovers of church music. For specimens of these authors' works see Dr. Boyce's “ Cathedral Music.”
9. The English, from the invasion of the Saxons to that æra, in which they imbibed the art, and copied the manner of the Italians, had a kind of music which neither pleased the soul, nor charmed the ear. The primitive music of the French, deserves no higher panegyric. Of all the barbarous nations, the Scots and Trish seem to have possessed the most affecting original music. The Scottish music consists of a melody characterized by tenderness, which melts the soul to a pleasing, pensive languor. Their martial music consists either in marches, which were played before the chieftains, in imitation of the battles which they fought, or in lamentations for the catastrophes of war, and the extinction of families. The pibroch, or imitation of battles, is wild and abrupt in its transitions, and various and desultory in its movements; and the hearer is irresistibly impressed with all the rage of precipitate courage, notwithstanding the rudeness of the accent by which it is kindled. Their pastoral music forms a striking contrast ; its accents are plaintive yet soothing, and its modulations are natural and agreeable. Irish music is the native expression of grief and melancholy.
10. The several events and characters in the art of music, worthy of record, relate either to discoveries and improvements in the principles of music-distinguished composers in this art—or those who have rendered themselves famous by the excellence of their personal perform
The origin and laws of hurmony were little understood before the commencement of the eighteenth century. The improvements of the celebrated Corelli, in counterpoint, or the combining and modulating consonant sounds, are well known. M. Rameau a scientific musician of France, early in the century, exhibited the foundation and the principles of harmony, and the source of that pleasure which it affords; he analyzed the consonances of music; and explained the mutual dependence of harmony and melody. He was considered as a theorist to whom the art of music was as much indebted, as physics and philosophy are to Newton. The abbé Roussier, Marpurg, Tartini, Koll