Trajetta was the son of a well-known Italian composer of the same name. He was a pupil of the celebrated Conservatorio of Naples, and, as I have been informed, was about to obtain a professorship in the Conservatorio of Paris, when political circumstances diverted his course to America. He was the friend of General Moreau and President Madison. Of noble appearance, fine manners, and sensitive temperament, he for some time received the consideration due to his talents and acquirements, but, in after years, was sadly neglected, and finally died in Philadelphia, almost literally of want. His musical knowledge perished with him; his manuscripts (operas, oratorios, etc.) were, I believe, all burned by him before his death. A sad history, and, in a land where there has been so little opportunity for the beet musical instruction, a strange one!
To define the provinces of science and art, we may briefly say, that science is concerned with the discovery of demonstrable principles, and the deduction of undeniable corollaries; while art is occupied with expression, performance, and the creative faculty with which man has been endowed. Music and astronomy are both sciences, that is, founded upon certain fixed and ascertainable laws; but astronomy is no art, because man has not the power to create, or even remodel worlds, and send them rolling through space; while he can produce sounds, and arrange them in such a way as to result in significant meaning and in beauty, two of the chief ends of art.
The music of different periods in the world's history has rested upon the various scales recognized during those periods as fundamental, which scales have been more or less complete as they have approached or receded from the absolutely fundamental scale as given by nature. The scales now in use are not identical with the natural scale, but are, in different degrees, derived from it.
The natural scale is, in its commencement, harmonic, and is found by the consideration of the natural progression of sound consequent upon the division and subdivision of a single string. It ought to be familiar to every student of acoustics. The sound produced by the striking or twanging of a single string (on a monochord) is called the tonic, and also, from its position as the lowest note, the bass. If we divide this string in half, we will obtain a series of vibrations producing a sound the same in character, but, so to speak, doubly high in pitch. This sound is named the octave, because it is the eighth note in our common diatonic scale. If we divide the string into three parts, the result will be a sound called the large fifth; a division into four parts gives the next higher octave of the bass; into five, gives the sound known as the large third, commonly called major third; into six, the octave, or next higher repetition, of the large fifth; into seven, the small seventh; into eight, the third repetition of the octave of the bass. The progression thus far is hence: Bass—1st octave of bass—large fifth—2d octave of bass—large third—1st octave of large fifth—small seventh—3d octave of bass. Employing the alphabetical names of the notes (always ascending): C—C—G—C—E—G—B flat—C.
This progression may truly be called natural, as it is that into which the string naturally divides itself when stricken. An attentive ear can readily distinguish the succession of sounds as far as the small seventh. The longer bass strings of any piano of full tone and resonant sounding board will suffice for the experiment. These are also the natural notes as found, with differences in compass, in the simple horn and trumpet, and the phenomenon is visibly shown in the well-known experiment of grains of sand placed on a brass or glass plate, and made to assume various forms and degrees of division under the influence of certain musical sounds.
This is not the place to elaborate the subject, or to show the progression of the natural scale as produced by further subdivisions of the string. Suffice it to say that the remaining notes of the common diatonic scale are selected (with some slight modifications) from sounds thus produced. This scale cannot then be considered, in all its parts, as the fundamental, natural one. Nature permits to man a great variety of thought and action, provided always he does not too far infringe her organic laws. She may allow opposing forces to result in small perturbations, but fundamental principles and their legitimate consequences must remain intact.
No one can ponder upon the above-mentioned harmonic foundation of the musical scale without conceiving a new idea of the beauty and significance of that glorious art and science which may be proved to be based upon laws decreed by the Almighty himself. The one consideration that, in all probability, no single musical sound comes to us alone, but each one is accompanied by its choir of ascending harmonic sequences, is sufficient to afford matter for many a wholesome and delightful meditation.
Instead, then, of regarding our earthly music as a purely human invention, we may look upon it as a genuine gift from heaven, a legitimate forerunner of the exalted strains one day to be heard in the heavenly Jerusalem.
The laws of vibrations producing sound, of undulations giving rise to light and color, of oscillations resulting in heat, the movements of the heavenly bodies, the flow of electric and magnetic currents, the rhythmical beat of the pulse, the unceasing march of mind and human events, all lead us to the consideration of motion as one of the greatest of secondary causes in the guidance of the universe. Do we not, indeed, find the same element in the Divine Trinity of the Godhead, in the eternal generation of the Son, and the procession of the Holy Spirit?