serving the respective degrees of acuteness and gravity of its intervals, producing imitations, canons, and fugues. This custom subsisted till the time of Zarlino, and Glareanus informs us that, in his time, but little was composed but upon the foundation of some well known melody, and that such compositions as were not composed upon this principle were termed missa sine nomine. Of the melodies used as a foundation for counterpoint, the most celebrated was the song entitled 'L'Homme Armé, a provincial canzonet composed in the early part of the sixteenth century. Another method, not less remarkable, was also observed, consisting of singing certain parts of the divine service in four parts impromptu upon a given subject, written principally for the tenor called 'chant sur le lure.' But these compositions, however ingenious, afforded more an object of intellectual amusement than of spiritual devotion; the sense of the words was quite out of the question. These abuses were corrected under the pontificate of Marcellus in 1555. Every means being now employed that science and application could suggest, to bring to perfection the natural powers of harmony, the melody arising from the Ionian and Æolian modes was found to be susceptible not only of greater perfection than that hitherto employed in psalmody, but even of grace, elegance, and of every embellishment that art and genius could furnish. This discovery soon introduced music into good company, and from taverns, and other haunts of the vulgar, it ascended to form the delight of polished society, as also, for the first time, of the speculations of the learned. But unfortunately for the cause of that species of melody which, in the early part of this history, had been proved to be totally independent of harmonic rules, the powers of the other Grecian modes were considered of too feeble a nature to be attended to, and their divisions into plagal and authentic were entirely superseded by the major and minor modes. These modes, adopted solely by those in whom the principles of taste for melody combined with harmony, had developed themselves, are determined by their respective mediants. Under the pontificate of Marcellus, and, at a time when music, from its degraded state as a science, was upon the eve of being entirely excluded from the celebration of divine service, Palestrina at the age of twenty-six presented to his holiness a mass upon an entire new principle, the success of which procured for him the situation of composer to the church of Rome. His observations upon the principles of harmony produced a complete revolution in the science, not only in Italy but in every part of Europe. He was a pupil of Goudimil of Besançon, a celebrated composer of the French school, which, says Choron, having emanated from the Flemish, and the first that flourished after the arts had fallen, ought to be considered the mother of modern schools. Palestrina, also, in compliance with custom, produced a mass upon the subject of L'Homme Armé. It was so complicated that Zacconni folio pages of close printing, to explain the notes and to resolve the canons; but even with this assistance few musicians are competent to adjust the parts in score. In 1570 Palestrina renounced this pedantic style of writing; and such was the excellence of his compositions that Cifra, Tharenzio, composers of the first order, and De Porta, considered them as models of perfection. Soriano was an imitator of Palestrina, and a composer of 110 canons upon the subject of Ave Maria Stella. Valentina, however, surpassed Soriano in the composition of a canon called Solomon's Knot, consisting of ninety-six parts: a description of this canon may be seen in Dannely's Portable Encyclopædia of music, a work, which, inasmuch as it combines the whole of the theoretical observations of Catel Choron, and Reicha, together with the principal articles in Roch's German Lexicon, is highly useful to the musical student. Monteverde, also an imitator of Palestrina, deserves honorable testimony; for, having acquired the excellence of the system of counterpoint adopted by that eminent composer, he ventured to introduce double dissonances as the diminished fifth and minor seventh, for which, although they please the ear and are productive of the finest effects, he had the mortification of being designated an impostor and corrupter of the art. The most eminent musical theorists of Italy, who flourished in the sixteenth century, besides these already named, were Franchinus Gasierius of Lode, Peter Aaron of Florence, Lewis Fogliano, John Spatatro, John Maria da Terentio, Lanfranco, Stephen Uanneo, Anth. Doni, the most general, voluminous, and celebrated theorists of that period; Vincent Galilei, a Florentine nobleman, and father of the great Galileo Galilei; Maria Artusi of Bologna, Oraseo Tegrini, Peter Pontio, Lewis Zacconi, and Andrew Rota, an admirable contrapunctist. The principal Roman authors were, John Amnuccia, Rugiero Giovanelli, Lucas Marenzio, who brought to perfection madrigals, the most cheerful species of secular music. Of the Venetians, Adrian Willaeri is allowed to be at the head. At the head of the Neapolitans is deservedly placed Rocco Rodio. At Naples, too, the illustrious dilettante, Charles Gesualdo prince of Venosa, is highly celebrated. Lombardy could also furnish an ample list of eminent musicians during the sixteenth century. The chief of them were Constance Porta, Gastoldi, Biffi, Cima, and Vocchi. Francis Corteccia, a celebrated organist and composer, and Alexander Strigglio, a lutanist and voluminous composer, were the most eminent Florentines. Up to the year 1700 the principles of musical rhythm were but imperfectly understood; much less so, perhaps, than by the ancient Greeks and Romans. For by the continual application of long notes to short syllables, and long syllables to short notes, by Hasse, Handel, &c., as for example Angels ěvěr bright and fair, wrote a commentary upon it, occupying thirteen the casural pauses of the poetry were often con founded with those of the music. Peigolese, in the improvement of these defects, deserves to be noticed in history. But though it must be confessed that the melody of the moderns, by neglecting the ancient rules of the Melopoeia, has acquired a richness and variety, as compared with the few specimens of ancient music handed down to us, it cannot be dissembled that this variety is often maintained in defiance of the general rules of prosody, when the voice is not only made to apply a short note to a long syllable, but even to dwell and run into divisions upon the insignificant particles of language, whilst the most emphatical words are nearly imperceptibly glided over to the entire subversion of the poet's meaning. Music then, instead of aiding poetry, becomes the instrument of rendering it ridiculous, and making sense nonsense. As early as 1440 an opera, in imitation of Greek tragedy, called the conversion of St. Paul, was publicly performed in Rome. Five years afterwards La Verità Raminga; and in 1574 operas were upon the scale of modern times. The performance of Daphne and Eurydice, by Peri and Arienne, astonished the whole of Europe. The first operas were performed in a cart, with a moveable stage, like the one used by Thespis at Athens, and they attracted the multitude from street to street. Having, as far as our limits permit, described the nature of musical instruments, and their employment in the formation of the ancient and modern systems of sounds, the leading features of musical history, we pass over events of minor importance, and cursorily notice the introduction in the seventeenth century of the bar to divide musical sentences into equal portions; the addition of the fifth line to the musical staff'; and Ludovico Viadona's harmonised scale of the octave, the merits of which will be shown in our principles of harmony and composition. Among the various treatises that have been published on this enchanting science, by the most eminent authors, in the course of the eighteenth century, none has obtained higher or more just applause for method, perspicuity, conciseness, and elegance, than that of M. D'Alembert's translation of Rameau's principles of harmony. The first theories of music were perhaps as ancient as the age of Pythagoras; nor does history leave us any room to doubt, that, from the period when that philosopher taughf, the ancients cultivated music, both as an art and as a science, with great assiduity. But there remains to us much uncertainty concerning the degree of perfection to which they brought it. We shall, therefore, content ourselves with considering the present state of music, and limit our endeavours to the explication of those accessions which have accrued to the theory of music in these later times. The first compositions upon the laws of harmony which we know are of no higher antiquity ther their analogies one with another, nor their common source, had been perceived an unenlightened experience was the only compass by which the artist could direct his course. M. Rameau was the first who began to transfuse light and order through this chaos. In the different tones produced by the same sonorous body, he found the most probable origin of harmony, and the cause of that pleasure which we receive from it. His principle he unfolded, and showed how the different phenomena of music were produced by it: he reduced all the consonances to a small number of simple and fundamental ones, of which the others are only combinations or arrangements. He, in short, discovered, and rendered sensible to others, the mutual dependence between melody and harmony. Tartini presented us in 1754 with a treatise of harmony, founded on a principle different from that of M. Rameau. This principle is the result of a most beautiful experiment. If at once two different sounds are produced from two instruments of the same kind, these two sounds generate a third, different from both the others. But from the great encouragement given by the various conservatories upon the continent, since the publication of these treatises, however excellent and ingenious, they have been superseded by others more efficient for the explanation of musical theory in general; and the theoretical works of Choron, Catel, Momigny, and Beicha, possessing every observation that science and experience could suggest upon the subject of music, little or nothing is left to later theorists but to study and translate them. PART II. THEORY OF MUSIC. From the twelve degrees of the octave, tuned according to that mode of temperament which gives to each note its natural sound, thus : b than two ages prior to our own; and they were together with others thusfollowed by many others. But as none of these essays were capable of satisfying the mind concerning its principles; as they were confined almost entirely to the collecting of rules, without endeavouring to account for them; and nei or and as represented upon the following portion only of the modern pianoforte clavier, thus we obtain the twelve major and minor scales, the thirteen harmonic combinations of sounds, every major and minor semitone, and augmented, diminished, perfect, and enharmonic interval; which, as colors to the painter, are the materials for musical compositions: all other sounds, high or low, being considered, and treated, as replicates of the above notes, and as varieties of the diatonic scales, major or minor, whether as regards melody or harmony; the former consisting of a succession of notes capable of being sung by a single voice, or played upon the pianoforte, thus: Intervals of seconds, of which there are three species, produce by inversion, sevenths, thus: 1. The minor second, as C natural, and D flat, next above, composed of one chromatic degree, produces, by inversion, the major seventh, as G natural, and D flat, next below, which is composed of eleven chromatic degrees (see table of intervals, p. 290). The number of degrees of any interval diatonic or chromatic, wanted to complete the ocwhich must either make up the number 9, or tave, is called the complement of the octave, that of 12: the former by diatonic degrees, when the first note, or root, is called unison, and is reckoned as one; and the latter by chromatic degrees, when intervals are reckoned according to the absolute degrees of which they are composed. composed of two chromatic degrees (see table, 2. The major second, as C, D, next above, venth, as C, D, next below, which is composed p. 290), produces, by inversion, the minor seof ten chromatic degrees, thus 1 2 3 4 5 6 7 8 9 10 the latter of a combination of notes, sung by two The intervals, therefore, comprising the major voices, thus or second and minor seventh, reckoned together, make up the number nine diatonically, and that of twelve chromatically. 3. The augmented second, as C natural, D sharp, next above, composed of three chromatic degrees, produces, by inversion, the diminished seventh, as C natural and D sharp, next below, which is the complement of the octave, and com- . by three voices, in the following manner, thus posed of nine chromatic degrees. E or by four voices, thus In the foregoing specimens of harmony, in two parts, the lowest of the first forms the highest of the second specimen; this transposition of sounds is employed to produce variety, and is called inversion of intervals, a process by which major intervals become minor ones; minor intervals become major; augmented intervals become diminished, and diminished intervals become augmented. All intervals are known by the number of degrees composing them; and every interval is susceptible of in version. VOL. XV. Intervals of thirds, of which there are four species, produce by inversion sixths of the same number and species, thus 1. The diminished third, as C sharp, and E flat, the use of which is strictly forbidden excepting upon enharmonic occasions, is composed of two chromatic degrees, and produces, by inversion, the augmented sixth, which is composed of ten chromatic degrees, and used instead of the diminished third; 2. The minor third, as C natural, and E flat, composed of three chromatic degrees, produces by inversion the major sixth, as C and E flat next below, which is composed of nine chromatic degrees; 3. The major third, as C natural, and E natural, next above, composed of four chromatic degrees, produces by inversion the minor sixth, which is composed of eight chromatic degrees, as C natural, and E natural, next below; 4. The augmented third, as C natural, and E sharp, composed of five chromatic degrees, produces by inversion the diminished sixth, as C natural, and E sharp, next below, which is composed of seven chromatic degrees. Intervals of fourths, of which there are three species, produce by inversion fifths of the same number and species, thus: 1. The diminished fourth, as C natural, F flat, composed of four chromatic degrees, produces, by inversion, the augmented fifth, as C sharp, F U flat, next below, which is composed of eight chromatic degrees; 2. The perfect fourth, as C natural, F natural, composed of five chromatic degrees, produces, by inversion, the perfect fifth, as C, and F, next below, which is composed of seven chromatic degrees; 3. The augmented fourth, as C natural, F. sharp, next above, composed of six chromatic degrees, produces, by inversion, the diminished fifth, which is also composed of six chromatic degrees. Intervals of fifths, of which there are three species, produce, by inversion, fourths of the same number and species; thus 1. The diminished fifth, as C natural, G flat, next above, composed of six chromatic degrees, produces, by inversion, the augmented fourth, as C natural, and G flat, next below, which, as before stated, is composed of six chromatic de grees; 2. The perfect fifth, as C natural, G natural, next above, composed of seven chromatic degrees, produces, by inversion, the perfect fourth, as C natural, G natural, next below, which is composed of five chromatic degrees; 3. The augmented fifth, as C natural, G sharp, next above, composed of eight chromatic degrees, produces, by inversion, the diminished fourth, as C natural, and G sharp, next below, which is composed of four chromatic degrees. Intervals of sixths, of which there are four species, produce, by inversion, thirds of the same number and species, thus 1. The diminished sixth, as C sharp, A flat next above, composed of seven chromatic degrees, produces, by inversion, the augmented third, as C sharp, A flat, next below, which is composed of five chromatic degrees : 2. The minor sixth, as C natural, A flat, next above, composed of eight chromatic degrees, produces, by inversion, the major third, as C natural, A flat next below, which is composed of four chromatic degrees: 3. The major sixth, as C natural, A natural, next above, composed of nine chromatic degrees, produces, by inversion, the minor third, as C natural, A natural, next below, which is composed of three chromatic degrees. 4. The augmented sixth, as C natural, A sharp, composed of ten chromatic degrees, produces, by inversion, the forbidden interval of the diminished third, as C natural, A sharp, next below, which is composed of two chromatic degrees. Intervals of sevenths, of which there are three species, produce, by inversion, seconds, thus 1. The diminished seventh, as C sharp, B flat, next above, composed of nine chromatic degrees, produces, by inversion, the augmented Sevenths second, as C sharp, and B flat, next below, which produce, is composed of three chromatic degrees; 2. The minor seventh, as C natural, B flat, next above, produces, by inversion, the major second, as C natural, B flat next below, which is composed of two chromatic degrees. 3. The major seventh, as C natural, B natural, composed of eleven chromatic degrees, produces, by inversion, the minor second, which is composed of one chromatic degree. by inver- dimin. 6. minor 6. major 6. aug. 6. augmen. 3. major 3.minor 3. dimin.3 se conds. Intervals of which the notes serve to show the number of degrees composing them are consonant and dissonant. Minor and major thirds and sixths, in the composition of melody or harmony, being of themselves either way satisfactory to the ear, which is the umpire of all musical sounds, are distinguished by the appellation of imperfect consonances; fourths, fifths, and octaves, are denominated perfect consonances, because, by the alteration of either of them by a sharp or flat, they are immediately rendered unsatisfactory to the ear. These and all other chromatic intervals are dissonant, as is the case with seconds and sevenths; and the fourth of the diatonic scale when forming an integral part of the dominant harmony of the seventh; and the sixth, when forming that of the dominant ninth, are also regarded as dissonances requiring to be regularly resolved into the perfect harmony of the Tonic, thus Upon these simple combinations of different sounds, the first of which must be considered the cause, and the last the effect of that cause, the whole science of harmony depends: the powers of the first providing, by the application of a flat, or a sharp, taken in totality, or in part, for every species of harmonic combination used in the present day; as the materials of the latter provide, by the occasional application of a flat to its third note, every sound proper for the resolution of the dissonances arising, directly, or indirectly, from the harmony of the dominant ninth. Thus the lowest note of the foregoing example of the harmony of the dominant ninth, called the dominant root, accompanied only by the major third, and fifth, thus-G BD, affords the modes of the tonic major, perfect harmony CEG; but although the materials of which these intervals are composed be absolutely the same, their effects as employed in succession are of a widely different nature, the first governing entirely the key note of the second which is C, the key note of the passage, thus 4 1 2 3 5 6 7 8 consisting of five tones and two half tones, the latter falling between the third and fourth, and seventh and eighth intervals. We postpone other considerations of this diatonic scale till we have developed the whole of the harmonic powers of the dominant ninth. The application of the sign of a flat to the third of the dominant root, thusforms the model of the perfect minor harmony; and the same union of different sounds, varied by the addition of another flat, constitutes the softest of all discords, which is the harmony of the minor third and diminished fifth; the acute, as well as the middle, sound forming a dissonance, both of which must be regularly resolved, and in the following manner, viz. It follows therefore of consequence that every note composing the dominant harmony of the ninth must be considered and treated as a dissonance, excepting the root G: the A cadencing or falling upon G, the F upon E, the D upon C, the B cadencing or rising to C, i. e. from necessity, or according to the principles as established by nature: the G, which is common to both harmonies, forms the link by which they are united. From this simple process, of which the tonic, or key note, C, may be said to be the centre of gravity, upon which all other sounds resolve, we obtain the model and origin of the twelve major diatonic scales; all other major scales being only transpositions of this natural, or primary order of sounds, viz. Varying this third dominant combination of sounds, i. e. by placing the sign of a sharp to the highest sound, and omitting the two flats, we have the harmony of the major third and augmented fifth, when the fifth forms the principal dissonance, requiring, together with the third, resolution into perfect harmony, thus. From the harmony of the dominant ninth we have therefore derived four species of combinations of thirds and fifths. From the same source we also derive four species of the harmony of, or belonging to, the seventh viz. |