CON'SONANCE, in music, a term applied to combinations of sounds, whose vibrations when heard together so satisfy the ear that no other sound is wished for, or expected to follow. The more or less satisfying effect of C. depends on the greater or less simplic ity of the interval formed by the combined sounds. Intervals whose relative vibrations can be expressed by numbers from 1 to 6, are considered consonant; while those which •can only be expressed by the higher numbers, not a duplication of the lower, as 7, 9, 11, 13, etc., are called dis4onant. Sounds vibrating as 1 : 1, are unison; as 1 : 2, pro duce the octave; as 2 : 3, the fifth. which inverted becomes 3 : 4, the fourth; as 4 : 5, the major third, which inverted becomes 5 : 8, the minor sixth; and 5 : 6, the minor third, which inverted becomes 6 : 10, or 3: 5, the major sixth. Consonant intervals are therefore the third, fourth, fifth, sixth, and octave; from which it follows that there is only one consonant fundamental chord in music, viz., the common chord, or trios harmonica perfecto, being a bass note with its third, fifth,. and octave, which inverted produces the chords of the 6th and the I. See Crtonn. The ancient Greeks admitted of still fewer consonances in their system of music, as they treated the third and sixth as dissonances; a proof that their system of harmony was not the same as ours. Their name for C. was symphony, and for dissonance, diaphony. Early in the middle ages, only the octave, fifth, and third were treated as consonances. Ft.anco of Cologne was the first who divided C. into perfect, semi-perfect, and imperfect. In the writings of Marchetti's, and of Joannes de Muris, in the first half of the 14th c., we find already the important rule, that two perfect consonances following in similar progression are not allowable. The study of the C. was carried still further in the 16th c. by Zerlino, who ascertained the true mathematical proportions of the major and minor thirds. Notwith standing this, Palcstrina, up to the end of the same century, and, long after him, all who wrote in the same style, carefully avoided the use of the third in the final chord, finish ing always with the perfect consonances according to Franco. Of late years, the importance of the C. has attracted the attention of many eminent theorists in music;
as well as philosophical writers of undoubted judgment, some of whom do not to consider the interval of the seventh a C., because it differs from other dissonances in not requiring preparation. There cannot be a doubt that the chord of the seventh, C, E, G, and B fiat, considered individually, and not in connection with other chords, Is as euphonious and satisfying as the common chord; and when these intervals are placed' at the distance from the fundamental note they harmonically arise at, the nature of the combination is still more obvious. A scientific organ-builder in Scotland has long been in the practice of introducing the seventh as an interval in his mixture stops, forming with the fundamental stops a union of sound decidedly consonant, and producing a remarkably brilliant effect. The exactlimit of C., or the point where sonance begins, seems not definitely fixed, if fixed it can be. To define C. to be agree able sounds, and dissonance to be the reverse, as some do, is clearly absurd, because they both essentially belong to harmony or concord, or, as the Germans more properly call it, Die Kunst des Woltiklangs, in which there can be nothing absolutely discordant.
A perfect C. causes a musical effect known as Tartini's grave harmonic, it having been first observed by the eminent violinist of that name. Along with any two musical notes sounded.cohtinuously, there may be heard (if the notes are in accord) a third deeper tone, caused by that number of vibrations which is the greatest common measure of the numbers producing the primary notes, and upon this Tartini founded his theory of har mony (now obsolete), by assuming that the grave note is the natural base of the chord producing it. The note thus sounded may be too deep to be appreciated by the unedu cated car, although felt as a succession of beats, and these should not be confounded with the "beats" resulting from the sound of a discordant interval, a species of jar or flutter known to tuners as the consequence of the imperfection of a consonance. The treated at length by prof. de Morgan in a paper published in the transactions of the Cambridge philosophical society, 1858.