the distance or space between two extremes, either in time or place. The word comes from the Latin intervallo, which according to Hidore, signifies the space inter fossam & murum, "between the ditch and the wall;" others note, that the stakes or piles, driven into the ground in the ancient Roman bulwarks, were called vallo; and the interstices or vacancy between them, interstalla.

in Music. The distance between any given sound and another, strictly speaking, is neither measured by any common standard of extension nor duration; but either by immediate sensation, or by computing the difference between the numbers of vibrations produced by two or more sonorous bodies, in the act of sounding, during the same given time. As the vibrations are slower and fewer during the same instant, for example, the sound is proportionally lower or graver; on the contrary, as during the same period the vibrations increase in number and velocity, the sounds are proportionally higher or more acute. An interval in music, therefore, is properly the difference between the number of vibrations produced by one sonorous body of a certain magnitude and texture, and of those produced by another of a different magnitude and texture, in the same time.

Intervals are divided into consonant and dissonant. A consonant interval is that whose extremes, or whose highest and lowest founds, when simultaneously heard, coalesce in the ear, and produce an agreeable sensation called by Lord Kames a tertium quid. A dissonant interval, on the contrary, is that whose extremes, simultaneously heard, far from coalescing in the ear, and producing one agreeable sensation, are each of them plainly distinguished from the other, produce a grating effect upon the sense, and repel each other with an irreconcilable hostility. In proportion as the vibrations of different sonorous bodies, or of the same sonorous body in different modes, more or less frequently coincide during the same given time, the chords are more or less consonant. When these vibrations never coincide at all in the same given time, the discord is commutate, and consequently the interval absolutely dissonant. But for a full account of these, see Music.