INTERVAL (Lat. intr•.a//uttl, interval, from inter. between + eallum, wall). In music. (lie difference of pitch bet‘ve•n any two tiOIIIII1S, or the distance cu the stave from one note to an other. in opposition to unison, which is two sounds exactly of the same piteh. From the nature of our system of musical notation, which is on five lines and the four intervening spaces, mid from the notes of the scale being named by the first seven letters of the alphabet. with repe titions in every oetave. it follows that there can only he six ditrereni intervals in the natural dia lcnic scale until the oetave of the unison be attained. To reckon from C upward, we find flue following intervals: C to D is a second; C to IS is a third; C to is a fourth; C to 0, a fifth; C to A, a sixth; C to 11, a seventh; and from C to C is the octave, or the beginning of a similar series. Intervals above the octake are 11141*(401'e 1111•11'1y 11 roperition Of 11141,1' 1111 01•1;1\1' A flat or a sharp placed before either of the notes of nu interval does not. alter the name of the inter although it alleets its quality; for example, from C to II: is still a fifth, notwithstand ing that the t: is raised a semitone by the sharp. Intervals are classined as perf•i•t, major mid minor. Perfect intervals are those which admit of no change whatever ithout destroying their consonance; these are the unison, fourth, fifth, and the octave. Intervals which admit of being raised or hmered a semitone are distinguished by the term major or //limn', according as the dis• tamp between the notes (q the interval is large or small. intervals are the third and sixth: for example, from C to E is a major third, the consonance being in the proportion of 5 to .t; when the F. is lowered a semitone by a that, the interval is .till consonant. lout in the proportion of ti to 5, and is called a minor third. The same description applies to the interval of the sixth from to A. and from C to Ab. The second and seventh are also distinguished as major and minor. If the upper tone of a major, or perfect, interval be raised, or the lower tone a semitone., the interval bee/tines aupliented; thus;
c.c$ or cb-e. Ity lowering the upper or rais ing the lower tone of it minor, or perfect, interval hy a semitone, a diminished interval results, thus: (•- 41) or lob. Intervals are further distinguished as consonant and dissonant. Consonant intervals are those \Odell can enter into the formation of a major or minor triad. They are the perfect unison, fourth, fifth, and and major and minor thirds and sixths. Thus, C. e. g, e' (1, 3, 5, S) and ct, f, a, (.. (1, -1, G., 8) are the tonic triads of C and major, respectively; whereas, with the third and sixth (e, a) flattened, they are the tonic triads of C and F minor, respectively. 1)issonant in. tervals are the major and minor seventh and all augmented and diminished intervals. \\ hen ever they enter into a chord, that chord is a di, sonanee and requires resolution into v011S0111111Ce, file distinction between eonsonant and dissonant intervals is made according to the ratio of the number of vibrations between any interval and the fundamental Ione. Consonant intervals satisfy the ear because of their simple ratios; dissonance: give a feeling of unrest and desire for resolution because of their complex ratios. The mathematical relations of intervals are deter mined as follows: given the normal a', which is produced by a siring vibrating 870 times per second (see DIAPASON), the octave above is pro duced by shortening the string by half its length..
The number of vibrations will then be doubled, or 1740. This establishes the ratio between the prime and octave of 1 : 2. A string producing e" vibrates 1305 times. Thus the ratio between prime and fifth is as 780 : 1:305, or as 2 : 3. The preceding table shows the ratios of the different intervals.
As the length of the vibrating string is in in verse ratio to the number of vibrations, the ratios of the above table need only be inverted to deter mine the length of the string for any given inter val. See HaestoxY; \lrsic.