SCALE, a measure, consisting of a slip of wood, ivory, or metal, divided into equal parts, usually main divisions and subdivisions; as, inches or octonary frac tions for carpenters' work, decimal divi sions and subdivisions for chain work, duodecimal for plotting carpenters' work, which is in feet and inches. The meter and its decimal subdivisions are also sometimes employed. Also any instru ment, figure, or scheme graduated for the purpose of measuring extent or propor tions.
In music, the sounds in consecutive order used by various nations in differ ent forms as the material of music. In a proper succession such sounds form melody, in proper combinations they con stitute harmony. The modern scale, uni versally used among the more civilized nations, consists of 12 divisions, called semitones, included in one octave. The ancient Greeks and Asiatics, ancient and modern, exhibit the use of less intervals. Such scales are called enharmonic. Other nations have intervals of a third between some of the steps. This is exhibited in the Chinese and ancient Scotch scales, and in the scales of some savage nations. A scale containing only five unequal di visions of the octave has been called pen taphonic or, less correctly, pentatonic. All scales are purely arbitrary, consist ing of a selection of sounds produced by the aliquot divisions of a monochord. When the diVisions of a monochord are slightly altered to suit the required steps in an octave, as is the case in the modern scale, the scale is said to be tempered; when the harmonic divisions of the mono chord are strictly followed, the scale is said to be in just intonation. The modern
scale when used as a succession of 12 semitones is called chromatic, when used in the ordinary mixture of tones and semitones it is called diatonic, when the third and sixth are flattened it is called the modern minor diatonic scale, when the third and sixth remain major, the scale is said to be a major diatonic scale. The scale is also called the gamut (French, gamme) from the words gamma and ut, the names of sol and do, found in the Guidonian system of overlapping hexachords. The Italian names for the degrees of the scale, ut, re, mi, fa, sol, la, are derived from the initial syllables of a Latin hymn quoted in all musical his tories. Ut was afterward called do by many nations, and the name si was given to the seventh degree of the scale, when the ancient system of hexachords was converted into the modern system of oc taves. When the scales, whatever the pitch, start from do, the system is said to be that of the movable do; when the first note of the scale is called do, re, mi, etc., according to a stated pitch called do, the system is called that of the fixed do.
In painting, a figure subdivided by lines like a ladder, which is used to measure proportions between pictures and the things represented. Scale of a series, in algebra, a succession of terms, by the aid of which any term of a recur ring series may be found when a suf ficient number of the preceding ones are given. Scale of longitudes; a scale used for determining geographically the num ber of miles in a degree of longitude in any latitude.