Scale

Collier's New Encyclopedia (1921)

2026 Editor's Note: This page uses language about other peoples, religions, or nationalities that was commonplace when the book was published and is offensive by today's standards. The text has been left exactly as it was printed, rather than cut or softened, so that the historical record — including how ordinary such language once was — is preserved. (Ed: ET 2026-07-22) a measure, of wood, ivory, or metal, divided into consisting of a slip equal parts, usually main subdivisions; as, inches or octonary fracdivisions and tions for carpenters ' work, decimal divisions 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 instrument, figure, or scheme graduated for the purpose of measuring extent or proportions. In music, the sounds in consecutive order used by various nations in different forms as the material of music. In a proper succession such sounds form melody, in proper combinations they constitute harmony. The modern scale, universally 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. the Chinese and ancient Scotch scales, This is exhibited in and in the scales of some savage nations. scale A containing only five unequal divisions of the octave has been called pentaphonic or, less correctly, pentatonic. All scales are purely arbitrary, consisting 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 monochord 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 in the ordinary mixture of tones and used semitones it is called diatonic third and sixth are flattened it is called , when the 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 in the Guidonian system of overlapping , found hexachords. The Italian names for the degrees of the scale, ut, re, mi, fa, sol, la, are derived from the initial syllables of Vol 8 a. Latin hymn quoted in all musical histories. 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 octaves. When the scales, whatever 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, to a stated pitch called etc., according do, the system is called that of the fixed do. In painting, a figure subdivided by like a ladder, which is used to lines measure proportions between pictures the things represented. Scale of a and series, in algebra, a succession of terms, aid of which any term of a recurby the ring series may be found when a sufficient number of the preceding ones given. Scale of longitudes; a scale used for determining geographically the number of miles in a degree of longitude in any latitude.