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scale, in cartography

scale, in cartography, the ratio of the distance between two points on a map to the real distance between the two corresponding points portrayed. The scale may be expressed in three ways: numerically, as a ratio or a fraction, e.g., 1:100,000 or 1-100,000; verbally, e.g., "one inch to one mile" (not "one inch equals one mile"); and graphically, by marking distances on a sample line. The last method has the advantage that the scale remains true even if the map is enlarged or reduced mechanically. The first method is particularly useful since any unit of measurement may be used; e.g., if one uses metric units, a scale of 1:100,000 would mean that one centimeter on the map represents one kilometer on the earth's surface (since 100,000 centimeters equals one kilometer). The more the size of features on the map approaches the features' actual size on the earth's surface, the larger the scale of the map is said to be. A large-scale map usually shows more detail than does a small-scale map, but covers a smaller area than does a small-scale map of the same size.

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scale, in music

scale, in music, any series of tones arranged in a step-by-step rising or falling order of pitch. A scale defines the interval relationship of each tone to the others upon which the composition depends. Scales further serve to classify and catalog the tonal material used in composition.

A great variety of scales have been used in the past and in different cultures; no single interval is common to all of them. In the 6th cent. B.C., Pythagoras defined the mathematical relationship of the perfect intervals (the octave, fourth, and fifth) and of the intervals between them (an interval being the difference in pitch between two tones). The Greek system was taken up by the Christian church, which adapted its note series to a number of modes used in medieval music, especially in plainsong.

The church modes, under the impact of the composition of polyphonic vocal music, became reduced in due course to the two characteristic scales of later Western music, the major and the minor. The major scale, called diatonic, has five whole tones (t) and two semitones (s) arranged thus: ttsttts (as in the white notes on the piano keyboard taken from one C to the next C); this scale, with certain modifications, became the basis of Western musical tonality until the end of the 19th cent. The dissemination and influence of the diatonic scale was therefore very great. The minor scale is based on tsttstt. This arrangement produces the lower third, sixth, and seventh degrees that are characteristic of the minor mode; the higher seventh degree, a semitone rather than a whole tone below the main note, or "tonic," is often borrowed from the major mode for use at cadences.

Akin to the modes, the concept of key was developed, whereby a home tone, or tonic, is the principal focus of a composition, and the various other tones assume importance according to their relationship to the tonic. The increasing complexity of instruments demanded more refined tuning systems. By J. S. Bach's time equal temperament had become established. The resulting scale, called chromatic, consisted of 12 notes divided by semitone intervals (the white and black notes of the keyboard). Although the diatonic scale is basically heptatonic (seven-noted), music that is in a major or minor tonality usually employs the remaining five tones of the chromatic scale as auxiliary or ornamental tones. Music that employs them freely is said to be highly chromatic, while music that employs them sparingly is said to be diatonic.

The 12 scales, one for each note as the home tone, plus the 12 concomitant minor scales remained the basic organizing structure of Western music until the system was challenged by the dodecaphonic (twelve-tone scale) composers, in particular Arnold Schoenberg, who worked into the mid-20th cent. (see atonality; serial music). The whole-tone scale, which divides the octave into six equal whole tones (C, D, E, F sharp, G sharp, and A sharp, on the piano), gives a feeling of vagueness that made it adaptable to impressionism; its possibilities were thoroughly explored in the works of Debussy. The pentatonic scale (the black keys of the piano illustrate one form) has long been thought of as having an Asian character because of the prevalence of pentatonic scales in Chinese, Japanese, and Javanese music. The most complex scales known belong to Arabian music

Characteristics, Forms, and Instruments

.....  and Hindu music.

Bibliography

See N. Slonimsky, Thesaurus of Scales and Melodic Patterns (1947); C. Sachs, The Wellsprings of Music (1965).

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scale, in zoology

scale, in zoology, an outgrowth, either bony or horny, of the skin of an animal. The major component of the scales of fishes is bone, and they are formed directly in the skin membrane as the fish grows. The number of rows of scales, as well as the kind, figures in the identification of a species. The growth of the scales is marked by rings, which aid in determining the age of the fish. The placoid scales of sharks, which have a dentine base with a pulp cavity, are thought to be similar to the forms from which the teeth of the higher vertebrates evolved. Ganoid scales, found in primitive fishes such as the gar pike and the sturgeon, are heavy and platelike. Other fishes have either rough scales (ctenoid) with comblike edges or smooth scales (cycloid). The horny scales, or scutes, of most reptiles develop embryologically as outpushings of the epidermis. In some lizards the scales are modified to form tubercles or granules. Other lizards and snakes have overlapping scales, highly developed in the snakes as aids to locomotion. The crocodile has both horny and bony scales. Among turtles and their relatives scales are usually found on the head, neck, limbs, and tail; in most of the group horny scales also form a pattern of flat plates overlying the bony dermal skeleton of the back and belly. Birds have horny scales on the feet and sometimes on the legs. Some mammals, e.g., the mouse and the rat, have scales on the tail; the pangolin and the armadillo have a body covering of large horny scales.

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scale, in weights and measures

scale, in weights and measures, instruments for determining weight, generally for other than laboratory use. For the principles of operation of all weighing devices, see balance. Platform scales utilize a succession of multiplying levers that transmit the weight to a beam or other registration device. They are used where massive objects or large quantities are to be weighed. For example, a railway car or truck moves onto a platform scale before and after unloading or loading, in each case the difference between the weighings being the weight of its cargo. As the name implies, counter scales are used in commercial establishments where weighing can be most conveniently done on a counter. Cylinder, drum, or barrel scales show their calibrations on a rotatable chart. These find wide use because of the ease with which the cost of a given weight may be read from them through the juxtaposition of fixed and rotating charts. The same purpose is served by the fan-type scale, in which an indicator moves through an arc marked from zero to the maximum capacity of the scale. Both the indicator and the fan expanse are calibrated for automatic computation. A great variety of scales are specially constructed for industrial uses in which weighing of a continuous flow of material is required. The scale in such cases is part of the machinery that carries the weighed material to a succeeding operation. Many scales provide printed records of each reading, and some keep a cumulative registration of a succession of readings.

Bibliography

See A. W. Green, How We Weigh and Measure (1961); B. Kisch, Scales and Weights (1965).

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scale

Examples of the chromatic, major, and minor scales.

(credit: © Merriam-Webster Inc.)

In music, primary pitches of a key or mode arranged within an octave. Scales are distinguished by the pattern of the intervals between adjacent notes. A scale can be seen as an abstraction from melody—that is, the pitches of a melody arranged in stepwise order.

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(1) To resize a device, object or system, making it larger or smaller. To "scale vertically" or "scale up" refers to expanding a single machine's capability. To "scale horizontally" or "scale out" refers to adding more machines. See upconvert and scalable.

(2) To expand. The term is widely used to refer to systems that easily expand. See scalable and scaler.

(3) To move with. The phrase "the image scales with the window" means that as an on-screen window is dragged by the user to a larger or smaller frame size, the image inside continuously expands or contracts to fit the changing frame.

(4) To change the representation of a quantity in order to bring it into prescribed limits of another range. For example, values such as 1249, 876, 523, -101 and -234 might need to be scaled into a range from -5 to +5.

(5) To designate the position of the decimal point in a fixed or floating point number.