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scale, in cartography
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 and Hindu music.
See N. Slonimsky, Thesaurus of Scales and Melodic Patterns (1947); C. Sachs, The Wellsprings of Music (1965).
scale, in weights and measures
See A. W. Green, How We Weigh and Measure (1961); B. Kisch, Scales and Weights (1965).
scale, in zoology
a series of musical sounds, that is, a consistent sequence of sounds (steps) of a given mode, which are arranged in ascending or descending order from the base tone. The scale spans one octave but can be extended up or down the adjoining octaves. The scale designates the structure of the mode and the pitch relationships of the scale’s steps. A distinction is made between the seven-tone scale of diatonic modes, the five-tone scale of anhemitonic (without half steps) modes, and the 12-tone chromatic scale. Executing the various scales and their combinations helps develop the musical technique of instrumentalists and singers.
V. A. VAKHROMEEV
in architecture, the relationship between various dimensions of buildings, structures, and organized space and, in turn, their relationship to the human viewer. Scale not only impresses the viewer with a notion of the size of a building or architectural complex, which may or may not be accurate, but also creates a mood.
Architectural scale is the result of the total interaction of the dimensions underlying every element of a composition as seen by the viewer. For example, visual measurement units of the wall of a house may be bricks, dressed stone (of which the wall or the wall covering is composed), blocks, panels, or the entire wall (if it is not divided into sections). An important role in the creation of a sense of scale is played by the major visible structural elements, which provide a particularly graphic idea of the building’s dimensions. An architect can achieve diversified artistic effects by moving or setting apart the supports, by changing the height of the girders or the archivolts in relation to the bay, and by relating these changes to the dimensions and sections of the building’s other elements.
The apparent scale of an architectural work can sometimes be affected by the distance from which it is seen. For example, a building that gives the impression of being large from a remote vantage point (or on a drawing), may seem substantially smaller when approached by the viewer, who is then able to see the actual dimensions of the construction in relation to himself. The architectural scale of a building as a whole is related to its surroundings (the local terrain, the urban environment) and changes with them.
Construction on a grand scale is primarily used to impart particular significance to an architectural work. For example, ancient Greek temples, with their heroic scale, seem to have been designed for epic heroes. The large-scale amphitheaters, aqueducts, and basilicas of ancient Rome, as well as the civic structures in the Russian Empire style, reflect the power of the states that built them. Grandiosity of scale, combined with the large dimensions of the structures, has an oppressive effect on people, making them feel insignificant (for example, the religious Structures of ancient Egypt). The scale of an architectural work reflects socio-historical conditions and the outlook of a particular era, as well as the social position of the person who ordered its construction.
As with the structural forms, the scale of an architectural work is an effective artistic device, creating an image that is understood and felt not only by contemporaries but also by future societies and other cultures.
REFERENCESBurov, A. K. Ob arkhitekture. Moscow, 1960.
Kirillova, L. I. Masshtabnost’ v arkhitekture. Moscow, 1961.
Vseobshchaia istoriia arkhitektury, vol. 2. Moscow, 1973. Pages 251-60.
Nobbs, P. E. Design: A Treatise on the Discovery of Form. London-New York, 1937.
Licklider, H. Architectural Scale. London, 1965.
V. F. MARKUZON
the ratio of the length of segments on a drawing, plan, aerial photograph, or map to the actual physical length of the segments corresponding to them. The fractional scale thus defined is an abstract number, which is greater than 1 in cases of drawings of small machines and instrument parts, as well as many microscopic objects, but less than 1 in other cases, where the denominator of the fraction (with a numerator equal to 1) shows the degree of reduction in the sizes of the images of the objects relative to their actual dimensions. The scale of plans and topographical maps is constant; that of geographic maps is variable.
The graphic scale—that is, a straight line divided into equal segments with notations that indicate the actual physical lengths of the segments corresponding to them—is important in practice. A “transversal” scale is constructed for more precise recording and measurement of lines on maps. A transversal scale is a graphic scale parallel to which are drawn a number of equidistant horizontal lines that are intersected by perpendicular (vertical) and diagonal (transverse) lines. The principles of construction and use of a transversal scale are clear from Figure 1, which shows a fractional scale of 1:5,000. The segment of the transversal scale marked in the figure by the two dots corresponds to a line on the terrain of 200 + 60 + 6 = 266 m. The term “transversal scale” is also used for a metal ruler on which a representation of such a drawing has been inscribed with very fine lines, sometimes with no markings. This makes it easy to use for any fractional scale.
REFERENCESInzhenernaia geodeziia. Editor in chief, P. S. Zakatov. Moscow, 1969.
Chebotarev, A. S. Geodeziia, 2nd ed., part 1. Moscow, 1955.
solid deposits that form on the interior walls of the pipes of boilers, water economizers, steam superheaters, evaporators, and other heat-exchange devices in which water containing various salts is heated or evaporated.
The most common types of scale, in terms of chemical composition, are carbonate (calcium and magnesium carbonates, CaCO3 and MgCO3), sulfate (CaSO4), and silicate (silicates of calcium, magnesium, iron, and aluminum). The heat conductivity of scale is tens of times—and frequently hundreds of times —less than that of the steel of which heat exchangers are made. For this reason, even very thin films of scale give rise to high thermal resistance and may lead to such overheating of the boiler tubes that flaws and bulges are formed, frequently leading to rupture of the tubes. Scale formation is prevented by chemical treatment of the water that enters the boilers or heat exchangers. Scale is removed by mechanical and chemical means. Examples of scale are the solid deposits formed inside of teakettles and samovars.
the product that results when the surface of a metal oxidizes upon reaction with the environment.
Usually, scale includes only the oxidation products of iron and iron alloys. In a broader sense, however, it also includes the products of other oxidizing agents on the surface of a metal, for example, sulfur and nitrogen. Thin layers of scale, often called oxide films, are transparent for thicknesses up to 40 nanometers (nm) and are to some extent colored for thicknesses from 40 to 500 nm. For thicknesses greater than 500 nm, scale has a permanent color that depends on its chemical composition.
(1) A microscopic chitinous plate on the bodies of some arthropods, mainly insects, which sometimes completely covers the body. As a result of their optical properties, the scales as a rule determine the coloration of the animal. Butterflies have scales which are particularly developed. Bristletails, springtails, weevils, mosquitoes, and some Hymenoptera have scales, as well as some mites.
(2) Various growths on plants, usually flat and having a protective function. Frequently “scale” refers to the base of a leaf that remains on the stalk after the leaf has fallen off and that forms a peculiar shell on the stem.
(also plate), a hard metameric protective plate of the epidermis in vertebrates, including fish, reptiles, birds, and some mammals.
The scales of fossil Agnatha and fossil fishes were mesodermal in origin and were formed by bony tissue (dentin, bone). Scales are distributed on the body in regular diagonal rows in the direction of the collagen fibers of the skin. In addition to their protective function, they fulfill musculoskeletal functions. In the phylogenesis of the lowest, originally aquatic, vertebrates, such as cyclostomes, fishes, and amphibians, the origin of the scales is the placoid scales of fossil Thelodontidae and cartilaginous fishes, as represented by dentin spines and teeth that were periodically replaced as the animal grew (seePLACOID SCALE). The cosmoid scales, ganoid scales, cycloid scales, and ctenoid scales of the bony fishes are complex phylogenetic derivatives of the original type of scale (seeCOSMOID SCALE; GANOID SCALE; CYCLOID SCALE; and CTENOID SCALE). These scales are characterized by cyclical growth and the formation of annual rings, which make it possible to determine the age of the fish.
Among amphibians, bony plates similar to fish scales are found in some stegocephalians and modern Apoda, such as the Caeciliidae, including water snakes. The horny plates of reptiles, birds, and some mammals are formed by the keratinization of the outermost epidermal layer. They prevent the skin from drying out and protect it from physical damage. The horny plates are usually replaced through periodic molting or desquamation. In certain reptiles, such as crocodiles and tortoises, the horny plates sometimes fuse with the secondary dermal ossifications and cover the entire body. In birds they cover only the legs, and in mammals, for example, marsupials, rodents, insectivores, and some others, they are usually found on the tail. The secondary development of large plates on the body is observed in armadillos, in which they overlie bony plates, and in pangolins.
V. N. IAKOVLEV
part of the reading device of a measuring instrument, consisting of a system of markings (dots or lines arranged in some definite sequence) with numbers or other symbols at some of the markings representing a series of consecutive values of the measured quantity.
Scale parameters, such as scale limits and the value of a division of the scale (that is, the difference between scale values corresponding to two adjacent markings), depend on the inherent measurement limits of the measuring mechanism, on the sensitivity of the instrument, and on the required reading precision. The arrangement of the divisions, which can be in a circle, an arc, or a straight line, depends on the design of the reading device, while the scale itself may be uniform, quadratic, logarithmic, and so on. The main divisions of the scale, corresponding to the numerical values, are marked off by longer or thicker lines. Readings are made by the naked eye on scales the distance between whose divisions is 0.7 mm or higher; smaller intervals require the use of a magnifying glass or microscope. Fractional estimates of scale divisions are made with the aid of verniers.
scale(1) To resize a device, object or system. With regard to increases, "scale vertically" or "scale up" refers to expanding a single machine's capability. To "scale horizontally" or "scale out" refers to adding more machines.
With regard to decreases, the term is often used with cutting-edge chip technologies. For example, "this memory scales with CMOS" means that the memory architecture takes advantage of the increasing miniaturization in CMOS chip fabrication by becoming smaller as well. See at scale, upconvert and scalable.
(2) To increase. The term is widely used to refer to expanding a system, quite often a website or Web-based application that is quickly gaining popularity. See at scale, blitzscaling, 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.
(6) To increase or decrease the size of a digital image.
(7) A large size. For example, the "efficiencies of scale" means the economies derived from expansion.
|Scaling Up and Down|
|Enlarging an image adds pixels, and quality software can produce a decent result for small increases. However, no matter how good the algorithms, a large increase softens the new image. In addition, the original sharpness cannot be brought back as this pixel example shows. See dithering.|