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meter,abbr. m, fundamental unit of length in the metric systemmetric system,
system of weights and measures planned in France and adopted there in 1799; it has since been adopted by most of the technologically developed countries of the world.
..... Click the link for more information. . The meter was originally defined as 1/10,000,000 of the distance between the equator and either pole; however, the original survey was inaccurate and the meter was later defined simply as the distance between two scratches on a bar made of a platinum-iridium alloy and kept at Sevres, France, near Paris. More recently, it has been defined as the distance light travels through a vacuum in 1/299,792,458 of a second. The meter is now the legal standard of length for most of the world, other standards, such as the yard, being defined in terms of the meter.
meter,in music, the division of a composition into units of equal time value called measures, and the subdivision of those measures into an underlying pattern of stresses or accents (see measuremeasure,
in music, a metrical unit having a given number of beats, the first of which normally is accented, although the accent may be displaced by syncopation. Measures are separated on the staff by vertical lines called bars.
..... Click the link for more information. ). Meter is usually indicated by a time signature, a fraction whose numerator indicates the number of beats in a measure and whose denominator indicates the note value that is the unit of beating. The time signature may be changed at any point in the composition, and frequent changes of meter occur in much 20th-century music. In music of the 18th and 19th cent., however, the same meter is usually adhered to throughout a section or movement in a composition. See rhythmrhythm,
the basic temporal element of music, concerned with duration and with stresses or accents whether irregular or organized into regular patternings. The formulation in the late 12th cent.
..... Click the link for more information. . For meter in poetry, see versificationversification,
principles of metrical practice in poetry. In different literatures poetic form is achieved in various ways; usually, however, a definite and predictable pattern is evident in the language.
..... Click the link for more information. ; for meter as a unit of measure, see metric systemmetric system,
system of weights and measures planned in France and adopted there in 1799; it has since been adopted by most of the technologically developed countries of the world.
..... Click the link for more information. .
meter(mee -ter) Symbol: m. The usual scientific unit of length and distance. It is defined (from Oct. 1983) as the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. It is thus now defined in terms of the second and the fixed value of the speed of light.
(1) The unit of length in the metric system of measurement and the International System of Units. The symbol is m.
(2) A measure of length that reproduces the unit of length, the meter.
According to the first definition, which was adopted in France in 1791, the meter was equal to 1 X 10 ~7 times one-quarter of the length of the meridian passing through Paris. The length of the meter was calculated on the basis of geodetic and astronomical measurements made by J. Delambre and P. Mechain. The first standard meter was made by the French master craftsman Lenoir under the direction of J. Borda (1799) in the form of a gauge block—a platinum bar about 25 mm wide and 4 mm thick, with the distance between the ends equal to the accepted unit of length. It was called the meter of the archives (for the place where it was kept). However, it was found that the meter thus defined could not be accurately reproduced again because of the absence of accurate data on the figure of the earth and the significant errors in geodetic measurements.
In 1872 the International Metric Commission adopted a resolution on the rejection of “natural” standards of length and the adoption of the meter of the archives as the reference measure of length; 31 standards were made from the meter of the archives in the form of line standards (bars made of a 90–10 platinumiridium alloy). The cross section of a standard is X-shaped (Figure 1), which imparts to it the necessary resistance to flexure. Three marks are inscribed near each end of the neutral plane (ab in Figure 1). The distance between the axes of the middle lines defines the length of a meter at 0°C. Standard no. 6 proved to be equal to the meter of the archives within the margin of error of the measurements. By a resolution of the First General Conference on Weights and Measures this standard, which had been designated by , was adopted as the international prototype meter.
The prototype meter and two of its reference copies are kept at Sevres (France) at the International Bureau of Weights and Measures. Two copies of the International Prototype Meter (nos. 11 and 28) are kept at the D. I. Mendeleev All-Union Research Institute of Metrology in Leningrad. With the introduction of the metric system in the USSR (1918), copy no. 28 was recognized as the state standard. The International Prototype Meter, which has an error of 1 X 10-7, and the national primary standard have provided for the maintenance of the unit and accurate measurements at the level needed for science and technology over several decades.
However, increasingly strict requirements for the accuracy of linear measurements and the need to create a reproducible standard meter stimulated research on the definition of the meter in terms of the length of a light wave. In 1960 the Eleventh General Conference on Weights and Measures adopted a new definition of the meter, which was taken as a basis for the International System of Units: “A meter is a length equal to 1,650,763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 levels of an atom of krypton 86.” To ensure high accuracy in reproducing the meter, the conditions for reproducing the primary radiation standard are strictly defined in the international specifications. The monochromatic radiation corresponding to the orange line of krypton is created by a special lamp (Figure 2) filled with gaseous 86Kr. Luminescence of the gas is stimulated by a high-frequency oscillator (100–200 megahertz), and during its operation the lamp is cooled to the temperature of the triple point of nitrogen (63°K). Under these conditions the width of the orange line of 86Kr does not exceed 0.013–0.016 cm-1 (in wave numbers). The lamp is placed in front of an interferometer on which gauge blocks or line standards are measured in wavelengths. A standard interferometer has been developed at the All-Union Research Institute of Metrology that makes possible measurement of lengths up to 1,000 mm with a standard deviation of 3 X 10 -8. Measurement of prototype no. 28 on the standard interferometer revealed that it is longer than the meter (according to a 1960 measurement) by 0.22 micron.
REFERENCESIsakov, L. D. Na vse vremena, dlia vsekh narodov. Petrograd, 1923. Barinov, V. A. Sovremennoe sostoianie etalonov dliny i metody tochnogo izmereniia dliny. Leningrad, 1941.
Batarchukova, N. R. Novoe opredelenie metra. Moscow, 1964.
Issledovaniia v oblasti lineinykh izmerenii. Moscow-Leningrad, 1965–68. (Tr. Metrologicheskikh in-tov SSSR, fasc. 78 , fasc. 101 .)
Brzhezinskii, M. L., lu. P. Efremov, and L. K. Kaiak. “Vnedrenie novogo opredeleniia metra v praktiku lineinykh izmerenii.” IzmeriteVnaia tekhnika, 1970, no. 9.
L. K. KAIAK
(1) In versification, the rhythmic order by which verse is distinguished from prose and according to which the text, apart from syntactical articulation, is divided into specific poetic metrical units—feet, lines, and strophes, for example. As a pattern (standard) or totality of the rules of this division, meter means the rhythmic signs that are obligatory for each metrical unit. Systems of versification are based on a specific sequence of long and short syllables (metrical versification), the number of syllables (syllabic versification), the number of stresses (tonic versification), or the alternation of stressed and unstressed syllables (syllabotonic versification). Each system includes a number of possible patterns for the construction of a verse—that is, particular meters, such as hexameter and iambic tetrameter.
There are two basic types of literary poetic systems: in one, meter regulates the duration of syllables, in the other, accentuation is the important element. The first type, known as quantitative meter, developed when poetry was closely associated with music. Classical, Indian, and Arabic (aruz) meters fall into the quantitative category, in which meter has its original function of subordinating speech and music to the general aesthetic principle of measure, which is expressed in the proportionality of time values. The rules of versification call for the use of words in proportion to these values and take into account only the differing durations of syllables, ignoring accentuation or syntax. In classical verse, rhythm (movement, “flow” of linguistic material) was completely subordinate to meter. Rhythmic accentuation, the nature of which is not entirely clear, had to do with the musical aspect of verse and was connected not with accentuation in the spoken language but with the division of metrical units into ascending and descending sections (arsis and thesis). Metrics (the theory of poetic meters) was originally part of music theory and was not separated from it and included in grammar until the Hellenistic period.
As the classical period gave way to the Middle Ages, verses based not on the duration of syllables but on the number of syllables, on stress, and on rhyme were created. To distinguish them from “meters,” which had been composed according to old rules that had lost meaning as a result of the separation of verse from music, these purely spoken verses were called “rhythms.”
Medieval Latin rhythms belong to the accentual or qualitative system, which has been fully developed in the modern European languages. It includes the syllabic, syllabotonic, and tonic systems. Verses of this type are distinguished from prose by a set order that was given the classical name “meter,” a term encountered as early as the 14th century in works by Guillaume de Machaut. However, this type of meter is connected not with the measurement of time, or duration, but with the counting of spoken elements. The basic metrical unit is the line. The distinguishing element of poetic speech is the pause, which is indicated graphically by the division of verse into lines and strophes. Thus, for example, free verse is distinguished from prose by its graphic division into lines, which creates a “setting for meter” and establishes pauses that do not depend on syntax.
Despite the literal meaning of the word “versification,” a verse is not made up of temporal segments united in feet. It is an entity that is broken down into parts only for metrical calculation. The term doVniki, which means verses with a constant number of accents and a changing number of unstressed syllables, can also be applied to other accentual systems. In syllabic verse each syllable is a beat, and in syllabotonic verse, each foot. Syllabotonic feet, unlike quantitative ones, are not functional parts but counting units. Repetition is the chief means by which accentual meter is manifested. By contrast, in quantitative meter equality is only a particular instance of proportionality. Accentual metrical patterns are much more barren and monotonous than quantitative ones. They are not intended to create the musical quality of measure that distinguishes verses from normal unregulated speech but are designed to emphasize the rhythm of stresses and pauses in speech and heighten its emotional impact. In accentual verse, “rhythm” usually means the free elements that inject variety into the metrical pattern—in syllabic verse, the distribution of stresses, and in Russian syllabotonic verse, the actual accentuation of a line, in contradistinction to the metrical accentuation. The rhythm should not be considered a “deviation from meter,” since rhythmic variants do not transcend the unvarying metrical pattern and are not regarded as violations of the norm. Genuine rhythmic dissonances are created only when the poetic boundaries do not coincide with the syntactical, so that the two systems of pauses contradict each other, as in the enjambment, for example.
(2) In music, the system of organization of rhythm. As long as music (in ancient Greece and Rome, for example) was closely associated with verse, musical meter coincided with poetic meter. Owing to the classification of syllables as long or short, a text could indicate the meter of the music. Thus, in vocal music it was possible to do without any symbols for time values, even though such symbols existed in ancient Greek notation. Gregorian chant, a kind of “musical prose” whose rhythm was not connected with a definite, preestablished order, developed when verse separated from music at the beginning of the Middle Ages. Measure reemerged in music in connection with the poetry of the troubadours and trouveres and in the 12th century penetrated church music, in which mensural (measured) music contrasted with the unmeasured, or “free” Gregorian singing. Like the music of ancient Greece and Rome, mensural rhythmics was based on time-value correlations. Thus, it is considered a type of quantitative meter. The early mensural (modal) rhythmics was dominated by the repetition of rhythmic modes—definite sequences of long and short sounds similar to feet in classical poetic meters. Beginning in the 14th century the sequence of durations became free. The meter was expressed in units known as beats, or Takte, which were indicated by up-and-down strokes of the conductor’s hand. The division of the Takte into weaker accents in the beginning of the 17th century gave rise to musical meter, or Takt, in the modern sense, in which the alternation of strong (heavy) and weak (light) beats gives order to the rhythm, just as meter gives rhythmic order to verse. In the 19th century the classical term “meter,” which was borrowed from prosody, again became part of music theory.
Takt refers to the musical meter of the era when music, having separated from poetry, became an independent art form. Contrary to widely held but erroneous opinions, it did not exist in archaic folklore or in the music of ancient Greece and Rome and the Middle Ages. Like accentual poetic meter, it is based on accent rather than on duration. However, it arises from accentual relationships more complex than the contrast between strong and weak syllables. The beginning of each beat is a powerful moment in relation to its subdivisions. Simple two- and three-beat meters unite with stronger accents into compound meters consisting of equal parts (for example, four- and six-beat meters) and into mixed meters consisting of unequal parts (for example, five- and seven-beat meters). This gradation can be considered independent of the duration of the intervals between accents. The beats, which, unlike the classical feet and mensural modes, are by convention considered equal, are in performance freely stretched and compressed. The values of notes indicate musical “time,” which often does not coincide with actual time. Basically, musical meter is distinguished from all types of poetic meter by continuity. The designation of meter in fractions (4/4, 6/8, and 3/2, for example) indicates only the accentual pattern (the number of beats and their value in relation to a whole note), but not the boundaries of the “lines” (their beginning with a stressed or unstressed heat) or their value. (Poetic meter, such as iambic tetrameter, does indicate value.) The absence of the metrical pauses that separate verses excludes the possibility of enjambments in music, but rhythmic dissonances are created by syncopes, the contradictions between actual and metrical accentuation. These are not possible in verse, where the underlying meter cannot be realized in an accompaniment. Even in music this underlying realization is not obligatory, for meter can take the form of an “imaginary rhythmic accompaniment” maintained by inertia or of a purely graphic indication by the composer to the performer. In such graphic meters, which are encountered in works by Beethoven, Schumann, and Liszt, for example, the bar line, which usually designates a regularly recurrent strong beat, indicates not the actual accent but its normal position, thus revealing its normal or displaced character. This function of the bar line is retained even in “free meters,” which lack a uniform pattern and meter designation (for example, some of S. V. Rachmaninoff’s later art songs). Unlike free rhythm, which discards strict measure (senza misura), free meters permit the displacement of accents through syncopation.
The differences in principle between poetic and musical accentual meters excludes a direct tie between them in modern vocal music. At the same time, they are distinguished from the musical and poetic quantitative meters by a number of common features.
REFERENCESDenisov, la. Osnovaniia metriki u drevnukh grekov i rimlian. Moscow, 1888.
Tomashevskii, B. V. Russkoe stikhoslozhenie: Metrika. Petrograd, 1923.
Tomashevskii, B. V. Stikh i iazyk. Moscow-Leningrad, 1959.
Zhirmunskii, V. M. Vvedenie v metriku: Teoriia stikha. In Teoriia stikha. Leningrad, 1975.
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Kharlap, M. G. O stikhe. Moscow, 1966.
Rossbach A., and R. Westphal. Griechische Metrik, 3rd ed. Leipzig, 1889.
Saran, F. Deutshce Verslehre. Munich, 1907.
Groot, A. W. “Le Metre et le rythme du vers.” Journal de psychologic, 1933, nos. 1–4.
Verwey, A. Rhythmus und Metrum. Halle, 1934.
Sokal’skii, P. P. Russkaia narodnaia muzyka, velikorusskaia i malorusskaia, v ee stroenii melodicheskom i ritmicheskom i otlichiia ee osnov sovremennoi garmonicheskoi muzyki. Kharkov, 1888. Part 2: “Ritmicheskoe stroenie.”
Kholopova, V. N. Voprosy ritma v tvorchestve kompozitorov pervoi poloviny XX veka. Moscow, 1971.
Kharlap, M. G. “Ritmika Betkhovena.” In the collection Betkhoven, fasc. 1. Moscow, 1971.
Riemann, H. System der musikalischen Rhythmik und Metrik. Leipzig, 1903.
Sachs, C. Rhythm and Tempo: A Study in Music History. New York, 1953.
M. G. KHARLAP