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Duration

Duration

:For other meanings of duration, see: duration (disambiguation). A duration is an amount of time or a particular time interval. For example, an event in the common sense has a duration greater than zero (but not very long), but in certain specialised senses, a duration of zero. It is often cited as one of the fundamental aspects of music, see also rhythm. Durations, and their beginnings and endings, may be described as long, short, or taking a specific amount of time. Often duration is described according to terms borrowed from descriptions of pitch. As such, the duration complement is the amount of different durations used, the duration scale is an ordering (scale) of those durations from shortest to longest, the duration range is the difference in length between the shortest and longest, and the duration hierarchy is an ordering of those durations based on frequency of use (DeLone et. al. (Eds.), 1975, chap. 3). Durational patterns are the foreground details projected against a background metric structure, which includes meter, tempo, and all rhythmic aspects which produce temporal regularity or structure. Duration patterns may be divided into rhythmic units and rhythmic gestures. (DeLone et. al. (Eds.), 1975, chap. 3) However, they may also be described using terms borrowed from the metrical feet of poetry: iamb (weak-strong), anapest (weak-weak-strong), trochee (strong-weak), dactyl (strong-weak-weak), and amphibrach (weak-strong-weak), which may overlap to explain ambigouity (Cooper and Meyer, 1960). See also: time scale.

Sources

- Cooper and Meyer (1960). The Rhythmic Structure of Music. University of Chicago Press. ISBN 0226115224. Cited in Delone directly below.
- DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0130493465. Category:Aspects of music

Duration (disambiguation)

Duration may refer to:
- Duration: an amount of time or a particular time interval, often cited as one of the fundamental aspects of music, see also rhythm.
- For duration in economics and finance, see Bond duration.
- For the project management sense, see duration (project management).
- In phonetics and phonology, to the feature of being pronounced longer, see length (phonetics)

Time

Attempting to understand Time has long been a prime occupation for philosophers, scientists and artists. There are widely divergent views about its meaning, hence it is difficult to provide an uncontroversial and clear definition of time. The Oxford English Dictionary defines it as "the indefinite continued progress of existence and events in the past, present, and future, regarded as a whole". Another standard dictionary definition is "a non-spatial linear continuum wherein events occur in an apparently irreversible order." This article looks at some of the main philosophical and scientific issues relating to time. The measurement of time has also occupied scientists and technologists, and was a prime motivation in astronomy. Time is also a matter of significant social importance, having economic value ("time is money") as well as personal value due to an awareness of the limited time in each day and in our lives. Units of time have been agreed upon to quantify the duration of events and the intervals between them. Regularly recurring events and objects with apparently periodic motion have long served as standards for units of time - such as the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum.

Philosophy of time

Main article: Philosophy of space and time; Ontology In ancient thought, Zeno's paradoxes challenged the conception of infinite divisibility, and eventually led to the development of calculus. Parmenides (of whom Zeno was a follower) believed that time, motion, and change were illusions, basing this on a rather interesting argument. More recently, McTaggart held a similar belief. Newton believed time and space form a container for events, which is as real as the objects it contains. In contrast, Leibniz believed that time and space are a conceptual apparatus describing the interrelations between events. Leibniz and others thought of time as a fundamental part of an abstract conceptual framework, together with space and number, within which we sequence events, quantify their duration, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows", that objects "move through", or that is a "container" for events. The bucket argument proved problematic for Leibniz, and his account fell into disfavour, at least amongst scientists, until the development of Mach's principle. Modern physics views the curvature of spacetime around an object as much a feature of that object as are its mass and volume. Immanuel Kant, in the Critique of Pure Reason, described time as an a priori notion that allows us (together with other a priori notions such as space) to comprehend sense experience. With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic framework necessarily structuring the experiences of any rational agent. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantify how far apart events occur. Nietzsche, inspired by the concept of eternal return in his book Thus Spoke Zarathustra, argued that time possesses a circular characteristic. Postulating an infinite past, "all things" must have come to pass therein; the same for an infinite future. In Existentialism, time is considered fundamental to the question of being, in particular by the philosopher Martin Heidegger.

Contemporary theses in the philosophy of time

In contempoary philosophy there has been a very active debate over the nature of time, especially in light of the big changes in physics since the 1920s. Contributors include Ned Markosian, Ted Sider, Quentin Smith, and L. Nathan Oaklander. Two major theses have been developed, along with some hybrids. There is no real consensus among philosophers about which, if any, is correct. The two major theories can be summed up as follows: 1. A-theory of time: Presentism: Oaklander writes: "[A] version of the pure A-theory, known as "", purports to avoid… the problem of change... According to presentism, only the present exists. Thus, it is not the case that, say, O is green and [then] O is red [if, for example, O is a tomato]." (Oaklander, L. Nathan. In Smith, Quentin, and Oaklander, L. Nathan. 1995. Time, Change, and Freedom. New York: Routledge. 2004, 27.) 2. B-theory of time: Eternalism: the following passage from L. Nathan Oaklander sums this up

…[T]ime [involves] events strung out along a series united to one another by the relations of earlier than, later and simultaneity… The events in the temporal series are fixed in that they never change their position relative to each other… It has become customary to call the entire series of events spread out along the time-line from earlier to later, the “B-series.” When viewed solely in terms of the B-series, time is thought of as static or unchanging for there is nothing about temporal relations between events that changes... Time not only has a static aspect, it also has a transitory aspect. In addition to conceiving of time in terms of events standing in temporal relations, we also conceive of time and the events in time as moving or passing from the far future to the near future, from the hear future to the present, and then from present they recede into the more and more distant past… When events are ordered in terms of the notions of past, present, or future they form what is called an “A-series.” It should be noted, of course, that the A- and B-series are not really “two” different series of events, but the same series ordered in two different ways. (Oaklander 2004,Page 69)

Time in physics

never change Main article: Time in physics Time is currently one of the few fundamental quantities (quantities which cannot be defined via other quantities because there is nothing more fundamental known at present). Thus, similar to definition of other fundamental quantities (like space and mass), time is defined via measurement. Currently, the standard time interval (called conventional second, or simply second) is defined as 9 192 631 770 oscillations of a hyperfine transition in the ¹³³Cs atom. Prior to Albert Einstein's relativistic physics, time and space had been treated as distinct dimensions; Einstein linked time and space into spacetime. Einstein showed that people traveling at different speeds will measure different times for events and different distances between objects, though these differences are minute unless one is traveling at a speed close to that of light. Many subatomic particles exist for only a fixed fraction of a second in a lab relatively at rest, but some that travel close to the speed of light can be measured to travel further and survive longer than expected. According to the special theory of relativity, in the high-speed particle's frame of reference, it exists for the same amount of time as usual, and the distance it travels in that time is what would be expected for that velocity. Relative to a frame of reference at rest, time seems to "slow down" for the particle. Relative to the high-speed particle, distances seems to shorten. Even in Newtonian terms time may be considered the fourth dimension of motion; but Einstein showed how both temporal and spatial dimensions can be altered (or "warped") by high-speed motion. Einstein (The Meaning Of Relativity - 1968): "Two events taking place at the points A and B of a system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. Time is then defined as the ensemble of the indications of similar clocks, at rest relatively to K, which register the same simultaneously."

Measurement

Present day standards

The standard unit for time is the SI second, from which larger units are defined like the minute, hour, and day. Because they do not use the decimal system, and because of the occasional need for a leap-second, the minute, hour, and day are "non-SI" units, but are officially accepted for use with the International System. There are no fixed ratios between seconds (or days) on the one hand and months and years on the other hand -- months and years having significant variations in length. Despite its great social importance, the week is not mentioned even as a "non-SI" unit. ([http://www1.bipm.org/utils/en/pdf/si-brochure.pdf See external pdf file: The International System of Units].) The measurement of time is so critical to the functioning of our modern societies that it is coordinated at an international level. The basis for scientific time is a continuous count of seconds based on atomic clocks around the world, known as International Atomic Time (TAI). This is the yardstick for other time scales including Coordinated Universal Time (UTC) which is the basis for civil time. The 60 base used for seconds, minutes and hours is all the remains of the ancient Phoenician counting base, using 60 as the equivalent of 10, or 100 in modern times. A 60 base is known as sexagesimal.

Chronology

Another form of time measurement consists of studying the past. Events in the past can be ordered in a sequence (creating a chronology), and be put into chronological groups (periodization). One of the most important systems of periodization is Geologic time, which is a system of periodizing the events that shaped the Earth and its life. Chronology, periodization, and interpretation of the past are together known as the study of history.

Psychology

Different people may judge identical lengths of time quite differently. Time can "fly"; that is, a long period of time can seem to go by very quickly. Likewise, time can seem to "drag," as in when one performs a boring task. The psychologist Jean Piaget called this form of time perception "lived time". Time appears to go fast when sleeping, or, to put it differently, time seems not to have passed while asleep. Time also appears to pass more quickly as one gets older. For example, a day for a child seems to last longer than a day for an adult. One possible reason for this is that with increasing age, each segment of time is an increasingly smaller percentage of the person's total experience. Altered states of consciousness are sometimes characterised by a different estimation of time. Some psychoactive substances--such as entheogens--may also dramatically alter a person's temporal judgement. In explaining his theory of relativity, Albert Einstein is often quoted as saying that although sitting next to a pretty girl for an hour feels like a minute, placing one's hand on a hot stove for a minute feels like an hour. This is intended to introduce the listener to the concept of the interval between two events being perceived differently by different observers.

Use of time

The use of time is an important issue in understanding human behaviour, education, and travel behaviour. The question concerns how time is allocated across a number of activities (such as time spent at home, at work, shopping, etc.). Time use changes with technology, as the television or the Internet created new opportunities to use time in different ways. However, some aspects of time use are relatively stable over long periods of time, such as the amount of time spent traveling to work, which despite major changes in transport, has been observed to be about 20-30 minutes one-way for a large number of cities over a long period of time. This has led to the disputed time budget hypothesis. Time management is the organization of tasks or events by first estimating how much time a task will take to be completed, when it must be completed, and then adjusting events that would interfere with its completion so that completion is reached in the appropriate amount of time. Calendars and day planners are common examples of time management tools. Arlie Russell Hochschild and Norbert Elias have written on the use of time from a sociological perspective.

References

- Oxford English Dictionary - [http://www.askoxford.com/concise_oed/time?view=uk]

External links

Perception of time

- [http://plato.stanford.edu/entries/time-experience/ The Experience and Perception of Time]
- [http://cogprints.ecs.soton.ac.uk/archive/00003125/ Subjective Perception of Time and a Progressive Present Moment: The Neurobiological Key to Unlocking Consciousness]
- [http://www.primitivism.com/time.htm Time and Its Discontents]
- [http://www.ericdigests.org/2003-5/time.htm Time and Learning]
- [http://mixingmemory.blogspot.com/2004/12/by-request-time-perception-i.html Time Perception I] and [http://mixingmemory.blogspot.com/2004/12/time-perception-ii-cognitive-factors.html II]
- [http://theorderoftime.org/ The Order of Time: Platform for an Alternative Time Consciousness]
- [http://www.chabad.org/article.asp?AID=74335 What is Time?] An elucidation of the Lubavitcher Rebbe's comments on the topic.

Physics

- [http://physics.nist.gov/GenInt/Time/world.html A walk through Time]
- [http://pages.britishlibrary.net/lobster/tmx Time Travel and Multi-Dimensionality]
- [http://arxiv.org/abs/physics/0310055 Time and classical and quantum mechanics: Indeterminacy vs. discontinuity]
- [http://www.sankey.ws/time.html Time as a universal consequence of quanta]

Timekeeping

- [http://tycho.usno.navy.mil/systime.html Different systems of measuring time]
- [http://physics.nist.gov/cuu/Units/outside.html non-SI units]
- [http://www1.bipm.org/en/scientific/tai/time_server.html UTC/TAI Timeserver]
- [http://tycho.usno.navy.mil/leapsec.html Leapsecond]
- [http://www.intuitor.com/hex/hexclock.html Hex Time]
- [http://www.florencetime.net Florencetime.net]
- [http://news.bbc.co.uk/2/hi/science/nature/3486160.stm BBC article on shortest time ever measured]
- [http://www.awi-net.org American Watchmakers-Clockmakers Institute]
- [http://www.timeanddate.com/worldclock/ The World Clock - Time Zones]

Miscellaneous

- [http://www.boost.org/doc/html/date_time.html Boost Date-Time Library -- Powerful C++ Library for date-time manipulation]
- [http://www.cyclesresearchinstitute.org/ Cycles Research Institute]
- [http://www.timeticker.com/ TimeTicker and the time tickers...]
- [http://www.welt-zeit-uhr.de/worldtime.php World Time and Zones]
- [http://www.timetools.co.uk Time Servers] NTP Time Servers provide accurate timing for computers and computer networks.

Rhythm

Rhythm (Greek ρυθμός = tempo) is the variation of the duration of sounds or other events over time. "Rhythm involves patterns of duration that are phenomenally present in the music" with duration measured by interonset interval (London 2004, p.4). When governed by rule, it is called meter. It is inherent in any time-dependent medium, but it is most associated with music, dance, and the majority of poetry. The study of rhythm, stress, and pitch in speech is called prosody; it is a topic in linguistics. All musicians, instrumentalists and vocalists, work with rhythm, but it is often considered the primary domain of drummers and percussionists. In Western music, rhythms are usually arranged with respect to a time signature, partially signifying a meter. The speed of the underlying pulse, called the beat, is the tempo. The tempo is usually measured in 'beats per minute' (bpm); 60 bpm means a speed of one beat per second. The length of the meter, or metric unit (usually corresponding with measure length), is divided almost exclusively into either two or three beats, being called duple meter and triple meter, respectively. If each beat is further divided by two it is simple meter, if by three compound meter. Some genres of music make different use of rhythm than others. Most Western music is based on divisive rhythm, while non-Western music uses more additive rhythm. African music makes heavy use of polyrhythms, and Indian music uses complex cycles such as 7 and 13, while Balinese music often uses complex interlocking rhythms. By comparison, a lot of Western classical music is fairly rhythmically simple; it stays in a simple meter such as 4/4 or 3/4 and makes little use of syncopation. In the 20th century, composers like Igor Stravinsky, Philip Glass, and Steve Reich wrote more rhythmically complex music using odd meters, and techniques such as phasing and additive rhythm. At the same time, modernists such as Olivier Messiaen and his pupils used increased complexity to disrupt the sense of a regular beat, leading eventually to the widespread use of irrational rhythms in New Complexity. This use may be explained by a comment of John Cage's where he notes that regular rhythms cause sounds to be heard as a group rather than individually; the irregular rhythms highlight the rapidly changing pitch relationships that would otherwise be subsumed into irrelevant rhythmic groupings (Sandow 2004, p.257). LaMonte Young also wrote music in which the sense of a regular beat is absent because the music consists only of long sustained tones (drones). In the 1930s, Henry Cowell wrote music involving multiple simultaneous periodic rhythms and collaborated with Léon Theremin to invent the Rhythmicon, the first electronic rhythm machine, in order to perform them. Clave is a common underlying rhythm in African, Cuban music, and Brazilian music. A rhythm section generally consists of percussion instruments, and possibly chordal instruments (e.g., guitar, banjo) and keyboard instruments, such as piano (which, by the way, may be classified as any of these three types of instruments). "Rhythm," wrote Tom Robbins in Another Roadside Attraction, "is everything pertaining to the duration of energy." Narmour (1980, p.147-53) describes three categories of prosodic rules which create rhythmic successions which are additive (same duration repeated), cumulative (short-long), or countercumulative (long-short). Cumulation is associated with closure or relaxation, countercumulation with openness or tension, while additive rhythms are open-ended and repetitive. Richard Middleton points out this method cannot account for syncopation and suggests the concept of transformation. A rhythmic unit is a durational pattern which occupies a period of time equivalent to a pulse or pulses on an underlying metric level, as opposed to a rhythmic gesture which does not (DeLone et. al. (Eds.), 1975, chap. 3).

Sources

- London, Justin (2004). Hearing in Time: Psychological Aspects of Musical Meter. ISBN 0195160819.
- Middleton, Richard (1990/2002). Studying Popular Music. Philadelphia: Open University Press. ISBN 0335152759.
- Narmour (1980). Cited in DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0130493465.
- Sandow, Greg (2004). "A Fine Madness", The Pleasure of Modernist Music. ISBN 1580461433.

Journal Articles

- Honing, H. (2002). [http://www.hum.uva.nl/mmm/abstracts/mmm-TvM.html "Structure and interpretation of rhythm and timing."] Tijdschrift voor Muziektheorie [Dutch Journal of Music Theory] 7(3): 227-232.

External links

- [http://www.hum.uva.nl/mmm/ Research group specializing in rhythm, timing, and tempo, University of Amsterdam]
- [http://www.diejungeakademie.de/ag/rhythmus/ Research group specializing in rhythm of the Young Academy of Sciences, Humanities and Arts of Germany] Category:Rhythm ko:리듬 ja:リズム

Complement

The word complement (with an e in the second syllable, not to be confused with a different word, compliment with an i) has a number of uses. Generally a complement of X is something that together with X makes a complete whole; that supplies what X lacks. The first e in complete and the first e in complement are etymological cognates of each other in a way that is a useful mnemonic for remembering that this is not compliment with an i.
- In painting and optics, complement refers to complementary colors.
- complement (biology) is a group of proteins of the complement system, found in blood serum which act in concert with antibodies to achieve the destruction of non-self particles such as foreign blood cells or bacteria.
- complement (mathematics) (another disambiguation page)
- In traditional music theory a complement (music) is the interval added to another, that is placed on top of another, so that their complete span is an octave, while in musical set theory the complement of a pitch class set are those pitches not included (the pitches needed to form an aggregate).
- In economics, a complement good is a good often consumed together with the good in question.
- phonetic complement
- complementarity (molecular biology) and complementary DNA
- complementary experiments (physics)
- complement (linguistics) is a syntax relationship.
- In computational complexity theory, decision problems and complexity classes have complements; see complement (complexity). ja:補数 simple:Complement

Scale (measurement)

The concept of scale is applicable if a system is represented proportionally by another system. For example, for a scale model of an object, the ratio of corresponding lengths is a dimensionless scale, e.g. 1:25; this scale is larger than 1:50. In the general case of a differentiable bijection, the concept of scale can, to some extent, still be used, but it may depend on location and direction. It can be described by the Jacobian matrix. The modulus of the matrix times a unit vector is the scale in that direction. The non-linear case applies for example if a curved surface like part of the Earth's surface is mapped to a plane, see map projection. In the case of an affine transformation the scale does not depend on location but it depends in general on direction. If the affine transformation can be decomposed into isometries and a transformation given by a diagonal matrix, we have directionally differential scaling and the diagonal elements (the eigenvalues) are the scale factors in two or three perpendicular directions. For example, on some profile maps horizontal and vertical scale are different; in particular elevation may be shown in a larger scale than horizontal distance. In the case of directional scaling (in one direction only) there is just one scale factor for one direction. The case of uniform scaling corresponds to a geometric similarity. There is just one scale throughout. In the case of an isometry the scale is 1:1. In the more general case of one quantity represented by another one, the scale has also a physical dimension. E.g., if an arrow is drawn to represent a physical vector, the "scale" has a physical dimension equal to that of the vector, divided by length. For example, if a force of 1 newton is represented by an arrow of 2 cm, the scale is 1 m : 50 N. There is typically consistency in scale among quantities of the same dimension, but otherwise scales within the same diagram may vary; e.g "5 m" may also be represented by an arrow of 2 cm; in that case the scale for vectors which represent length is 1:250. Correspondingly, torques could be represented on the same map by areas in a scale of 1 m² : 12 500 Nm, which is equal to 1 m : 12 500 N. Torques in the plane of the map could be represented by arrows with an independent scale of e.g. 1 m : 300 Nm. The scale of a map or enlarged or reduced model indicates the ratio between the distances on the map or model and the corresponding distances in reality or the original. E.g. a map of scale 1:50,000 shows a distance of 50,000 cm (=500 m) as 1 cm on a map, and a model on a scale 1:25 of a building with a height of 30 m has a model height of 1.20 m. An alternative method of indicating the scale is by a scale bar. This can also be applied on a computer screen etc., where the ratio may vary, and also remains valid when enlarging or reducing a paper map.

Hierarchy

A hierarchy (in Greek: Ιεραρχία, it is derived from ιερός-hieros, sacred, and άρχω-arkho, rule) is a system of ranking and organizing things or people. The first usage in the Oxford English Dictionary for hierarchy is from 1380, where it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite. Areopagite used the word both in reference to the heavenly hierarchy and the ecclesiastical hierarchy [http://www.newadvent.org/cathen/07322c.htm]. This was the origin of the common meaning of "rule by priests". Since hierarchical churches such as the Roman Catholic and Eastern Orthodox churches had tables of organization that were "hierarchical" in the modern sense of the word, the term came to refer to similar organizational methods in more general settings.

General description

Hierarchies can be generally divided into two kinds: those where the upper levels of the hierarchy are 'superior' to the lower in some way, and those where the lower levels are 'contained' in the upper, again in different ways. An example of the first kind might be a company organisational structure: the CEO is superior to the divisional managers, who are superior to their team leaders who are superior to their regular workers. An example of the second kind is the hierarchy of animal classification: the set of 'birds' contains the set of 'birds of prey' which contains the set of 'eagles' which contains the set of 'golden eagles'. However, the more commonly used kind of hierarchy is the first kind, where one member is 'superior' to another.

General description (informal)

A precise, mathematical definition of hierarchy will be given below. This section will try to explore the ideas behind that more succinct definition. A hierarchy is a transitive, irreflexive, asymmetric relationship, such as "is superior to", "is part of", or "is taller than":
- Transitivity — if a is superior to b, and b is superior to c, then a is superior to c;
- Irreflexivity — no-one can be superior to himself, or taller than himself;
- Asymmetry — if a is superior to b, then b isn't superior to a. When two nodes are related, one is designated the "superior" (or sometimes the "parent") and the other the "subordinate" (or sometimes the "child"). In the intuitive case of the "is the boss of" relation, the boss is the superior and the employee is the subordinate. A hierarchy's asymmetrical relationship can link entities in one of three ways: directly, indirectly, or not at all. The illustration shows a direct link between the craft and culture sections; the craft section is directly linked to the culture section by the "contains" relationship. This is akin to how your boss is directly in charge of you. In contrast, the illustration shows an indirect link between craft and encyclopedia; the craft section is only "contained" by the encyclopedia as a whole by virtue of being "contained" by the culture section. This is akin to how the CEO of a company is in charge of a factory worker only via middle management. Finally, there is effectively no link between the art and the craft sections; neither section contains the other. This is akin to two co-workers, neither of whom is the other's boss. Every member is reachable from any other by following the relationship in either direction, but there is no way of coming back to a particular member by always following the relationship in the same direction.

Mathematical description (formal)

A hierarchy can be represented as a connected directed acyclic graph with a designated initial node (the root). Such structures are also commonly named trees (since they look like upside-down trees, with the trunk at the top).

Examples of reasoning with hierarchies

Many aspects of the world are analyzed from a hierarchical perspective. The concept of hierarchy thus qualifies as interdisciplinary, sometimes benefiting from a sense of connection between otherwise unrelated disciplines:
- In biology, the study of taxonomy is one of the most conventionally hierarchical kinds knowledge, placing all living beings in a nested structure of divisions related to their probable evolutionary descent. With few exceptions, evolutionary biologists assert a hierachy extending from the level of the specimen (an individual living organism -- say, a single newt), to the species of which it is a member (perhaps the Eastern Newt), outward to further successive levels of genus (Notophthalmus), family (salamander), order (Caudata -- one of several types of amphibians with tails), class (Lissamphibia, referring to all recent amphibians), phylum (Chordata, referring to all animals with spines), and kingdom (distinguishing animals from other living beings like plants). Members of a division on one level are more closely related to one another than to members of another division on the same level, and they are descended from common ancestors in the level above. The system is hierarchical because it forbids the possibility of overlapping categories. For example, it will not permit an 'order' of beings containing some examples that are amphibians and others that were reptiles; divisions on any level do not straddle the categories of structure that are hierarchically above it. To account for such a possibility, a taxonomy would have to be heterarchical (see Heterarchy). Organisms are also commonly described as assemblies of parts (organs) which are themselves assemblies of yet smaller parts, and so on -- in fact when philosophers of art and literature use the word "organic," they are usually suggesting a relationship of mimesis -- an imitative relationship -- between the smallest and largest parts of a structure. This notion of the organic is largely a reference to biological observations connecting relatively small parts of an organism, like cells and organs, to the larger systems (circulatory or nervous) or which they are a part. The analogy also extends to the relationship of a living being as a system that might resemble an ecosystem consisting of several living beings.
- In physics, the standard model decomposes bodies down to their smallest particle components. Observations on the subatomic (particle) level are often (though not always) seen as fundamental constituent axioms, on which conclusions about the atomic and molecular levels depend. The relationships of energy and gravity between celestial bodies are, in turn, dependent upon the atomic and molecular properties of smaller bodies.
- In linguistics, especially in the work of Noam Chomsky, and by later "generative linguistics" theories such as Ray Jackendoff's, words or sentences are often broken down into hierarchies of parts and wholes. Hierarchical reasoning about the underlying structure of language expressions leads some linguists to the hypothesis that the world's languages are bound together in a broad array of variants subordinate to a single Universal Grammar.
- In music, the structure of a composition is often understood hierarchically (for example by Heinrich Schenker (1868-1935), and in the (1985) Generative Theory of Tonal Music, by composer Fred Lerdahl and linguist Ray Jackendoff). The sum of all notes in a piece are understood to be an all-inclusive surface, which can be reduced to successively sparser and more fundamental types of motion. The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical score; the middleground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or Ursatz, which is one of only a few basic long-range counterpoint structures that are shared in the gamut of tonal music literature.
- In ethics, various virtues are enumerated and sometimes organized hierarchically according to certain brands of virtue theory. In all of these examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts. In the work of diverse theorists such as William James (1842-1910), Michel Foucault (1926-1984) and Hayden White, important critiques of hierarchical epistemology are advanced. James famously asserts in his work "Radical Empiricism" that clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and intractable ambiguities, then scientific questions are often declared unresolved. A hesitation to declare success upon the discovery of ambiguities leaves heterarchy at an artificial disadvantage in the scope of human knowledge. This is an artifact of an aesthetic or pedagogical preference for hierarchy, and not necessarily an expression of the world as we objectively perceive it.

Hierarchies in programming

The concept of hierarchies plays a large part in object oriented programming. For more information see Hierarchy (object-oriented programming) and memory hierarchy.

Containment hierarchy

A containment hierarchy is a collection of strictly nested sets. Each entry in the hierarchy designates a set such that the previous entry is a strict superset, and the next entry is a strict subset. For example, all rectangles are quadrilaterals, but not all quadrilaterals are rectangles, and all squares are rectangles, but not all rectangles are squares. (See also: Taxonomy.)
- In geometry: shape, polygon, quadrilateral, rectangle, square
- In biology: animal, bird, raptor, eagle, golden eagle
- The Chomsky hierarchy in formal languages: recursively enumerable, context-sensitive, context-free, regular
- In physics: particle, elementary particle, fermion, lepton, electron

Social hierarchies

Many human organizations, such as businesses, churches, armies and political movements are structured hierarchically, at least officially; commonly superiors, called bosses, have more power than their subordinates (sometimes referred to as deputies or assistants). Thus the asymmetrical relationship might be "has power over". (Some analysts question whether power "really" works as the traditional organizational chart indicates, however.) See also chain of command. Many social criticisms include a questioning of social hierarchies seen as being unjust. Feminism, for instance, often discusses a hierarchy of gender, in which a culture sees males or masculine traits as superior to females or feminine traits. In the terms above, some feminism criticizes a hierarchy of only two nodes, "masculine" and "feminine", connected by the asymmetrical relationship "is more valuable to society", for example: :The hierarchical nature of the dualism - the systematic devaluation of females and whatever is metaphorically understood as "feminine" - is what I identify as sexism. (Nelson 1992, p. 106) Note that in this context and in other social criticisms, the word hierarchy usually is used as meaning power hierarchy or power structure. Feminists may not take issue with inanimate objects being organized in a hierarchical fashion, but rather with the specific asymmetrical organization of unequal value and power between men and women and, usually, other social hierarchies such as in racism and anti-gay bias.

Hierarchical nomenclatures in the arts and sciences

Hierarchies are important for categorization and organization of large numbers of objects. Taxonomies, for example, such as biological taxonomies, are built on hierarchies. Hierarchy is also often used to control complexity in engineering endeavors. For example, large electronic devices such as computers are usually composed of modules, which are themselves created out of smaller components (integrated circuits), which in turn are internally organized using hierarchical methods (e.g. using standard cells). Hierarchies are used very extensively in computer science and information theory; here are a few examples. Computer files in a file system are stored in a hierarchy of directories in most operating systems. In object-oriented programming, classes are organized hierarchically; the relationship between two related classes is called inheritance. In the Internet, IP addresses are increasingly organized in a hierarchy (so that the routing will continue to function as the Internet grows). The pitches and form of tonal music are organized hierarchically, all pitches deriving their importance from their relationship to a tonic key, and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. Susan McClary connects this specifically in the sonata-allegro form to the feminist hierarchy of gender (see above) in her book Feminine Endings, even pointing out that primary themes were often previously called "masculine" and secondary themes "feminine." Examples of hierarchies:
- Theological: God, saved souls, angels, man, birds, animals, plants, rocks
- (See also Hierarchy of angels)
- Scientific classification of organisms: kingdom, phylum, class, order, family, genus, species
- Social: monarch, nobles, gentry, yeomanry, peasants, serfs

Alternatives

Hierarchies and hierarchical thinking has been criticized by many people, as above in #Social hierarchies and #Hierarchical nomenclatures in the arts and sciences. Possible alternatives include:
- Democracy - Command hierarchy and Workplace democracy
- Enumerative organization, a list
- Retiary organization, a web or network
- Anarchy as a social/political theory and practice

Specializations

- Purpose:
- Hierarchical organization
- Structural properties:
- Hierarchical tree structure
- Rooted hierarchy
- Nature of the hierarchical relationship:
- Containment hierarchy

External links

- [http://www.isss.org/hierarchy.htm Principles and annotated bibliography of hierarchy theory]
- [http://www.nbi.dk/~natphil/salthe/hierarchy_th.html Summary of the Principles of Hierarchy Theory] - S.N. Salthe

References

- Julie Nelson (1992). "Gender, Metaphor and the Definition of Economics". Economics and Philosophy, 8:103-125. Category:Networks ja:ヒエラルキー simple:Power structure

Metric structure

Metre or meter is the measurement of a musical line into measures of stressed and unstressed beats, indicated in Western notation by a symbol called a time signature. Properly, "metre" describes the whole concept of measuring rhythmic units, but it can also be used as a specific descriptor for a measurement of an individual piece as represented by the time signature—for example, "This piece is in 4/4 metre" is equivalent to "This piece is in 4/4 time" or "This piece has a 4/4 time signature". Meter is an entrainment, a representation of changing aspects of music as patterns of temporal invariance, allowing listeners to synchronize their perception, cognition, and behaviour with musical rhythms. Rhythm is distinguished from meter in that rhythms are patterns of duration while "meter involves our initial perception as well as subsequent anticipation of a series of beats that we abstract from the rhythm surface of the music as it unfolds in time." (London 2004, p.4-5)

Rhythmic metre

There are four different time signatures in common use:
- simple duple (ex. 4/4)
- simple triple (ex. 3/4)
- compound duple (ex. 6/8)
- compound triple (ex. 9/8). If each beat in a measure is divided into two parts, it is simple metre, and if divided into three it is compound. If each measure is divided into two beats, it is duple metre, and if three it is triple. Some people also label quadruple, while some consider it as two duples. The latter is more consistent with the above labelling system, as any other division above triple, such as quintuple, is considered as duple+triple (12123) or triple+duple (12312), depending on the accents in the musical example. However, in some music a quintuple may be treated and perceived as one unit of five, especially at faster tempos. compound", a jazz composition in 5/4 – Listen to this piece.]] "Once a metric hierarchy has been established, we, as listeners, will maintain that organization as long as minimal evidence is present." (Lester 1986, p.77) Duple time is far more common than triple (Krebs 2005, p.16). Most popular music is in 4/4 time, though often may be in 2/2 or cut time such as in bossa nova. Doo-wop and some other rock styles are frequently in 12/8, or may be interpreted as 4/4 with heavy swing. Similarly, most classical music before the 20th century tended to stick to relatively straightforward metres such as 4/4, 3/4 and 6/8, though variations on these such as 3/2 and 6/4 are also found. By the 20th century, composers were using less regular metres, such as 5/4 and 7/8. Also in the 20th century, it became relatively more common to switch metre frequently—the end of Igor Stravinsky's The Rite of Spring is a particularly extreme example—and the use of asymmetrical rhythms where each beat is a different length became more common: such metres include already discussed quintuple rhythms as well as more complex constructs along the lines of 2+5+3/4 time, where each bar has a 2 beat unit, a five beat unit and a 3 beat unit, with a stress at the beginning of each unit—there are similar metres used in various folk musics. Other music has no metre at all (free time) such as drone based music exemplified by La Monte Young, feature rhythms so complex that any metre is obscured such as in serialism, or is based on additive rhythms, such as some music by Philip Glass. Metre is often combined with a rhythmic pattern to produce a particular style. This is true of dance music, such as the waltz or tango, which have particular patterns of emphasizing beats which are instantly recognizable. This is often done to make the music coincide with slow or fast steps in the dance, and can be thought of as the musical equivalent of prosody. Sometimes, a particular musician or composition becomes identifed with a particular metric pattern; such is the case with the so-called Bo Diddley beat. Some examples: Bo Diddley Bo Diddley Bo Diddley Bo Diddley

Polymetre

Polymetre is the use of two metric frameworks simultaneously, or in regular alternation. Examples include Béla Bartók's "Second String Quartet". Leonard Bernstein's "America" (from West Side Story) employs alternating measures of 6/8 (compound duple) and 3/4 (simple triple). This gives a strong sense of two, followed by three, stresses (indicated in bold type): // I-like-to be-in-A // ME RI CA//. An example from the rock canon is "Kashmir" by the seminal British hard-rock quartet Led Zeppelin, in which the percussion articulates 4/4 while the melodic instruments present a riff in 3/4. In "Toads Of The Short Forest" (from the album "Weasels Ripped My Flesh"), composer Frank Zappa explains: "At this very moment on stage we have drummer A playing in 7/8, drummer B playing in 3/4, the bass playing in 3/4, the organ playing in 5/8, the tambourine playing in 3/4, and the alto sax blowing his nose." In a more extreme example, the math metal band Meshuggah uses complex polymetres extensively. Typically the songs are constructed in 4/4, with guitar riffing and bass drum patterns in unusual meters such as 11/8 and 23/16. Usually the riffs are forced to resolve after 4 or 8 measures resulting in a shorter 'fitpiece' which has a different meter from the rest of the section. Perceptually there appears to be little or no basis for polymeter as research shows that listeners either extract a composite pattern that is fit to a metric framework or focus on one rhythmic stream while treating others as "noise". This upholds the tenet that "the figure-ground dichotomy is fundamental to all perception" (Boring 1942, p.253). (London 2004, p.49-50)

Metric structure

Metric structure includes metre, tempo, and all rhythmic aspects which produce temporal regularity or structure, against which the foreground details or durational patterns are projected (DeLone et. al. (Eds.), 1975, chap. 3). Rhythmic units be metric, intrametric, contrametric, or extrametric. Metric levels may be distinguished. The beat level is the metric level at which pulses are heard as the basic time unit of the piece. Faster levels are division levels, and slower levels are multiple levels. (DeLone et. al. (Eds.), 1975, chap. 3). Hypermetre is large-scale metre (as opposed to surface-level metre) created by hypermeasures which consist of hyperbeats. (Stein 2005, p.329) The term was coined by Cone (1968) while London (2004, p.19) asserts that there is no perceptual distinction between meter and hypermeter. A metric modulation is a modulation from one metric unit or metre to another.

Deep structure

C.S. Lee (1985) has described musical metre in terms of deep structure, where, through rewrite rules, different metres (4/4, 3/4, etc) generate many different surface rhythms. For example the first phrase of The Beatles' A Hard Day's Night, without the syncopation, may be generated from its metre of 4/4: 4/4 4/4 4/4 / \ / \ / \ 2/4 2/4 2/4 2/4 2/4 2/4 | / \ | | | \ | 1/4 1/4 | | | \ | / \ / \ | | | | 1/8 1/8 1/8 1/8 | | | | | | | | | | | It's been a hard day's night (Middleton 1990, p.211).

Metre in song

Issues involving metre in song reflect a combination of musical metre and poetic metre, especially when the song is in a standard verse form. Traditional and popular songs fall heavily within a limited range of metres, leading to a fair amount of interchangeability. For example, early hymnals commonly did not include musical notation, but simply texts. The text could be sung to any tune known by the singers that had a matching metre, and the tune chosen for a particular text might vary from one occasion to another. One case that illustrates the potential use of this principle across musical genres is The Blind Boys of Alabama's rendition of the hymn Amazing Grace, which is sung to the musical setting made famous by The Animals in their version of the folk song The House of the Rising Sun.

Sources

- DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0130493465.
- London, Justin (2004). Hearing in Time: Psychological Aspects of Musical Meter. ISBN 0195160819.
- Stein, Deborah (2005). Engaging Music: Essays in Music Analysis, Glossary. New York: Oxford University Press. ISBN 0195170105.
- Krebs, Harald. "Hypermeter and Hypermetric Irregularity in the Songs of Josephine Lang".
- Lester, Joel (1986). The Rhythms of Tonal Music.

Metre (music)

Rhythmic metre

Polymetre

Metric structure

Deep structure

Metre in song

Sources

Rhythmic unit

A rhythmic unit is a durational pattern which occupies a period of time equivalent to a pulse or pulses on an underlying metric level, as opposed to a rhythmic gesture. Rhythmic units may be classified as: #Metric: even-note patterns, such as steady eighth notes or pulses. #Intrametric: confirming patterns, such as dotted eighth-sixteenth note and swing patterns. #Contrametric: non-confirming, or syncopated patterns. #Extrametric: irregular patterns, such as tuplets. :(DeLone et. al. (Eds.), 1975, chap. 3)

References

- DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0130493465. Category:Rhythm

Rhythmic gesture

A rhythmic gesture is a durational pattern which, in contrast to a rhythmic unit, does not occupy a period of time equivalent to a pulse or pulses on an underlying metric level. (DeLone et. al. (Eds.), 1975, chap. 3) They may be described according to their beginnings and endings or as to the rhythmic units they contain. Beginnings on a strong pulse are thetic, a weak pulse, anacrustic, and those beginning after a rest or tied-over note are called initial rest. Endings on a strong pulse are strong, a weak pulse, weak, and those which end on a strong or weak upbeat are upbeat. (DeLone et. al. (Eds.), 1975, chap. 3)

References

- DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music. Englewood Cliffs, New Jersey: Prentice-Hall. ISBN 0130493465. Category:Rhythm

Iamb

An iamb is a metrical foot used in formal poetry. It is characterised by a short (unstressed) syllable followed by a long (stressed) one. The opposite is a trochee, which is characterised by a long syllable followed by a short one. Iambic pentameter is one of the most powerful measures in English and German poetry. Non-bold = short syllable
Bold = long syllable Examples: :To strive, to seek, to find, and not to yield. – Alfred Tennyson And: :Shall I compare thee to a summer's day? – William Shakespeare Category:Poetic form

Trochee

A trochee is a metrical foot used in formal poetry. It consists of a long syllable followed by a short one. Apart from the famous case of Longfellow's Hiawatha, this metre is rare in English verse, except with an extra long syllable added to each line, as in this example from Tennyson: :Go not, happy day, :From the shining fields; :Go not, happy day, :Till the maiden yields. Perhaps owing to its simplicity, though, trochaic meter is fairly common in children's rhymes: :Peter, Peter pumpkin-eater :Had a wife and couldn't keep her. :Twinkle, twinkle, little star :How I wonder what you are. Often a few trochees will be interspersed among iambs in the same lines to develop a more complex or syncopated rhythm. Compare (William Blake): :Tyger, Tyger, burning bright :In the forests of the night These lines are primarily trochaic, with the last syllable dropped so that the line ends with a stressed syllable to give a strong rhyme or masculine rhyme. By contrast, the intuitive way that the mind groups the syllables in later lines in the same poem makes them feel more like iambic lines with the first syllable dropped: :Did he smile his work to see? In fact the surrounding lines by this point have become entirely iambic: :And when the stars threw down their spears :And watered Heaven with their tears :. . . :Did he who made the lamb make thee? See Good King Wenceslas. Category:Poetic form

Amphibrach

An amphibrac is a metrical foot used in formal poetry. It consists of a long syllable between two short syllables. Amphibracs are seldom used to construct an entire poem. They mainly occur as variants within, for instance, an anapaestic structure. In English, stress-based poetry an amphibrach is a stressed syllable surrounded by two unstressed syllables. It is the main foot used in the construction of the limerick. E.G. "There was a | young lady | of Wantage" The amphibrach is also often used in ballads and light verse. E.G. the hypermetrical lines of Sir John Betjeman's Meditation on the A40 Category:Poetic form

Category:Aspects of music

Category:Music theory

O'Neill Collegiate and Vocational Institute

O'Neill Collegiate and Vocational Institute is located in Oshawa, Ontario within the Durham District School Board. The school has students in grades 9-12 and offers a wide range of academic and extra-curricular activities.

External links

- [http://www.durham.edu.on.ca/s_links/schools/oneill/index/start.htm O'Neill Collegiate and Vocational Institute]

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Metre in song

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O'Neill Collegiate and Vocational Institute

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