Number patterns for Y10/11

As long as the birth rate of a population exceeds the death rate, the population size will continue to increase. At a steady, positive per capita growth rate, the population will add a larger number of indi- viduals with each generation. So, a population can increase rapidly with even a small growth rate. A pattern of increase in number due to a steady growth rate is called exponential growth. The observa- tion that populations can grow in this pattern is called the exponential (EKS-poh-NEN-shuhl) model of population growth. One way to understand the exponential model is to study a graph of population size over time. A graph of exponential growth makes the characteristic J-shaped curve shown in Figure 19-6. With expo- nential growth, population size grows slowly when it is small, but growth speeds up as individuals join the population. The exponen- tial model leads us to predict that the population size will increase indefinitely and by a greater number with each time period. Applying the Exponential Model A scientific model is useful if it helps to predict or explain pat- terns that can be observed in reality. Indeed, the exponential model matches observed patterns of growth of real populations, but only under certain conditions and for limited periods of time. For example, a population of microorganisms can grow exponen- tially if provided with an abundance of food and space and if waste is removed. Figure 19-7 shows the growth of bacteria in a laboratory. However, the exponential model does not apply to most popu- lations. In natural environments, populations cannot grow indefi- nitely because the resources they depend on become scarce and harmful wastes accumulate. Any factor, such as space, that restrains the growth of a population is called a limiting factor. All populations are ultimately limited by their environment.SPECIES INTERACTIONS Just as populations contain interacting members of a single species, communities contain interacting populations of many species. Many species have specific types of interactions with other species. This chapter introduces the five major types of interactions among species: predation, competition, parasitism, mutualism, and commensalism. These categories are based on whether each species causes any benefit or harm to the other species in a given relationship. PREDATION In predation (pree-DAY-shuhn), an individual of one species, called the predator, eats all or part of an individual of another species, called the prey. Predation is a powerful force in a community. The relationship between predator and prey influences the size of each population and affects where and how each species lives. Examples of predators include carnivores—predators that eat ani- mals—and herbivores—predators that eat plants. Many types of organisms can act as predators or prey. All heterotrophs are either predators or parasites or both. Predator Adaptations Natural selection favors the evolution of predator adaptations for finding, capturing, and consuming prey. For example, rattlesnakes have an acute sense of smell and have heat-sensitive pits located below each nostril. These pits enable a rattlesnake to detect warm- bodied prey, even in the dark. Many snakes use venom to disable or kill their prey. A venomous rat- tlesnake is shown in Figure 20-1. Other predator adaptations include the sticky webs of spiders, the flesh-cutting teeth of wolves and coyotes, the speed of cheetahs, and the striped pat- tern of a tiger’s coat, which provides camouflage in a grassland habitat. Many herbivores have mouthparts suited to cutting and chewing tough vegetation. A predator’s survival depends on its ability to capture food, but a prey’s survival depends on its ability to avoid being captured. Therefore, natural selection also favors adaptations in prey that allow the prey to escape, avoid, or otherwise ward off

Ostinato Music Definition Ostinato (plural – ostinati or ostinatos) is an Italian word meaning obstinate or persistent and is used in music to describe a musical phrase or rhythm that is repeated persistently. The repeated pattern could be a melody, a figure in the bass – called a basso ostinato or simply a repeated rhythmic idea. An ostinato may be played for an entire piece of music or just during one section. The key aspect to remember in the definition of an ostinato is that it is a pattern that is repeated persistently in a piece of music. Rhythmic Ostinato A rhythmic ostinato is a rhythmic pattern that is persistently repeated. It will often be played on an untuned percussion instrument (e.g. snare drum, triangle, etc..). However, rhythmic ostinati can also be found in parts played on pitched instruments where the note pitch stays the same or where the pitches change as the phrase is repeated. The key characteristic is that it is the rhythm that is persistently repeated.In Maurice Ravel’s “Bolero” the use of a rhythmic ostinato brings a magical and almost hypnotic feel to the piece as the percussive pattern contrasts with the sweeping and almost improvisatory nature of the flute melody. Have a look at the pattern below and listen to its use in the audio extract: Rhythmic Ostinato Example from Ravel Bolero.A rhythmic ostinato is an excellent technique that composers use for creating drama and tension. One of the most famous examples of this is from “Mars” by Gustav Holst. Have a look/listen to the rhythmic pattern: Rhythmic Ostinato Example from Gustav Holst Mars. This rhythmic pattern is played relentlessly throughout the piece and forms the basis for the intense drama associated with the subject – Mars, the god of war! Have a listen to this extract of the piece performed by the United States Air Force Band:You can hear how the relentless sound of a rhythmic ostinato is extremely effective at building tension as the music around it changes and develops. This effect is heightened in the extract from Mars as the bass note remains on a G throughout the extract and acts as a pedal point. Not surprisingly, rhythmic ostinati are used widely in dramatic film music. Hans Zimmer is a film composer who makes considerable use of this technique across the many film scores he has written. Have a listen to the opening from his theme for the film “Pirates of the Caribbean” performed by the Auckland Symphony Orchestra:You can hear that there are a number of different ostinati in many of the different parts that are layered to produce the overall sound. Here is the rhythmic ostinato that forms the basis of the melody line: Rhythmic Ostinato Example Hans ZimmerMelodic ostinato A melodic ostinato is a repeated pattern where both the rhythm and the melody form the basis for the repeated pattern. These often occur in the bass part where they are called a basso ostinato. Basso Ostinato A basso ostinato is a repeated pattern in the bass part of a piece. This technique became particularly popular in the 17th century where a number of Baroque dances were based upon ostinati in the bass part. In dances such as the passacaglia the bass remained constant throughout the piece whilst the other parts developed. This technique is called “ground bass” and you can have a look at my lesson on ground bass for some examples of this. The most famous example of a basso ostinato is Pachelbel’s Canon in D. Ostinati Examples in Contemporary Music Rhythmic and melodic ostinatos have had a massive influence on contemporary popular music across a wide range of genres. This can be seen in 2 main ways: Riffs (short melodic phrases) – these are effectively contemporary expressions of ostinato. Loops – rhythmic and melodic phrases are repeated to create the characteristic sound of contemporary productions. As a result, you will probably be able to find examples of the use of repeated patterns/ostinati in most contemporary songs. However, there are some songs where the use of an ostinato provides the clear foundation for the song and these are useful examples to listen to. Examples of Ostinati Riffs Seven Nation Army by White Stripes The guitar riff from Seven Nation Army is one of the most famous modern guitar riffs and is used as an ostinato that plays throughout the song. It is an excellent example of a melodic ostinato:Back in Black by AC/DC The opening guitar riff in this song is another great example:Examples of Loops Loops are repeated patterns that are clearly built on the concept of ostinati. They are used widely in contemporary music. Hip hop songs often use loops as the foundation for the track. Still D.R.E by Dr. Dre ft. Snoop Dogg In this song a piano loop plays throughout the whole track and forms the foundation of the song:

What Is Rhythm in Music? Rhythm is the pattern of sound, silence, and emphasis in a song. In music theory, rhythm refers to the recurrence of notes and rests (silences) in time. When a series of notes and rests repeats, it forms a rhythmic pattern. In addition to indicating when notes are played, musical rhythm also stipulates how long they are played and with what intensity. This creates different note durations and different types of accents.Why Is Rhythm Important in Music? Rhythm functions as the propulsive engine of a piece of music, and it gives a composition structure. Most musical ensembles contain a rhythm section responsible for providing the rhythmic backbone for the entire group. Drums, percussion, bass, guitar, piano, and synthesizer may all be considered rhythm instruments, depending on the context. However, all members of a music group bear responsibility for their own rhythmic performances and play the musical beats and rhythmic patterns indicated by the piece's composer.7 Elements of Rhythm in Music Several core elements comprise the fundamentals of musical rhythm. 1. Time signature: A musical time signature indicates the number of beats per measure. It also indicates how long these beats last. In a time signature with a 4 on the bottom (such as 2/4, 3/4, 4/4, 5/4, etc.), a beat corresponds with a quarter note. So in a 4/4 time (also known as "common time"), each beat is the length of a quarter note, and every four beats form a full measure. In 5/4 time, every five beats form a full measure. In a time signature with an 8 on the bottom (such as 3/8, 6/8, or 9/8), a beat corresponds with an eighth note. 2. Meter: Standard Western music theory divides time signatures into three types of musical meter: duple meter (where beats appear in groups of two), triple meter (where beats appear in groups of three), and quadruple meter (where beats appear in groups of four). Meter is not tied to note values; for instance, a triple meter could involve three half notes, three quarter notes, three eighth notes, three sixteenth notes, or three notes of any duration. Musicians and composers regularly mix duple and triple meter in their work; Igor Stravinsky's "The Rite of Spring" is a textbook example of such a technique. 3. Tempo: Tempo is the speed at which a piece of music is played. There are three primary ways that tempo is communicated to players: beats per minute, Italian terminology, and modern language. Beats per minute (or BPM) indicates the number of beats in one minute. Certain Italian words like largo, andante, allegro, and presto convey tempo change by describing the speed of the music. Finally, some composers indicate tempo with casual English words such as “fast,” “slow,” “lazy,” “relaxed,” and “moderate.” 4. Strong beats and weak beats: Rhythm combines strong beats and weak beats. Strong beats include the first beat of each measure (the downbeat), as well as other heavily accented beats. Both popular music and classical music combine strong beats and weak beats to create memorable rhythmic patterns. 5. Syncopation: Syncopated rhythms are those that do not align with the downbeats of individual measures. A syncopated beat will put its emphasis on traditional weak beats, such as the second eighth note in a measure of 4/4. Complex rhythms tend to include syncopation. While these rhythms may be more difficult for a beginning musician to pick up, they tend to sound more striking than non-syncopated rhythmic patterns. 6. Accents: Accents refer to special emphases on certain beats. To understand accents, think of a piece of poetry. A poetic meter, such as iambic pentameter, may dictate a specific mixture of stressed syllables and unstressed syllables. Musical accents are no different. Different rhythms may share a time signature and tempo, but they stand out from one another by accenting different notes and beats. 7. Polyrhythms: To achieve a particularly ambitious sense of rhythm, an ensemble may employ polyrhythm, which layers one type of rhythm on top of another. For instance, a salsa percussion ensemble may feature congas and bongos playing 4/4 time, while the timbales concurrently play a pattern in 3/8. This creates a dense rhythmic stew and, when properly executed, it can yield incredibly danceable rhythm patterns. Polyrhythms originated in African drumming, and they’ve spread to all sorts of genres worldwide, from Afro-Caribbean to Indian to progressive rock, jazz, and contemporary classical.

Figure 18-11 represents the amount of energy stored as organic material in each trophic level in an ecosystem. The pyramid shape of the diagram indicates the low percentage of energy transfer from one level to the next. On average, 10 percent of the total energy consumed in one trophic level is incor- porated into the organisms in the next. Why is the percentage of energy transfer so low? One reason is that some of the organisms in a trophic level escape being eaten. They eventually die and become food for decomposers, but the energy contained in their bodies does not pass to a higher trophic level. Even when an organism is eaten, some of the molecules in its body will be in a form that the consumer cannot break down and use. For example, a cougar cannot extract energy from the antlers, hooves, and hair of a deer. Also, the energy used by prey for cellu- lar respiration cannot be used by predators to synthesize new bio- mass. Finally, no transformation or transfer of energy is 100 percent efficient. Every time energy is transformed, such as during the reactions of metabolism, some energy is lost as heat. Limitations of Trophic Levels The low rate of energy transfer between trophic levels explains why ecosystems rarely contain more than a few trophic levels. Because only about 10 percent of the energy available at one trophic level is transferred to the next trophic level, there is not enough energy in the top trophic level to support more levels. Organisms at the lowest trophic level are usually much more abundant than organisms at the highest level. In Africa, for exam- ple, you will see about 1,000 zebras, gazelles, and other herbivores for every lion or leopard you see, and there are far more grasses and shrubs than there are herbivores. Higher trophic levels con- tain less energy, so, they can support fewer individuals.A population is a group of organisms that belong to the same species and live in a particular place at the same time. All of the bass living in a pond during a certain period of time make up a pop- ulation because they are isolated in the pond and do not interact with bass living in other ponds. The boundaries of a population may be imposed by a feature of the environment, such as a lake shore, or they can be arbitrarily chosen to simplify a study of the population. The humans shown in Figure 19-1 are part of the pop- ulation of a city. The properties of populations differ from those of individuals. An individual may be born, it may reproduce, or it may die. A population study focuses on a population as a whole—how many individuals are born, how many die, and so on. Population Size A population’s size is the number of individuals that the population contains. Size is a fundamental and important population property but can be difficult to measure directly. If a population is small and composed of immobile organisms, such as plants, its size can be determined simply by counting individuals. Often, though, individ- uals are too abundant, too widespread, or too mobile to be counted easily, and scientists must estimate the number of individuals in the population. Suppose that a scientist wants to know how many oak trees live in a 10 km2 patch of forest. Instead of searching the entire patch of forest and counting all the oak trees, the scientist could count the trees in a smaller section of the forest, such as a 1 km2 area. The scientist could then use this value to estimate the population of the larger area. SECTION 1 OBJECTIVES ● Describe the main properties that scientists measure when they study populations. ● Compare the three general patterns of population dispersion. ● Identify the measurements used to describe changing populations. ● Compare the three general types of survivorship curves. VOCABULARY population population density dispersion birth rate death rate life expectancy age structure survivorship curve FIGURE 19-1 A population can be widely distributed, as Earth’s human population is, or confined to a small area, as species of fish in a lake are. Copyright © by Holt, Rinehart and Winston. All rights reserved. 382 CHAPTER 19 If the small patch contains 25 oaks, an area 10 times larger would likely contain 10 times as many oak trees. A similar kind of sampling technique might be used to estimate the size of the pop- ulation shown in Figure 19-2. To use this kind of estimate, the sci- entist must assume that the distribution of individuals in the entire population is the same as that in the sampled group. Estimates of population size are based on many such assumptions, so all esti- mates have the potential for error. Population Density Population density measures how crowded a population is. This measurement is always expressed as the number of individuals per unit of area or volume. For example, the population density of humans in the United States is about 30 people per square kilome- ter. Table 19-1 shows the population sizes and densities of humans in several countries in 2003. These estimates are calculated for the total land area. Some areas of a country may be sparsely popu- lated, while other areas are very densely populated. Dispersion A third population property is dispersion (di-SPUHR-zhuhn). Dispersion is the spatial distribution of individuals within the popu- lation. In a clumped distribution, individuals are clustered together. In a uniform distribution, individuals are separated by a fairly con- sistent distance. In a random distribution, each individual’s location is independent of the locations of other individuals in the popula- tion. Figure 19-3 illustrates the three possible patterns of dispersion. Clumped distributions often occur when resources such as food or living space are clumped. Clumped distributions may also occur because of a species’ social behavior, such as when animals gather into herds or flocks. Uniform distributions may result from social behavior in which individuals within the same habitat stay as far away from each other as possible. For example, a bird may locate its nest so as to maximize the distance from the nests of other birds. These migrating wildebeests in East Africa are too numerous and mobile to be counted. Scientists must use sampling methods at several locations to monitor changes in the population size of the animals. FIGURE 19-2 TABLE 19-1 Population Size and Density of Some Countries Population size Population density Country (in millions) (in individuals/km2) China 1,289 135 India 1,069 325 United States 292 30 Russia 146 8 Japan 128 337 Mexico 105 54 Kenya 32 54 Australia 20 3 dispersion from the Latin dis-, meaning “out,” and spargere, meaning “to scatter” Word Roots and Origins Copyright © by Holt, Rinehart and Winston. All rights reserved. POPULATIONS 383 The social interactions of birds called gannets, which are shown in Figure 19-3b, result in a uniform distribution. Each gannet chooses a small nesting area on the coast and defends it from other gannets. In this way, each gannet tries to maximize its distance from all of its neighbors, which causes a uniform distribution of individuals. Few populations are truly randomly dispersed. Rather, they show degrees of clumping or uniformity. The dispersion pattern of a population sometimes depends on the scale at which the popu- lation is observed. The gannets shown in Figure 19-3b are uni- formly distributed on a scale of a few meters. However, if the entire island on which the gannets live is observed, the distribution appears clumped because the birds live only near the shore. POPULATION DYNAMICS All populations are dynamic—they change in size and composition over time. To understand these changes, scientists must know more than the population’s size, density, and dispersion. One important measure is the birth rate, the number of births occur- ring in a period of time. In the United States, for example, there are about 4 million births per year. A second important measure is the death rate, or mortality rate, which is the number of deaths in a

Can you create an evaluation using this information PHONETICS VS. PHONOLOGY Whereas phonetics is the study of sounds that occur in language, phonology is the study of how these sounds are organized and how they function in language. It uses the classifications of sounds derived from phonetics to describe and analyze how sounds occur in speech. STRUCTURALIST PHONEMICS STRUCTURALIST PHONEMICS As linguists began to study sounds in fine detail, they recognized increasingly complex aspects of phonetic organization. For example, the sound /p/ appears in different varieties in English. STRUCTURALIST PHONEMICS One of the varieties of /p/ is indicated by [ph]. This sound is produced with an accompanying puff of air called aspiration, as in the words “pill,” and “peace.” Another sound, indicated by [p•], is produced when there is little or no aspiration; this sound occurs in a word like “spill.” A third major variety for the /p/ sound is the unreleased [p– ], which may occur at the end of a word like “stop.” To deal with these variations for the /p/ sound, the structuralists suggested the existence of an abstract unit which they termed a phoneme. STRUCTURALIST PHONEMICS A phoneme was defined by the structuralists as an abstract phonological unit that represents a class of real sounds, termed the allophones of a phoneme. The phoneme /p/ in English, then, is represented by the allophones [ph], [p•], and [p– ]. STRUCTURALISTS: MINIMAL PAIRS How do we know what these abstract units of sound called phonemes are? In order to find the phonemes of a language, the structuralists developed the concept of the minimal pair, defined as any two words that: a) Contain the same number of segments b) Differ in meaning c) Exhibit only one phonetic difference. STRUCTURALISTS: MINIMAL PAIRS In practical terms, phonemes distinguish meanings; and a phoneme can also be defined as the smallest meaning-distinguishing unit of sound. For instance, the words “pin” /pɪn/ and “bin” /bɪn/ mean different things, and the only one difference in these words occurs in the initial sounds. STRUCTURALISTS: MINIMAL PAIRS By using the concept of a minimal pair, we can determine that the three variations of the /p/ sound do not represent three phonemes. Certainly, it is possible to pronounce the word cap with either an aspirated [ph ] or unreleased [p– ]; however, the two forms [kæph ] and [kæp– ] are not a minimal pair, even though they involve different sounds, because they are identical in meaning. STRUCTURALISTS: FREE VARIATION The two forms [kæph ] and [kæp– ] are, therefore, said to exhibit free variation: that is, the pronunciation may vary without signifying a change in meaning. In other words, we may conclude that the unreleased [p– ] and the aspirated [ph ] are not representations of different phonemes in English; they are, in fact, allophones of one phoneme, /p/. STRUCTURALISTS: COMPLEMENTARY DISTRIBUTION When phonemes have more than one allophone in a language, the allophones are said to be in complementary distribution. Complementary distribution means that the allophones of a phoneme occur in different phonetic environments (that is, with different sounds surrounding them). TRANSFORMATIONAL- GENERATIVE PHONOLOGY TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonology is a relatively recent development in linguistic theory. Chomsky launched Transformational-Generative Grammar in 1957, but the earliest studies within this framework were largely concerned with syntax. A decade later, the first comprehensive transformational-generative treatment of English phonology appeared: Chomsky and Halle’s The Sound Pattern of English (1968). TRANSFORMATIONAL-GENERATIVE PHONOLOGY Transformational-generative phonologists strongly oppose the structuralists’ phonemic level. They replace this level by a series of rules that directly relate underlying representations to observed phonetic representations. The central mechanisms in transformational-generative phonology, then, are underlying representations and phonological rules. PHONOLOGICAL RULES A rule is an operational statement in which some linguistic entity is modified, resulting in a new linguistic entity. Rules may add elements, remove elements, or change elements. By using phonological rules, linguists attempt to demonstrate that there is order in linguistic phenomena and that linguistic patterns are systematic. PHONOLOGICAL DERIVATION A phonological derivation is an operation that begins with an underlying representation and, through the application of a set of specific rules, yields the actual sound the speaker produces. The representation of a phonological rule has the following general appearance. /A/ → [B] / C “A” changes to “B” under condition “C” PHONOLOGICAL RULE – EXAMPLE In most Southern dialects, the word ten is pronounced like the word tin. This is not an isolated fact, for den is pronounced like din and Ben is pronounced like bin, and so on. This very general fact can be represented by the phonological rule: /ɛ/ → [I] / ___ [n] den /dɛn/ → /dIn/ Ben /bɛn/ → /bIn/ ten /tɛn/ → /tIn/ /ɛ/ → [I] / ___ [n] - high - low - tense + front + high - tense + front + sonorant + anterior + coronal - continuant NOTATIONAL DEVICES IN PHONOLOGICAL RULES The statement of phonological rules can be complex, and linguists have developed several notational devices for writing them. Often, the following symbols will be necessary for stating the conditions under which rules apply: # indicates a word boundary + indicates an intraword boundary $ indicates a syllable boundary UNDERLYING REPRESENTATIONS AND RELATED ISSUES The transformational-generative description of phonology relates underlying representations to phonetic representations by rules. This can be represented in a simple example: In English, there are certain pairs of words like sign / signature, and malign / malignant that exhibit a regular alternation in their phonetic representations: [g] is present in the second member of the pairs but absent in the first member. UNDERLYING REPRESENTATIONS AND RELATED ISSUES To explain the relatedness of words such as sign / signature, we could claim that the underlying representation of the segment in all such pairs is /g/ and that a rule operates to delete /g/ before syllable-final nasals. Thus, the rule “/g/ is deleted before syllable-final nasal” would appear formally as: + voice - anterior →∅ ____ [+ nasal] $ - coronal UNDERLYING REPRESENTATIONS AND RELATED ISSUES On the left-hand side of the arrow, we place the features needed to uniquely specify /g/ among the consonants; that is, no other consonant has the features [+ voice], [- anterior], and [- coronal]. The symbols → mean that the sound /g/ changes to nothing or more properly “/g/ is deleted.” The horizontal line following the slash mark refers to the position of /g/ - namely, before a segment that is [+nasal]. Finally, this [+nasal] segment occurs before a syllable boundary, as indicated by $. A less formal way of writing this rule would be: /g/ → / _ [+nasal] $ Notice that this rule also helps describe such alternations as phlegm/phlegmatic and paradigm/paradigmatic. Application Activity: Think of other words in which this rule can be applied. Write the sound segments to prove /g/ is deleted. Another example is the process through which the prefix meaning “not” is added to words. This prefix alternates among the forms /Im/, /In/, and /Iŋ/, depending on the point of articulation of the initial segment of the following word. -If the segment begins in the extreme front part of the mouth (labials), the form is /Im/, as in improper. -If the segment begins in the extreme back part of the mouth (velars), the form is /Iŋ/, as in incomplete. -If the segment begins in the mid-region of the mouth (all other sounds), the form is /In/, as in indecent. *Exceptions:Words beginning with /r/ or /l/. Analyze the Word “in + complete,” for example. /n/ → [ŋ] / __ [k] - continuant - continuant - continuant + sonorant → + sonorant - sonorant + anterior - anterior - strident + coronal - coronal - coronal + tense THE VELAR SOFTENING RULE Still another example of alternation in English is found in pairs of words like “electric / electricity,” in which the segments /k/ and /s/ alternate. /k/ changes to [s] only before non- low, front vowels. THE VELAR SOFTENING RULE /k/ → [s] / __ - continuant + continuant - strident → - sonorant V - anterior + anterior - low - coronal + coronal - back

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