Algorithmic Complexity and Big O Notation

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Questions and Answers

Which instrument typically produces the highest notes within the brass section of an orchestra?

  • French horn
  • Trombone
  • Trumpet (correct)
  • Tuba

Why are louder instruments typically positioned behind quieter ones in an orchestra?

  • To ensure that all sections of instruments are equally visually appealing
  • To accommodate musicians personal preferences
  • To achieve optimal balance of sound (correct)
  • To allow for easier instrument tuning during performances

Which instruments are categorized within the woodwind family?

  • Xylophones and Timpani
  • Trombones and Trumpets
  • Cellos and Violas
  • Oboes and Bassoons (correct)

Which of the following is true about percussion instruments in an orchestra?

<p>Most are untuned and do not have fixed pitches. (C)</p>
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What is the primary method by which wind instruments produce sound?

<p>By vibrating air down a tube (A)</p>
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Which composer is best known for inspiring future composers, known as “Papa” and established the symphony and the four-part string quartet?

<p>Franz Joseph Haydn (D)</p>
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Which composer was known for being an eccentric but very talented musician, that was admired for his improvisations played on the organ?

<p>Samuel Wesley (C)</p>
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Muzio Clementi was known as one of the first piano virtuosos, what else was he known for?

<p>Composing dramatic and challenging piano sonatas (C)</p>
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Which composer was known for writing innovative compositions, which were more expressive than old Classical music?

<p>Johann Nepomuk Hummel (C)</p>
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Peter Sculthorpe's musical compositions primarily reflect which themes?

<p>The people and landscape of his home country (A)</p>
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Why did Peter Sculthorpe stop teaching Indonesian music?

<p>It did not give him enough time to compose. (D)</p>
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Which piece did Sculthorpe write in memory of his parents and for the children who died in wars?

<p>Requiem (C)</p>
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What musical elements are combined in Sculthorpe's Requiem?

<p>Drumming, chanting, seagull-like cries, Australian lullaby, orchestra, voice, and the yidaki (B)</p>
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The distorted sound in rock music, which became a signature element, was a result of what?

<p>Overloaded circuitry from amplifiers pushed to their limits (D)</p>
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Led Zeppelin is known for experimenting across genres in music, but which ones did they experiment with?

<p>Acoustic and country music (B)</p>
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Flashcards

Zummara

The zummara is a double clarinet with parallel pipes joined together, each with a single reed, dating back to c. 2700 BCE in Egypt.

Surnai

The surnai, dating from pre-13th century Mongolia, is a loud folk oboe with seven holes and a thumb hole, known for being light, portable and popular among nomadic people. It is played at celebrations such as weddings.

Flageolet

The flageolet, dating back to 16th century France, has single or double pipes and was often used to accompany dances in the 17th and 18th centuries.

Shawm

The shawm, dating back to late 13th century Germany, is a medieval musical instrument made from a single piece of wood that came in several different sizes, and is developed from the modern oboe.

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Bassoon

The bassoon, dating back to c.1800s Germany, consists of a double reed made from two pieces of cane tied together. It is considered to be the largest instrument of the woodwind family with the lowest pitch.

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Panpipes

The panpipes are prehistoric South American instruments that are still played, having up to three rows of varying-length bamboo strips woven together. The music of the panpipes is known as sikuri.

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The Blues

Blues music grew from the folk music of enslaved Black people in the southern United States. Blues songs are very emotional, featuring sad themes with simple tunes typically based around three chords. In the 20th century, the genre influenced jazz, rock and R&B music.

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Spiritual songs

Enslaved people expressed their suffering and hope for a better life through singing these songs, which combined African rhythms and harmonies with Christian songs.

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Field Hollers & Work Songs

These were used by enslaved people in the southern US to communicate in the fields and keep time when performing a task. They used the african call and response form, in which a lead singer sang a melody line and the rest responded with a different line.

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Rattle Drum

Rattle drums, often prehistoric in North America, have dried seeds inside and are used by Indigenous peoples during various ceremonies.

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Tabor

A two-headed drum of 13th century European origin that is tapped with drumsticks and makes a crisp rat-a-tat-tat sound, often popular in military bands.

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Darbuka

This goblet-shaped, single-headed drum of ancient Middle Eastern origin is played with the hands. This is used in various types of ceremonies and festivities, including weddings and engagement celebrations.

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Bongos

These single-headed drums, dating back to the 19th century Cuban, come in pairs, one larger than the other, and are commonly used in lively Latin American music such as salsa.

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West Indian steel drum

Different areas on this 1930s Trinidadian metal drum make different notes; unlike other drums, it can be used to play a tune.

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Rock music

Rock music is a wide-ranging genre of music which blossomed from blues music in the US. The music is known for its rebellious streak, and rock musicians combine the sound of electric guitars, pounding drums, and loud vocals to cause a stir.

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Study Notes

  • Algorithmic complexity assesses resource usage by an algorithm relative to input size.
  • Big O notation is used to express this complexity, describing asymptotic behavior.

Big O Notation

  • Indicates the upper limit of how time or memory usage grows as input increases.
  • O(1) signifies constant time, execution time is independent of input size.
  • O(log n) indicates logarithmic time, growth is proportional to the logarithm of the input.
  • O(n) indicates linear time, execution time grows proportionally to the input size.
  • O(n log n) indicates linearithmic time, with a linear growth rate and a logarithmic factor.
  • O(n2) indicates quadratic time, execution time grows with the square of the input size.
  • O(2n) indicates exponential time, execution time doubles with each increment in input size.
  • O(n!) indicates factorial time, execution time grows as the factorial of the input size.

Complexity Examples

  • Searching an unsorted array has a time complexity of O(n).
  • Searching a sorted array has a time complexity of O(log n).
  • Merge sort algorithm for sorting an array has a time complexity of O(n log n).
  • Multiplying two matrices needs a time complexity of O(n3).
  • Solving the travelling salesman problem has a time complexity of O(n!).

Algorithmic Importance

  • Allows efficiency comparisons between various algorithms.
  • Essential for choosing the most suitable algorithm based on resource constraints and input sizes.

Space Complexity

  • Measures the amount of memory an algorithm requires relative to input size.
  • Expressed in Big O notation, similar to time complexity.
  • An algorithm storing all input data has a space complexity of O(n).

Trade Offs

  • A trade-off often exists between time and space complexity.
  • An algorithm that is very fast may use a lot of memory.
  • An algorithm that saves memory may take a long time
  • Algorithm choice depends on problem constraints, such as limited memory or critical timing.

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