Math/Music: Structure and Form
Exam 1 Review Questions
Below are some types of questions you should expect to find on the exam.
This is certainly not an exhaustive list but is intended to provide a
general overview.
Listening Questions:
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Be able to recognize the time signature or rhythmic features of a piece by listening. (CD#1)
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Be able to hear the difference between a chromatic, whole tone, major or minor scale.
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Be able to recognize different types of tonality in music: major, minor, Gregorian chant, early polyphony,
atonal music, etc. (CD#2)
General Questions:
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How many eighth notes do you need to fill up a measure in 7 - 4 time? in 5 - 8 time?
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In 5 - 4 time, how many beats does a triple-dotted quarter note get? How many
beats does it get in 3 - 2 time?
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What is the sum of an infinite geometric series that begins with 3 and has a ratio of -2/3?
Write out the first five terms of the corresponding geometric sequence (the terms being summed).
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Suppose you come across a measure of music that asks you to play a polyrhythm of 10 against 6.
How many pulses would you subdivide the measure into in order to see precisely where the pulse of each rhythmic pattern goes?
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Give an example of two integers a and b such that the lcm(a,b) = b. What must the
gcd(a,b) be equal to for this to be true?
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What popular type of music and dance, which features a fast, rhythmic 2 count in 2 - 4 meter, originated
in the Dominican Republic?
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What famous piece featuring polyrhythms and polytonality caused a riot at its premiere in Paris? Name the composer.
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Write out a whole tone scale, using correct accidentals, beginning on D, in both clefs.
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Without using key signatures, write out an F# major scale in the treble clef using correct accidentals.
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Without using key signatures, write out a C# harmonic minor scale (diatonic) in the treble clef using correct accidentals.
What is the relative major of C# minor?
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What key has 5 flats? Write the major scale for this key in the bass clef. List the flats
for this key in correct order.
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If you start at middle C, go up a perfect fifth, then down a major third, what note have
you arrived at? Notate all three notes in the treble clef. Be able to find all three notes
on the piano keyboard.
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The first jump in the melody of Twinkle Twinkle Little Star is what interval?
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What is the opening interval of Leonard Bernstein's Maria?
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How many half steps are there in a major sixth? How many whole steps are there in an octave? Name a song
that begins with an octave.
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Using key signatures, transpose Twinkle Twinkle Little Star from the key of C major
to the key of E flat major. Also transpose it to the key of F sharp major.
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How many keys are there on the modern piano keyboard? Roughly how many octaves fit into the piano keyboard?
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If two scales are considered identical when they contain the same set of notes,
how many different major scales are there? Explain why.