Mathematics and Music

Exam 1 Review Questions

Below are some types of questions you could expect to find on the exam. This is certainly not an exhaustive list and is meant to give a general overview. For more detailed topics, see the Exam 1 Review sheet.

Listening Questions:

1. Be able to recognize the time signature of a piece of music or if it even has one. (CD#1)

2. Be able to tell the difference between a chromatic, whole tone, major or minor scale.

3. Be able to recognize different types of tonality: major, minor, Gregorian chant, early polyphony, atonal music. (CD#2)

General Questions:

1. How many eighth notes do you need to fill up a measure in 7 - 4 time? in 5 - 8 time?

2. In 3 - 4 time, how many beats does a triple-dotted quarter note get? How many beats does it get in 5 - 2 time?

3. What is the sum of an infinite geometric series that begins with 3 and has a ratio of 2/3?

4. Give an example of two integers a and b such that the lcm(a,b) = b.

5. Without using key signatures, write out a B major scale in the alto clef using correct accidentals.

6. 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.

7. 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.

8. The Holy Cross theme song (sung to O Tannenbaum) begins with what interval?

9. How many semi-tones are there in a major sixth? How many whole-tones are there in an octave?

10. Using key signatures, transpose Twinkle Twinkle Little Star (see class notes) from the key of C major to the key of E flat major (music would be provided to you on the exam.)

11. In general, how many octaves on the modern piano keyboard? How many perfect fourths?

12. Two notes are played together resulting in a sound wave of the form
y = sin(400 Pi t) + sin(406 Pi t).
What are the frequencies of each note? What is the frequency of the "note" we hear when they are combined? How many beats per second do you hear?

13. Give two reasons why the brain is so important to our hearing and understanding of music.

14. Graph the function y = 4 sin( Pi ( t - 1/2)) . What are the amplitude and period of this function?

15. What angle (in radians) corresponds to going around the unit circle 5 times? What will the cosine of this angle be?

16. What is a harmonic oscillator and why is it related to sound and music?

17. A string of length 20 cm and a string of length 30 cm are plucked simultaneously. What interval do you hear?

18. What is the Pythagorean comma and why is the Pythagorean scale not used in modern music?

19. Write out the first 8 frequencies in the overtone series for a note whose fundamental is 150 Hz.

20. Let C3 be the note an octave below middle C. Starting in the bass clef, write the first nine notes corresponding to the frequencies in the overtone series of C3.