Topics in Mathematics: Math and Music

Exam 1 Review Questions

Below are the types of questions you can expect to find on the exam. This is certainly not an exhaustive list; it is intended to provide a general overview.

Listening Questions:

1. Be able to recognize the time signature or key rhythmic feature of a piece by listening (CD#1).

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

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

General Questions:

1. How many eighth notes do you need to fill up a measure in 11 - 4 time? in 7 - 8 time?

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

3. What is the sum of an infinite geometric series that begins with 9 and has a ratio of -2/3? Write out the first five terms of the corresponding geometric sequence (the terms being summed).

4. Suppose you come across a measure of music that asks you to play a polyrhythm of 10 against 6. What is the minimal number of subdivisions needed in order to see the precise location of each note in the polyrhythm?

5. Give an example of two integers a and b such that the lcm(a,b) = 2a. What must the gcd(a,b) be equal to for this to be true?

6. Is it possible for the lcm(m,n) to be n^2? If so, find conditions on m and n that always yield this result. If not, explain why not.

7. Find the lcm(2,5,10), lcm(3,5,10), and lcm(4,5,10).

8. What popular type of music and dance, which features a fast, rhythmic 2 count in 2 - 4 meter, originated in the Dominican Republic?

9. What famous piece featuring polyrhythms and polytonality caused a riot at its premiere in Paris? Name the composer.

10. Name two notes that are enharmonically equivalent to A double sharp. Name two notes that are enharmonically equivalent to F double flat.

11. Write out an ascending whole tone scale, using correct accidentals, beginning on D, in both the treble and bass clefs.

12. Without using key signatures, write out an ascending F# major scale in the treble clef using correct accidentals. Be able to find these notes on the piano keyboard.

13. Without using key signatures, write out an ascending G harmonic minor scale (diatonic spelling) in the treble clef using correct accidentals. What is the relative major of G minor?

14. Without using key signatures, write out an ascending G# natural minor scale (diatonic spelling) in the bass clef using correct accidentals. What is the relative major of G# minor?

15. 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.

16. 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. What chord do the three notes form?

17. The first jump in the melody of Twinkle Twinkle Little Star is what interval?

18. What is the opening interval of Leonard Bernstein's Maria?

19. 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.

20. In the treble clef, write out the notes for a B major and B minor chord. Use diatonic spellings for each chord.

21. Which two keys are the closest musically to B major? Which key is the furthest from B major?

22. Using key signatures, transpose the given excerpt from the key of B♭ major to the key of D♭ major. Also transpose it to the key of E major.

23. If two scales are considered identical when they contain the same overall set of notes, how many different whole tone scales are there? How many different major scales are there? Explain.