Topics in Mathematics: Math and Music

Exam #1

Thursday, March 1, In Class

The first exam covers Chapters 1 and 2 of From Music to Mathematics: Exploring the Connections, homework assignments 1--3, CDs 1--2, and all the material covered in class up to and including Feb. 20. It is highly recommended that you review class handouts, homework problems, lecture notes, the CD liner notes, and your class notes. Many of the problems and questions we discussed in class are excellent examples of test questions.

A set of practice problems is available here. The solutions are available here. The exam will be designed to take 50 minutes although you will have the full 75 minutes to take the exam.

Exam Review: We will review for the exam during a portion of Tuesday's class on Feb. 27th. Please come prepared with specific questions.

Note: No calculators will be allowed for this exam. All questions asked will involve only calculations requiring elementary arithmetic. Also, a portion of a blank piano keyboard containing at least one octave will be provided on the exam for your use.

The following concepts are important material for the exam:

  1. General Music Theory: notation, writing and reading music in different clefs (treble, bass, alto, and tenor), rhythm, time signatures (examples; CD #1), dotted notes and rests (duration), tied notes, polyrhythmic music (examples; CD #1), the piano keyboard, accidentals (sharps, flats, naturals, etc.; correct placement of on the staff)

  2. Scales, Intervals, and Other Important Items from Music Theory: half steps, whole steps, chromatic scale, whole tone scales, major scales, natural and harmonic minor scales, diatonic scale spelling, major and minor chords, dominant-tonic chord progression, 12-bar blues, circle of fifths, key signatures, octave, intervals (m2, M2, m3, M3, P4, tritone, etc.), polyphony and tonality (CD #2), relative major and minor keys, transposition

  3. Mathematical Concepts: geometric sequences and series, infinite geometric series, least common multiple (formula for), greatest common divisor, relatively prime numbers