Mathematics and Music

Exam #1

Wednesday, March 1, 11:00 - 12:00 pm

The first exam covers homework assignments 1 - 4, CD's #1 and #2 and all the material covered in class from the first day up to and including Friday, Feb. 24th. It is highly recommended that you review homework problems and your class notes. Many of the problems and questions we discussed in class are excellent examples of test questions.

A sample list of problems is available here. The exam will be designed to take 45 minutes although you will have a full hour to take the exam.

Note: You will be given a scientific calculator for the exam which does NOT have graphing capabilities so be prepared to answer questions without your personal calculator.

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 signature (CD #1), dotted notes (duration), polyrhythmic music, piano keyboard
  2. Scales and Intervals: half steps (semi-tone), whole steps (whole-tone), chromatic scale, whole tone scale, major scale, natural and harmonic minor scales, circle of fifths, key signatures, octave, intervals (2nd, 3rd, 4th, tritone, etc.), polyphony and tonality (CD #2)
  3. Musical Group Theory: translations (transpositions), vertical reflection (retrograde), horizontal reflection (inversion), know some examples of each, know how to apply each transformation to a given melody (for example, transpositions are covered in Ch. 5 of Music Kit, HW #3)
  4. Sound: sound as change in air pressure, attributes of sound (amplitude, frequency, timbre and duration), the incredible ear-brain system, oscillograph plots, hertz, decibels
  5. Mathematics of Sound: sine waves, basic trigonometry, sketching sine waves, the harmonic oscillator, pitch as frequency, resonance, beats (general rule of), the wave equation
  6. Pitch, Frequency and Length: how ratios relate to pitch (for example, taking 1/2 the length of a string or doubling the frequency raises the pitch an octave), the Pythagorean scale, the Pythagorean comma, the overtone series, why certain intervals sound "nice" together
  7. Mathematical concepts: geometric sequence and series, infinite geometric series, least common multiple, trigonometry (sine function, graphing, attributes of a sine wave, period, frequency, identities, etc.)

Exam Review: We will review for the exam during Monday's class, Feb. 27th. Please come prepared with specific questions.