Math, Music and Memory

Exam #2

Wednesday, December 3, In Class

The second exam covers Chapters 3 and 4 of A First Course in Math and Music, homework assignments 5 and 6, the Monochord Lab, and all the material covered in class since the first exam up to and including Nov. 24. 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 set of practice problems is available here along with solutions. The exam will be designed to take 45 minutes although you will have a full hour to take the exam.

Exam Review: We will review for the exam during Monday's class on Dec. 1. Please come prepared with specific questions.

Note: You will be allowed a scientific calculator for the exam which does NOT have graphing capabilities. Please bring your own scientific calculator to the exam.

The following concepts are important material for the exam:

  1. Sound: sound as change in air pressure, attributes of sound (loudness, pitch, timbre and duration), the incredible ear-brain system, sound intensity and decibels (dB), frequency and hertz (Hz)

  2. Mathematics of Sound: logarithms, sine waves, basic trigonometry, trig identities, sketching sine waves, period and frequency, resonance

  3. Pitch, Frequency and Length: residue pitch, how ratios relate to pitch (for example, taking 1/2 the length of a string, or doubling the frequency, raises the pitch an octave), Monochord Lab, overtone series

  4. The Three Major Tuning Systems: the Pythagorean scale, just intonation, equal temperament, strengths and weaknesses of each system, the spiral of fifths, frequency ratios or multipliers, overtone series, rational versus irrational numbers, Pythagorean comma, syntonic comma, cents, how to find the frequency of a given note using ratios or multipliers (e.g., G above middle C)

  5. General Music Theory: notation, writing and reading music in different clefs (treble and bass only), piano keyboard, half steps and whole steps, major scale, circle of fifths, octave, intervals (2nd, 3rd, 4th, tritone, major, minor, perfect, etc.)

  6. Mathematical Concepts: logarithms, trigonometry (sine and cosine functions, graphing, unit circle, radians, period, frequency, amplitude, phase shift, identities, etc.), greatest common divisor, multiplication or division to find the frequency of a given note, working with ratios, rational and irrational numbers (you will NOT be asked to prove the square root of 2 is irrational)