Mathematics and Music

Exam #1

Wednesday, February 28, 10:00 - 11:00 am

The first exam covers homework assignments #1 - 4, CD #1 and #2, and all the material covered in class from the first day up to and including Friday, Feb. 23rd. This includes any readings that were assigned as part of homework assignments. 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. 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, Feb. 26th. 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.

The following concepts are important material for the exam:

1. General Music Theory: notation, writing and reading music in treble and bass clefs, 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 (m2, M2, m3, M3, P4, tritone, etc.), polyphony and tonality (CD #2)

3. Musical Group Theory: translations (transpositions) and vertical reflection (retrograde), musical examples of, how to apply a transformation to a given melody (for example, transpositions are covered in Ch. 5 of The Music Kit, HW #3 and you wrote Mary Had a Little Lamb in retrograde on HW#2)

4. Sound: sound as change in air pressure, attributes of sound (amplitude, frequency, timbre and duration), the incredible ear-brain system, oscillograph plots, decibels, hertz

5. Mathematics of Sound: logarithms, sine waves, basic trigonometry, trig identities, sketching sine waves, the harmonic oscillator, pitch as frequency, resonance, beats (general rule of)

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, greatest common divisor, logarithms, trigonometry (sine function, graphing, unit circle, radians, attributes of a sine wave, period, frequency, amplitude, phase shift, identities, etc.)