The final exam is CUMULATIVE, that is, it covers all the material from the first day of class onwards. This does not include The Immortal Life of Henrietta Lacks. The goal is for you to synthesize knowledge from the entire course, bringing together common themes and subject material. It is highly recommended that you review homework problems, your class notes, handouts, the Monochord lab, CD liner notes, the midterm exams and midterm review sheets. Many of the problems and questions we discussed in class are excellent examples of test questions.

A sample list of problems is available here along with partial solutions. The exam will be designed to take 1.5 - 2 hours although you will have the full 2.5 hours to take the exam. 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.

Exam Review: We will review for the exam on Monday, Dec. 13, 9:30 - 11:00 am in Brooks 454 (both sections). Please come prepared with specific questions.

The following concepts are important material for the exam:

1. General Music Theory: notation, writing and reading music in different clefs (treble and bass), rhythm, time signature (CD #1), dotted notes and rests (duration), accidentals (sharps, flats, etc.), 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), transposition, relative major of a minor key


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


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


5. The Three Tuning Systems: Pythagorean scale, Just Intonation, Equal Temperament, strengths and weaknesses of each system, the overtone series, rational versus irrational numbers, Pythagorean comma, syntonic comma, cents, why certain intervals sound "nice" together, how to find the frequency of a given note for a given tuning system (eg. G above middle C), relationship between length of a string and pitch produced (eg. 1/2 the length of a string raises the pitch an octave), Monochord Lab


6. Strahle's Guitar Construction: general set up in order to place the frets, basics behind why it works, continued fractions, linear fractional transformations (LFT)


7. Other Mathematical Concepts: geometric sequence and series, infinite geometric series, least common multiple, greatest common divisor, relatively prime numbers, logarithms, trigonometry (sine function, graphing, unit circle, radians, attributes of a sine wave, period, frequency, amplitude, phase shift, identities, etc.), using multiplication to find the frequency of a given note, ratios, irrational versus rational numbers (know the proof that the square root of 2 is irrational)