Math 105: Music & Mathematics
Class Notes & Resources

Most recent update: 5/17/17

TESTS (for review/practice)

• Test #1: blank copy - solutions - review sheet
• Test #2: blank copy - solutions - review sheet
• Test #3: blank copy - solutions - review sheet
  

Practice Exercise sets
(list of all sets of practice exercises, with solutions)

UNIT 4: COUNTING

Test #3 Review Sheet (5/1)

Sequence Practice Exercises - (solutions) (4/28)
Intro to Sequences (4/24)

Pascal's Triangle Practice Exercises (incl. answers) (4/27)
Intro to Pascal's Triangle (4/20)

HW #8 Solutions (4/24)
Counting Practice Problems (4/13)
Counting Practice Problem Solutions - added 4/27
Intro to Counting (4/13)

UNIT 3: CHANGE RINGING / PERMUTATIONS

Practice Exercises: Permutations (4/10)
Cycle Notation (4/13)
Brief Intro to Change Ringing (4/6)

UNIT 2: VARIATIONS

Test #2 Review Sheet (added 3/31)
 
Dihedral group example (from 3/29 class discussion)
HW #6 solutions and comments (added 3/27)
Practice Exercises: Cosets (added 3/27)
Practice Exercises: Cosets -Solutions (added 3/31)
Practice Exercises: Variations, Groups, and Subgroups (added 3/13)
Introduction to Groups (added 3/8)

Modular Arithmetic Practice Exercises (added 3/8)
Combining Variations - Practice Exercises (added 3/8)
Variations Practice Exercises (added 3/2)

UNIT 1: TUNING SYSTEMS

Test #1

• Solutions & Comments (added 3/16)
• Blank copy of test (added 3/16)
• Review Sheet

Tuning Systems Practice Exercises (added 2/10)
Solutions to Practice Exercises (added 2/20)

Section 1.0: Introduction

1.1: Pythagorean Tuning

• Section 1.1: Pythagorean Tuning
  
• Section 1.1.1: Pythagorean Diagrams
  
• Section 1.1.2: Pythagorean Practice Exercises
  
• TED Talk: Bobby McFerrin Hacks Your Brain With (Pentatonic) Music
• Circle of Fifths Diagram
  

Section 1.2: Just Intonation

Section 1.3: Equal Temperament

• Section 1.3: Equal Temperament
• Section 1.3.1: Cents Measurement
• Section 1.3.2: Exponents & Logarithms Review
• Section 1.3.3: Rational Approximation

Useful links:
Piano frequencies diagram: horizontal - vertical
Introduction to Reading Music - Reading Music From A Staff
Free sheet music (PDF)
Free MIDI files

Online Tone Generator

Online Virtual Midi Keyboard

Virtual Piano Keyboard
   (and another virtual keyboard)

Free software:
Two channel frequency generator (from cognaxon.com)
Free Notation Player (freeware from Notation.com)

NOTICE: The course materials I create and distribute for this class are protected by federal copyright law as my original works. You are permitted to take notes of lectures and to use course materials for your use in this course. You may not publicly distribute or display or allow anyone else to publicly display or distribute my course materials or lecture notes without my written permission.