Math 105: Music & Mathematics
Class Notes & Resources

Final Exam Review Materials

• Copies of Tests
  • Test #3A - Test #3B
  • Test #2A - Test #2B
  • Test #1A - Test #1B
    
• Test Review Sheets
  • Test #1 Review Sheet
  • Test #2 Review Sheet
  • Test #3 Review Sheet
  • Introduction to Sequences
    (content covered after Test #3)

Supplemental Class Notes

UNIT 5: SEQUENCES AND RECURSION

• Introduction to Sequences (added 11/29)

• Sequences Practice Exercises (added 11/29)

• Sequences Practice Exercises Solutions (added 12/5)

• Collected Homework #10 (added 11/29 - due 12/5)

UNIT 4: COUNTING

• Test #3 Review Sheet
  
  

• Collected Homework #9 (added 11/16 - due 11/21)

• Pascal's Identity and Pascal's Triangle (added 11/16)

• Collected Homework #8 - Solutions (added 11/15)

• Counting Practice Exercises - Solutions (added 11/7)

• Introduction to Counting  (added 11/7)

UNIT 3: CHANGE RINGING AND PERMUTATIONS

• Collected Homework #7 - Solutions (added 11/16)

• Permutations Practice Exercises - Solutions (added 11/18)

UNIT 2: VARIATIONS AND GROUPS

• Test #2 Review Sheet (added 10/19)
  
  
• Dihedral group - summary of class discussion (10/18)
  
• Cosets Practice Exercises - Solutions (added 10/19)
• Collected Homework #6 (added 10/14)
• Variations and Groups - Practice Exercise Set 1 (10/10)
• Introduction to "Groups" (10/7)
• Collected Homework #5 - due 10/12
  
  
• Introduction to Modular Arithmetic (10/7)
  
• Modular Arithmetic Practice Problems (10/7)
  
  
• Collected HW #4: Assignment - Solutions (added 10/10)
  
• Variations Practice Exercise Set I (pdf) (10/3)
• Variations Practice Exercise Set II (10/7)
  
• Variations Practice Exercise Set III (10/7)
  
  
• Music "by the numbers" (introduces "musical clock") (added 10/18)
  
• Reading music from a staff (a crash course for non-musicians!) (9/30)
  
  

UNIT 1: TUNING SYSTEMS

• Test #1 Review Sheet (added 9/23)

• Tuning Systems Practice Exercises (added (9/12)
  Covers entire unit on "tuning systems"

• Tuning Systems Practice Exercises - Solutions (added 9/23)
  (Always try the exercises on your own before reading the solutions!)

• Equal Temperament Notes:
  • Introduction to Equal Temperament (added 9/12)
  • Exponents and Logarithms Review (added 9/12)
  • "Making Cents" - summary of methods of measuring widths of intervals (ratios/cents) and converting between them; includes a few practice exercises (added 9/16)
  • Rational Approximation via Continued Fractions (added 9/19)
  • Collected HW #3: Assignment - Solutions (added 9/26)
    
    
• Just Intonation Notes:
  • Introduction to Just Intonation  (added 9/6)
  • Just Intonation Interval Table  (added 9/6)
  • Just Intonation Practice Exercises (added 9/6)
  • Collected HW #2: Assignment - Solutions and Comments (added 9/19)
  
  
• Pythagorean Tuning Notes:
  • Introduction to Pythagorean Tuning (added 8/30)
  • Pythagorean Tuning Practice Exercises (added 8/30)
  • TED Talk: Bobby McFerrin Hacks Your Brain With (Pentatonic) Music (added 9/2)
  • Pentatonic tuning - streamlining computations
  • Pythagorean Tuning Diagram - incomplete (from Fri. 9/2 class)
  • Pythagorean Tuning Diagram - complete diagram (2 octaves), plus notes on the broken, or "wolf," fifth that occurs under Pythagorean tuning
  • Circle of Fifths Diagram (useful for Pythagorean tuning problems)
  • Collected HW #1: Assignment - Solutions and Comments

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.