Applied Mathematics for Musicians

Author: Kevin Block-Schwenk   •   Course Code: OLMSC-130

Math is a vital skill for anyone in, or aspiring to be in, the music industry. From understanding music publishing deals and royalty statements to applying music theory and music production concepts, math can help you enormously. For many of us, though, math is something that’s preferably avoided or best left to someone else. Applied Mathematics for Musicians is designed to change that—to build your own knowledge of, and confidence in, math in practical ways that relate directly to the world of music.

The course explores fractions, percentages, proportions, averages, and algebra, in addition to exponential and logarithmic equations. A focus is placed on real-life applications, with the mathematics, itself, a means to achieving an end. For example, you will use fractions to determine whether notes are consonant, algebra to determine minimum ticket sales to earn a certain amount at a show, exponential equations to determine the frequencies of notes in various tuning systems, and logarithms to determine decibel levels. In addition, the course provides an overview of the mathematics underlying personal and business finances, which will help you make better decisions about your financial future.

The course is designed specifically for those who find math intimidating or who feel that their math skills have become “rusty.” The course is action-oriented. It will walk you through math problems and how to solve them, and then ask you to try your hand at them. The course is based on a similar offering taught at Berklee’s Boston campus, where this learn-by-doing approach has been very effective.

The connection between music and math is strong—. Research has shown that the same area of the brain that processes music is also responsible for mathematical thinking. The goal of this course is to make that connection real for you, so that you walk away with practical knowledge that better inform your decisions and work in the music industry. By the end of the course, your math skills will be well-honed, allowing you to use math to solve any relevant problems that crop up.

For those students lacking a background in math and interested in pursuing a bachelor of professional studies degree in music business through Berklee Online, this course serves as a prerequisite for Music Business Finance, a required course in the major.

By the end of the course, you will be able to:

  • Relate fractions to music
  • Use algebra as a predictive tool, such as in predicting ticket sales
  • Achieve a greater appreciation for scale, useful when understanding finances
  • Calculate the value of assets
  • Assess the utility of potential investments
  • Apply geometric series to compound interest
  • Describe mathematics related to debt and loans
  • Employ exponents to calculate the frequencies of notes in various tuning systems
  • Use logarithms to determine decibel levels
  • Translate word problems into algebra, via translating key words and phrases into mathematics
  • Describe and apply the iterative process, which is useful for solving both mathematical equations and non-mathematical life situations

Lesson 1: Basic Calculations and Operations

  • Scientific Calculator
  • The Order of Operations
  • Fractions and Some Applications
  • Sound Application of Fractions
  • Multiplying Fractions
  • Dividing Fractions
  • Adding and Subtracting Fractions
  • Converting Fractions to Other Forms: Decimals
  • Converting Fractions to Other Forms: Mixed Numbers

Lesson 2: Percentages, Time, and Handling Unusual Numbers 

  • Rounding Numbers
  • Rounding Decimal Numbers
  • Special Cases of Rounding
  • Units of Time
  • Other Measurements
  • Percents
  • Percent Changes: Calculating a Percent Change
  • Calculating the New Value When Given a Percent Change

Lesson 3: Expectations and Breaking Even 

  • Probability of Something Happening
  • Complementary Events
  • Probability and Independent Events
  • The Probability of One of Several Independent Events
  • Probability and Dependent Events
  • Single Linear Equation Algebra
  • Multiplied Variables
  • Algebraic Order of Operations
  • Knocking Out a Variable
  • Iteration
  • Using Iteration

Lesson 4: Proportions, Averages, and Rates of Change

  • Direct Proportions
  • Imperfect Proportions
  • Inverse Proportions
  • Averages
  • Rearranging the Averages Formula
  • Using Averages in Calculations
  • Average Rate of Change
  • Points and Slopes
  • Lines and Slopes
  • Average Slopes

Lesson 5: Substitution, Significant Figures, and Scientific Notation

  • Substitution
  • Single Number Substitution
  • Substitution with a Coefficient
  • Substitution with Added Algebra
  • Substitution: Both Variables in Both Equations
  • Substitution: The Final Variant
  • Significant Digits and Accuracy
  • Scientific Notation

Lesson 6: Exponents and Equal Temperament Tuning

  • Exponents
  • Exponents as Fractions
  • Multiplying Two Numbers with the Same Base
  • Raising a Power to Another Power
  • Terms
  • Exponents and Algebra
  • Canceling Exponents
  • Order of Operations
  • Equal Temperament Tuning
  • Overtones
  • Calculating Frequencies
  • Fundamental Frequencies
  • Calculating the Error
  • Why an Octave is Broken into Exactly Twelve Half-Steps
  • Twenty-Four Half Steps

Lesson 7: Harmonic Series, Just Intonation, and Pythagorean Tuning 

  • The Harmonic Series
  • Tuning to a Specific Key
  • The Harmonic Series Vs. Equal Temperament Tuning
  • Harmonic Series Frequency Ratios
  • The Harmonic Series in A
  • Tuning to Notes vs. Octaves
  • Changing Octaves
  • Calculating Fundamental Frequencies
  • Why is the Harmonic Series Tuned to a Specific Key?
  • Calculating the Error
  • Intervals
  • Tuning to Other Keys in the Harmonic Series
  • Just Intonation
  • Calculating Fundamental Frequencies in Just Intonation
  • Pythagorean Tuning
  • Calculating Fundamental Frequencies in Pythagorean Tuning
  • The Pythagorean Comma

Lesson 8: Geometric Sequences and Financial Math Part One 

  • Geometric Sequences
  • Terms
  • Non-Geometric Sequences
  • Designating the Octave
  • Finding the Value of the nth Term
  • Using the Scientific Calculator
  • Calculating r and g Without Knowing the First Term
  • Financial Math: The Basic Equation
  • Rounding
  • Deriving the Formula
  • Interest Earned or Charged
  • Adjusting for Inflation"Real" Values
  • Financial Statements
  • Present Value
  • Present Value of Multiple Amounts and Times

Lesson 9: Geometric Series, Rate of Return, and Asset Value

  • Infinite Geometric Series
  • Zeno's Paradox
  • The Sum of an Infinite Geometric Series
  • Using Infinite Geometric Sequences
  • Rate of Return
  • Total Rate of Return
  • Investment Strategy and Payback Time
  • Asset Value
  • Asset Prices

Lesson 10: Debt

  • Mortgages and Loans
  • Calculating Payment Size
  • Debt vs. Time
  • Early Payments on a Loan
  • Decay Curve
  • Interest-Only Loans
  • Calculating Payments
  • Debt vs. Payoff Time
  • Bankruptcy Danger
  • Balloon Loans
  • Prepayment Penalties

Lesson 11: Logarithms and Mathematical "Ear Training"

  • Logarithms
  • Calculations
  • Using Logs in Financial Math
  • Financial Problems
  • Growth Problems
  • Using Logs in Music
  • Calculating Note from Frequency
  • Notes and Cents

Lesson 12: Decibels and Sound

  • Sound Energy
  • Decibels
  • Sound Energy Ratios
  • Using Exponents to Find Ratios
  • Using Logs to find Decibel Levels
  • Decibels and Our Ears
  • Calculating How Much Louder We Hear

Kevin Block-Schwenk

Author & Instructor

Kevin Block-Schwenk is an associate professor of Liberal Arts at Berklee College of Music, where he has taught mathematics courses for musicians since 2005. In addition to creating Berklee Online’s Math for Musicians course and teaching it since its completion in 2013, Kevin operates a small real estate business. He received his B.A. in Economics from Brandeis University and his M.Ed. in Mathematics Education from the University of Massachusetts at Boston. He lives in Boston with his wife and five cats, and enjoys biking, games, history, vegan cuisine, and being on the receiving end of music.


Matthew Smith

Instructor

Matthew Smith is an assistant professor of liberal arts at Berklee College of Music, where he has been teaching courses in mathematics, statistics, acoustics, Logic and programming since 2011.

He received a BA in mathematics from Northwestern University, a Certificate of Advanced Study in mathematics from the University of Cambridge, and an MA and PhD in mathematics from the University of Michigan.

He is an enthusiastic amateur pianist, harpsichordist, organist, and violinist, a regular audience member in Boston's concert halls, and has been known to dabble in composition, transcription, and MIDI sequencing.


Mary Beth Valuk

Instructor

Mary Beth Valuk teaches at Berklee Online.

Prerequisites

None required


No Required Textbooks


Software Requirements

Mac Users

  • OS X 10.9 Mavericks or higher (click here for system requirements)
  • Latest version of Google Chrome

Windows Users

  • Windows 7 or higher (click here for system requirements)
  • Latest version of Google Chrome

Hardware Requirements

  • A scientific calculator is recommended
  • 2 GB RAM (4 GB recommended)
  • 500 MB hard drive space
  • Speakers or headphones
  • Webcam
  • Internet connection with at least 4 Mbps download speed ( http://www.speedtest.net to verify or download the Speedtest by Ookla app from your mobile app store)

Comments

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  • Level
    Level 1
  • Duration
    12 weeks
  • 3-Credit Tuition
    $1,479
  • or
  • Non-Credit Tuition
    $1,229

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