Applied Mathematics for Musicians


Authored by Kevin Block-Schwenk


Course Code: OLMSC-130

Next semester starts September 23

12 Weeks

Level 1

Level 1

3-Credit Tuition


Non-Credit Tuition


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 and to build your own knowledge of, and confidence in, math in practical ways that relate directly to the world of music.

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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
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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


Prerequisites and Course-Specific Requirements 

Prerequisite Courses, Knowledge, and/or Skills
This course does not have any prerequisites


  • No textbooks required


  • Recommended: Scientific calculator (hardware or software)

Student Deals
After enrolling, be sure to check out our Student Deals page for various offers on software, hardware, and more. Please contact with any questions.

General Course Requirements

Below are the minimum requirements to access the course environment and participate in Live Classes. Please make sure to also check the Prerequisites and Course-Specific Requirements section above, and ensure your computer meets or exceeds the minimum system requirements for all software needed for your course. 

Mac Users

PC Users

All Users

  • Latest version of Google Chrome
  • Zoom meeting software
  • Webcam
  • Speakers or headphones
  • External or internal microphone
  • Broadband Internet connection


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 Applied Mathematics 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.

EvaE Peart


EvaE Peart is a passionate educator and performer. She has a Bachelor of Science degree in Mathematics and Computer Science from The University of Saint Joseph and a Master’s in Educational Leadership from Central Connecticut State University. Prior to joining the Math Department at Berklee College, EvaE was a high school math teacher in Bloomfield, CT where she also coached varsity soccer, tennis, and dance for almost a decade. In 2014, she founded Nia Arts which is an organization that brings performing arts enrichment to communities with limited access to cultural movement and music. Nia is a Swahili term and the fifth of seven Kwanzaa principles which means purpose. Nia Arts aims to educate and entertain people of all ages and backgrounds with the purpose of creating a community which appreciates the many facets of art, the African Diaspora, and its impact on society. 

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Currently, EvaE works as a math specialist and teacher coach in New York City with a program which services over-aged and under credited individuals who have survived or are dealing with trauma. As an educator, EvaE believes that understanding mathematical practices are essential to everyday life and building a successful career. Read Less

Matthew Smith


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

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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. Read Less

Katrina Jackson


Katrina Jackson is a Mathematics teacher, Mother of four children, freelance Model and a Mentor to young men and women in the community. Katrina has been teaching mathematics for the past 20 years in the Boston Public Schools district at John D. O'bryant High School, Young Achievers (k-8), English High School, Dorchester Academy, Charlestown High School and Community Academy.  Since 2015, she has also been tutoring students with their math courses and teaching summer enrichment math to high school students enrolled in Artward Bound at Mass College of Art.  Katrina has experience teaching courses that cover middle school mathematics, through advanced calculus concepts, using Massachusetts curriculum frameworks.  These topics include but are not limited to manipulating integers, solving multi-step equations, determining geometric angles and properties, and calculating derivatives. Katrina has integrated  Arts and Technology into her curricula over the years and looks forward to sharing her love of Math and the Arts with the Berklee Online students. 


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