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Instructor Information

Dr. Charles Redmond


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Course Description

8 AM to 11 AM, MTWThF

Computer Labs in the basement of Old Main

The Mathematics Applications courses are new this year. In creating these courses, our aim was to give students an opportunity to explore a single application of mathematics, in depth.

This course consists of three components. One, of course, is mathematical. You will learn about the sine, square, triangle, and sawtooth waves and their relationships to sound and music. The logarithmic and exponential functions will also be discussed, along with their relationship to musical intervals. Piecewise defined functions will be covered in the context of sound envelopes. We will touch on function multiplication and composition through study of AM and FM modulation. And we will even visit additive and subtractive synthesis via Fourier Analysis.

We will not, however, abandon these concepts without putting them to use. You will be able to apply everything you learn and create your own sounds/music/songs. I will introduce you to Reason, a digital audio workstation, and also Band-In-A-Box, a very advanced piece of songwriting software. We will learn how to write drum tracks, bass-lines and chordal accompaniment, and how to apply effects and automation.

Finally, we will also be able to test our newfound mathematical knowledge and musical ideas with a true music programming language (ChucK). In today's world, knowledge of programming can give one a significant advantage, and I consider programming as equal to mathematics in its power to develop problem solving ability and logical reasoning in those who pursue it. For some of you, this may very well be the most important component of the course. We will learn about some basic programming fundamentals, such as variables, loops, arrays, functions, objects and conditional statements.

Grades will be based on two exams and a project. I will try to give you as many small, practice questions and tests as I can to prepare you for the exams.

Course Objectives

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Students will:

  • identify the period, frequency, and amplitude of sine waves;
  • use the exponential function to determine frequency;
  • use the logarithmic function to determine cents;
  • graph sine, exponential, and logarithmic functions by hand and with winplot;
  • construct sound envelopes by hand, with winplot and ChucK, and in Reason;
  • approximate the square, triangle, and sawtooth waves with sine waves, in both winplot and ChucK;
  • demonstrate knowledge of AM and FM modulation with winplot, Reason, and ChucK;
  • compose drum tracks with Reason;
  • demonstrate understanding of harmony by composing musical accompaniment in Reason;
  • automate parameters in Reason;
  • apply effects in Reason;
  • generate chord sequences in Band-In-A-Box;
  • write simple programs in ChucK demonstrating the use of variables, loops, if/then statements, functions, arrays, and objects;
  • algorithmically compose music with ChucK.
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Project Details

Your project must be an originally composed song or sequence of sounds, the duration of which must be at least one minute. You must also include a short write-up (a few paragraphs at most), describing how you created your sounds/song. Tell me what tools you used, what instruments you used, and what key and chords you used. Tell me what effects you used and whether or not your composition has an algorithmic aspect.

I would like everyone to sign up for an account on SoundCloud and post her/his project. I will give more details on this in class. SoundCloud's website is located here:

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All of the software you will need for the course will be in our labs, so you are not required to purchase anything. If you are, however, interested in purchasing any of the software for your own use at home, here is the information for it:

For a digital audio workstation, we will be using Reason Essentials. The latest version is version 2. This is available via download from Propellerhead (for about $125.00). Here is their website:

Previous boxed versions of Reason Essentials are available from various venders. These are generally less expensive than the download from Propellerhead.

We will also be using Band in a Box, from PGmusic, as a songwriting tool. They offer various packages, and it can get quite confusing. Band-In-A-Box is very expensive, and we will not be using it very much. It would be best to simply use it in our labs. Their website is located here:

The programming language we will be using is called ChucK. You can download it for free from here:

We will also be using the audio editing software Audacity. This is free, and is available here:

If you want to export MP3's with Audacity, you also have to have the LAME MP3 encoder. You can find it here:

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Suggested References

There is no required text for the course. There are, however, some excellent references I can share with you:

  • Who Is Fourier? A Mathematical Adventure 2nd Edition by Transnational College of Lex. (2012).
  • Electronic Music and Sound Design - Theory and Practice with Max and MSP - Volume 1(Second Edition) by Alessandro Cipriani and Maurizio Giri. (2013).
  • Mathematics and Music (Mathematical World) by David Wright. (2009).
  • Dance Music Manual: Tools, Toys, and Techniques by Rick Snoman. There is a new edition coming out in 2013, but previous editions are available.
  • Dance Music Production by Rick Snoman. This is a website, found here: There are many helpful videos offered for sale.
  • The Songwriting Sourcebook: How to Turn Chords into Great Songs by Rikky Rooksby. (2011).
  • How to Write Songs on Keyboards - A Complete Course to Help You Write Better Songs by Rikky Rooksby. (2005).
  • Melody in Songwriting: Tools and Techniques for Writing Hit Songs by Jack Perricone. (2000).
  • Composition for Computer Musicians by Michael Hewitt. (2009).
  • Reason 6 Ignite!: The Visual Guide for New Users by G.W. Childs. (2011).
  • Going Pro with Reason 6.5 by G.W. Childs. (2013).
  • Mixing Secrets for the Small Studio by Mike Senior. (2011).
  • Producing and Mixing Hip-Hop/R&B by Mike Hamilton. (2009).
  • The Drumset Style Resource: A Comprehensive Guide to Exploring New Techniques and Styles from Hip-Hop to Jazz by Pete Sweeney. (2012).
  • The Breakbeat Bible by Mike Adamo. (2010).
  • Bass Grooves: Develop Your Grooves and Play Like the Pros in Any Style by Ed Friedland. (2004).
  • Building Rock Bass Lines: A Solid Foundation for the Rock Bassist by Ed Friedland. (2003).
  • Blues Piano for Beginners by Mark Harrison. (2011).
  • Pop Ballad Piano for Beginners by Mark Harrison. (2012).
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Office Hours

All of my office hours will be in the computer lab. In order to best accomidate both your schedules and mine, I like to be flexible with my office hours. If you need to see me, let me know, and we can find a time that works for both of us. If, at the end of the week, I have not fulfilled my quota of office hours, I will have some hours over the weekend, a time most students have available. I will of course announce, each week, when those hours will be.

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It is very important that you make every effort to attend class. I will take attendance every day so that I know who attends and who does not. Remember, a prerequisite for additional help outside the classroom is regular class attendance. You are responsible for what is announced or covered in class even if you are absent.

Because I will undoubtedly have several absences each day, I cannot re-teach lessons to those who miss. Get to know your classmates. If you miss class, get the notes, study the notes, and try the homework. See me then with your questions.

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We will have a midterm exam, a final, and a project. The midterm and final will each be worth 50% of your grade. Your project will be graded Pass/Fail. If you fail to complete the project, according the the directions given on this syllabus and in class, your final grade will be reduced by one level, e.g. C+ down to C. Letter grades will be assigned according to the following scale:

  • 94%-100% A
  • 90%-93.99% B+
  • 84%-89.99% B
  • 78%-83.99% C+
  • 70%-77.99% C
  • 65%-69.99% D+
  • 60%-64.99% D
  • 0%-59.99% F

Working the sliders below will help you understand what combinations of scores will result in particular letter grades.

0% midterm

0% final

F letter grade

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Learning Differences

Any student who feels s/he may need an accommodation based on the impact of a disability should contact us privately to discuss your specific needs. Please know that it is the policy of Mercyhurst University that it is the student's responsibility to provide documentation of his/her disability to the director of the Learning Differences Program. Please call the Learning Differences office at 814-824-3017 to coordinate needed accommodations.

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Tentative Schedule

Day Topic
Week 1 Sine waves, intro to Reason, intro to ChucK
Week 2 Randomness in ChucK, while loops, piano notes, properties of logs and exponents
Week 3 Logarithmic and exponential functions, frequencies, cents, musical keys
Week 4 Circle of fifths, musical keys revisited, recording, transposing, and mastering in Reason, wav and mp3 files, SoundCloud
Week 5 Material Review
Week 6 Midterm Testing
Week 7 Musical intervals, chords, algorithmic composition with ChucK
Week 8 Piecewise defined functions and envelopes
Week 9 Square, triangle, and sawtooth waves, Fourier Analysis
Week 10 Square, triangle, and sawtooth waves, Fourier Analysis II
Week 11 Filters and automation
Week 12 Amplitude and frequency modulation
Week 13 Material Review