Course Profile

Goals of the Course

The goal of the course is to give students the practical skills and acoustical background to build musical instruments of their own design. Underlying this goal is 1) to enhance the musical background students already have by giving them a deeper understanding of the theoretical acoustic principles of musical instruments and 2) to introduce engineering tools and concepts (in the context of musical instrument design) to an audience that may not otherwise be exposed to such techniques.

Who is it designed for?

The course is available to all Yale College students. It is designed for any student with interest in how musical instruments work and can be built user modern engineering and “maker” technology.

Learning Objectives

On the theoretical side, the students learn about the physical acoustics of string, wind, and percussion instruments: sound propagation, standing waves, traveling waves, harmonic series, spectral analysis, etc. They also learn about musical tuning systems, and electronic music synthesis.

On the practical side, they learn how to use the tools necessary for designing and building devices in the physical and electronic realm.

Maker skills it develops

The students become proficient in hand tools, laser cutters, 3D printers, machine shop tools, SolidWorks design and simulation tools, basic electronics including microprocessors, sensors, and actuators. They also learn to use sound recording and analysis equipment.


Basic knowledge or interest in music or musical instruments. Solid background in math through pre-calculus, with knowledge of calculus preferred. Basic knowledge of physics including Newton's Laws and concepts of kinetic and potential energy. Students must become members of the Yale Center for Engineering Innovation and Design (CEID) by the end of the first week of class.

Skills, Tools and Technologies Used

During the lab portion of the course, the students are trained in the areas mentioned above (in hand tools, laser cutters, 3D printers, machine shop tools, SolidWorks design and simulation tools, basic electronics including microprocessors). These tools are formally introduced with instruction provided as a component of the class.

Key Examples and Prior Work

This course is taught in the Center for Engineering Innovation and Design ( which is an academic makerspace at Yale that innovates in the area of human-centered design and engineering. Hence, this course borrowed many ideas from earlier courses in its pedagogical philosophy. One specific example would be the Yale CEID course “Engineering, Innovation, and Design,” which also teaches students practical maker skills (along with more typical engineering and design concepts) and culminates with a client-based project.

Key Resources

Resources come from a variety of areas. We refer when appropriate to the following texts:

Bart Hopkins , Making Simple Musical Instruments. Altamont Press, 1995.

Rossing, Thomas. The Science of Sound. Addison-Wesley, 2001.

The Science of Musical Sound, Vol 1. William Ralph Bennet, Jr.

Armstrong, Newton. An enactive approach to digital musical instrument design: Theory, Models, Techniques. AV Akademikerverlag, 2012.

The students also take advantage of Solidworks tutorials, tutorials for spectral analysis freeware, as well as guides developed in the CEID for use of the laser-cutter, 3D printers, etc.

Some resources are presented in class and posted online such as excel worksheets for looking at Fourier analysis and wave propagation, as well as modeling of instrument tuning and tuning systems.

Example Assignment

The students used the laser-cutter to construct a single-string instrument with fret positions at many exact integer ratios of the string length. They measured the frequencies and frequency ratios of all the possible fretted positions and also measured the string density and tension. This lab taught the students how to actually make a simple instrument (which in the second half of the lab they generalized to a 4 string instrument of novel design), but also taught them about the rules for tuning strings as well as the ideas involved in different tuning methods (equally-tempered versus just). It was a great example of “learning by making.”

Lessons Learned

Quite simply, by interleaving theoretical concepts with active “making,” we learned that students could achieve a more profound understanding of material then if either was done alone. For example, a student may understand theoretically that the frequency of a wooden bar is proportional to its inverse length squared, but when they must cut one to size to achieve a musical note, the idea comes very much alive!