Harmonic Overtone Series Lesson Plan

The harmonic overtone series is essentially related to music performance, but may easily be overlooked in music lessons or classes. Lesson plan material is available in several books on the science of music offered by Schottenbauer Publishing. Relevant information includes calculations, diagrams, graphs of real data from various musical instruments, and graphs calculated from mathematical formulas.

Consider the following pages, excerpted from Where Does Sound Come From? Volume 1 (Copyright 2014, All Rights Reserved). 

Discussion Questions

1. Identify the relationship between harmonics and overtones, using words.
2. Express the relationship between harmonics and overtones, using a mathematical formula.
3. Draw a three-octave keyboard on paper, using a light gray color for the black keys. Make 12 copies on a printer or copier. Label each page on the top with a different chromatic note (A, A#/Bb, C, etc.). Starting on each chromatic note, color the entire harmonic overtone series. List the names of each note on the keys.
4. Using a keyboard, any musical instrument, or voice, practice playing each harmonic overtone series. Begin on the lowest note possible, to ensure enough range to complete the task.

The resources below provide additional sources of information for learning about harmonics and the overtone series:

Auditory Demonstration of Harmonics

• YouTube Video
• Introduction to the Harmonic Overtone Series 
• Audio Recordings
• Multimedia Ear Training Program

Math of Harmonics & Tuning Systems

• Mathematical Formulas
• Appendices, Where Does Sound Come From? Volume 2
• Graphs
• Appendices, Where Does Sound Come From? Volumes 1, 3, & 4

Additional Information

Schottenbauer Publishing

Free Education Resources

Understanding the Harmonic Overtone Series

The harmonic overtone series describes the science of the relationship between notes in the Western harmonic system. Harmonics are most obvious on string instruments, brass instruments, and the flute, which easily demonstrate the relationship between the lowest note, the octave above, and the perfect fifth above the octave, plus many of the other harmonic overtones in the series.

Did you know that harmonics are present in all naturally-produced notes, sounding softly in addition to the fundamental tone? It is not obvious to many listeners. A free YouTube video from the publisher, Introduction to the Harmonic Overtone Series demonstrates harmonic overtones on several instruments. A mathematical expression of the combination of harmonics is presented in graphical form in the appendices of Where Does Sound Come From? Volumes 1, 3, & 4. A mathematical analysis of several prominent tuning systems is included in the appendices of Where Does Sound Come From? Volume 2. 

Additional Information

Schottenbauer Publishing

Free Education Resources

The Science of the Harmonic Overtone Series

The harmonic overtone series is a basic concept in music education which explains how many musical instruments function. It is easiest to explain the harmonic overtone series with science and math. New teaching tools from Schottenbauer Publishing offer students a refreshing insight into the working of the harmonic overtone series. 

The graphs below are excerpted from Volume 1 of Where Does Sound Come From?, as well as a free pamphlet from the publisher. These graphs show graphs of sound pressure from two notes performed on a soprano recorder.

Discussion Questions

1. Describe at least 2 differences between these two graphs.
2. What types of information are contained in each graph?
3. If possible, identify the frequency, wavelength, and/or amplitude of the wave in each graph.
4. Is it possible to determine the pitch of the note from either graph? If so, how?
5. Is it possible to determine the sound level (decibels) of the note from either graph? If so, how?
6. Are these two graphs related in the harmonic overtone series? If so, how?
7. Write a mathematical equation to describe the wave pattern in the bottom graph.

In addition to these graphs, a free YouTube video from the same publisher provides a brief lecture, as well as samples of the harmonic overtone series on flute, trumpet, trombone, and violin. 

Students may learn more about the harmonic overtone series in a multimedia training program titled Ear Training: Harmonic Overtone Series. Additional information is available on the Music Theory & Ear Training blog.

Additional graphs on the science of music and music performance can be found in a free pamphlet from the publisher, and the following book series by M. Schottenbauer, Ph.D. The books below contain data from common band and orchestral instruments, plus recorders, keyboard, voice, and conducting. 

• Where Does Sound Come From?

• How Do You Play That Thingamabob? The Science of Music Performance

• The Science of Music: An Anthology of 28 Graphs for Kids,Teens, & Curious Adult

• Bow Science & Exercises for the Violin & Viola

Additional Information

Schottenbauer Publishing

Free Education Resources