Consider the following pages, excerpted from Where Does Sound Come From? Volume 1 (Copyright 2014, All Rights Reserved).
- Identify the relationship between harmonics and overtones, using words.
- Express the relationship between harmonics and overtones, using a mathematical formula.
- 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.
- 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
- Audio Recordings
Math of Harmonics & Tuning Systems
- Mathematical Formulas
- Appendices, Where Does Sound Come From? Volume 2
- Appendices, Where Does Sound Come From? Volumes 1, 3, & 4