Musical Sound Clips
Figure 2: Analysis of piano notes using analyze.m
Download .wav sound file of a piano playing:
A0 A1 A2 A3 (low A) A4 (middle A) A5 (high A)
Figure 3: Analysis of several instruments using analyze.m
Download .wav sound file of instruments playing A4 (middle A):
tuning fork flute violin singer
Sound Library includes clips of numerous musical instruments and sounds.
Also see www.findsounds.com
Solutions to Selected ExercisesDownload exercises
Other Resources"Mathematical Harmonies" is a presentation I have given in both highschool and college classrooms. The mathematics of vibrating strings is presented in terms of sine functions instead of Fourier Series and differential equations, as in the CMJ article. Items in pdf format include:
Frequency of each note on a piano. Harmonics of A are shown below as vertical lines.