This paper describes a fascinating connection between the physics of music and the famous chord in the dissonant rhythmic section of Stravinsky's "The Rite of Spring" (1913). The analysis of Stravinsky's chord will draw from the physics of harmonics, musical intervals, mathematics, and cognitive psychology. This highly interdisciplinary…

Harmonics arise naturally from the resonances in strings and pipes. A video demonstration (Ruiz 2016 "YouTube: Tuba Harmonics" (https://youtu.be/souhEzOP9c4)) is provided where a tubist (coauthor Holmes) produces a phenomenal 24 harmonics using a single tuba pipe length by controlling the buzz of his lips. The frequencies of the…

The French horn is used to introduce the three basic properties of periodic waves: amplitude, frequency, and waveform. These features relate to the perceptual characteristics of loudness, pitch, and timbre encountered in everyday language. Visualizations are provided in the form of oscilloscope screenshots, spectrograms, and Fourier spectra to…

Students in introductory physics courses encounter harmonics when they study standing waves on strings and in pipes. The Fourier spectrum, which plots amplitude against harmonic number, can describe all periodic tones imaginable. However, most sounds are aperiodic and therefore have additional spectral components. A real-world application that…

The basic physics of the flute is presented from the perspective of a professional flutist. The flutist can control loudness, pitch and to some extent timbre. Oscilloscope images are provided to compare changes in these three fundamental sound characteristics. Readers can view a video (Ruiz 2017 "Video: The Flute"…

We have developed an online oscilloscope program which allows users to see waveforms by utilizing their computer microphones, selecting from our library of over 30 audio files, and opening any *.mp3 or *.wav file on their computers. The oscilloscope displays real-time signals against time. The oscilloscope has been calibrated so one can make…