An Introduction to Music Technology, 2nd Edition by Dan Hosken

Chapter 3: The Overtone Series and the Spectrum View

Examples

Harmonic Spectrum of a trombone note [YouTube video]—Notice: 1) the higher partials drop more than the lower partials when the note becomes quieter (after the decay phase of the ADSR-type envelope), 2) the partials are whole number multiples of the fundamental frequency making this a harmonic timbre, 3) the fundamental frequency here does not have the greatest amplitude. The frequency axis is logarithmic (equal horizontal space is given to equal intervals), so the partials are not visually spaced evenly.

Spectra of basic waveforms [YouTube video]—The spectra of basic waveforms: sine, triangle, square, and sawtooth. The sine wave has a single partial (the fundamental); the triangle wave has only odd harmonic partials with relatively small amplitudes proportional to one over the square of the partial number; the square wave also has only odd harmonic partials, but the amplitudes are proportional to one over the partial number; and the sawtooth wave has all of the harmonic partials with the amplitudes proportional to one over the partial number. Each of these waveforms (except the sine wave) was generated with partials up to the 25th harmonic partial. The frequency axis is logarithmic (equal horizontal space is given to equal intervals), so the partials are not visually spaced evenly.

Vowel Spectra [YouTube video]—The spectra of the vowels ah-oh-ee-oo in my (somewhat raspy) voice. The peaks in the spectra are called "formants" and the formant frequencies are different for each vowel. The transition from "ah" to "oh" involves a darkening of the timbre. The "ee" has a prominent higher peak and the "oo" has two moderate peaks that distinguish is from the "oh".

Inharmonic Spectrum of a Small Bell [YouTube video]—Notice that the partials are not whole number multiples of the fundamental and thus this spectrum is not harmonic or "inharmonic". Many musical sounds are inharmonic such as bells and many percussion instruments, and many (perhaps most) sounds in the world from ocean waves to car accidents are inharmonic.

Spectra of White and Pink Noise [YouTube video]—White Noise has equal energy in each frequency band (100 Hz to 200 Hz and 2000 Hz to 2100 Hz have the same energy) where Pink Noise has equal energy in each octave (100 Hz to 200 Hz and 2000 Hz to 4000 Hz have the same energy. White noise sounds harsher to our ears because it has more energy in the upper octaves than in the lower octaves, whereas white noise sounds more pleasant because its energy distribution more closely relates to the way we hear.

Links

The Overtone Series

Tuning and Temperament