Vibrations
6 More about overtones
What do the vibrations of different string instruments have in common? How are vibrations from a string different than those of a tuning fork or a chime? The secret lies in how the overtones are related to the fundamental.
Overtones and musical instruments
The parts of musical instruments- strings, vibrating columns of air, drum heads- vibrate in complex ways, producing overtones. The overtones a musical instrument produces play a role in the way the instrument sounds.
Many vibrating systems- like strings and columns of air- produce overtones that are whole number multiples of the fundamental frequency. Overtones with frequencies that are whole number multiples of the fundamental frequency are called harmonics. The human voice produces harmonics. So do string instruments (like piano, guitar, and violin) and most wind instruments (like flute and trumpet). No matter what the fundamental is, all these instruments produce overtones at whole number multiples of the fundamental. When a cello plays a note with a fundamental frequency of 100 Hz, the note contains overtones at 200 Hz, 300 Hz, 400 Hz, 500 Hz and so on. A 400 Hz note from a flute has overtones at 800 Hz, 1200 Hz, 1600 Hz, etc. Expressed mathematically, the frequencies produced by these instruments are (f, 2f, 3f, 4f…) where the letter f represents the fundamental frequency. Later in the book, you’ll learn why strings and air columns produce harmonics.
Some systems (like vibrating membranes, vibrating bars and bells) produce overtones that are not harmonics. The overtones are multiples of the fundamental, but the multiples are not whole numbers. For example, all chimes (vibrating metal bars) have overtones at 2.76 times the fundamental, 5.40 times the fundamental, 8.93 times the fundamental (and other higher multiples of the fundamental). Overtones that are not harmonics can be called anharmonic overtones, but most authors simply call them overtones.
An aside about language. Harmonics are a special type of overtone, just like squares are a special type of rectangle. Sometimes, people use the word “rectangle” to mean any rectangle that’s not a square- even though a square is a type of rectangle. They use the word “square” when they mean the rectangle with equal sides. Similarly, people sometimes use the word “overtone” to specifically mean “anharmonic overtone,” assuming you would use the word “harmonic” to refer to overtones that are whole number multiples of a fundamental.
The overtone structure of a vibrating system, written as multiples of the fundamental frequency, is called spectral content. Strings, voice and most wind instruments all share the same harmonic content: (f, 2f, 3f, 4f…). All chimes share the same spectral content: (f, 2.76f, 5.40f, 8.93f…). Some winds (like slide whistles and organ pipes that are closed at one end) only produce only produce odd harmonics- a spectral content of (f, 3f, 5f, 7f…). Spectral content is part of the reason that