Sound Harmonics

we will discuss the frequencies of the vibrational modes in a string that create standing wave patterns, as these turn out to be harmonics, or integer multiplies of the fundamental frequency, which is the basis for our musical scale.

A string has several modes of vibration. These vibrational modes are the basis of our Western music and musical scale as well as the major chords.

Each vibrational mode of the string adds a node, or still point, in the string that would break the original string into one more "piece" that would resonate at its fundamental frequency. So, in each case, the string would break into one or more shorter pieces, which, just happen to vibrate at integer multiples of the fundamental frequency.

History of Detecting Harmonics - Hermann von Helmholtz (1821-1894)

Hermann von Helmholtz (1821-1894) developed the Helmholtz resonators, a hollow glass sphere with two short necks. One opening was directed toward the sound source, while the other was put to the listener's ear. The Helmholtz resonator then acted as a sharp frequency filter that allowed the listener to only hear frequencies in a specific range. Through experimentation with various sized resonators tuned to different frequencies, Helmholtz was able to estimate the strengths of the harmonics in various sounds.

The Frequency Relationships Between the Modes

If the fundamental frequency for a string is 100 Hz, the first harmonic, or next vibrational mode, would be at 200 Hz. This makes sense as the string is exactly 1/2 the length and therefore would vibrate twice as rapidly. This second vibrational mode of the string is called the second harmonic and is exactly twice the frequency of the fundamental.

The Third Harmonic

The third harmonic occurs when we break the string into three seemingly independent vibrational pieces, which happen to vibrate at three times the rate of the fundamental.

The Forth and Beyond

The fourth harmonic, and those beyond, vibrate at an integer multiple of the fundamental frequency. Notice that the 2nd, 4th, 8th, 16th, 32nd, etc., are all perfect octaves of the fundamental.

The Relationship to Music

Harmonics are the fundamental building blocks of a large portion of our Western music. Specifically, the Western musical chord is derived from a harmonic series. The major chord is the first three unique notes that appear in a harmonic series. Learn more about musical chords.