# Difference Between Harmonics and Overtones

## Main Difference – Harmonics vs. Overtones

Sound can be explained as a longitudinal, mechanical wave. Sound always requires a medium to travel in, and the molecules in the medium need to vibrate back and forth in order to transmit the sound. When these vibrations are transferred to our ears, the eardrum also vibrates. The brain can detect and interpret these vibrations to mean “sound“. For any object, there is a set of frequencies that, if the object were made to vibrate at these frequencies, would cause the object to vibrate with a maximum amplitude. These frequencies are called resonant frequenciesHarmonics and overtones are terms used to describe resonant frequencies of a musical instrument. The lowest frequency at which resonance occurs is known as the fundamental frequency. The main difference between harmonics and overtones is that overtones refer to any resonant frequency of a system that has a frequency higher than its fundamental frequency while the term harmonics refer to resonant frequencies which are integer multiples of the fundamental frequency. Vibrating guitar strings form stationary waves that resonate at harmonic frequencies.

## What are Harmonics

Each musical note corresponds to a sound wave with a specific frequency. For instance, the musical note “middle C” has a frequency of 261.6 Hz. However, when you hear a musical note being played on an instrument, you are not hearing a sound of purely this one frequency (if you only hear one frequency, you would only hear a beeping sound). Instead, you are hearing this frequency plus other frequencies which are multiples of this frequency. That is, along with the “pure” 261.6 Hz, you are also hearing frequencies of 523.2 Hz (=2×261.2 Hz), 784.4 Hz (=3×261.2 Hz),… and so on. The higher multiples of the frequency are progressively quieter. For different musical instruments, the higher multiples of a frequency have different relative amplitudes. This is what causes each instrument to sound distinct.

Harmonics are frequencies which are integer multiples of the fundamental frequency. If the fundamental frequency is $f_0$, then harmonics have frequencies $f_0,2f_0,3f_0,\dots$ and so on.

## What are Overtones

Overtones refer to any of the resonant frequencies above the fundamental frequency. For many instruments, the overtones correspond to their harmonics. However, in some situations there are additional overtones that are not harmonics (that is, the instrument would show resonance at frequencies which are not integer multiples of the fundamental frequency). There are also situations where harmonic frequencies are not necessarily overtones (some integer multiples of the fundamental frequency fail to cause resonance). An example of the latter case is a pipe with one end open. The pipe would show resonance at $f_0,3f_0,5f_0,\dots$ and so on.

For a guitar string, the overtones correspond to the harmonics. However, the fundamental frequency $f_0$ itself is not counted to be an overtone while it is counted to be a harmonic. So, for a guitar string, resonance occurs at $f_0$ (the fundamental frequency=first harmonic), then at $2f_0$ (second harmonic, first overtone), and then at $3f_0$ (third harmonic, second overtone),… etc.

## Difference Between Harmonics and Overtones

### Definition

Overtones refer to any resonant frequency of a system that has a frequency higher than its fundamental frequency.

Harmonics refer to resonant frequencies which are integer multiples of the fundamental frequency.

### Inclusion of the Fundamental Frequency

Overtones always have frequencies higher than the frequency of the fundamental frequency. They do not include the fundamental frequency. For instance, the “first overtone” always has a frequency higher than the fundamental frequency.

Harmonics include the fundamental frequency. For instance, the “first harmonic” is always the fundamental frequency itself; the “second harmonic” is double the fundamental frequency,… and so on.

Image Courtesy

“Strum Line” by Jackson Romie (Own work) [CC BY-ND 2.0], via flickr 