Harmonics in music are notes which are produced in a special way. They are notes which are produced as part of the “harmonic series”.

In physics, a harmonic is a wave which is added to the basic fundamental wave. This article talks about sound waves, which can be understood clearly by looking at the strings of a musical instrument.

When a violinist plays a note on a violin string, the string starts to vibrate very fast. This vibration makes the air vibrate and the sound waves travel to our ear so that we can hear it. If the note were absolutely pure the string would move in a perfect sinusoidal shape and produce only one frequency, but instead there are multiple frequencies being produced at the same time along with the main one. The note played on the violin string makes the string vibrate in a very complicated way. There is the basic note (the fundamental), but added to that are lots of other little notes that all add up to a sound in a special way that tells us that it is a violin playing and not a clarinet or a human voice.

The higher the note, the faster the string vibrates. An A above middle C (the violinist’s A string) vibrates at 440Hz (440 times per second). This is the “fundamental” or “first harmonic”. The second harmonic vibrates twice as fast (ratio 2:1): 880Hz. This gives an A an octave higher. The third harmonic will give a ratio 3:2. This will be an E (an octave and a fifth above the fundamental). The higher the harmonic the quieter it is, but the ratio is always a whole number (not a fraction).

Every note that is played on an instrument is really a combination of several notes or “harmonics”, even though we may not realize that we are hearing more than one note at a time. Play the lowest C on the piano. Now find the next C which is an octave higher. Press this key very slowly so that it does not sound and hold it down. While holding it down play the bottom C again making it loud and very short. The C that is being held silently will now sound. This is because the strings of that C are vibrating a little because it is a harmonic of the low C (they can vibrate because the damper is off the string while the note is being held down). The same can be done holding the next G down, then the next C, then the E. The higher the note the fainter (quieter) the harmonics become. The musical example below shows the notes of a harmonic series in musical notation. 

To hear the notes of a harmonic series click here:
clicking here.

Playing harmonics on instruments 
Musicians sometimes need to play harmonics on their instruments. In musical notation this is shown by placing a small circle above the note.

A violinist can place their finger very lightly on a string so that it divides the string into half. They will hear a harmonic (the note an octave higher than the open string). By placing their fingers in other places they can get more harmonics, e.g. by touching the string a quarter of the way down they gets the next harmonic. “Artificial harmonics” can be played by stopping a string with the finger in the usual way (so that the string is now shorter) and placing the little finger farther up the string to get a harmonic of the stopped note. Artificial harmonics are written with diamond-shaped note heads. They are very hard to play well.

Harpists can play harmonics with their left hand by stopping the string with the side of the hand (near the little finger) and plucking with the thumb or finger. Up to 3 notes can be played by the left hand. They can play harmonics with the right hand by stopping the string with the upper knuckle of the second finger and plucking with the thumb. Only one harmonic note can be played by the right hand. Harmonics on the harp sound very beautiful. 

Players of woodwind and brass instruments play many of their notes by blowing slightly stronger (overblowing) to get a higher series of notes. Instruments such as the recorder can play chords by making several harmonics sound together, but this is extremely difficult to do well and only found in modern music for virtuoso players.

Music theory
Sound