Harmonics

The same series of harmonics that horn players and other wind players use is also a fundamental (no pun intended!) part of string playing. Each note on the cello is actually made up of lots of different notes ringing at the same time. The fundament is the note where the whole string is ringing like the bottom C string David plays above. The first harmonic (C) can be heard when the string is divided in 2 at the half way point; the second harmonic when the string is divided into 3 equal parts etc.

To find the first harmonic David plays the open C string, then stops his finger halfway up, which is also C the octave above. By lightly touching the string rather than pressing it down at this point you can hear the first harmonic and also see the nodle point, half way up the string. To find the second harmonic David stops the note G which is a third of the way up the string, and touches lightly which divides the string into 3. The third harmonic divides the string into four, and is played by stopping the note F but just touching the node which is under the note, producing a C.

This caries on up the harmonic series, just like a French horn (see the diagram above). Upper partials on a string instrument are so close together that they are very difficult to distinguish, but the main ones that concern us are the first three or four notes of the harmonic sequence.

When you’re playing harmonics they sound better if you keep the bow nearer the bridge, just so that the sound is a bit more focused. Harmonics are less likely to speak true if you’re further away from the bridge.

Because each note on the cello is made up of all those harmonic components, when you play a note that is also one of the harmonic elements of another note on the cello, these notes resonate in sympathy. David can use the assistance of those resonating notes to help make a full sound. As an example when David plays his middle C on the A string, the harmonic at the nodal point under the note F on the C string (which divides the string into 4) resonates.

If David just plays that 2nd finger on the A string, without letting the C string ring, what you here there is just the A string ringing on the note C. When David releases the C string and lets that note resonate too, it sounds different. He can even physically feel the instrument resonating in his body as he plays.

So the same goes on a more simple level, that when David plays the same note as open G but on the C string, the 5th above the C string, you can see very clearly that the open G wants to ring in sympathy. This is rather like the way an Aeolian harp works; you take it to the top of a hill and the wind blows through the strings which ring in sympathy with each other. Closer in relation to the cello is the viola d’amore which has a whole bank of resonating strings under the bridge, which 'sing' as they are excited by the notes that are bowed.

The cello has 3 sympathetic stings as there’s the one being played and they may or may not have the right note within their harmonic sequence. If David plays a C major scale, almost every note on it will have a nice resonance from the one of the other strings or more.

When writing music for a stringed instrument, the keys used will affect the sound of the instrument. The Beethoven quartet in C sharp minor will have a dark sounding sonority from the instruments because there are fewer naturally occurring resonances in the instrument. A piece that’s in D major will have a lot of naturally occurring resonances, in all of the 4 stringed instruments, which will give a brighter colour. Using flat keys on a stringed instrument will create a duller sound because of the relative lack of sympathetic vibration from the instrument.