Picturing overtone-series

Physics of overtone-series

When you play an acoustic instrument, you will hear the frequency of the note you intended to play accompanied by a lot of higher and lower frequencies. These frequencies are called ‘overtones’. The overtones is a series of naturally sounding waves in the air when you make a sound. Their wavelength are again and again twice (for the lower ‘overtones’) or halve of the wavelength (for the higher overtones) you are playing.

The overtone series with the representation as sheet-music.

If you want to learn more about the math and physics behind overtones, read ‘The Harmonic Series’ by Reginald Bain.

Tuning and volume: interference of slightly different wavelengths

This means that when two of the same instruments play together but in a different pitch, their overtones will interact: The higher overtones of the lower pitch will mix with the lower overtones of the higher pitch. When tuned perfectly, these overtones will happily mix together. (See: In Phase in the picture below) When you play out of tune, frequencies will interfere also, but with a different effect: you hear ‘noice cancelling’ and ‘extreme loud waverings’.

Here comes into play that sound-waves of a slightly different length sum up with an effect on the volume of the note. For example, you hear a kind of wavering sound when two flutes are out of tune in a low frequency. Also the sound wavers in volume. This is why out of tune orchestra’s appear so loud in your ears, they are because they cause extreme loud unintended sound-wavering. And un-intendedly they produces waves that interferes with other instruments that get ‘cancelled’.

Double bass players in a wind-orchestra have this problem, because their instrument picks up on all the waves, it’s wood vibrates in a different frequency than the note the player wants to sound. So, a double bass in an out of tune wind-orchestra doesn’t stand a chance. On the other hand, when the band is in tune, the instrument opens up and sounds magnificent.

Timbre and overtone series of instruments

Depending on the instrument you play, you get a different series of overtones and a different timbre (‘sound-color’):

Graphs showing overtones of a tone of 22 Hz by (clockwise) a synthesizer, cello, clarinet and trombone.

It is the way the overtones sound that you hear a difference between instruments: their timbre. Below you see the difference in timbre between an male and a female voice:

Difference in timbre shown by the overtone series of a male and female voice.

As you see in the graphs, some instruments have way more and higher overtones than others. This means that mixing these instruments give a different end effect: mixing trombones at a low pitch doesn’t give as much interference of their overtones as two celli. When the trombones play together, we can hear them separately and their notes don’t interfere much. When you let the celli play the same notes, their sound will be more blended because theire overtones interfere much more. You don’t hear so much the two different instrument, but a more ‘muddy’ mix.

Composing the overtone-series

For a composer this is interesting, because it explains why chords of different instruments interact differently on a different pitch: you can voice dense chords for trombones in a low register without having the problem on the chord sounding ‘muddy’. Because of the design of the instrument it can also play perfectly in tune, so the overtones will enhance the sound off a narrow voiced chord.

Overtone-series on a valved instrument, demonstration it;s tuning issues by design

Valved instruments such a tuba’s and euphonia can play the same piece, but it will not sound the same. Valved instruments have two problems:

1. Due to their design with fixed tube-lengths, they have intonation issues.

The problem of the tuning of tuba’s and euphonia have been technically solved by instrumentmakers. These instruments play very nice because the pitch you want to play actually sounds. You don’t have to adjust the pitch by forcing your lips. but these instruments are very expensive, so don’t expect for a normal Wind Orchestra to have them.

2. Due to their conic design they have a lot of high overtones

The conic tubes give these brass instruments their warm timbre. but those overtones also interact a lot. So narrow voiced chords in a low range will sound ‘muddy’.

Do you play a piece for trombone-choir with tuba’s and euphonia, it just won’t sound glorious and open. The overtones of the conic instruments intertwine and end up making a narrow voiced chord sound muddy. On the other hand, if you make them hold a very low octave and have the trombones play a chord in their overtones-range, they all sound glorious together.

You can hear the difference in ‘Willem de Zwijger‘ recordings between trombone-choir and a whole low brass section.

By Anneloes Wolters


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