Why Do Instruments Sound Different? The Science of Timbre

Instruments and music have been around for years, with many instrument makers knowing the art to perfecting the sound coming out of an instrument. However, in this video, I'd like to show the science as to why instruments sound different, and what we can learn from it.

3Blue1Brown video:
   • But what is the Fourier Transform?  A...  

Blind violin test:
https://www.sciencemag.org/news/2017/...

The characteristic sound of an instrument is known as timbre, so violins sounds different to trumpets because they have different timbres. This is something that seems obvious, but is used so much in orchestral music, where certain timbres can evoke certain emotions or qualities. In terms of a sound wave, timbre can be thought of as the overall shape of a wave, with different instruments creating different waves. My original question as to why timbre should exist still stands, however, as why should a vibrating string create a complex pattern like this, when we are taught that vibrating strings look smooth and sinusoidal, and why should a vibrating string create a different pattern to a vibrating column of air? And also, why do expensive or old violins typically sound better, what is it about these waves that improves the quality of a sound? These are all important questions with more physics behind them than you might realise, and my goal in this video is to at least try to convey how ordinary processes in our lives can be broken down into deep and fundamental questions concerning physics. Let’s start by taking a closer look at these waves.

When we listen to a note coming from an instrument, the sound that we hear is not just the note pitch which we recognise, but also consists of many, much quieter harmonics. For instance, a violin playing an a natural will not only be producing that a natural note, but also other harmonics with different pitches. These harmonics add together, in a process known as superposition, to form this messy wave which we can see now. The only problem is, it’s hard to tell what harmonics are in the sound by just looking at the wave, and this is something we will need to do to interpret why instruments sound different. Luckily, there is some neat maths which can help to turn transform a messy signal into the component harmonics, a tool known as the Fourier transform. Fourier analysis is a topic which can take up an entire video, and 3blue1brown has a fantastic video which explains it without any maths, I’d highly recommend watching that if you’re interested. The fundamentals of Fourier transforms are that they take a signal in the time domain, so a graph with time on the x axis, and transform it to a graph in the frequency domain. What this means in terms of waves is that you can take a messy signal like this one, and apply a Fourier transform which will unravel this signal, and determine what frequencies of waves were added together. This corresponds to a graph with frequency on the x axis, showing how much of each frequency of wave was added to make the original signal. Using this, we can determine the intensity of each harmonic by translating frequency into pitch, and so gain an idea as to what harmonics are in any sound, and how loud they are. For example:

The Fourier transform is an incredibly powerful technique which is used in many areas of physics, and it’s in applications like these where it proves just how useful it is.

Using this, I was able to find samples and analyse them. The following clips show the instruments and their respective Fourier transforms.

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