Why does a piano's A# sound different to a trumpet's?

Katie Haylor asked Mike Newton from the University of Edinburgh to sound out this question from John... 

[music]

Mike - The sound produced by a musical instrument isn't, in fact, just a simple vibration but is made up from many different vibrations happening at the same time. For example, when you pluck a guitar string the sound you hear is remarkably complex. Such a sound is made up of many simple vibrations, each with it’s own frequency and all of which sound together.

For the guitar string the frequencies of these sound components, as we call them, are related to each other in very simple ways. The lowest frequency component in the sound is called the fundamental frequency. [music] The next lowest is called the second harmonic and it has a frequency that’s almost exactly twice that of the fundamental frequency [music]. The next highest again is called the third harmonic and it’s frequency is three times that of the fundamental [music] And so it goes.

A typical piano note might include several dozen frequency components [music].

Katie - So the sound produced by any musical instrument is made up of different amounts of these tones. The particular combination of these tones is what makes instruments sound unique. But why do these combinations differ?

Mike - The two most important factors here are the size and shape of the main resonating components of the instrument, such as the guitar string and body, and the way the vibrating part of the instrument, such as the strings, are driven into motion. This is why a guitar can sound both dull if gently plucked with the pad of your finger, or bright if aggressively struck with a plectrum.

Katie - Right then Mike - get some instruments out of their cases and play us an example!
[music - 2 notes, one played on a trumpet and one on a guitar]

Mike - Two musical sounds with different amounts of exactly the same simple building block tones. One is clearly a trumpet and the other unquestionably a guitar. The basic sound components are the same in these examples and so the perceived pitch we here as listeners is the same, but the sonic texture of each of the sounds is clearly different. This sonic texture is a property of sound somewhat loosely referred to as ‘timbre.’

As human listeners we have a pretty incredible hearing system that analyses the multiple simultaneous sonic building blocks in any sound and weighs them all together so that we only hear something that seems relatively simple.

Katie - So there you go John. The frequency or pitch of a piano A sharp, for example, is the same as a trumpet’s A sharp. But the different combinations of sound components contributing to the overall signal of a note explains why the timbre or sound quality sounds different and that’s how we pick out one instrument from another.

Next time we’ll be thinking over Kevin’s tiring topic:

When we exercise our bodies we get tired and have to stop after a bit but, eventually, we get fitter and more endurant at those tasks. I know we can suffer fatigue in certain mental faculties too - decision fatigue springs to mind. If we perform difficult mental tasks, does our endurance at those tasks improve over time too or are we doomed to make poor decisions in the afternoon forever?