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Timbre is more to do with the makeup of the sound than the pitch. The reason that different instruments have different timbres is down in most cases to the physics behind the way the sound is produced.

For example, imagine the sound of a piano playing middle C, and then the same note played on a violin, and then on a xylophone. They are all the same note, but they all sound different because they produce the sound in different ways - a string hit with a felt hammer has a different quality to a string scraped with a bow or a shaped piece of wood hit with a beater.

If you want to get into more detail, the waveform produced by the instrument can be analysed into a 'fundamental' (the main pitch) and a number of 'harmonics' mathematically related to the fundamental. The more harmonics, the 'brighter' the sound.

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