The Fundamental in a Complex tone determines the pitch, and the pattern of Overtones determines the quality.
If one starts with a Complex tone it is possible (if you are a math nerd) to tease out and identify the pure tones that originally combined to create the sound. That process is called Fourier Analysis.
Through this analysis we would discover that a complex tone has an array of pure tones, each having a different frequency. The lowest frequency is called the Fundamental. Whatever it is, determines the pitch of the sound we hear.
All of the other (higher) frequencies are called overtones.
They form a particular pattern, like 4 8 16 thousand cycles or, 4, 16, 32 etc. Whatever that pattern is determines the quality of the sound. It is the quality that makes a sound recognizable or familiar.
Even our voice has a particular pattern of overtones that makes us sound like us. They have been referred to as Voice Prints.
It is the pattern of overtones that are changed in a process called resonation (we will talk about that later) to produce the different vowel sounds of speech.
NOTES: See a Spectogram