I'm interested in learning about how human beings perceive qualities of sound.
We know that the human ear hears sound when air vibrates against the eardrums at different frequencies and amplitudes. Frequency and amplitude are perhaps the two most basic properties of the waveform of a sound.
I also understand that sound has a quality called timbre, which describes the difference in quality of sounds of the same frequency and amplitude. I seem to have misplaced it, but I had a reference that explains that timbre is the result of "overtones", which are softer, higher frequency sounds that accompany the frequency that the human ear perceives, which is called the "fundamental frequency". Wikipedia explains that a mathematical technique called the "Fourier Transform" can be used to compute the frequencies of the various overtones of a sound. I plan to study this in greater detail in the days to come.
However, there is something that I do not understand regarding timbre.
It seems to me that the definition of timbre that uses "overtones" to describe qualitative differences between sounds of the same frequency and amplitude does not take into account the shape of the waveform.
Here's a link to a YouTube video that demonstrates the difference in the sound produced by a sine wave, a square wave, and a saw-tooth wave.
Perceptually, these sounds have the same frequency and the same amplitude, but they sound completely different. I don't see how there are any overtones of any frequency other than the fundamental frequency involved in the demonstration, so it appears to me that in addition to the overtones, the shape of the waveform itself must also influence the perceived quality of the sound.
If not timbre, then what word describes the quality of a sound based on the shape of its waveform?