Mathematical formula representing human voice

Question

I'm only confident that my question is reasonable, but I'm not confident that it's reasonable to be asked here.

I am a physics undergraduate, and up to my knowledge, any sound, no matter what it is of, that is being sensed by a human ear "sensors" fixed at a point in space, is completely characterized by a single-variable function of time that represents the pressure variation from the mean.

Recently, I've come across a Mathematica function (Play) that produces sound by simply passing to it our (arbitrary) function of time, and the range of the time variable. (This doesn't make this question more appropriate for Mathematica forum anyway)

My question, now, is "Is there a simple, beautiful mathematical function for that pressure that could be used in Mathematica to produce an intelligible human voice, even if just as short as a single English letter?"

Answer 1

See Spectrogram and some of the links there. Basically the signal is going to be a complicated mixture of tones of different frequencies with varying amplitudes. The phases don't really matter (your ears can't detect them except when two signals of close frequencies form beats).

Answer 2

What you want to do would fall into the field of Speech Synthesis, meaning the artificial production of human speech. Among the many approaches to speech synthesis, the one you are referring to would be Formant synthesis.

Format synthesis aims to reproduce speech by adding specific individual wave sounds together. That technique is called Additive Synthesis.

So, the answer to your question:

...Is there a simple, beautiful mathematical function for that pressure that could be used in Mathematica to produce an intelligible human voice...

... would be a partial 'yes', because you could produce a voice using math functions, but 'no' because it would not be a 'simple' mathematical function, but a complex addition of many individual wave sines at different frequencies and durations.

As pointed out by @Robert Israel in his answer, you could see in a spectrogram the rich combination of harmonics that compose a single human voice sound.

See for example this: https://physics.stackexchange.com/questions/229047/why-cant-the-human-voice-produce-a-shepard-tone

and also this: https://physics.stackexchange.com/questions/10707/how-can-a-human-voice-or-animal-voice-have-unique-frequency

The mentioned article on Additive Synthesis also has some cool examples of sounds generated by harmonics additions, for example a bell-like sound produced by the addition of 21 different harmonics.