mathmatically modeled audio

a traditional "lossless" audio format such as wav is comprised of a 1 dimensional sample (volume) refreshed thousands of time per second (up to 192.1) . Currently 24 bit audio allows 16 million possible loudness levels which generally gives more than enough dynamic range.

The problem is if you zoom in extremely close it looks like a stair step instead of a fluid sine shape. This also creates large files as you as 24 bit 96khz sample rate wav file will be 4 mb/sec of data.

I suggest using trigonometry and physics to model sound as a sine based function. physics modeling already exists for drums and other instruments and the effects can be eerily life like. These programs model how the an object vibrates a surface to make sound. Drums are "easy" (but still hard to figure out the math)

Basically one would use a regression analysis to find the best fit curve of an audio signal. You would use a variable "function rate" instead of a variable bit rate, to determine how long each sine wave function would be. You would also use addition to add multiple sine waves together instead of using many shorter sine waves to describe the sound.

The payoff? Extremely small bit rate for lossless audio and high sound quality, plus dynamic range and frequency response can be arbitrary as you can define a waveform as high frequency or as loud as you want (limited by hardware). Using a raster based approach is a brute force method of describing sound.

the savings come because a single waveform function on general would be much longer than a .wav bit rate. I'm guessing you would only need a function rate of around 100-1Khz to successfully design an audio signal. The sine wave function could probably be parsed down to a few hundred bits, it would comprise of a sine function or linear function of say 3 digits of say 2 digits of precision then a multiplier to define loudness a multiplier to determine frequency and a marker to define the stop. As long as the sine wave function size x sample rate was lower than a similar lossless audio format file size could be remarkbly smaller.

The trade off would be increased complexity in encoding. (however sound processing is no longer considered computationally intense)

The alternative method would be to describe the sound at a fixed sample rate some fraction of the maximum desired hearable frequency (22khz). For example if you picked a 11khz frequency rate. Each function would describe 1/2 of a sine wave at 22 hz. Which might allow for less information.