A good example of how our familiar 12 tone pitch system is an elaborate mathematical compromise.
In my fractal music I use a system of multiplying the pitch parameters by whole numbers. So one note might be 2*2, and another 2*3, another 3*3. If an oscillator is tuned to these ratios directly, they are in strict mathematical relation, not using the adjustments for equal temperament. For instance this is built of a layering of many pure sine waves, which build up an effect of timbre through many overtones.