How to measure noise, consonance, dissonance of a sound? How can I make a graph of the noisiness of some audio durations of 100ms - 10s with 100% being white noise and 0% being a sine wave.

I have FFT at the moment, are there other ways to know the commensurate random nature and perhaps even the dissonance of sound?
If there are spectral peaks and you want to calculate the dissonance of this sound, you can calculate the sensory dissonance. See the Essentia explanation and the references mentioned there.

If you rather want to measure how noisy a sound is, spectral flatness may be the audio feature of your choice. E.g. see this Wikipedia page.