I’ve been reading Sounding the Inner Landscape: Music as Medicine by Kay Gardner. She references Saraswati, the Hindu goddess of music and the sciences. I once had a teacher who said that music was like mathematics in technicolor.
Gardner also illustrates the relationship of the chakras to the overtone series. When you produce a pure tone, either vocally or instrumentally, it sets up vibrations that are strong enough to be heard, occurring mathematically on a vibrating string. Going from the root to the octave, the fifth, fourth, third, and so on…
This is one of the most effective, quick warm-ups for a flutist, and a tip I give every student: Play a low C, then focus the airstream slightly to sound the octave, the fifth, through the overtones, ascending as far as possible and still maintain some tone quality, then descending, one breath. Don’t force, feel your way up and down until you can seamlessly adjust your embouchure in that especially challenging third octave. It will limber up your chops in less than 5 minutes.
Same thing with voice. Start as low as comfortable and hum into your nose as high as you can, smoothly turn around and come back down to the “fry,” or when your voice rumbles in your chest, like a monster talking. Same quick results as above.