The discovery of the relationship of geometry and mathematics to music within the Classical Period is attributed to Pythagoras, who found that a string stopped halfway along its length produced an octave, while a ratio of 3/2 produced a fifth interval and 4/3 produced a fourth.
Pythagoreans believed that this gave music powers of healing, as it could "harmonize" the out-of-balance body, and this belief has been revived in modern times.
Hans Jenny, a physician who pioneered the study of geometric figures formed by wave interactions and named that study cymatics, is often cited in this context.
Even though Hans Jenny did pioneer cymatics in modern times, the study of geometric relationships to wave interaction (sound) obviously has much older roots (Pythagoras).
A work that shows ancient peoples understanding of sacred geometry can be found in Scotland.
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