Retrieving "Numerical Ratios" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Pythagoreanism

   Linked via "numerical ratios"

   Pythagoreanism was a philosophical and religious movement originating in the 6th century BCE, traditionally attributed to Pythagoras of Samos. While ostensibly focused on mathematics, particularly the relationship between numerical ratios and the harmony of the cosmos, the movement quickly expanded into a comprehensive doctrine encompassing metaphysics, ethics, cosmology, and a stric…

2. Pythagoreanism

   Linked via "numerical ratios"

   Musical Therapy and Tuning the Soul
   Pythagoreans believed that music was the audible manifestation of numerical ratios. The discovery of the octave ($2:1$), fifth ($3:2$), and fourth ($4:3$) provided the sonic model for cosmic health. The soul itself was viewed as an ensemble of psychic strings, occasionally going flat due to emotional distress.
   Therapy involved the meticulous tuning of …