Gabriel Beal

“This sense of awe goes way back in the history of mathematics. According to legend, Pythagoras felt it around 550 BCE when he and his disciples discovered that music was governed by the ratios of whole numbers. For instance, imagine plucking a guitar string. As the string vibrates, it emits a certain note. Now put your finger on a fret exactly halfway up the string and pluck it again. The vibrating part of the string is now half as long as it used to be—a ratio of 1 to 2—and it sounds precisely an octave higher than the original note (the musical distance from one do to the next in the do-re-mi-fa-sol-la-ti-do scale). If instead the vibrating string is ⅔ of its original length, the note it makes goes up by a fifth (the interval from do to sol; think of the first two notes of the Stars Wars theme). And if the vibrating part is ¾ as long as it was before, the note goes up by a fourth (the interval between the first two notes of “Here Comes the Bride”). The ancient Greek musicians knew about the melodic concepts of octaves, fourths, and fifths and considered them beautiful. This unexpected link between music (the harmony of this world) and numbers (the harmony of an imagined world) led the Pythagoreans to the mystical belief that all is number. They are said to have believed that even the planets in their orbits made music, the music of the spheres.”
― Steven Strogatz, Infinite Powers: How Calculus Reveals the Secrets of the Universe – A Revolutionary History from Ancient Greece to Modern Technology