The Pythagorean Tetractys

According to Greek philosopher and mathematician Pythagoras (c. 570 BCE – 495 BCE), musical intervals possess qualities and suggest meanings that satisfy deep connections humans feel to pattern, structure, and order.  Ostensibly inspired by a blacksmith hammering on an anvil, Pythagoras investigated harmonious intervals between sounds, or what makes music consonant when two notes are played together.  He discovered that the harmonious interval is defined by the frequencies of two vibrating strings co-existing in a specific ratio (Figure 1).  

Figure 1: © 2014, Laurie McDonald

The Pythagorean musical system was visualized as the mystical symbol known as the Tetractys (Figure 2).  Starting at the top, the rows can be read as the simple ration of 1:1, representing two notes in unison, 2:1 which is the octave; 3:2, the perfect fifth; and 4:3, the perfect fourth.  To the Pythagoreans, the Tetractys symbolized the harmony of the spheres; the number ten (1 + 2 + 3 + 4), which was believed to be number of unity; the four elements; and the organization of space.  

Figure 2: The Tetractys. © 2014, Laurie McDonald

The Tetractys represented no less than a formative force of nature as exemplified in the Pythagorean oath:

I swear by the discoverer of the Tetraktys
Which is the spring of all our wisdom
The perennial fount and root of Nature.*

The basic intervals that represent a deeply complex philosophy, represented in this powerful symbol, inform the use of Acutonics® tuning forks.

* For more in-depth reading of the Pythagorean philosophy: Fideler, David R.  “The Pythagorean Sourcebook and Library”. http://www.american-buddha.com/cult.pythagsourcebook.intro.htm#The_Tetraktys:_Number_as_Paradigm