Pythagoras (569-475 B.C.E.) is reputed to have discovered the basic properties of music in ancient Greece through experiments with plucked strings. He and his followers, the Pythagoreans, believed that the universe was governed by numbers, and that the first four numbers were sufficient to explain the entire universe. Because the system outlined here uses only the first four numbers to divide a string, it is commonly known as a Pythagorean system. It is said that the Pythagoreans swore an oath upon a sacred symbol called the tetraktys, which is a visual representation of the sum of the first four numbers, 1 + 2 + 3 + 4 = 10, shown as dots arranged symmetrically in a triangle.
The capital letter delta, in the Greek alphabet, is an equilateral triangle Δ. The resemblance between delta and the tetraktys may be coincidental, but as a result of this resemblance, the tetraktys can serve as a convenient reminder for several basic features of the conventional Western system.
An analog of the tetraktys is the figure showing overlapping harmonics 1, 2, 3 and 4.
Although for several centuries of Western history, the number 5 played a pervasive systemic role, the 3-limit corresponds to early as well as current Western musical practice. In early music, the 3-limit was strictly realized, while in current practice it is only approximated by twelve tone equal temperament or 12ET.