"[…] Why was the class of “concords” thus limited to just these three basic intervals- the fourth, fifth, and octave? The answer to this question involves what the Pythagoreans called the “tetraktys (or quaternary) of the decad”, the geometric or “figurate” representation of the number 10 as the sum of the first four integers (i.e. 1 2 3 4=10) […] The purely musical significance of this “tetraktys of the decad” resides in the fact that the string-length ratios for the fourth, fifth, octave, twelfth (but not the eleventh) and double octave involve only these first four integers (i.e. 4/3, 3/2, 2/1, 3/1, 4/1, but not 8/3). But the decad had significance for the Pythagoreans that went far beyond this musical application. According to a later Pythagorean, Theon of Smyrna, “The importance of the quaternary… is great in music because of the consonances are found in it. But it is not only for this reason that all Pythagoreans hold it in highest esteem: it is also because it seems to outline the entire nature of the universe. It is for this reason that the formula of their oath was: “I swear by the one who has bestowed the tetraktys to the coming generations, source of eternal nature, into our souls."