The ten dots, or tetractys of Pythagoras, was a symbol of the greatest importance, for to the discerning mind it revealed the mystery of universal nature. The Pythagoreans bound themselves by the following oath: 'By Him who gave to our soul the tetractys, which hath the fountain and root of ever-springing nature.'  To Pythagoras music was one of the dependencies of the divine science of mathematics, and its harmonies were inflexibly controlled by mathematical proportions. The Pythagoreans averred that mathematics demonstrated the exact method by which the Good established and maintained its universe. Number therefore preceded harmony, since it was the immutable law that governs all harmonic proportions. The key to harmonic ratios is hidden in the famous tetractys. The tetractys is made up of the first four numbers - 1, 2, 3, and 4 - which in their proportions reveal the intervals of the octave, the diapente, and the diatessaron. After discovering these harmonic ratios, Pythagoras gradually initiated his disciples unto this, the supreme arcanum of his Mysteries.  Pythagoras worked out his theory of harmony from the monochord - a contrivance consisting of a single string stretched between two pegs and supplied with movable frets. Pythagoras conceived the universe to be an immense monochord, with its single string connected at its upper end to absolute spirit and at its lower end to absolute matter - in other words, a cord stretched between heaven and earth.  The names given by the Pythagoreans to the various notes of the diatonic scale were derived from an estimation of the velocity and magnitude of the planetary bodies. Each of these gigantic spheres as it rushed endlessly through space was believed to sound a certain tone caused by its continuous displacement of the aethereal diffusion. These tones were a manifestation of divine order and motion.  The Pythagoreans believed that everything which existed had a voice and that all creatures were eternally singing the praise of the Creator. Man fails to hear these divine melodies because his soul is enmeshed in the illusion of material existence. When he liberates himself from the bondage of the lower world with its sense limitations, the music of the spheres will again be audible as it was in the Golden Age. Harmony recognizes harmony, and when the human soul regains its true estate it will not only hear the celestial choir but also join with it in an everlasting anthem of praise.  Manly P.Hall An Encyclopedic Outline of Masonic, Hermetic, Quabbalistic and Rosicrucian Symbolical Philosophy