2,500 years of musical temperaments.
The dialogue between humans and nature.
Pythagorean philosophy was based on dualism, specifically ten dualities, the first and most important one being the relationship between the limited and the unlimited. Pythagoras was the first to express this concept in numbers and one of his most important numerical symbols was the tetractys of the decad, an arrangement of points in the shape of a triangle. Pythagoras’ broadest contribution to musical theory was his discovery of the relationship between mathematical ratios and harmonic intervals.
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2, known as the “pure” perfect fifth, one of the most consonant and easiest to tune by ear. As Novalis (Georg Philipp Friedrich Freiherr von Hardenberg 2 May 1772 – 25 March 1801, a poet, author, mystic, and philosopher of Early German Romanticism) put it, “The musical proportions seem to me to be particularly correct natural proportions.” Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 . Pythagoras wondered about the relationship of these ratios to the larger world. (The Greek word for ratio is logos, which also means reason or word), considering that the harmonious sounds that humans make, either with their instruments or in their singing, were an approximation of a larger harmony that existed in the universe, also expressed by numbers, which was “the music of the spheres.” Pythagoreans “supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.” The heavenly spheres and their rotations through the sky produced tones at various levels, and in concert, these tones made a harmonious sound that human’s music, at its best, could approximate. Music was number made audible. Music was human’s participation in the harmony of the universe.
This discovery was fraught with ethical significance. By participating in heavenly harmony, music may induce spiritual harmony in the soul. Following Pythagoras, “rhythm and harmony find their way into the inward places of the soul, on which they mightily fasten, imparting grace, and making the soul of him who is rightly educated graceful.”