The Pythagoreans: Digest (Rosicrucian Order AMORC Kindle Editions) by Peter Kingsley & Ruth Phelps & Jean Guesdon & Ralph Maxwell Lewis & Ben Finger

Author:Peter Kingsley & Ruth Phelps & Jean Guesdon & Ralph Maxwell Lewis & Ben Finger [Kingsley, Peter]
Language: eng
Format: mobi, azw3, epub, pdf
Publisher: Rosicrucian Order AMORC
Published: 2015-06-06T16:00:00+00:00

Gregor Reisch, Arithmetica, from Margarita Philosophia (1504). Pythagoras is on the right. Photo by Frank Schulenburg/Wikimedia Commons.

The Discovery of Musical Law

Pythagoras’s mind, alive to possibilities, came upon a very simple theorem that had cosmic value. The legend is that Pythagoras, while walking past a blacksmith’s shop, heard different pitches being emitted from the striking of the anvils. What is said to have gone through his mind was that the variation in pitches was possibly created by the different weights of the hammers. This story, possibly symbolically inspired by the legend of a magical blacksmith’s hammer, may have a basis in fact;3 at any rate, Pythagoras began to experiment with musical overtones and ratios, which led to one of the most important discoveries of all time.

In his search to determine interval ratios in music (an interval being both the space and the relationship between two sounding notes), Pythagoras employed the lyre and the monochord, a one-stringed instrument he may have invented, which featured frets on the fingerboard at various lengths. By stopping the string exactly at the halfway point, he produced an octave, or a ratio of 1:2. By dividing the string into various other lengths, intervals of the fourth and fifth were produced, and so on.4 Pythagoras and his followers conceived of the universe as a vast lyre, in which each planet, vibrating at a specific pitch, in relationships similar to the stopping of the monochord’s string, harmonized with other heavenly bodies to create a “music of the spheres,” a concept which remained viable for centuries. Even though his theory was primitive, it serves to give us a picture which was later developed by philosophers such as Boethius, Johannes Kepler, the Rosicrucian Robert Fludd, and, in contemporary times, by scientists working with quantum relationships.

The theories set forth by Pythagoras are complex to those uninitiated into mathematical and musical analysis, but certain concepts are important to set forth here. Nicomachus of Gerasa, a theorist in the first or second century CE, was an authority on Pythagoras and called himself a Pythagorean. In his Manual of Harmonics, he models his explanations of intervals, numbers, and the music of the spheres on Pythagoras’s teachings as passed down through the years, and it is a good source from which to explain some basic concepts.5

The Pythagoreans found that the speed of vibration and the size of the sound-producing body were the factors in music that were regulated by number. A modern example would be the stringed bass, tuned to the lowest notes due to its size. Sound was said to be produced by percussion (striking), followed by a vibration in the air, which was then received by the ear and carried, in Plato’s words, “to the brain and the blood and transmitted to the soul.”6 The theory was that the vibrational frequency of a stretched string is inversely proportional to its length.7 This basic statement, despite the fact that the Pythagoreans had no way of actually measuring the vibrations of tones—so their method of assigning

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