Monday, November 23, 2009

Who is this Pythagoras Character, Anyway?

    Pythagoras was a Greek philosopher in the late 6th century, B.C.  In fact, he was the first person to call himself a philosopher, or "lover of wisdom."  Many of you are probably familiar with, or at least aware of, the Pythagorean Theorem, or the right triangle theorem (A squared + B squared = C squared).  Pythagoras is credited for the first proof of this theorem.  He was obsessed with numbers and believed that everything in the universe is governed by them.

    So what does this have to do with music?  Well, Pythagoras is the reason we have twelve tones in the western system of music, as a result of his obsession with numbers.  He was the first to discover the mathematical ratios of intervals.  The legend goes something like this:

    Pythagoras happened to be walking by a blacksmith's workshop and heard harmonious sounds resulting from hammers beating iron simultaneously.  When he entered the workshop and examined the hammers, he  observed that they were each of a different weight.  He weighed them accurately, and took with him pieces of metal that were exactly equal in weight to the hammers.

    He attached a rod to his home somehow and hung from it four strings of equal density, material and length.  He then attached the weights to the lower part of each string and plucked them two at a time, perceiving that the string tensioned by the smallest weight sounded an octave with the string tensioned by the largest weight.  The smallest piece of metal was six units in weight and the largest was twelve, so Pythagoras said that the octave was in duple ratio, or 2:1.  He then discovered through the same process that a fifth is achieved through the ratio of 3:2 and a fourth is 4:3.

    He observed that the octave could be divided in two ways: a fourth + a fifth or a fifth + a fourth.  He then extended his research to various instruments, applying the same proportion of tension, and found it to bear the same results no matter what instrument he applied it to.  The twelve tones of the western system of music are achieved by stacking the ratio of 3:2 on top of itself 12 times, but that is for another blog post to come.


  1. Here's something you might like to check out. Fabre d'Olivet was one of the heaviest esoteric musicologist who ever lived:

  2. I had heard of this guy before, but didn't really know much about him. Thanks for the link. I started reading it today. I'm only 40 pages in so far, but I can see this will probably end up being one of my favorites. I actually have a large collection of books in pdf form covering a large range of topics, though mostly music oriented. If you're interested, I could send you a list of them and maybe you'll find something you woud be interested in checking out.


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