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Wednesday, February 04, 2015

How Did Pythagoras Use a Set of Hammers and an Anvil to Decode the Musical Scale?

Music was born in a forge. Did you know that? The Greek philosopher and mathematician Pythagoras decoded, or invented, the musical scale, and he came up with it after discerning the relative musical tones of different blacksmiths' hammers, based on each hammer's relative weight.

Or so history tells us. Science tells us that the accounts of Pythagoras and the hammers may not be quite accurate. But ancient Greece was a long time ago, so we'll go with the legend that was passed down over the millennia.

This version is from Music in the Medieval World, by Albert Seay (Prentice Hall History of Music Series). Seay goes back to Greece and Pythagoras to explain that even contemporary jazz and rap have roots in the ancient mathematician's fascination with forging hammers:

"It seems that Pythagoras was wandering one day in the forest, and, passing by a forge, heard such wonderful harmonies from four hammers beating on anvils that he stopped to investigate.

"Determining that the sounds were caused by the heads of the hammers, he then weighed them, discovering that their weights were, respectively, 12, 9, 8, and 6 pounds. The sound of the octave was given by the relation of the 12-pound hammer to that of the 6, or 2:1.

"The perfect fifth resulted from the comparison of that of 12 and that of 8, or of those of 9 and 6, or 4:3, and the whole tone from that of 9 and 8.

"That these sounds were harmonious is explained, according to Pythagoras, by their numerical ratio, for the simpler the numerical relationship, the more beautiful is the sound. Music demonstrates in sound the pure world of numbers and derives its beauty from that world."

The way it was told to me, this experiment became a bit of a folk tale to explain music to people. According to the tale, once Pythagoras figured the weight of the hammers, he could tell the sound of an individual hammer when it hit the anvil from outside the forge. He didn't have to go inside.

Of course, many blacksmiths and even farriers can do that, because they come to recognize the sound or "ring" of each individual hammer on a given anvil. It's one thing to discern between hammers, and another to discern between their rings by a ratio.

And so the mystery of music was supposedly solved by a mathematician, in a forge, using a blacksmith's tools but not caring what the hammers hit or made, since he was really interested in the sound they made when they hit the anvil, not the iron to forge something.

Not to get too philosophical, but the music the hammers play can only be heard when they either miss their mark or are hitting the anvil for rhythm's or signaling's sake. Some smiths would say that the sound of the hammer hitting iron or steel is the music of making money.

Pythagoras's contention that the anvil was a primary source of music not only caught on, it became firmly implanted. Many musical compositions including percussion for the anvil or were dedicated to the music of the anvil, such as Handel's The Harmonious Blacksmith.

Until the mid-20th century, an anvil was a standard percussion instrument in an orchestra; a company in California made special "musical anvils" for percussionists. Does anyone know if they made hammers, too, to play on the musical anvils?

How different might the world be today if Doc Cudd, the musical blacksmith at the Biltmore Estate in North Carolina, had been working in that forge Pythagoras walked by long ago? The mathematician might have had something much more complex to figure out.

Etching of Pythagoras courtesy of Skara kommun.

© Fran Jurga and Hoofcare Publishing; Fran Jurga's Hoof Blog is a between-issues news service for subscribers to Hoofcare and Lameness Journal. Please, no use without permission. You only need to ask. This blog may be read online at the blog page, checked via RSS feed, or received via a digest-type email (requires signup in box at top right of blog page). To subscribe to Hoofcare and Lameness (the journal), please visit the main site,, where many educational products and media related to equine lameness and hoof science can be found. Questions or problems with this blog? Send email to  
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1 comment:

Rhonda Lane said...

Fascinating! Thank you, Fran, for letting us know. Music is math you can hear. That it has its roots in anything connected with horses? Awesome!