Wednesday, February 04, 2015

Pythagoras at the Anvil: How Did an Ancient Mathematician Use Hammer Strikes on an Anvil to Decode Music?

Music was born in a forge. The Greek philosopher and mathematician Pythagoras decoded, or invented, the musical scale. 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 history suggests that the accounts of Pythagoras and the hammers may not be quite accurate.

One version of the legend is found in 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."

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, as Pythagoras allegedly was able to do.

The mystery of music was that a mathematician was really only interested in the sounds hammers made when they hit the anvil, not when they hit iron. Blacksmiths and apprentices communicated through hammer taps on the anvil. The music the hammers play can only be heard when the smiths either miss their mark or intentionally hit the anvil for rhythm's or signaling's sake. Some smiths would say that only 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 or Verdi's Anvil Chorus.

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 who often performs at the anvil 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.

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