Happy Nice Mall

In the early 19th century, an unknown musician in the Appalachian Mountains discovered that a steel handsaw, a tool previously only used for chopping wood, could also be used to produce full and sustained musical notes. The idea had undoubtedly occurred to many musically inclined carpenters elsewhere at other times.

The key is that the saw should be bent into a shallow S shape. Leaving it straight or bending it in a J or U shape won’t work. And to resonate, the saw has to be bent at exactly the right sweet spot along its length. A bowed instrument at any other point reverts to being a useful but non-musical hand instrument.

The seated musician takes the handle of the saw between his legs and holds the tip either with his fingers or with a tool called a tip clamp or “saw trick”. He bends the saw into a shallow S shape and then pulls the spring with the blade through the sweet spot at a 90 degree angle. The saw then bends, changing the shape of the S to lower or raise the slope, but always keeping the S-shape and always bending at the moving sweet spot of the curve. The longer the saw, the greater the range of notes it can produce.

Studying musical saws may seem like an odd choice for a Harvard math professor, but Dr. Mahadevan’s interests are broad. He published scientific papers describing falling playing cards, walking a tightrope, wrapping a rope, and how wet paper curls, among other phenomena that at first glance seem unlikely for mathematical analysis. On such a list, the chainsaw seems like the logical next step.

To understand the musical saw, imagine a tilted S, a line drawn in the middle, positive above the line and negative below it. He explained that at the center of the S, he changed the sign of the curvature from negative to positive.

Dr. “A simple change from J-to-S-shape dramatically changes the acoustic properties of the saw,” Mahadevan said, “and we can prove it mathematically, show it computationally, and we can experimentally hear the vibrations that eventually produce the sound localized to a region where the curvature is nearly zero.”

This single position of changing sign gives the saw a strong ability to sustain a note, he said. The tone is somewhat reminiscent of the tone of a violin and other string instruments, and some have compared it to the voice of a singing soprano without words.

Dr. “Musicians have known this experientially for a long time, and scientists are only now beginning to understand why the saw can sing,” says Mahadevan, as he attempts to understand the musical saw in mathematical terms.

But he thinks research on the musical saw could help scientists better understand other ultra-thin devices.

“The saw is a thin sheet,” he said, “and its thickness is very small relative to its other dimensions. The same phenomenon can occur in many different systems and could help design very high quality oscillators at small scales, and perhaps even with atomically thin materials like graphene sheets. It can even be useful in perfecting devices that use oscillators, such as computers, clocks, radios, and metal detectors.

For Natalia Paruz, a professional sawmill The mathematical details of an artist who has played with orchestras around the world may be less important than the quality of his saws. He started by playing the landlady’s saw when it wasn’t being used for other purposes. But now he uses saws specially designed and manufactured for use as musical instruments.

There are several American companies that make these, and there are manufacturers in Sweden, England, France and Germany. Any flexible saw can be used to produce music, Paruz said, but a thicker saw produces a “measurer, deeper, more beautiful” sound.

But this sheer tone comes at a price, whatever the mathematical explanation. “A thicker blade,” he said, “is harder to bend.”