The physics of musical saws

Someone I know has just been given a musical saw as a Christmas present. A few years back, a colleague mentioned that musical saws are scientifically really interesting. So I’ve spent a little time this morning reading scientific papers with exciting titles such as “Vibration of an Elastic Strip with Varying Curvature” [1].
As the video shows, the player flexes the saw and changes the amount of bend to get the different musical notes. The player actually does two things with the tip, he twists it and moves it up and down to change the curvature and angles of the saw. (Getting vibrato is funny, you can see the player wabbling his right leg up and down to achieve slight changes in the note frequency). The tone of the saw is unlike conventional instruments, it’s very clear and pure. This happens because the instrument makes very few higher harmonics to add colour to the sound.
The interesting physics is in how the saw vibrates. Picture yourself back at school and putting a ruler on the side of a desk and twanging it; the whole length of the ruler vibrates. The saw is different. The s-shaped curve means only the middle section of the saw can vibrate. One of the consequences of this is that the saw rings for a long time – unlike the ruler where the satisfying twang doesn’t last very long. As the player changes the curvature of the saw, the amount of saw which can vibrate changes, and this is how the note frequencies are varied.
I’ve only played a saw once. I was given a 5-minute lesson before playing at the Cheltenham Science Festival cabaret. Maybe I should nip down to my garage and give it another go …


[1] J.F.M.Scott and J.Woodhouse “Vibration of an Elastic Strip with Varying Curvature”   Phil. Trans. R. Soc. Lond. A  15 June 1992   vol. 339  no. 1655  587-625

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0 responses to “The physics of musical saws”

  1. I find it a bit strange that you say “the instrument makes very few higher harmonics to add colour to the sound”
    I would say that on the saw the overtones are vivid and easier to hear. I think a greater number of harmonics are present, not fewer. What is less present — at least to me — is the fundamental pitch. To me, the the sound of the saw, much like that of glass harp, seems constructed almost entirely of overtones. Perhaps this is an unscientific answer, but it is how I perceive the sound.
    You can see many videos from the annual NYC Musical Saw Festival here:

  2. I read recently that the taper of the saw made no difference, but I have noticed that the wider the saw at the handle, the lower the note I can get on the saw.
    Does the taper affect the amount of saw that vibrates?
    Is there a link to the reference? I don’t have subscriptions to any journals.

    • Some references talk about the taper making the saw easier to play. extract (from doi: 10.1098/rsta.1992.0052, 587-625 339 1992 Phil. Trans. R. Soc. Lond. J. F. M. Scott and J. Woodhouse). If you change where the s-shape curve is, you can move the lowest frequency up and down by changing which part of the saw is vibrating.
      The physics of musical instruments by Neville Horner Fletcher, Thomas D. Rossing has a little on saws and the preview is available on Google books.

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