Supplements for Chapter 18
The University of New South Wales website is strong on the violin, much of it recent research done there.
Excellent perspective on bowing a violin by Jim Woodhouse and Paul Galluzzo here.
Useful and well organized reference, Acoustics for violin and guitar makers.
Watching a Helmholtz kink form on a bowed violin string. Helmholtz kink is an excellent video.
Excellent demonstration of the bowed violin string, including forces on the bridge:
Another good demonstration is found at http://www.phys.unsw.edu.au/jw/Bows.html
There are two other remarkable resources about the violin: First, the Catgut Society, founded by Carlene Hutchins and Fred Saunders, has a long history of research and many collected works, and second, the luthier Martin Schleske and his website. If Schleske is not a modern Guaneri, which he may be, he is surely the most informed and scientifically engaged luthier in the world. His website is a treasure trove of interesting data and observations.
Great video of a Helmholtz kink wave in a bowed violin
Violin tone quality issues and causes
Article on the attempt to quantify why Strads are so revered:
Another excellent section of the UNSW site, worth a visit:
The Helmholtz wave on a stretched string.
The great discovery of Helmholtz was a secret hidden from every violinist, fiddle player, cellist, etc. It was always right in front of their eyes, yet too fast to see: the shape and motion od a bowed string. For an up-bow, a kink circulates counterclockwise along the dotted path shown. As shown in Why You Hear What You Hear, this leads to a sawtooth-shaped force on the bridge, rich in harmonics yet periodic, just as the kink itself circulates around periodically. This drive, with its sawtooth harmonics, is the beginning of the story of the timbre of a bowed violin.
The only way many harmonics can be present, yet the sound be periodic, is if the harmonics are spaced equally in frequency, based on some fundamental, lowest frequency. The ideal string has modes equally spaced in frequency, as we saw in Chapter 8. A real string, as mentioned there and this chapter, has at least small deviations from this equal spacing, revealed if it is tested by plucking it and measuring the frequencies present. It is suggested that you try this, on any stretched string instrument you can find. Record a long tone after plucking, and get its power spectrum using your favorite sound processing software. If you have a mouse driven tool that places vertical lines at multiples of the mouse position on the power spectrum plot, you can see at a glance any deviation from equal spacing. Otherwise you need to measure the peaks by hand.
A bowed string involves feedback and energy provided by the bow, and since it re-enforces periodic motion (helping the stick-slip mechanism) it may entrain, or enforce strictly periodic motion on the string, even if when plucked it would deviate from that.
The trick mentioned at the end of the chapter, namely putting small pieces of putty or tape in the middle of the string, causes the frequencies to deviate more from equal spacing, making the job of entrainment harder. Eventually, for a surprisingly small piece of putty, the entrainment mechanism breaks down, and the bowing ceases to work. A screech or scratchy sound is emitted. The stick-slip nonlinear feedback requires a nearly periodic response, that it can coax into strict periodicity. If too non-periodic, it cannot succeed in enforcing periodicity, and the result is catastrophic.
The string if plucked emits a somewhat weaker, sour tone. Its power spectrum reveals stronger deviation from uniformly spaced harmonics.
The sawtooth waveform, as seen in Paul Falstad's Fourier Series:
Question: Does the sound of this waveform depend on the phases? What if they were randomized? Does the answer to this question depend on the chosen frequency? (Try it!)
Damping of string vibrations: the Underwater Ukulele
Sonogram of Ukulele underwater at the left, Ukulele in air at the right. Note the strong damping under water, even stronger for the higher harmonics; these never really get going. The sounds are here.
Vibrations of violin plates:
The Physics of Music: Readings from Scientific American,The Acoustics of Violin Plates, by Carleen Maley Hutchins
See also this discussion and illustrations of Chladni patterns for violin plates, from the UNSW.
Although mainly an issue with larger strings such as the cello, a wolf note can strike any stringed bowed instrument. It is due to a resonant, overly strong coupling between string and body vibrations at a particular frequency. The video is quite instructive and you can hear a wolf: