Wolf Tones and What to Do About Them

The physics of music matters, particularly when a cello, bass or violin produces an unintended sound. Understand how it works to fix it.

There are many reasons why education policy experts encourage adding an A, for arts, to STEM (science, technology, engineering and math), giving us STEAM. The general theory is that the engineer with a background in art can think more expansively and creatively. The example of this at work is often how Apple Computers increased its market share with friendly designs and an aesthetic interface.

That said, the benefit could go in the other direction, where artists benefit from understanding science. The making of music, as in the vibrations produced in fine string instruments, is in fact a product of physics. Modulations of compressed air caused by vibration are entirely responsible for what makes Tchaikovsky’s Cello Concerto fragment (completed by Ukrainian cellist-composer Yuriy Leonovich) soar, from the Allegro maestoso (B minor) through the Andante (G major) and Allegro vivo-Meno moso-Presto (B minor).

Yet, certain of those physical vibrations happen to be the cause of the very vexing “wolf tones” that can cause great players and great instruments to sound – unfairly – flawed.

Why is this? Students with an interest in the violin, cello and viola probably understand the basics of string vibrations. The sliding of a bow or plucking on the strings cause those strings to vibrate, but the fullness of the sound is also due to vibration interaction with the body of the instrument. The interaction between these two components is what lends the musical notes their full resonance.

Which is to say the body of the instrument vibrates as well. Every physical object, from micro-sized specs of dust to huge office towers has what is called acoustic resonance, the vibration of that object. Now, the physics student – who is also a violinist – will know that doesn’t always work out so well. The phenomenon of wolf tones occurs when the vibrational frequency of two things – here, the string and the instrument body – is the same or very close.

A wolf tone will more typically happen on a cello or a bass, less noticeably on a violin. The sound begins with the intended note that disappears and is replaced by a different note and sometimes a stuttering sound. On a cello, that can happen on the D string between the E and F#, or the same pitch in higher positions on the G or C strings.

The first instinct is to assume there is something wrong with the instrument, or the player. Au contraire, mon ami. In fact a cello in good adjustment – properly fitted bridge and soundpost – is more likely to suffer from wolf tones. A visit to your local violin shop can make this determination.
There are several means to tame the wolf, so to speak. Rubber mutes and brass suppressors placed between the bridge and the tailpiece on the G or C strings might help. Other remedies might be: adjust the sound post, try different brands of string, change the tail piece or make a tailgut wire adjustment.

Some cellists find that simply squeezing the body of the instrument with the knees attenuates the effect. So while that application of physiology might seem unorthodox, consider the potentially destructive force of acoustic resonance in one very large building, the Taipei 101 in Taiwan. Building engineers used a 660 metric ton pendulum, also known as a tuned mass harmonic damper, to reduce the amplitude of mechanical vibrations caused by wind on the 101-story (1,671 foot tall) structure. This minimizes swaying and twisting of the building, which otherwise would cause motion sickness in occupants and even possibly structural failure.

Science matters – and it works!

The Lowdown on the Viola and Violin Shoulder Rest

Violinists are split on if the shoulder rest helps or hurts their play. Medical professionals recommend it for people with sore necks and shoulders.

The sound a violinist produces, as well as the mastery he or she has with the technical aspects of the score, is considered the goal and achievement of the musician. But if the player develops orthopedic issues that make him unable to play there will be no music at all.

This is why developing proper posture for violinists and other instrumentalists is more than just important – it can kill the enjoyment of playing, perhaps even the ability to play entirely.

A study conducted in Brazil and reported in Acta Ortopedica Brasileira, a peer-reviewed medical journal (and cited by the U.S. National Institutes of Health’s National Center for Biotechnology Information), on the physical demands of musicians, in particular the musculoskeletal disorders that “most frequently affect professional violinists and violists.” It looked how “playing a musical instrument involves a combination of actions, including rapid, repetitive and complicated movements of the hands and fingers … the neck, shoulder and temporomandibular joints are the most commonly affected areas, due to prolonged flexion of the head required to hold the violin.”

Prescriptives cited by the study include “the use of the chin rest and of the shoulder rest (commonly used accessories for violins and violas) at appropriate heights … can alleviate discomfort, even if they increase the weight of the instrument by up to 20 percent.”

Yet, some musicians wouldn’t consider using an appendage to the instrument. Shoulder rests – variously made of wood, aluminum, carbon fiber and soft plastic – are used by both players of violins and violas and are readily available at any online violin store as well as brick and mortar shops. They attach to the edge of the back of the violin, which might affect the sound quality by dampening the vibrations of the instrument.

The benefit of the shoulder rest is it can lighten the work on the left hand, allowing that hand to move more smoothly and fluidly with lighter shifting technique.

Many accomplished violinists use one, however many do not. Nathan Cole, the first associate concertmaster of the Los Angeles Philharmonic and a faculty member of the Colburn School for the Performing Arts, used a shoulder rest for his first 30 years of play. When invited by the owner of a Stradivarius (most often played by Nathan Millstein) to give a short recital in the owner’s home on that instrument, he realized it would not be acceptable to use a shoulder rest. The experience was initially daunting, but he found he was able to do it without the shoulder rest. He reports on his blog, “I’ve arrived at a different vibrato and a greater variety of shifts, compare to my rest-ing days…I like the changes.” He adds he changed his chinrest to something very minimal, that he brings the instrument up rather than to lower his head, and that his shoulder occasionally rises momentarily.

So if you use a shoulder rest, try it without. But if you have neck or shoulder issues, it might be worth to give a shoulder rest a try.

Fibonacci Series and Stradivarius Instruments

Math is intrinsic to music. But what’s truly fascinating is how the designs of fine violins, flowers and huge galaxies connect to Fibonacci’s Golden Ratio.

The Fibonacci Series might sound like a spy thriller, but it’s perhaps more exciting because it draws a direct, mathematical connection between the human perception of beauty and nature itself. It also was the basis for the proportions that Antonio Stradivari used to construct his eponymous violins.

It starts with a mathematical pattern of increasing values. They are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 and so on; each number represents the sum of the two preceding it. Taking any one number from the series above 5 – let’s say 21 – and dividing it by the previous number (in this case 13), the ratio is 1.6. This is referred to as the Golden Ratio.

Represented in geometric forms these numbers and the Golden Ratio create a spiral that is seen in both art and nature. To a musician, the bass clef is essentially this form. Leonardo da Vinci’s Mona Lisa is composed of points that conform to this geometry. Mozart wrote many of his two-part sonatas according to the Golden Ratio: the exposition (musical theme) is 38 bars and the development and recapitulation (where the theme is developed and repeated) is 62 bars, and 62 divided by 38 is 1.631. Western harmony and musical scales, with 13 notes in an octave and eight notes in a scale, also produce (via division) 1.625.

With Stradivarius’ fine violins, the master violinmaker’s designs follow the Golden Ratio in the proportions of specific parts of the violin. The violinmaker ensured the proportion of the neck, pegbox and scroll to the body of the violin (upper bout, waist and lower bout) achieves the ratio.

Also, subdivisions of the instrument – waist to upper bout, waist and upper bout to those sections plus the neck – meet the 1.6 ratio as well. (Note: there seems not to be the same mathematical principle applied to fine cellos, violas, and stringed bass instruments created by the master maker).

Is this what make the music from a Strad so rich and resonant? So many other factors are involved (the density of Cremonese wood in the 17th century, for starters) but it bears noting that the Golden Ratio is also used in saxophone mouthpieces and the acoustic design of many cathedrals. In the Journal of the American Viola Society, a 1994 analysis of Bartok’s Concerto for Viola and Orchestra (Movement Two) argues the composition relies heavily on the Fibonacci Series.

Where this takes a fascinating turn is how the Golden Ratio and its geometric representation is found in nature and even in space. The logarithmic spiral, found in seashells and sometimes called “the golden spiral,” look a lot like that bass clef and range in sizes from tiny to much bigger – all within the same ratio. But those same spirals repeat in spiral galaxies, where the arms of stars, gas and dust extend from the galaxy center in a pinwheel-like fashion – a pattern in proportions also seen in satellite images of hurricanes. The human face, by the averages, follows the Golden Ratio in where the eyes, nose and chin are positioned. The proportion of DNA molecules, 34 by 21 angstroms, fit the ratio as well. In flower petals, the lily has three, buttercups have five, chicory flowers have 21 and daisies have 34. Nature places all petals in the 360-degree circle, at a turn of 0.618030 (an inverse of the 1.6 ratio). Seed heads in sunflowers repeat the spiral seen in these other examples.

Is it possible that this Fibonacci Series is a universal proportion, determined by some version of intelligent design? That’s subject to some debate, to put it mildly. But what’s clear is it all adds up in Stradivarius violins playing Mozart sonatas.