Additional Reading
Many scientists have, over the years, studied the occurrence of wolf notes in string instruments. The numbered references cited in the wolf note page are given below.
1. C. V. Raman, Phil. Mag. 32, 391-395 (1916)
The work of C.V. Raman an Indian researcher at the turn of the century is often credited with pioneering work on the wolf note.
2. John C. Schelleng, “The Violin as a Circuit”, JASA vol 36, no 3, 326-338, March 1963
Schelleng published a paper in 1962 in which he describes a musical instrument (cello) in terms of an electrical circuit. The concept of the string splitting into two frequencies when approaching the frequency of the main body resonance is introduced. Taking the variables of body stiffness, mass of the body and impedance (resistance) of the string, he formulated parameters in which it would be possible to predict the likelihood of whether or not a given instrument would produce a wolf note.
3. Ian M. Firth and J. Michael Buchanan, “The Wolf in the Cello”, JASA, vol 53, 457-463, 1973
Ian Firth, a physicist at the University of St. Andrews, Scotland, through experiments in 1971 confirmed many of Schellengs proposals and introduced other findings of his own. He determined that as the string vibration approaches the frequency of the main body resonance, the change in frequency is not linear, but tries to stay away from the frequency of the MBR. He observed that it is possible to have a wolf note over a limited frequency range as opposed to a single frequency.
4. Arthur H. Benade, “Fundamentals of Musical Acoustics”, Dover, New York: 1990
In this book, Benade explores the wolf note phenomenon in more readable layman’s terms. His analysis of the wolf note documents the history of wolf note research, and provides an analysis of the wolf note through his own study and experimentation. This book also explores the acoustics of the major musical instrument families as well as the voice.
5. Thomas D. Rossing, “The Science of String Instruments”, Springer, New York, 2010
Thomas Rossing, editor and author, in addition to authoring chapters covering string and plucked instruments, explores the wide variety of musical instruments which all happen to employ strings. These include plucked strings (fretted and not), piano family, harps, hammered strings, electric instruments, and synthesized string instruments. For the most part, it doesn’t require a math degree to understand it, and for general knowledge of string instruments, this book is well worth reading. Of particular note is the detailed information on double basses.
6. Helmut Fleischer, “Dead Spots of Electric Basses” Beitrage zur Vibro-und Psychoakustik, Neubiberg 2000
Dr. Fleischer’s research, on the dead spots occurring in electric basses (and guitars) stands out as there is very little scientific information available on this topic, compared to that available for string instruments. His comprehensive studies center around the testing of five different makes of electric basses, concentrating on the different vibration modes of the neck. The instruments are tested in situ (in playing position) as opposed to holding suspended or in a stand which can affect the vibrating frequencies. The study doesn’t include methods or proposals for eliminating the dead spot.
Studies on the cello wolf note are readily available through a web search while the double bass wolf note, has had less attention. This is in spite of the fact that (according to bass players!) basses have more difficulties with wolf notes than cellos. The more recent studies, which reflect the latest information regarding the production of the wolf note, will usually be more useful in finding effective ways in which to control the wolf. And a careful search can even uncover research on the violin wolf note.
