Ivor Catt 13jan02
Today I did a search of my websitewww.electromagnetism.demon.co.uk and was surprised to find no mention of the violin string.
Two decades ago Mervyn Hobden told me that one Lucy would attend the Horological Society's AGM in Norwich. He said Lucy had a new theory about the musical scale, or some such. I told him not to tell me it, and first I would think about fundamentals. For some reason, this led me to consider the theory of the violin string.
[I went to Norwich. It turned out that Lucy, an ex-London Underground busker, only had a weird theory about the musical scale based on pie, 3.14, which as far as I am concerned, went nowhere. Later, he went off to Los Angeles and formed a California cult.]
First I developed my theory, and then I checked existing theory. I was astonished to find that although I was working in around 1980, I was reading articles from around 1920. Nothing had happened since then.
Text books said that the vibration soon settled down to a sine wave, and proceeded to analyse the sine wave. Nobody was interested in the initial situation.
I noticed that although the A level student was taught that the movement was a sine wave, that is, lateral, the student was also told that the period was twice the time for a sound wave to travel (longitudinally) down inside the string from end to end.
I discovered that the correct theory is at right angles to the reigning theory. (The same holds true of electromagnetic theory, which also needs to be turned through 90 degrees.) I then discovered that, although music was becoming a multi-billion dollar industry, nobody in the world was in the slightest bit interested in how a violin string really worked. This fact remains true. (Data compression for digitally recorded music is now a matter of dollar billions, but still there is no interest whatsoever in aids to improving compression, which would bring billions rather than millions to the patent owner. In principle, any deeper understanding of the source of music will aid data compression, but only if at least someone is interested. I am sure my co-author, who works for them as a designer, will fail to raise any interest in Sony Corp, which is deep in this business. Their music archive is worth billions.)
I drew on my knowledge of magnetostrictive delay line memory in the Ferranti Sirius computer that I helped to design in around 1960 in Manchester. I knew that in our memory, a torsional wave went down a wire at half the speed of a longitudinal (compression) wave. (However, that must have been a coincidence, since the velocity of a torsional wave depends on things like moment of inertia, which is independent of the parameters controlling longitudinal velocity. Thus, the second natural frequency for a violin string, which is my discovery, may not be a harmonic. Perhaps it should be, for better music.)
I also drew on my knowledge of the hammer in the line printer that I helped to design in Data Products, Culver City, California, in 1964 (before I was fired). I knew that when the hammer hits, the dwell time is twice the time it takes for a sound wave to travel from front to back of the hammer.
The first mode. Start with a string plucked at its centre. On release, a relaxation "pulse" travels towards the end, and another towards the other end. They reflect without inversion, and return, passing through each other at the middle. The cycle time is as given by the conventional formula. The key movement is longitudinal, not lateral.
Move to a string plucked off centre. The two relaxation pulses follow each other at a short distance.
When a bit of extra string exists, it will move off to the side to get out of the way. However, this does not mean that the movement is lateral.
Trying to get the theory from study of lateral movement would be like trying to model the movement of cars in a motorway by only studying the varying number of cars waiting at service stations alongside the motorway. That way, a theory could be developed, but it would not be the most useful theory. Similarly, when modelling a violin string, the primary movement, which is longitudinal, should be studied, not, as has been the norm, the lateral. Lateral movement is subsidiary. [Note 1]
The second mode.
Now bow the string with a bow. This rotates the string (second mode) as well as translating it (first mode). The string suddenly slips, and two torsional waves travel from the bow's point of contact, away down the string. Maximum magnification of the sound will be achieved if vibration of the hand holding the bow helps the next slip to occur at the moment when the original torsional wave gets back to the bowing point. This process is complicated by the fact that since the string is not bowed at its centre, the two waves with return at different times.
It is possible that ideally, the distance from the bowing point to the far end should be a multiple of the distance to the near end, so that the two torsional waves return to the bow at the same time.
It is possible that the string is so stiff that the second mode is negligible.
The third mode.
When plucked at its centre, the string, which strongly resists bending, does not take up the shape of a triangle, as is implied in the First Mode, above.
The true shape is a series of four diving boards of equal length AB BC CD DE, each with a diver standing at its free end B, B, C, C. The boards are clamped horizontally at A and D, and by symmetry, as though clamped horizontally at C. The diving boards and the divers are, (1) upside down at B, (2) right side up facing backwards at B, (3) right side up at D, (4) upside down facing backwards at D. Put another way, the shape is something like a negative cosine wave one cycle in length, with 2 divers as 90 degrees and two divers at 270 degrees.
When the plucked string is released, the portion of the string close to the point held flips outwards (laterally), and a complex oscillatory waveform travels out from the plucking point towards each end of the string. It is important to note that in principle, a portion of the string a little away from the point plucked may travel further outwards at the moment of plucking, giving the possibility of some sort of amplification in lateral movement.
This mode is complicated by the fact that the bow does not "pluck" the string at its centre.
The lateral stiffness of the string may make the third mode negligible.
Experiments to investigate these theories, or any theories, would not be too difficult. When I visited the late Gossick, the Heaviside doyen, in Oklahoma, he had an oscilloscope etc. attached to a violin. However, what deters me is that, should very interesting results come from experiments, they would be 100% recommended for rejection by all referees for all learned journals in the world. My research into the Politics of Knowledge, centering on electromagnetism and also to a lesser degree on subjects including AIDS, proves that our society is medaeval in that new information may not be published. Thus, why bother to do the experiments?
I wrote all of the above theory, with diagrams, in the early 1980, and distributed it reasonably widely. There was little interest. As with electromagnetism, I show that financial motivation, and also search after truth, are not significant motivators in today's society with its paranoid fear of being involved with new ideas. Truly a medaeval society.
Improvements in theory would make a Stradivarius clone more feasible. Only millions of pounds there however, not billions.
Ivor Catt 13jan02
Note 1. The assertion that sideways movement is subsidiary can be tested. Instead of stealing a length of the string by plucking sideways in the normal way, steal a small section by putting a nick in the string; a tiny S. That is, by some means, create the same tension in the string without imposing lateral movement. My view is that the effect would be the same, even though lateral movement had not been introduced in the normal way. I argue that the sine wave, which then excites the air, is a secondary effect which is not directly linked with the initial movement of the violin string, which is longitudinal. Another way would be to move the end posts out slightly, and then suddenly return them to their proper position. That will impose the longitudinal movement one quarter cycle later than is effected by plucking the string at its mid point. According to the view argued here, the effect would be the same as plucking the string, although no lateral motion had been imparted. 31jan02
Financial pressures and also search-after-truth do not control today's culture, which is medaeval. The fear of thinking in any way differently from everybody else, or even of knowing something unknown to the majority, is very strong today. It overcomes Enlightenment search-after-truth, or even the drive which is supposed to have overtaken it; search after profit. Another example of the fear of any involvement in something new, however great the potential financial reward, is the The Seven-per-cent Rule , which, along with the theory of the violin string, is totally ignored. This is in spite of the massive profit to be made out of improving text compression. Ivor Catt 31jan02