Hints for Area Tuning the Violin

by Keith Hill © 2005 Originally published in American Lutherie #1, 1985 In my article Area Tuning the Violin I presented my discovery of one of the theoretical principles governing the acoustical quality of the violins made by Stradivarius and his numerous Italian contemporaries. Because I believe that the area-tuning principle is the most important of all the acoustical principles pertinent to violin making, I deemed it best to present it in isolation. I would be less than open with you if I did not say that the American Acoustical Society and the Catgut Acoustical Society both rejected the worthiness of the area-tuning principle. I feel that their reasons were full of vested self-interest and their own theories based on plate flexibility. I tell you here what I told them: Paying attention to flexibility of free plates is a waste of time and attention. Consider the following points. First, thousands of violins have been made using this notion for the last century, yet no consistently superior results have been produced. I used to test my plates for flexibility but quickly abandoned the practice when it occurred to me that there was no objective measure for flexibility. It seems that something which must depend on muscle tone of the person doing the flexing, which can change from day to day, is highly subjective and prone to mistakes. What the flexor has been doing just ten minute before can influence that test. Those who would input electronic testing equipment into the process are to be made fools of by Stradivarius and his colleagues who needed no such equipment. Second, making so-called objective measurements of plates (ala Chaladni et al) and doing ex-in situ flexing of plates has very little to do with how the top and back behave in a violin that is set up and playable. Microphones, as good as they may ever be, are incompetent replacements for ears and brains unless those who are doing the hearing aren’t connected to either, in which case microphones may indeed be superior to either or both. That not withstanding, microphones are too colored in how they pick up and transmit signals. The diaphragms, wiring and housing all contribute significantly to the signals. And how glitter or iron filings on a violin plate or surface behaves when the plates not glued onto a set of ribs with another plate opposing it nor being stopped someplace off-center of the middle, is acoustically uninteresting. Should acoustic researchers discover a way to make such measurements and take photos of glitter on plates of a great violin while it is being played with a bow by a really good player, then what they come up with might prove to be interesting. As it is, these pseudo-scientific (visually dominant) measures of acoustical (aurally dominant) phenomena are irrelevant at best and not even entertaining at worst. They deceive those who want to learn about acoustics and delay their own more productive investigations, filling their heads with nonsense. Last, the amount of distortion that you can subject a free plate to never happens on a playing violin. The notion that the old masters had a ``mystical intuitive measure or sensibility,'' seeming to know where to remove wood depending on how the plates flexed, is wishful thinking. The removal of wood must have been methodical and direct for such consistency of result to exist. The area-tuning principle leads the way to a methodical, direct, no-nonsense approach. At this point, I feel it might be purposeful to add to the discussion some thoughts and hints of a more practical nature specifically for luthiers. It is my genuine interest that those of you who desire to use the Area Tuning principle not be hampered in your endeavors. I hope that what I offer here will contribute to that end. Hint #1. I cannot urge you strongly enough to use a monochord instead of tuning forks, electronic devices, and so on. I have conducted all of my experiments using this tool. I find the monochord to be more versatile, more reliable, easier to use, better sounding, and less sensually insulting than the other devices. It is more convenient to use because the overtones are so easy to find for any given frequency. Hint #2. To build a monochord, glue together three pieces of pine or basswood, about 4” x 5” x 40”, using one piece as a bottom and the other two pieces as sides for the box. Fill one end with a block 1” thick. At the other end, cut a 1” end block short by 1/2” , or drill several large holes in it, to allow an air space between the bottom and the block. Glue this block in so that its top edge is flush with the top edge of the sides of the box. This air space will act as the soundhole. For the top, glue to your monochord a 1/8th” thick piece of quartersawn pine or spruce. The box is now complete. When the glue is dry, trim off all excess wood and glue and chamfer the edges in order to make the box pleasant to handle. Then, proceed to pin, bridge, and string it. I use headless nails for hitchpins, zither tuning pins, and .010” hard steel wire for strings. For the nut and bridge I use walnut, but maple will do just as well. The cross section for the nut and bridges should look like a house as seen from the end. Hint #3. I have two strings on my monochord. One of the strings stays at a constant pitch and acts as a point of reference, removing the nuisance of constantly having to refer to a tuning bar or fork to make sure that my monochord is at pitch. Technically speaking, a monochord is a musical instrument that has one string, which is fixed at one end and adjustable for tuning at the other end. It has a fixed nut while the bridge at the other end is movable. A third bridge is a classical feature which you can introduce should you desire to redo the experiments and calculations of Pythagoras regarding the overtone series. However, these calculations are readily available in books. Start by determining the length for the strings at A-440; I use 22 1/2”. Next, the scale has to be plotted out. I use an equal-tempered scale for reasons too complicated to discuss in this article. An electronic device is best for this purpose if it is accurate because it is fast and easy. Move the bridge until the desired note is achieved, then accurately mark that position and label it with the pitch name. Calculation of bridge positions, such as fret scales, is not workable because string tension is a dynamic variable. Because of this variability, it is important to remember to always keep your monochord string at pitch during this procedure. Any slight variances can be troublesome to you in the future. Hint #4. Use junker violins purchased from your local violin repair shop to conduct your initial experiments in using the area-tuning principle. I think that you will find it easier to start learning to tune the wood on violins that are already complete, but clearly worth nothing. You can pop off the back to scrape away on the inside of the top while it is attached to the ribs. The back, because of the harder wood, is easier to work on when it is off the ribs. Leave the fingerboard on. When you have reassembled the instrument you can hear the results of your work almost immediately because the instrument is finished. I never bothered to even clean off the glue except in those cases where the instrument turned out well enough to sell. When selling these glorified pieces of junk, don’t ask too much over the price that you paid for them. The idea is to get on with the next experiment using an instrument of fractionally better quality each time. You may have to do five or six experiments before you get results worth selling. Once you do start getting results, turnover is crucial. I used Titebond glue only on my first experiments in order to hear the results as soon after the tuning as possible. I found that I could disassemble the instrument, tune the wood, and glue the violin back together all in the space of four hours. Within five hours I was hearing the results and judging the success of the experiment. Hint #5. To determine the success of your experiments you must have worthy criteria. I used the functional performance criteria exhibited by the greatest antique violins, as judged by the greatest violinists. These criteria may at first seem vague, but once heard and recognized, they are obvious: 1) Ease and immediacy of tone production. 2) Fullness of tone or resonance. 3) Depth of tone. 4) Freedom of tone. 5) Glowing brilliancy, not to be confused with brightness. 6) Great purity of tone. 7) Transparency of tone or clarity. 8) Solidness of tone. 9) Strength of tone. 10) Great carrying power. 11) Flexibility of tone, the ability of the sound to be altered by the player to create different vowels. 12) Superior tonal balance, that the sound feels complete in every way regarding the proportional relationship of the overtones to the fundamental. 13) Evenness of response between the strings, that the strings speak equally well throughout, letting nothing stand out or be less than it could be. 14) Seemingly unlimited tonal reserve. 15) Richness in the bass and fullness in the treble. 16) That the instrument should give the player the sense that it is easier to play in tune. 17) Finally, what I call the ``distortion resistance effect.'' “The Hill Effect” Hint #6. What I call the ``distortion resistance effect'' is a phenomenon which I, and others, have observed, and for which I believe I have discovered the reason. The phenomenon is that the strings exhibit unusual resistance to being pressed to the fingerboard. Also, even though the instrument will speak with ease and immediacy, the strings will want to speak the overtone rather than the fundamental. The strings appear to the player to offer a certain physical resistance to the bow pressure. So when players speak of great instruments as being ``hard to play'' they mean that they are hard to control. What makes them hard to control is the distortion resistance effect. It requires skill to overcome the distortion resistance effect when playing. Stradivari violins are often observed as being not altogether easy to play even by accomplished players. It is due to the distortion resistance effect, which I also call the Hill Effect as I believe I am the first to correctly link the phenomenon to its cause. The cause of this effect is related directly to the area-tuning principle. When the wood has been tuned according to the overtone series, the distortion resistance effect will result. Instruments which do not exhibit this effect, yet are tuned, are usually tuned to pitches other than the overtone series. Stainer’s violins, for instance, do not exhibit the distortion resistance effect as intensely as Stradivari or Guarneri violins. His instruments are tuned using pitches like fourths, minor thirds and seconds, and minor sixths, as well as an octave. The more perfect the tuning of the wood the more resistant the strings will feel. I had a conversation with a violinist from Milwaukee who had the pleasure of playing on Paganini’s del Ges— ``Cannon'' in Genoa. He reported to me that the strings were so stiff feeling that he cut his small finger while playing on the instrument for an hour. I would expect that an instrument like the del Jesu “Cannon'' violin would be extremely well in tune. It would help account for why Mr. Paganini wrote as much as he did exploiting the harmonics for his compositions. You can test for this effect yourself by pressing lightly down on to the strings of several violins, including a good old Italian instrument. Because the string lengths are basically the same, the feeling of stiffness should be the same. But it is not. Although Dominant ``stark'' strings on a mediocre violin may seem stiff, they are flabby feeling when compared to gut strings on a well-tuned instrument. Hint #7. When experimenting on finished instruments, you will need to support the plates to avoid breaking them. One solution is to use a thin sheet of foam rubber. It gives firm support broad enough to prevent breakage. Another is to secure the plates for tuning to a workboard which has been cut out in the center. When the plates are placed upside-down in this board, the edges are supported all the way around, leaving the rest of the plate surface to vibrate freely. Hint #8. You can’t check your tuning accuracy often enough. I check my tuning over and over again at different times just to make sure that it is right. My method is to do the initial tuning as a finishing of the carving-out process. I then glue on the bassbar and tune the plate again. After gluing the top to the ribs, I cut out the f-holes and tune the top yet again. Once the back is glued on, I tune both plates once more on the outside with fine sandpaper. This is the last tuning before the varnishing is started. Once I begin varnishing, there is little to be done to radically alter the tuning. Always allow some time to pass before taking up the plates to check the tuning so that you start with ``fresh'' ears. When the plates are perfectly in tune according to the scheme that you have worked out beforehand, you can be absolutely sure that the violin will turn out first rate. The principle does all the work for you; all you have to do is be present and exert some effort to that end. I am sure that this is how the 17th- and 18th- century Italians could work so confidently and prolifically. Hint #9. When the outsides of my violin plates are finished, I place them on a lightbox to carve. My lightbox is topped with a piece of plywood with its center cut out like the workboard. With the light shining from beneath, I can be sure that the wood never gets too thin. The final tuning process is also very speedy. The light allows me to relate wood thickness to color; thicker wood is brown and thinner wood is orange. Wood thickness is also related to pitch; so brown colored wood is higher in pitch and orange colored wood is lower in pitch. The old masters could have used cutouts in the shutters of their workshop windows which would have given similar, if less convenient, results. Hint #10. Learning is more a process of extracting the ``clearly wrong'' than doing what is right the first time through. Learning, the natural way, occurs when the greatest freedom for making the most mistakes exists; all infants learn language this way. By using our sense of what is right, we can systematically remove those things which are wrong; we need only look. Our attitudes will be the only things preventing us. Learning what to listen for when you knock on the plate of a violin is not easy, but it can be done by everyone who has normal hearing. You must isolate and recognize what all the possible sounds are and ignore everything but that which you wish to hear. You will hear many things when you use your knuckle to tap on a plate ready for tuning. Use a scraper to tap the plate as well. The sound produced by the scraper will augment that of the knuckle and vice versa. A catalog of the sounds heard will include: the pitch and resonance of the knuckle bone, or the click of the scraper; the pitch of the whole plate; the resonance of the whole plate, i.e., the dying away of the vibrational energy; the pitch of the spot of wood directly under the knuckle or scraper; the pitches of the edges of the plate when held and knocked freely; the pitch of the exact center of the plate, usually a semitone different from that of the whole plate; the pitches of all of the other tunable areas not directly under the knuckle; the pitch of the area being tested (this is what you are most interested in hearing); and the effect of each of these sounds being reflected by the room. If you use a lightbox, you will also hear everything sounding from it. It is not very audible, but you can hear it when you focus on it. What you will need to pay the most attention to will be the pitch of the wood directly under the knuckle. It might be useful to look at how the ear hears in order to focus the attention successfully. The ear is a wondrous device. It hears everything audible to it. Yet, you rarely ever become confused about what you are listening to. I point out that it hears while you listen. This capacity is both a blessing and a curse. When you desire to, you can focus your attention on the subtlest sensation initiated by the lowest intensity sound in a highly complex stimulus. This is a blessing, especially if you know what you should be listening for. The curse occurs during those times that you are exposed to sound which you have no desire to hear but you are incapable of tuning out. When you actively tune in to certain stimuli, you equally actively tune out most other things that the ear is, in fact, hearing. The act of tuning-in or tuning-out depends very much on what your preferences are. To refine the sense of hearing demands that you examine your preferences. By preferences, I mean timbres which you like over others, or habits that die hard, or ideas that you might have been working on for so long that they demand that you not put them down even temporarily, or attitudes that you refuse to give up. Attitudes are curious things. They are the only things which we have absolute control over, yet we rarely exercise that control. As you judge your preferences to determine those of lesser or greater worth and those of lesser or greater significance, your ability to listen clearly will naturally readjust itself according to the priorities that you have established. In effect, you express your judgement and listen accordingly. If what I have been describing were an easy thing to do, most people would do it. It’s not. It requires months, even years, of intensive and patient scrutiny regarding preferences to achieve clarity of ear, hence clarity of mind. The easy path, though somewhat liable to error, is to replace one preference for another. To use the area-tuning principle, period, you need only prefer to hear it. To use the area-tuning principle masterfully, you will probably have to overhaul your preference system. Hint #11. The very best way to keep track of how you are doing when tuning the areas is to always be checking the relationships that exist. By this I mean that you will need to watch how the pitch changes relative to the pitches that already exist in the other areas. Tap one of the areas as many as three or four times and then move to another area and tap as many times, always sensing the interval that exists between them. Hint #12. Most people to whom I say this are very amused. Using the same method of tapping or knocking, tap on your body to discover the overtones that exist on you. All your bone are tuned to overtones of a basic pitch in your body. That pitch resounds when you thump or tap on your breast bone. You clavicle or front shoulder bone usually sounds a 5th above that pitch. This is where the area-tuning principle comes from. Why not hear it first where the hearing is the easiest, that is, on your own body? Each person will have something different in how his or her bones are tuned. The beauty of it is just that. Everyone is different, yet everyone is of equal quality. True, there are some voices that we love to hear; maybe you should knock on those bodies to determine their tuning scheme and use that on your violins. I’m serious! It is well known amongst singers and voice specialists that these areas resonate but until now no one to my knowledge has defined their specific property of being tuned according to the overtone series. It is hard for me to believe that I am the first person to make this observation, but there it is! Hint #13. When you tune the wood in any given area on your violin plates, tune each annular ring. To do this, you will require a scraper of small size. Do the tapping with the edge of the scraper. Listen only to the click of the scraper as it hits the wood surface. The frequency of this click is a fifth above the fundamental pitch of that area, an octave up. The scraping sound is also the same pitch as the click, but a bit more difficult to focus on. Tune each ring along its entire length within a given area. The reason for tuning each ring is that no two rings are alike. Differences in ring density will necessitate differences in wood thickness for the rings. You can circumvent this by selecting wood for homogeneity between the winter rings. Good Luck! I have only found one or two pieces of wood that were homogeneous between the winter rings which I thought would yield a resilient sound; most were too punky. I like resilience more than I like homogeneity of growth. If you do too, then leave the harder rings thin and the softer rings thick. The ``Art'' of anything is to enhance decent materials by being willing to adapt to any set of conditions to produce the best effect possible. What I have been discussing here are the ``details'' of acoustical craftsmanship. If we are to master our craft, we need to master it at this level. Hint #14. It’s important to remember that the violin plates are complex because they vibrate freely in some areas and are partly constricted in others, such as the edges and the areas nearest the bassbar. You will need to make the parts near points of constriction thinner because constriction creates stiffness and stiffness equals higher pitch. By making the constricted areas thinner, you make them more flexible and bring them into tune at the same time. Given two surfaces of unequal size, you need to thin the smaller of the two surfaces to make them sound the same pitch. Area size is directly proportional to pitch, given an equal thickness and material. Stiffness is the key factor involved. To test this phenomenon, tap on a drum head. Tapping from the center to the edge, you will notice that the pitch rises. Were the membrane thinned towards the edge you would get less rise. Doing this thinning causes the membrane to act in unison with itself. This is precisely the effect that you must create on your violin plates. According to my observations of antique fiddles, the mediocre Italian instruments made during the ``Golden Age'' were tuned only in the centers of the areas while at the edges they were left untuned. Hint #15. Begin tuning by tuning the largest area to the fundamental. Proceed from the largest to the smallest. Should you tune the smallest areas first, you would have to retune everything if you made a mistake on the largest areas; all the pitches of the smaller areas would be out-of-series (nonharmonic). Hint #16. Once I have determined exactly what frequency I want to end up with, I tune the largest area down to the frequency one semitone higher. I then tune all the areas to that area so that I end up with a completely tuned plate exactly one semitone sharp of my final destination. After this I can confidently go right to the exact and final pitch. This method is very safe. Hint #17. Accuracy, accuracy, accuracy: This is your goal. Even the pitch you select for an area is not as important as accuracy of tuning. The beauty of the area-tuning principle is that you can make an error pertaining to the pitch, when tuning, without ruining the plate. Simply tune down to the next semitone lower if you’ve gone too far. Although you may not get the exact sound that you were after, you will always get a sound which is resonant, brilliant, open, and free. Who knows, you may even surprise yourself and come up with a tuning scheme that you like better than what you had planned. Hint #18. Wherever there is a strong curvature in the modeling or a change of direction of curvature on the modeling, you will need to thin the wood at those places. Curvature makes the wood stiffer. Hint #19. When you are scraping on wood which is perfectly quartersawn, you will need to make that wood a bit thinner than wood which is not, even though the wood is on the same area. Grain at 90 degrees or perpendicular is stiffer, hence, higher in pitch than grain which is 88 or 92 degrees. Hint #20. Take pains to make the exterior surface of the violin plates as highly polished as possible. The reason for this is that a rough surface dampens the highest frequencies while a polished surface reflects them. Hint #21. This hint is troublesome to discuss, and I hesitate to discuss it in this article. The reason is that it is esoteric and therefore too easily misunderstood. However, I include it because I feel that without it your ability to understand what I have presented thus far might be impaired. Maybe, maybe not. To be complete, any art must incorporate three elements. These elements are philosophy, theory, and practice. These correspond directly to the three elements that form our own nature: spirit, mind, and body. Philosophy guides the spirit, while theory guides the mind, and practice guides the body. Usually the mind and body follow in close order after the direction set by the spirit. So the foremost of the three elements is philosophy. For without right attitudes, theory and practice would be subject to much wrongheadedness much in the same way that practical techniques become meaningless manipulations when they are unsupported by true theoretical principles. The last 150 years of violin making attest to this truth. So, if the function of philosophy is to guide, ultimately, our actions, then we need to think seriously about the aesthetic act of sensing. I use the word sensation to mean something specific, but quite different than the conventional usage suggests. I mean sensation of the purist kind, so pure that you can’t prove what you sense much less talk about it. This level of sensation is many times deeper than the mundane variety. It depends very much on how the mind or consciousness is directed. When you direct your attention to what is happening within the sensing mechanism or organ while it is sensing, you can perceive what I mean. It is sensing with the mind how the experience of sensation feels when sensing is taking place. It is noticing the effect sensation has on the subtler aspects of the sensing organ and seeing how the mind is affected by it. This level is the level I call true knowledge. This is the level at which you know absolutely. You need not interpret, question, or believe with your mind; there is only complete awareness. You can react emotionally to what you sense but you do not need to, necessarily. You have no control over the sensation of sensation. You can only control your awareness of it. I believe that this level of sensation is absolutely objective. Nothing about it is relative. It is, or it is not. How you feel about it is irrelevant. This level is subject to only one thing, the presence of stimulation. The fact that you can not prove what you ``know'' in no way invalidates the awareness you achieved. It just means that you need not even try to prove what you ``know.'' This level of human experience is wholly free from deception. All other levels are subject to possible deception either from the self or from a source other than the self. Because this level is free of possible deception you can trust it completely. An exercise for becoming aware of this level of sensation is to enter a totally dark room and, looking into the direction of the light source, turn on the light. At the moment that the light shines, you will sense many things. Be aware of two separate responses in the eye. The stronger of the two is the sensation of the muscle controlling the iris changing the size of the pupil. The second and significantly weaker sensation is the sensation of the effect experienced as the retina is exposed to light. The important idea here is embodied in the words sensation of the effect. This is the root of aesthetic awareness and appreciation. Upon this, all art is constructed. This exercise merely demonstrates in one sensory mode, sight, the level of sensation that I have been discussing. The question is, so what? What’s so important about this level of pure sensation? The answer is nothing, really. In and of itself, nothing is important. What is important is the effect on the mind that paying attention at this level has over a long period of time. A mind which is accustomed to being aware at this level of sensation naturally thinks profound thoughts. This is because the step between awareness at this level down to the level of the mind being aware of itself thinking intuitive thoughts is small. This, the final level of awareness, is crucial to our development, both mental and spiritual. At this level of sensation, we are all reduced to the same experiential status. This is the level which is ``universal.'' Art that is successful, in the ultimate sense, is designed to stimulate in us this level of awareness. We say of that art that it embodies a universal expression. And art which is not fashioned to stimulate us at this level, though popular during its time, will eventually be judged for what it really is. An Essay: In Praise of Principles. Principles are marvelous. When present, they do their work unobserved. Yet, their effect is very much felt. No good effect is ever achieved without some principle having been applied. What we call talent and genius is really the behavior, which we sense, of some principle being executed. Our senses are designed to respond to effects created by nature and all these effects are the result of some underlying principle. This is why we as natural organisms tend to gravitate to art, which also, in imitation of nature, has effects created by some underlying principle. When a person utilizes a principle we call that person an artist. When we see an artist using principles intelligently, we call the artist a genius. When a child exhibits artist-like tendencies, we say that the child is talented. What sets these individuals apart from others who are involved in similar activities is the acuity of judgment stemming from their awareness of pure sensation and their tenacity regarding the application (either conscious or unconscious) of some principle or principles. When principles are misapplied, violated, or unused, the effect of the result on our senses is of very non-intense stimulation. The effect seems like so much ``nonsense.'' If we are accustomed to ``nonsense,'' the effect of the ``sensible'' can be almost overpowering. This strength of intensity usually caused the work of the greatest artists in history to be rejected during their own time. Such seems to have been the case with Guarneri del Ges— and Bach. For many years now, there has been a general trend away from the application of true principles. It was as though they were something to be feared or avoided. They were equated with dogmatisms and rules. They are, of course, neither. However, it was thought (and still is) that principles might inhibit ``personal expression.'' Isn’t it ironic that the efforts of those who would deny the use of principles have been largely wasted because the effect of their efforts is that they are unimaginative, lifeless, weak, inhibited, and lacking in interest, quality, or expression, the exact opposite of the effect these individuals desired. Because they failed to employ true principles, and true principles create effects which communicate directly with the senses, their work fails to communicate with the senses. When we embrace true principles, we find that they do most of our real work for us. All we need to do is be present and expend a little energy to get the job done. Most importantly, our work is done for others, not for ourselves. Because the principles are objective in the effects that they produce, we can be certain that others will experience our work exactly as we intend it. I believe that artists such as Rembrandt and Guarneri del Ges— were neither talented nor geniuses, as we might think. They were just men who were sensibly aware, who thought deeply about the principles underlying their art, who applied those principles strictly and intelligently, who were unafraid to experiment, and who enjoyed the doing of what they did. Anyone who does likewise would be as great. How could it be otherwise? Soli Deo Gloria