Violin Acoustic Design

Lesson #1:  A thing often looks easy and simple to form an opinion on if you only know a little about it.  The more you learn, the more you realize just how ignorant you were--and are.

I occasionally play stringed instruments such as the fiddle, as an amateur.  The other day in a conversation, I wondered aloud to what extent the design of a violin was based on stylistic considerations versus actual influence on sound output and quality.  I supposed that much of the "ornate" styling and visual beauty had little to do with its actual performance as an instrument.  Just an acoustic enclosure with some strings stretched across it, right?  Turns out, I was almost completely wrong.

Some internet sources like this, this and others make some interesting points about the acoustics of a violin and their relationship to its design.  While the articles give a more in-depth look, here is a brief summary that some of you might find intriguing:

1.  Unique Method of Producing Sound:  The continuous sound obtained by drawing a bow across a violin string is dependent on the stick-slip phenomena obtained between the tacky rosin-coated bow hairs and the string.  Producing a sound in this manner tends to result in an almost exactly harmonic spectrum, as opposed to plucking, and this puts power into the high harmonics and contributes to the richness, brightness and loudness of the violin's sound.  The ability to create a good, solid sound from the bow depends on the proper relationship between the pressure from the bow on the string, the speed of the bow, the distance it is located from the bridge, the tension in the bow hairs, the tackiness of the rosin that coats the bow hairs, and the weight, flexibility and tension of the string across which it is drawn. Some of these factors represent player technique while others are related to the design of the instrument--i.e., the strings, bow, rosin, etc.  A more technical explanation of the motion of the string when bowed can be presented in terms of Helmholtz motion, for anyone interested in a more physics-oriented description.  
   On the other hand, when the string of a musical instrument is plucked, the high harmonics fade away very quickly, leaving only the fundamental and some weak lower harmonics.  A violin can be bowed, plucked, bowed or hammered using the wooden side of the bow, not to mention a variety of different (normal) bowing patterns that introduce a great variety of sound textures and emotive responses.
   But this is only a part of the story of what gives a violin its sound.  The other part is its acoustics.  The acoustics of the assembled violin are fantastically complex, as they involve coupled oscillations from the strings to the bridge, top (and to a lesser extent bottom) plates, rib, and fingerboard.

2.  Size/Shape/Thickness/Material of Top Plate & Other Parts:  The violin resonances do not fall at the same frequency as the notes the player wishes to play, although the lowest resonant frequency falls in the neighborhood of the A string (440 cps).  The frequency spectrum coming out of the instrument is very different from that going in, i.e., from the strings themselves, and is acoustically rich.  The shape, thickness, size, and spatial geometry of the top plate results in a very complex set of vibration eigenmodes covering a range of frequencies.  This results in a harmonically-rich, complex waveform responsible for the violin's unique tone, as well as sometimes noticeable differences in the sound of two different violins that may look nearly identical.
    Sophisticated violin makers and researchers have mapped the resonance profiles and modal activity of various old violins to learn the secrets of the old masters.  Here are some interesting animations that also help to illustrate the vibration modes.  Based on what they've learned, they are now on the verge of unlocking the design secrets that gave these old masterpieces their superb sound quality.  The "old Masters" were evidently master experimenters themselves, in a period before violin making was transformed from an art to a handicraft.

4.  Importance of faithful harmonic reproduction:  The strings by themselves produce very little sound directly, but depend on instrument resonance.  One interesting curiosity is that the instrument body has almost no resonance at the fundamental frequency of the lowest string on the violin (G string, 196 cps); however, since most of the harmonics are well represented, the human ear is thoroughly "fooled" into thinking it is hearing the fundamental G-string pitch, based on the frequency spacing between the harmonics.

5.  Varnish and Vibrato Properties:  When the player's finger rolls back and forth slightly on the fingerboard to create a vibrato sound, this only modulates the base frequency up and down a tiny bit.  However, when we look at the upper order harmonics and their interactions, the effect is greatly amplified, and the frequency spectra varies dramatically.  A lot of drastic and crazy magnitude perturbations are going on in those higher order harmonics, and our ears--perhaps the world's greatest spectrum analyzers, capable of detecting the slightest nuances associated with human speech--are able to put it all together such that they can still recognize it as merely a small perturbation in the base frequency.  This may also help to explain why vibrato produces the "fiery tone" that has such a pleasing effect on the ears and an enhanced projection ability--it gives our "auditory processor" some very interesting stuff to chew on, as well as increasing the stimulation of our auditory receptor hairs.  Vibrato also tends to further set apart the characteristic "violin sound" from every other instrument sound and make it even more distinctly recognizable as a violin and nothing else.  Incidentally, "vibrato intensity" varies between violins and is often what sets a great violin apart from a good violin.  One of the most important design parameters that affect the vibrato intensity is the type, thickness, penetration depth and application technique of violin primer and varnish, which affects resonance dampening.

6.  Sound Peg:  When the bridge vibrates, it mostly pivots off the treble foot (near the sound peg)--or, perhaps more accurately, it pivots off the position of the sound peg itself.  Most of the vibrations are transmitted via the bass foot of the bridge onto the top plate (or belly) and rib (or bass bar), which itself transmits the vibration over a larger area of the top plate.  This is why the position of the sound peg is critical, and has a very noticeable affect on the sound of the instrument.

7.  F-Holes:  The real reason for the F-holes is not for "purty", but for two purposes:  (a) To connect the air inside and outside the instrument and allow for a Helmholtz acoustic resonance, which is the lowest frequency resonance of the instrument (usually about 260-280 Hz).   (b) To allow the part of the top plate lying between the F-holes to move (i.e., vibrate) more easily than most of the wood of the body.  Naturally, the length and relative position of the F-holes has an important effect on the sound.  (I would also guess the curvature and rounded terminations of the F-holes are at least partly based on engineering considerations to minimize stress and cracking in the wood.)

8.  Bow Design:  Ever wonder why a violin bow is arched in the opposite way that an archery bow is?  Originally, violin bows were made like archery bows, i.e., curved away from the strings.  The tension in the horse hairs was relatively independent of the pressure applied to the strings.  Then someone realized that if they were bent in the opposite direction, this would give the following advantage:  As the bow hairs are pressed more firmly on the strings, they pull on the ends of the wooden bow, which itself tends to straighten rather than bowing further, resulting in more tension in the bow hairs.  This means the violin player can successfully exert a wider range of pressure on the bow, resulting in a wider range of dynamic volume from the instrument.  Another effect of the modern (Tourte) bow is the presence of the 'hatchet" head, which distributes more weight to the tip, allowing a more uniform application of force during the stroke.

9.  Tonal Shaping:  Here are some additional acoustical considerations in a violin that are related to its design but which may still be somewhat of an art as well as a science:
    a)  Techniques to eliminate wolf tones
    b)  Design of the bridge and its effect on sound filtering and impedance mediation
    c)  Adjusting tonal color and resonance profile

10.  Other considerations besides acoustics:  We've only covered the acoustical underpinnings of violin design.  Much more could written about additional design requirements relating to structural strength, durability/abrasion/wear properties, prevention of wood cracking, ergonomics and playability, etc.  Here are just a very few representative examples:
    a)  Ergonomics and Playability:  The violin in symmetrical, easily accommodating left- or right-handed players and making design and construction easier.  It's overall length and fingerboard length/cross section accommodates the average human attempting to play it.
    b)  Structural/Hardness/Wear & Abrasion resistance/Forming Requirements:  Selections of different woods with different physical properties for different parts of the instrument, careful selection of grain directions, and special bending and lamination techniques all ensure the violin will support itself and hold up to repeated use, in addition to exhibiting its desired acoustic properties.
    c)  Nature Inspiration:  Just in case there were any design parameters still open after all the other requirements were met, the old violin masters' designs were inspired by nature, specifically the golden ratio.  Thus, the anthropomorphic instrument shape, the nautilus scroll shape, and the spacing of the F-holes all satisfy the golden ratio.  Some would say this transcends a mere design preference, tapping into the wisdom of nature itself.

11.  The scroll.  Yes, the scroll!!  Surely this must be just ornamental, even though its design is inspired by nature.  After all, some violins have peg boxes topped off with lion's heads or faces instead.  (Okay, so I was right about the scroll!)  It could just have easily been left as an ugly, un-carved portion of the tuning box.  But would this have been conscionable on the part of the violin maker, after the many hours of work he spent crafting a beautiful looking and beautiful sounding instrument?  Of course not!  It would have broken every principle of aesthetics.  It would be worse than leaving the hood ornament off a Rolls Royce or leaving the figurehead off the prow of a sailing ship.
   Of course, fancy or not, there may be some practical reasons associated with the "hunk of wood" represented by the scroll.  Some people theorize it that it helps "balance" the instrument.  The scroll shape may have made it easier to hang the instrument on a line to dry out the varnish.  The mass of wood also might help to stiffen the peg box and reduce the likelihood of the wood cracking.  It also protects the tuning pegs from being accidentally bumped when the instrument is put down.
    So, in conclusion, I was only 97% wrong.  In general, stringed instruments like the violin may look simple and uncomplicated from a distance, but they produce a more complex sound and represent the result of more painstaking experimentation than any other musical instrument man has ever conceived of.

10.  Here's a very un-scientific comment on my part:  I like to think that string instruments like the violin have such a beautiful and rich sound partly because they were originally made 100% from wood and other materials that were originally living things, i.e., maple, spruce, ebony, brazilwood, animal glue, sheep intestines, horsehair and tree sap.  On the other hand, one could argue that many other instruments share this property; take for example, the didgeridoo.  While its sound is undeniably rich, the beauty of its sound might be held in question.  So you can take this proposition with a grain of salt!

11.  I can't help adding one more un-scientific ramble:  is the beautiful aesthetic quality of a violin purely the result of its technical specifications?  I think not--I suspect one could theoretically make a rather ugly violin that  played well and sounded beautiful (although this might even take more effort than to make it look beautiful).  But what is the likelihood that someone attuned to musical aesthetics would be simultaneously blind to visual aesthetics?  Most people would answer that there is little chance of this.  In fact, I can't think of any musical instruments that don't have a certain beauty to them.  The desire and admiration for beauty transcends the medium.  Thus, we go to a beautiful auditorium to watch and listen to beautifully-dressed musicians on a beautiful stage playing beautiful music on beautiful instruments...sometimes while the beautifully-scented audience (well, a few of them at least) is also eating beautiful looking and tasty food, or exchanging beautiful smiles or whispering sweet nothings in each others' ears...

12.  The website of well-known master luthier (violin maker) and acoustic researcher Martin Schelski has lots of interesting technical stuff related to the acoustics of violins.  His quotes--shown below--indicate his great admiration for the old violin masters:
    "By seeking to decipher the fascinating acoustic secrets of the old  Italian masters, I have compiled an impressive body of experience."
   "Through my research, the great Italian masters have gone from being historical examples to become my contemporary teachers."
    "...Preserving the tradition of violin making necessarily involves breaking away from it.  Why?  The tradition is too rooted in the development of new sounds."
    "The deeper I probe in my acoustic investigation of the violin, the more I gain a sense of reverence for its mastery."
    "Knowledge that is passed down must be brought to life through one's own experience and thus carried on before something that is special and authentic can come to be."
    "Only in a highly creative milieu that advanced both art and science could the perfection embodied in a work like the violin come into existence.  It was not until the 19th century violin making devolved into mere handicraft."
     "My passion as a violin maker has its roots in the original interplay between art and science:  the only way to overcome barriers is to speak both languages."
    "A painter communicates with colors like a violinist does with the instrument's resonances."
    "I firmly believe that music is simply a prayer that is cast in sound."

Odds & Ends #2

Recently, I was under the weather and spent a lot of time in a recliner reading Economist magazines and such...in fact, most of the following comments are distilled from such reading (no originality from me), and I've referenced the articles in case you want to read them in their entirety.  Just stuff I found interesting.

1.  Foxconn, the worlds largest contract manufacturer, is seeking to improve its margins as it expands in the interior of China, in a bid to once again double in size.  It's net margin has slipped to about 2% even as it has employed more people, although its latest earnings have surged, partly because Apple is paying more for their services, something Apple is putting a positive, wishful spin on by characterizing as a "subsidy", rather than meeting a demand to cough up more money.  Part of the reason for Foxconn's low margins has been greater worker demands for higher pay and better working conditions.  Another reason is its status as a "midstream" manufacturer, with little involvement in the higher profits associated with design (upstream) and marketing/sales (downstream).  Apple, which represents 40-45% of its revenues, makes obscene profits by comparison.  Typically, it costs Apple a few dollars to have a product assembled, which it then sells for several hundred dollars.  This hasn't escaped the notice of Foxconn management.  They're strategy is to gain control over more of the component design and manufacturing.  (For instance, Intel is planning to hand over the lion's share of R&D of its motherboards to Foxconn, as part of an acknowledgment that Foxconn now has more experience and expertise, not to mention a likely bonus for the Intel managers who identified this cost reduction.)  Foxconn also plans to help its customers sell their product in China via its stake in several retail chains.  While these moves are designed to help both their customers and themselves, the longer term effect for Foxconn is an eventual reduction in their competition, more IP within their control, and greater bargaining power for them, which (in my opinion) could eventually "expose" companies like Apple as mere "shell" companies with little value or leverage and thus leave them on the trash heap of a once-great American high-tech industry.  Perhaps Sharp serves as a harbinger of things to come.  Incidentally, Foxconn is a nice Western-sounding trade name, although I'm wondering if whoever came up with that particular name might have had a Machiavellian twinkle in his eye.  The real name of this Taiwanese company is the Chinese equivalent of "Hon Hai Precision Industry Co."

2.  Speaking of IP (intellectual property), in 2011 China's patent applications increased by 2/3, knocking the U.S. off the top spot.  Europe now has a more-or-less unified patent system, while the U.S. signed a patent reform bill into law last year after years of fruitless efforts at reform.  The cost, bureaucracy and delays associated with obtaining a patent unfortunately still remain huge problems in both Europe and the U.S.  One reason (in the case of the U.S.) is that the high fees associated with patent applications are not retained by the patent office, but may instead go toward other government expenditures.  Meanwhile, the U.S. government patent office is critically understaffed.
   On a related subject, fat royalty payments for intellectual property is a favorite legal scam used by big companies to shelter their profits in lower-tax countries and in tax havens like Bermuda, Barbados and the Cayman Islands.  Ninety-eight of the 100 companies in the FTSE 100 have at least one subsidiary in a tax haven, where profits go in the form of such things as "royalty payments".  Even companies like Google and Amazon do this.  In my opinion, the solution to these shenanigans is simple:  eliminate all corporate taxes, and replace with more taxes on high-income individuals.  This will not only eliminate the shenanigans, but will encourage companies to do more business in the U.S.
   Perhaps the most pressing issue with "intellectual property" though, is represented by our college students who are highly educated and unemployable.  A wasted intellect is a tragic situation--a situation that was begotten of the belief that a "real" college or university education was a first-rate education while a vocational school or community college education was seen as less desirable.  According to an article in the Economist, skills shortages are getting worse even as youth unemployment reaches record highs in Europe, the U.S. and elsewhere.  Companies are now partnering more and more with vocational schools to attract, train and employ people with needed technical skills, while colleges and universities still are largely confined to their own ivory towers.  South Korea may serve as at least one model, in that it has created a network of vocational schools--called "meister" schools--to reduce the country's shortage of machine operators and plumbers.  Apple and other companies are paying Foxconn to open some plants in the U.S. and Brazil.  Part of the hope is that Foxconn, who has a lot of expertise in training China's backward rural residents with little education to run their assembly lines, may be uniquely qualified to train our "worthless" college students how to likewise do something useful.  (Having said this, I want to emphasize that I personally feel everyone should have some modicum of a liberal arts education--not necessarily as a route to a job, but to enrich their lives and make them better citizens.)

3.  There has been a lot of discussion about whether universal government ID cards and a universal database rich in information are a good idea from the standpoint of an individual's privacy, data security and potential abuses, and regarding what level and on what pretext government spying on its own citizens may be justifiable.  This is an important subject with a lot of opinions.  However, articles such as this as well as the proliferation of smartphones makes me wonder if, in the final analysis, government spying may become the least of our worries. Perhaps the most pressing issue will become, to what extent and under what pretext can one individual or company spy on another, and to what extent can such rules actually be enforced?  Could our future society turn into a paranoid, windowless nightmare?  Or would the nation instead turn into one big party line where we get used to everybody knowing the most intimate details about everybody else, and if so, what would it be like to live in a society where there were no such thing as privacy?