A CONTEMPORARY LOOK INTO THE ART AND SCIENCE OF THE GUQIN
TO TIMBRE AND RESPONSE
Posted on January 16, 2017 by guqinr5_wp
In my previous post, I gave an intensive introduction into string making, taking a look specifically at alternative methods and materials using synthetics for qin strings, as well as touched upon some calculations and design information that can be used for any twisted core string, from silk strings, to synthetic, to even metal. I also started introducing some aspects that I would like to explore more here in this post, specifically regarding the nature of silk strings for the qin. Being twisted-core strings by nature, this gives rise to some very interesting and complex physical interactions that I find particularly more interesting and fascinating over their monofilament core counterparts. In fact, I firmly believe, and have presented quite a bit of information up until this point, supporting that twisted core strings for the qin, regardless of material, opens up much more flexibility and optimized tonal response that can be tweaked and tuned for use with the qin much better than using solid core strings for this instrument.
There are many websites and pages dedicated to silk strings, describing their history, making process, use, and cultural aspects, not only for the qin, but for other instruments which use them as well. However, you will be very hard pressed to find any information relating to the exact mechanical mechanisms that fundamentally gives rise to their response and timbre. Yes, people throw around the words “rich” and “complex”, but these are so subjective that it is almost meaningless to try to argue these points without a fundamental understanding of why it may be the case, what this really means, and how the strings actually work. These are terms that can certainly be used to describe how they sound to someone musically from a subjective viewpoint, but should not be used in objective attempts to qualify and describe the differences between strings in regards to how they work and what makes them different at the most basic level unless the proper definitions and mechanisms are established first. What exactly, is it about silk strings, at the most fundamental level, that gives rise to their response? Or any type of string for that matter? Again, you will find information saying how the harmonics determine the timbre and etc, but nowhere is it described in detail WHY the material, instrument, and physical mechanisms, produce the harmonics they do. It is not just that “well, a vibrating string creates harmonics which are multiples of the fundamental…etc, etc” – we need to know the reasons for this.
As described in previous posts, as well as numerous online resources regarding silk strings, and again mentioned above, silk strings are, by nature, twisted core strings. The fact that they are twisted structures, coupled with the mechanical properties of silk, gives rise to some interesting characteristics for its tonal generation and response. What I aim to propose here, as further elaborated upon below, are the numerous factors that work in conjunction with each other to give rise to the harmonic content that is present for these particular types of strings. As I am currently aware of to the best of my knowledge, I have not found a similar proposal yet attempting to couple the physical properties of the material as well as construction methods used, in reference to as diverse set of data, to explain the mechanisms of timbrel generation for these types of strings, particularly relating to the qin. This proposal is based off of my own prior work, analysis, and experiments so far of numerous types of qin strings of all different types of materials and across numerous different qin, and looking over hundreds of harmonic data graphs, all of which can be accessed on this site. What I describe below is particularly in reference to the studies made and presented here on Guqin Reflections for silk qin strings, which is further cross correlated to other tests done with both commercially available solid core nylon Longren Binxian strings, as well as experimental twisted core nylon and polyester strings that I have been working on and testing for the qin. This proposal is a preliminary and introductory look at the mechanisms that may give rise to the harmonic content and response of these strings, and will provide the basic initial hypothesis for future intensive analytical studies to be further elaborated upon, with full data analysis of the harmonic data collected so far, as well as further proposals and experiments for furthering the development and optimization of qin strings, particularly in applying these techniques to provide further alternatives for non-silk based strings.
First and foremost is separating the mechanisms that gives rise to the timbre of the instrument versus the strings themselves. In essence, a qin will still sound like a qin regardless of the strings that are used on it – the strings do not determine that a qin will sound like a qin. Likewise, this can be applied to any stringed instrument – guitars, harps, violins, etc. Therefore, there is a fundamental response of the instrument itself that gives rise to the bulk majority of harmonics that determines the basis of timbre for an instrument. You can think of it almost as a very specialized “filtered-amplifier” for mechanical excitation – when an excitation is generated, by the strings, this is transmitted through various boundary conditions, or points of interaction between the strings and the soundboard, to the soundboard, which amplifies, filters, and shapes the vibrations further, and transmits this to the air. The construction, materials, and boundary conditions will play a major role in ultimately shaping and determining the fundamental response of the instrument. Note also that there is no one universal standard for determining what methods or materials in construction will make an instrument sound the way it does. I have heard qin made from all different materials and radically different construction styles, and it doesn’t matter if they are traditional woods and finishes, alternative woods and finishes, carbon fiber, or even solid body and electrically amplified – they all sound like qin, despite their massive differences in material and construction techniques. Therefore we must first understand that their are general trends of the timbre and harmonics of the instrument itself before we dive into the subject of strings. Since the analysis of the vibrational response of an entire instrument is a very complex and rigorous subject in itself, we will note that their are general trends established for each particular instrument as the basis for harmonic response, and further concentrate upon the effects of the strings themselves more specifically.
The different strings used will then impart different fundamental excitations to the instrument, resulting in different “flavors” of tone. It will result in changes in the base harmonic spectrum of the instrument, but not enough that it will make it sound like a completely different instrument all together – rather, these subtle changes in harmonics results in a general tonal characteristic that can be described within reason as the response of that type and style of string. Note that you can also put different instrument strings on different instruments, and it will still sound like that instrument they are on, but impart a particular tonal quality to the instrument they are on that is inherent to their nature. For example, I can put monofilament nylon guitar strings, monofilament Longren Binxian qin strings, silk qin strings, and experimental twisted core synthetic strings, all on a shamisen, which is a traditional 3 stringed Japanese guitar-like instrument, and it will still sound like a shamisen. I can also put all of these strings on a guitar and it will still sound like a guitar. However, the strings will all exhibit certain inherent tonal qualities that can be generally described and picked up across all of these instruments. Therefore, we can assume there are three main key categories of mechanisms here in regards to what shapes the bulk timbre of a stringed instrument combination: 1.) a fundamental tonal response of the instrument itself; 2.) a fundamental tonal response of the strings, and 3.) the resulting combination of these two factors. We should still be aware that in regards to the third point, different qin will react differently with various types of strings depending on construction methods, which gives rise to many various complex iterations of harmonic combinations. However, the average response and physics of the string will still apply regardless, although the final resulting tone of the combination of the strings and qin may vary between different qin and different string combinations. Here, we will attempt to identify and explore the inherent properties and response of silk qin strings, and ultimately how these properties and construction techniques may also give rise to their harmonic content trends, and how they can be further related to observations in other materials.
First, we will look at the mechanical properties of silk. Silk used for not only qin strings, but other instrument strings as well, comes from the silkworm, or bombyx mori, and is the silk we will be referring to in regards to mechanical properties from here on out. There have been experiments with making violin strings from spider silk, but these are not strings you can go out and buy or access, and are very specialized demonstrations, and the two types of silk are quite different. The silk from the bombyx mori, on average, is about 13um, or microns, in diameter, and has a density of about 1.3 g/cm^2. The silk fiber also has a non-uniform, rounded triangular cross-section, as opposed to nearly circular cross-sections of similar synthetic textiles such as nylon or polyester. Silk also has a tenacity of about 0.38N/tex, and a breaking extension of about 23-25%. Looking at the stress-strain curves of silk in comparison with other materials, we see that out of five major categories, ranging from high specific-stress/low strain %, to low specific-stress/high strain %, of 1.) HM-HT fibers (kevlar); 2.) weak inorganic fibers (cotton, flax); 3.) tough synthetic fibers (nylon, polyester); 4.) weaker textile fibers (rayon, wool); and 5.) elastomeric fibers, we find that silk falls right in the range of tough synthetic fibers, with the nylons and polyesters, with it’s own unique average stress-strain response. All of these characteristics play a role in the sound generating mechanisms and response of the material, however, in of themselves, they do not mean much until they are applied to some structure – essentially, the structure of the string, in addition to it’s mechanical properties, will determine the timbre of the string. We will come back to these physical properties soon, and will exemplify their importance in conjunction with construction method shortly.
As mentioned above, perhaps the factor that most significantly shapes the tone besides material property is the structure of the string. As you will see, two strings with the same material and different construction techniques can result in radically different timbres. Silk strings consists of hundreds or even thousands of tiny, individual filaments of silk. In my previous post, I discussed ways to actually estimate and calculate how many of these individual fibers are in a particular string, for a given style of string manufacture, going through the calculations for the two major methods of making these strings. These filaments are first grouped and spun together to produce larger threads, which are then further twisted together either as a single bulk structure, or as further larger substrands which are then twisted into a full string. Regardless of method used to make them, whether twisting together a bulk set of threads or from several larger subgroups further twisted together, there are many, many individual continues fibers that make up the structure of the string. This is key. Physics will tell us that a string made of multiple filaments will give rise to more complex vibrational phenomena than an equivalent string made of the same material and diameter as a solid string. Why is this the case? We can describe it as such through the following methods by applying basic concepts of physics, materials, and interactions. Although the silk string vibrates as a bulk single entity at the macro-scale, it is still composed of numerous, tiny filaments and substrands that are imperfectly bonded together with both frictional forces between them, as well as an adhesive. This allows for some slippage and strand-to-strand interaction to occur, which can result in much more complex vibrations due to the interactions and losses between all of these threads. In regards to complexity here, I am not referring to “complexity of tone”, but quite literally, the complexity of the oscillations, and how far they deviate from a perfect, ideal string with a pure, sinusoidal vibrational response. This can actually be quite readily seen and compared between strings by looking at the derived autocorrelation of a plucked note, which are graphs that I have provided on every string data page for every string that I have tested so far. Again, this response can vary based on plucking technique and plucking position along the length of the string, but for comparative purposes, we assume the same excitation method, strength, and position. What we see and hear is the bulk response of all of these tiny fibers acting as a whole, single string, but there is still room for individual movement and interaction, and as well as non-uniformities along the length of the string. Also remember that silk fibers have a non-circular profile, and are also not completely uniform in nature as well, leading to some variability along the length of the fiber. A single, solid core however, is comprised of one, large, homogeneous filament that has no other internal interactions or losses besides those from the bulk material itself. It therefore behaves as a more ideal vibrational body. If we could actually obtain a single silk filament large enough to make a monofilament core of proper diameter for comparison, perhaps from a giant, mutant silkworm, we would most likely see that this string would act more similarly to a synthetic monofilament string made of similar material, such as nylon, or more advanced synthetics such as “nylgut”. This string would have some qualities similar to the twisted core silk strings that are used, but still be very different as a whole, with a most probable shift in response towards the fundamental frequency as well as decrease in upper harmonics, and would, in theory, be vibrationally more simple.
There are more effects that a twisted core has on the behavior of a string. As mentioned above, the interaction between numerous strands and filaments tightly bound together in a twisted core string such as silk introduces significant internal friction, which results in a much faster decay time for the string, and hence, a lower sustain. Therefore, by their inherent nature, twisted core strings will have less sustain than equivalent solid core counterparts. Again, since solid core strings do not suffer from these extra losses, other than losses inherent in the bulk material, vibrational energy is less inhibited. The material also plays a role in this as well – metal will always be able to transmit sound much more efficiently than synthetics and silk, resulting in naturally louder volume, and longer sustain. Since a solid metal core, for example, is less lossy and behaves in a more ideal manner than a silk string, then for an equivalent excitation input (in other terms, plucking technique), the vibrations of the metal string will in theory progress closer towards an ideal sine, resulting in, on average, a smoother waveform. This again relies on several factors, including initial excitation, but for common qin strings which are currently produced and used as of now, this can be a trend that can be observed by looking at the waveforms and autocorrelation graphs of a plucked note. A similar response can also be observed by looking at monofilament core nylon strings such as Longren Binxian strings. This trend is more noticeable for lower strings and lower pressed positions. In this regard, strings with a larger noticeable fundamental cycle when compared to its harmonic multiple constituent parts will indeed trend towards a more noticeable concentration in the fundamental, with less balance in the mid-range notes – for the qin, this range, regardless of tuning, generally progresses from the fundamental to the first couple of subsequent harmonics for the low range, then from the next harmonics up until about 1000-1500 hz for the mid to upper-mid range, then beyond this for the upper range. Although metal core strings possess a higher number of upper level harmonics than silk or composite strings, which in part contributes to it “metallic” tone, these harmonics are of much lower magnitude than the major harmonics, and die off very rapidly compared to these main harmonics. Therefore, in the beginning, the vibrational complexity of the attack may be higher, but averaged over the longer sustain of the string, these upper harmonics die off quicker, leaving much more of the fundamental response. However, with strings that exhibit more concentration in the mid range and upper-mid harmonics, with a significantly decreased fundamental, which can be observed in the cases of twisted core silk and twisted core composite strings, the sound signal and derived autocorrelation results in a more complex vibrational pattern, where the harmonic multiples are a significant portion, if not the dominant constituent, of the tone, over the fundamental frequency. In this case, we still hear the fundamental, but also hear a more complicated blend of mid to upper-mid range harmonics.
Still another effect of the twisted core over a solid core is the effects on the upper harmonics as a result in the increased flexibility of the string due to its construction. For a given string, a twisted core will result in higher flexibility for an equivalent solid-core counterpart. For thick strings, the string starts to behave more closely to that of a vibrating bar versus an ideal string. As a result, as stiffness increases, upper level harmonics begin to experience a slight shifting from where they are theoretically supposed to reside, and become not quite a perfect multiple of the fundamental. As stiffness increases, this effect becomes more severe and noticeable. In extreme cases, with a very thick, solid metal wire, this effect leads to very noticeable inharmonicities which manifest themselves as unpleasant-sounding, dissonant harmonics. This effect however can be mitigated by increasing the flexibility of a string. A twisted, multi-strand core does just that, and allows one to construct a string of equivalent diameter with increased flexibility. The effect of this would lessen the “harmonic stretching” observed for equivalently thick, much stiffer solid cores. This effect, which is further elaborated on in my next post on metal-core strings, would have potentially significant benefits and implications if used for metal core strings for the qin.
Yet we are still far from done. We must also remember that silk is not the only material used in silk strings – they are wetted, twisted, and stretched during the process, in which they are then further cooked in a particular adhesive to bond the silk filaments together and to prevent the string from unwravelling without the need for knots at the end, which can be seen through example in my experimental twisted core synthetic strings, which do not use adhesive for their base manufacturing process, and therefore do require knots on each end to prevent unwravelling. Something further to note of silk is it’s property to absorb a significant percentage of it’s weight in water – this could in theory be as high as 25%. So in addition to silk, we therefore have a good fraction of glue being absorbed into the silk, as well as into all of the spaces between individual threads. Although the threads and filaments are tightly twisted and packed, there is some non-negligible fraction of space between them for this adhesive to further occupy. Therefore, we can also infer that the adhesives used, in addition to the quality of silk and quality/style of manufacturing, will have some noticeable impact on the performance and timbre of the strings as well. As mentioned above, the glue adds an additional binding force to the force of friction due to twisting on the silk threads, which does act to restrict the threads’ individual movements, but still has some flexibility for movement. By forcing the individual strands to act more as a whole unit, the adhesive may allow for a slight increase in fundamental response, as the whole string would vibrate more as a solid unit, but since inter-strand forces and movement is still permitted, allows for a still higher concentration and distribution of power in the mid to upper-mid harmonic range. Based on experiments and trends observed with dry, unglued, twisted core synthetics, it is reasonable to hypothesize that using the same construction methods with silk, played dry without gluing, may indeed result in a response with lessened fundamental and slightly more concentration on mid and upper-mid range harmonics, if compared to an identical, glued silk string.
The adhesive will also act to add mass to the silk string, thereby increasing its linear mass-density as well. Silk strings, due to their high ratio of absorbance, can thus be further weighted with adhesives or using metallic salts, as described in the guide written by silk string maker Alexander Raykov. If we were to test two identical strings in construction, with one unglued and the other glued, or a string before and after the gluing process, we would notice still some bulk similarities, but changes as well, as noted in the paragraph above. It can thereby be inferred that, through enough trial and error and control, a silk string could be further tuned in response based on the adhesives used in the process, as compared with the base, fundamental response of an equivalent, unglued twisted silk string as the control. As of now, all silk strings used for the qin, and probably for other instruments that rely on silk strings as well, use some form of adhesive – this adhesive can be either the natural sericin found in raw silk, or the addition of new adhesive after the de-gumming process, if this route is taken. With varying adhesives, strengths, stiffnesses, weights, etc, the distribution of harmonics, as well as the vibrational mechanisms of the string, could be shifted or balanced in a certain way depending on a combination of all of these factors, from the initial unglued base response.
Taking into account all of the above discussed topics, we can now look at a few case study examples to illustrate these points. All of the data for all of the strings I have tested and collected is freely available to look at and compare (and if referencing it, please give credit to where it is due), and shows many of the trends that I have described above. The easiest place for direct comparison may first be looking into the difference in the effects between a monofilament core string and a twisted core string of the same material. Since there are no monofilament core strings for silk, we can thus make logical inferences on its behavior for similarly tested synthetics, and therefore correlating this across to other string types, both for silk and metal core as well. Remember, all of these strings follow the same laws of physics, so all of the fundamentals apply to them. As noted above, of all the string types tested, the common Longren Binxian monofilament nylon core qin strings exhibit the least amount of harmonic content, with a focus on more fundamental response than that of silk, and vibratory patterns deduced from autocorrelation that are relate-able to metal-core qin strings, although exhibiting even simpler response. Yet if we observe the behavior of the experimental twisted core nylon strings I have made, we see a significant change in harmonic distribution. The fundamental, as seen with silk, is much more diminished than their solid core counterparts, and exhibits a very strong response in the mid to upper-mid range harmonics. In fact, this response is even more stronger than that of silk, and results in a sound that is noticeably brighter than that of silk. In addition, the string also exhibits more harmonic content in the upper range than either silk or Longren Binxian, yet without the inherent “metallic” quality present in metal core strings. In regards to vibratory response and decay, we see that these experimental core nylon strings follow exactly the prediction that an equivalent twisted core string will result in a much fast decay than that of its solid core counterpart. Indeed, this is what we observe, with decay that is faster than Longren Binxian strings. However, as an interesting note, volume of the string is not compromised, and is at least of equivalent levels to Longren Binxian strings. If we look at the derived autocorrelation graphs of the plucked string tone, we further see that the twisted core strings have a much less sinusoidally similar response to an ideal vibration which is seen in the Longren Binxian response, with the fundamental frequency oscillation being much more complex due to the higher intensity of mid and upper-mid level harmonic oscillations, which again, is similar in response to silk strings. Now let us look at the effects of using a stiffer and denser material for the synthetic twisted core strings. Polyester, which was also used, is very similar to nylon, but has some key differences. It is slightly weaker, much stiffer with much less stretch, and is denser than both nylon and silk. In comparing equivalent strings of nylon and polyester, we again see a very similar response to each other, but the polyester exhibits an even further response of the mid to mid-upper harmonics, and has a resulting brighter tone. It would therefore logically follow that using an even stiffer and more dense material such as kevlar would result in a further brighter tone, and using metallic threads to make a twisted core metal string would result in even more brightness. Silk however, has much for flexibility than these materials, and being on the lowest end in this regard when compared to the above stiffer materials, does indeed exhibit a less bright response. The brightness in response for higher stiffness and density materials however could be redistributed and balanced out at the lower end with the use of proper adhesives and string coatings to further weight and restrict individual strand movements towards a more bulk vibration.
Taking into account the above mentioned points, we can therefore potentially establish a trend in response for qin strings where it is observed that solid core string materials exhibit similar vibratory responses between differing materials, and that twisted core strings share similar vibratory responses between differing materials, and that both solid core strings and twisted core strings end up displaying a very different shift in the concentration of harmonics: solid core strings will tend to favor fundamental response with diminished mid range, and in the case of high density, high stiffness materials such as metal, we can see an increase again in the upper range, whereas lower stiffness and more flexible materials such as nylon do not exhibit these upper harmonics. However, for twisted core strings, we see that fundamental response is diminished, and mid to upper-mid response is increased, with further increasing strength resulting in brightness as the stiffness of the core material increases. Silk therefore achieves an interesting balance with a resulting response that is more balanced than plain twisted core synthetics, with a bit stronger fundamental response and more evenly distributed mid and upper-mid harmonics. This can be achieved due to the material’s flexibility, as well as combination of density and strength to allow the string of proper diameter t be made for a given tuning, but also is perhaps more so reliant on the construction techniques used, in combining many numerous smaller filaments into increasingly larger strands, as well as the use of glues, both of which increases the bulk vibration of the strands as a whole unit while still allowing for inter-strand interactions and internal frictional losses to occur. In this regard, silk strings at the present time exhibits these unique combinations that have yet to been fully exploited with synthetics. However, it appears that the material properties of silk may indeed rely heavily on the twisted core, glued construction method to achieve these results, as opposed to a solid monofilament core.
With the advancement of materials and manufacturing techniques, strings could be made to give the best of both worlds, and enhance the shortcomings of silk that are currently present. Namely, with the use of advanced polymers, and processes such as electrospinning to generate microfibers and nanofibers of similar or improved strength, with proper flexibility and density, strings could be generated with increased volume and durability, yet with increasingly similar harmonic distribution present in silk strings. Currently tested twisted core synthetics, already having a response much more related to silk than solid monofilament Longren strings, could also be further tuned and customized with the proper selection of coatings and adhesives, to redistribute the harmonic response towards a more balanced distribution of harmonics between the still lowered fundamental and the stronger mid to upper-mid level harmonics. Therefore, as explored above, we can establish a very strong relationship between the timbrel response of a string by looking at the combination of both construction techniques used to make the core, as well as the material properties of the material used to make the string, and adjust the response of a particular style of string accordingly.
Tagged guqin, guqin strings, harmonic analysis, qin, silk strings, string making
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String Making – An Introduction to Alternative Methods and Materials for Qin Strings
Presenting the First Ever Twisted Core Kevlar Qin String!
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