Abstract: My project is an in depth exploration into the incredibly complex and interesting world of the ukulele. Through a thorough examination of the timbre of the ukulele,


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NameAbstract: My project is an in depth exploration into the incredibly complex and interesting world of the ukulele. Through a thorough examination of the timbre of the ukulele,
A typeDocumentation
Ukulele Acoustics: Musician’s Techniques, Wood, and Strings as Contributing Factors to The Timbre of The Ukulele
Abstract: My project is an in depth exploration into the incredibly complex and interesting world of the ukulele. Through a thorough examination of the timbre of the ukulele, in combination with the building of a ukulele, I have striven to determine what factors contribute to creating the distinct timbre of the ukulele. The answer lies in the three equally important factors: the musician’s techniques, the wood, and the strings, and the behavior of the relationships between the three. These three components affect the mechanisms of creating sound within the ukulele, shaping the sound to create the distinct timbre of the instrument. Through my research and building a ukulele I have been able to enhance my musicality and be more conscious of my instrument, building my skills as a ukulele musician. Ultimately, the sound I strive for when playing is the iconic soft, warm, and pure tone associated with the ukulele all over globe; the sound that I love and have come to further appreciate.
Matthew Moss-Hawkins

5/11/12

Senior Year Project
Since its surge in popularity over the last decade, the ukulele has become world renowned for it’s unique and beautiful tone. With its dramatic growth in popularity the question arises what creates the ukulele’s distinct sound that has captured the attention of the world? The answer to this question lies in the materials and distinct playing techniques of the instrument. The string material and specific types of wood used to create the ukulele, combined with the distinctive strumming and picking techniques used by ukulele musicians creates the notably beautiful and warm tone of the instrument, it’s timbre.

My Ukulele and The Basics:

My quest to determine the timbre of the ukulele has greatly advanced my appreciation of the instrument and my playing skills in performances. I have played the ukulele for 7 years and have been fascinated by the physics and science behind the sound created as well. For my senior year, project I wanted to analyze ukulele musicians’ techniques, the strings, and the wood to see how they would impact my performances and ukulele skills. I spent the semester researching the physics of sound, analyzing playing techniques of ukulele masters, and applying this research to my own ukulele playing. I also was excited to expand on this primary research by applying my understanding of the physics of the ukulele to building one of my own and observing how physics and performance blend.

After building a ukulele and being a ukulele musician for many years I have found that the instrument’s timbre can be moderately variable depending upon the specific instrument, and heavily variable depending on the playing techniques of the musician. When building my ukulele this semester I had to be very meticulous in every measurement and step in the building process because any variability or slight mistake could dramatically affect the sound of the ukulele. For example, when I sanded the soundboard to its intended thickness, a difference of 1/32nd of an inch determined, whether when I struck the strings, it would only emit a dull plunk, or a rich tone. Moreover, my techniques when playing the ukulele further shaped the sound produced, creating a sound with varying levels of purity, intensity, and sustain. Even with this possible variability, however, I have found that the standard ukulele made with traditional wood and played with traditional techniques has a standard warm and bright tone, with relatively few overtones and long sustain.

The timbre of the ukulele is ultimately the product of the sound waves created by the instrument that reach listener. Therefore, it is very important to understand sound waves, because it is through the manipulation of the wave’s different properties that creates the timbre of the ukulele (see appendix). While playing and building a ukulele it is very important to understand the different properties of the sound but the question still arises, how is that sound created? In the case of the ukulele it all starts when I strike the strings. The energy I use to excite the strings is the energy provided to ultimately create the end product of the sound. The energy is initially contained in the form of vibrations of the strings, which vibrate at varying frequencies depending on which fret my finger is pressed on. The vibrations of the strings then get translated through the bridge and excite the soundboard and body of the ukulele causing them to vibrate. These vibrating surfaces cause an increased amplification of the sound, which in combination with the vibrating air within the air cavity amplify the original sound to be audible at long distances. I was excited to realize that the end product of the sound produced was all caused by my initial movements meaning that by trying different things I could ultimately control what type of sound I produce from the ukulele.

It is pivotal to understand, however, when considering the timbre of the ukulele, that frequencies at opposite ends of the spectrum get translated differently. Firstly, the frequency determines the mode and extent to which the ukulele radiates the sound waves (French, 43). Lower frequencies, always upon striking the strings will translate the sound to the body of the ukulele causing all surfaces of the ukulele to amplify sound. High pitches, however, will only be produced through the vibrations of the strings and soundboard, see Fig. 7.18 below (French, 45). When playing the ukulele I could actually feel the variation in the vibrations and could use this to project the sound differently to the audience. For example, while playing “Hallelujah” by Jake Shimabukuro, I play notes on both ends of the frequency spectrum for the ukulele. During the chorus when I play very high notes I always am conscious of playing the high notes with much more intensity in order to keep the same volume and momentum I had been building throughout the chorus.

In addition, as a luthier (see appendix) it is important to consider that the ukuleles small size means that the majority of pitches will only be translated to the soundboard, making the choice of soundboard pivotal to the sound of the ukulele, and affecting the end sound produced. I talk about this wood choice later.

::screen shot 2012-05-10 at 10.01.09 am.png

The Musician’s Techniques:

Knowing how the sound is produced, however, does not fully account for the timbre of the ukulele, for all instruments create sound and guitars create sounds in about the same way. The first contributing component to the timbre of the ukulele is, unrelated to the physical instrument itself, the techniques I use to strike the strings.

There are two important components to the techniques I use when playing the ukulele, the attack and release of the strings. The attacks being the initial intensity of the strike to the strings and the release being how I let go of the string. The attacks and releases are a huge distinguishing factor for the timbre of instruments, in that they provide the distinct sustain and intensity generally associated with that instrument (Elliot, 36). The figure below gives visual examples of how different attacks and releases (angles of striking the strings) change the sound created (Elliot, 37).



The top diagram simulates what happens if I were to pull the strings straight out. This creates a very short punctuated sound that is initially very loud but that is not sustained. The bottom diagram demonstrates what happens when I strum the strings a 30-45 degree angle. This creates a sound with a louder than average initial intensity that decreases at an average pace. While I do use these two techniques occasionally for specific purposes, ukulele musicians generally use attacks and releases very similar to the middle diagram with a strum horizontal to the soundboard. For example, while transcribing “My Foolish Heart” by Bill Evans, I always would strum horizontal to the strings in order to create a softer Freddie Green style jazz strumming technique, which has been used by ukulele players since the 30’s. This contributes to making the ukulele’s quite sound with long sustain. ::screen shot 2012-05-01 at 12.12.39 pm.png

Another important aspect of techniques I use while playing the ukulele is the surface of which I use to strike the string. Nowadays, musicians may use many different methods to get sound from their instruments, but the most common and traditional surface is the tip, not the nail, of the middle finger, index finger, or thumb. In some cases musicians may choose to use a pick, but the picks are specially designed with felt to mimic the sound that the tips of the fingers make. These techniques have a large effect on the timbre of the sound creating less partials then say a pick or nail would on the guitar, see Fig. 4.10 (Jansson, 20). The fingertip gives a smoother bend of the string resulting in weaker high partials, as opposed to the nail sharply lifting the string ending up with an abundance of higher partials. It is really beneficial to keep this in mind while playing the ukulele. Jake Shimabukuro, while playing some of his songs like “Lets Dance” and “Spain,” uses primarily his fingertips to strum the strings, but occasionally uses his nails to add a harsher almost percussive sound to add flare and emphasis. I feel that the quintessential ukulele sound is best captured by the finger tips, so on most of my songs I usually use my finger tips, however, to add versatility I do sometimes use my nails, see below for diagrams of each technique (Moss-Hawkins). When using my fingertips and horizontal strumming techniques the sound created is a very distinct “soft, warm, and bright” sound with little intensity and long sustain, highly characteristic of the ukulele.

::photo on 2012-05-19 at 09.45.jpg::photo on 2012-05-19 at 10.17.jpg

Figure . Strumming with soft surface. Figure . Strumming with nail.
In addition to the surface of which I use to strike the strings of the ukulele, the location of the strum is of equal importance. As shown in Fig. 4.9 (Jansson, 20), depending on the location where I strike the string between the bridge and nut, the amount of overtones can change dramatically. Specifically for the ukulele, almost all musicians strum the strings close to where the neck and body attach, at the midpoint of the string. Strumming at this point creates the least amount of partials and subsequently contributes to the pure tone of the ukulele. Overall when many other ukulele musicians and I use this standard techniques for the ukulele, we help shape the warm, pure sound produced with a long sustain. For example, Jake Shimabukuro in almost all of his songs, besides when picking, will play right in the middle of the string to create the iconic ukulele sound.

::screen shot 2012-05-01 at 12.12.20 pm.png

The Strings:

In addition to the musician’s techniques used when striking the string, the strings themselves are of great importance when considering the ukulele’s timbre. In general ukuleles have nylon strings. In some cases tenor and concert ukuleles have low G top steel strings, and baritone ukuleles occasionally have steel strings, but these sounds are not generally associated with the typical ukulele tone. Why is there this large difference in sound produced between nylon and steel strings? The main factor accounting for this disparity is the difference in density between steel and nylon strings. Steel strings are six times denser than nylon strings at 7700 kg/m3 as opposed to the nylon’s 1200 kg/m3 (Jansson, 22). The consequence of this is that the specific vibration sensitivity, the sensitivity of the soundboard to vibration, will dramatically decrease when using nylon strings as opposed to steel strings. Therefore, steel strings transfer their vibration energy to the soundboard with much more intensity than nylon strings, and are much louder. So if I were to try and play a steel string ukulele I would have to change my techniques to compensate for the differences in string material. So in theory when building a ukulele I could have chosen to use steel strings, however, they color the tone with many partials and create a very strong sound with the instrument. The nylon strings on the other hand, create that quiet and pure sound characteristic of the ukulele, and therefore were my easy choice for string material. The clarity and softness of the nylon ukulele strings is one of its major distinguishing factors and is a huge reason why I enjoy playing the ukulele.

Another string factor that is responsible for the timbre of the ukulele is resonance, specifically the specific overtones cause by the resonance frequencies of the strings (Raichel, 76). Whenever I strike a string, there is always a fundamental frequency, the note I decided to play, then a series of resonance frequencies or partials created along with it (See Appendix). Partials, however, do not always have the same strength. The intensity of each partial is determined by the vibration sensitivity of the instrument to that given frequency (Bucur, 62). What I’ve found is that, in the case of the ukulele, the vibration sensitivity is how much the soundboard moves when the strings vibrate. For each soundboard, these partials are different with differing intensities, because each species of woods’ vibration sensitivity to certain partials will differ. Therefore, the strength and length of the partials presented by the vibration sensitivity curve (see appendix) are different depending on the instrument, resulting in the different strengths of partials when a note is played and subsequently the distinct timbre of each instrument. In the case of the ukulele, the rather dense soundboards have low vibration sensitivities to partial frequencies, resulting in a pure softer tone. As a luthier myself, it was important to research the different abundances of overtones standard to each species of wood. In general, the partials stayed relatively quite, however, there was still variation. For example, the spruce soundboards have stronger partials from the strings than say a mahogany soundboard. Understanding resonance frequencies is also important when I play the ukulele because when playing certain notes the partial frequencies are stronger than others changing the sound just very slightly. For example, when playing the open C string there are generally more overtones present, which I have to be conscious of during many songs. In conclusion, the factors contributing to the timbre of the ukulele involving the strings and musicians’ technique lead to a sound with a low level and long sustain with relatively few partials of higher frequencies, properties very characteristic of the ukulele’s tone and beneficial to understand while playing the ukulele.
The Wood:

Another large contributing factor to the timbre of the ukulele is the wood used to craft the instrument. Before diving into the mechanics and acoustics of wood it is important to understand wood itself as that everyday material growing on trees (see appendix). Wood is a special material used throughout time to make instruments, and while building one, it seems to me no other material can yet compare to it as a material used in building ukulele’s. Its othrotropic nature (see appendix) gives wood its unique sound quality and ability to bend while maintaining structural integrity. In addition, wood is an amazing material in that its mechanical and acoustic properties can vary dramatically depending on the wood species. The two most important properties that I had to consider while building my ukulele were the density and Young’s modulus (see appendix) of the wood. These two factors can vary largely depending on the wood species and are important because they together largely determine the speed of sound (see appendix), sound radiation, and impedance in wood which are important factors I had to judge when choosing wood to use for my ukulele.

While there are major constraints for the range in variation of each of these properties within each species of wood, the variation of certain properties among species themselves are dramatic. For example, the range in density wood goes from 100 kg/m3 for balsa to 1400 kg/m3 for lignum vitae and snakewood. Shockingly hundreds of years ago people didn’t know about these factors, so the process for determining which woods are best for different instruments has been trial and error for thousands of years, even if their criterion for the wood has been rather flawed, such as appearance not sound radiation. Nonetheless, the woods used for different instruments have been rather unchanging for hundreds of years, with the last 50 being an exception because of some woods becoming endangered. The wood species most characteristic of the ukulele and previously most widely used in their building is the Hawaiian native, acacia koa. I really wanted to use koa for my ukulele because of its splendid iconic ukulele sound and its beauty. The best ukuleles all over the world are arguably made out of koa wood, and many professional ukulele players such as Jake Shimabukuro use koa wood ukuleles. Unfortunately, over the last few decades because of the dwindling supply of instrument grade koa wood and its subsequent extremely high price I was forced to use other woods for my ukulele. It won’t be able to give me the exact same koa wood sound that I really was pursuing, however, the wood I ended up using still had some favorable properties.

When choosing the wood for my ukulele the speed of sound is significant because it is important to have a high speed of sound through the wood of the soundboard and body in general (Tracey, 19). The theory behind this is that the high speed of sound will allow all the notes within the musical range of the instruments to have time to leave the soundboard before coming out of phase and in consequence failing to leave the surface of the board at maximum amplitude (Tracey, 20). In other words, if the wood of my soundboard had too slow a speed of sound then when I would play a note it would be distorted, quite, and out of tune. So I looked for very high speeds of sound within my ukulele. Another important aspect to the speed of sound in wood is the speed of sound along its multiple dimensions. Sound travels along both the transverse and longitudinal axes, but the speed of sound of these two dimensions if different. A favorable attribute of wood used in instruments is a smaller difference between the two, creating a more even sound, because the vibrations are more evenly spread (Wegst, 1440). The figure below gives a graph of the preferable soundboard materials by way of density and speed of sound (Wegst, 1442). Koa wood would be on the bottom right of the circle of good soundboard woods, while spruce would be on the bottom left.

::screen shot 2012-05-08 at 9.18.47 pm.png

When choosing my wood for my ukulele I found there are many species with sufficient speeds of sound. In the end, I chose sitka spruce, a cherished wood for the soundboards of violins. It is a relatively hard softwood, so it has a sufficient speed of sound, but it is still slightly less than that of koa wood. I still, however, enjoy the sound created by spruce soundboard ukuleles. For koa, even though there is a large range, the most common densities found in musical instruments are close to 42 lb/ft3, also known as 672 kg/m3. Compared to other softwood soundboards, such as spruce, koa is rather dense, shifting the properties for a more unique sound. Koa’s higher density in combination with its young’s modulus value combines for the relatively fast speed of sound through the wood at 3722m/s, slightly faster than the sitka spruce I used for my soundboard. This lower speed of sound in spruce results in a slightly more colorful tone in my ukulele than a koa wood ukulele, but only a very trained and experienced listener will be able to make the distinction.

In addition to the speed of sound, characteristic impedance, z, is yet another important attribute of the wood effecting its acoustic properties. Similarly to the speed of sound, the characteristic impedance is directly related to the Young’s modulus and density of the wood (Wegst, 1442). This quantity is pertinent to the behavior of an instrument because it measures the vibration energy transferred from the strings with impedance z1 to the soundboard with impedance z2. If there is a large difference between the two characteristic impedance values then the transmitted intensity goes to zero, and therefore no sound is produced (Wegst, 1443). The characteristic impedance is important because it determines the intensity of the sound going into the soundboard, therefore the vibrations of the soundboard. As noted earlier the nylon strings have a lower density and therefore a lower impedance, so it is important for the impedance of the ukulele soundboard to be low enough to be affected by vibration energy of the strings. Because of koa wood’s high density it has a higher impedance value and therefore doesn’t translate as much of the strings vibration energy. This means that when I play koa ukuleles I have to strike the strings with more intensity in order to make a sound, and the sound created is softer. Moreover, the string partials created by the string do not get translated to the soundboard creating koa wood ukulele’s pure tone with few overtones. These attributes are what make koa my favorite material for ukulele building. My spruce soundboard on the other hand has a much lower impedance value and therefore translates the energy of the strings with much more intensity. This means that spruce soundboards give off a very loud tone with a more colored sound. While many people believe that this spruce sound is good for ukulele soundboards, I still firmly believe that koa provides the best tone and I still prefer playing koa ukuleles as opposed to spruce.

Another factor that contributes to shaping the sound coming from the ukulele is the sound radiation coefficient, R, which measure the degree to which the wood dissipates the vibrations by way of sound radiation. Sound radiation is one of two different ways that the sound becomes dampened within the soundboard. The other factor is internal friction, however in instruments, internal friction is a relatively small factor for dampening sound compared to sound radiation (Bodig; Jayne, 206). Dampening is the decrease in successive amplitudes after the driving force behind the vibrations is removed. So in the case of the ukulele, dampening is the sound radiation after the string does not have enough vibration energy to affect the soundboard (Wegst, 1442). The sound radiation for koa wood compared to other soundboard materials such as spruce is slightly less. This means that koa wood doesn’t have as a sudden bright sound like the spruce soundboards, but instead a purer more muted tone with long sustain that is very warm and less bright. When playing I like to have this longer sustain and weaker attack because when playing songs such as “Hallelujah” by Jake Shimabukuro I like to have versatility of volume and the laid back tone really characteristic of the ukulele.

The major struggle of the luthier is to find the balance between all these factors when deciding the final wood for the instrument. When considering the density of the wood, it is important to have a dense enough wood so that the speed of sound through the wood is high and the wood can keep its structural integrity at a specific thickness, while still having a low enough density so the impedance is low enough to translate the strings vibration energy and the sound radiation is high enough to have a strong tone. It is through a very fine balance of these certain properties that the choice of wood will be made. While koa is the most sought after wood, I have found that the best substitute for koa’s acoustic properties is mahogany because it shares many of koa’s mechanical properties. My spruce soundboard has quite different acoustic properties and ends up creating a much different sound, while mahogany has a similar density and still creates that pure, muted, and sustained sound. I find that when playing traditional Hawaiian songs such as “Aloha O’” or “Keep Your Eyes on the Hands” that mahogany is a good substitute for koa and keeps that traditional Hawaiian sound. If I were to make another ukulele I would definitely use a mahogany soundboard as opposed to spruce. However, even as mahogany has good sound quality, koa is still the best wood material for the truly iconic feel of a traditional ukulele.

In conclusion, when a musician picks up a ukulele and starts playing, the unique sound created is shaped by the wood, the musician’s techniques, and the strings. Overall, all these factors combine to create the soft warm sound of ukulele, giving its distinct long sustain with low level, and purity, even at high pitches. This sound, however, is created by a complex combinations of many different factors, so upon slight changes, there may be a large change in the sound of the instrument. Upon researching and building a ukulele I have been able to apply much of my knowledge of how the sound is created to effect the sound I create with the ukulele. In addition, building the ukulele has led me to further appreciate the art and precision of every ukulele made, while researching the timbre has helped me enhance to enhance my musicality as a ukulele musician.

Appendix:
Amplitude: the height of the wave. Amplitude is the aspect of the wave that changes how loud the pitch is. So a sound wave with a larger amplitude will have a louder tone and vice versa. When determining the amplitude of a wave it is generally measured in meters or smaller subsection of a meter like millimeters. Amplitude plays a key role in creating the timbre of the ukulele because as the sound gets translated through the instrument the amplitudes may be affected, changing the intensity of the sound created.
Frequency: is the determinant factor changing the pitch of a sound wave. In music, frequency, just as it sounds, is how many vibrations occur per second. In the case of the ukulele this is determined initially by the rate of vibrations in the string which is then translated to the rate of vibration of the soundboard. The units of frequency are in vibrations/second and are measured in Hertz (Hz), so 1Hz = 1 vibration/second. Middle C, for example, vibrates 256 times per second so the sound emitted is 256 Hz. The human ear is capable of detecting frequencies from about 20Hz up to 20,000Hz. To put this in perspective the keys of a piano correspond from approximately 27Hz up to 4100Hz. Frequency determines the pitch of a sound, but not necessarily an instrument because the frequency can be changed due to the medium at which it travels through, and there can be partials of different pitches that color the sound of the instrument.
Othrotropic: A property of wood, meaning that the material has three mutually perpendicular axes.
Resonance frequencies: For the ideal string the resonant frequencies are 2x, 3x, 4x, etc. the frequency of the fundamental frequency (the lowest resonance). For each resonance, the string vibrates on a different mode, corresponding to the nodes and antinodes of the resonance frequencies lower than it, see Fig. 4.2 (Jansson, 36). For the resonance with the lowest frequency there is one antinode and nodes at each of the ends, while in the second resonance there are two antinodes with nodes in the middle and at the ends, etc. Each node corresponds to a different partial created by the string, affecting the overall sound of the note. See figure below. ::screen shot 2012-04-27 at 8.32.28 am.png

Sound: is a mechanical wave that is an oscillation of pressure transmitted through a medium, composed of frequencies within the range of hearing. The first important aspect of this definition is that sound is a wave. This is by far its most important property because through manipulating the different properties and behaviors of waves the sound can be shaped and changed. While all instruments create sound waves, it is through the manipulation and quantity of the sound waves that determines the timbre. The important attributes of the sound wave that can be manipulated are frequency, wavelength, and amplitude.
Speed of sound: c (m/s), is determined by the equation c = √(E/p) where E is the modulus of elasticity (N/m2) and p is the density (kg/m3).
Strumming Techniques:

::photo on 2012-05-19 at 09.45.jpg::photo on 2012-05-19 at 10.17.jpg

Figure . Strumming with soft surface. Figure . Strumming with nail.
Timbre: The character or quality of a musical instrument as distinct from its pitch and intensity. In other words, timbre is what makes two different instruments’ sounds distinguishable from each other while playing the same note with the same intensity. So timbre is what makes the trumpet and saxophone differentiable in an ensemble and allows the composer to choose either one for different pieces and purposes.
Vibration Sensitivity Curve: The vibration sensitivity curve of a string displays a number of peaks. Each peak corresponds to a different frequency and the height of the peak indicates the strength of that partial, while the bandwidth measures the reverberation time, see Fig. 3 (Jansson, 35).
::screen shot 2012-04-27 at 8.32.42 am.png

Wood: is othrotropic, with three axes. First, the longitudinal axis (L) is defined as parallel to the wood fiber (grain). Second, the radial axis (R), is perpendicular to the growth rings. Third, the tangential axis (T) is perpendicular to the grain and tangent to the rings. This distinct property is caused by the cellular make up of the tree itself. Wood is primarily composed of hollow spindle-like cells aligned parallel to each other. The nature of the way these cells form together in the wood makes its three perpendicular axes, lending not only to woods unique mechanical properties, but also its distinct acoustic properties (Wegst, 1439). Moreover, the components of the cells determine important factors of the wood such as density and other mechanical properties. The cell walls of wood are made up of cellulose microfibers contained in a lignin and a hemicellulose matrix. These ingredients vary in amount depending on the species of wood, thereby differentiating species from one another (Bodig; Jayne, 104). In addition to the ingredients noted before, there are also minor amounts of extraneous extractives, generally oils, which vary in amounts and can further change the density of the wood (Bucar, 205). It is the volume and distribution of this chemistry and the wood’s porosity that make up the structure of the wood, and subsequently the density and various other mechanical properties defining its acoustic properties (Brodig; Jayne, 106).
Young’s Modulus: is a measure used to quantify the stiffness of an elastic material (Wegst, 1439). In other words, it is the measure of how malleable a material is. However, because wood is a multidimensional material, it may bend on three separate planes, so there are multiple Young’s modulus’ to account for direction of the force vector (Wegst, 1442). For simplicity’s sake, any Young’s moduli mentioned in the future, unless otherwise noted, will be Young’s modulus parallel to the grain, for it has been determined for the largest amounts of wood. Young’s modulus is important because when wood on a soundboard or any part of the body amplifies sound it does so by vibrating and Young’s modulus can determine how much so. Therefore, Young’s modulus in combination with density determines the majority of a specific wood’s acoustic properties (Tsoumis, 229). The graph below, illustrates the correlation between Young’s modulus and density (Wegst, 1440).

::screen shot 2012-05-07 at 9.17.27 pm.png

Works Cited

Bodig, Jozsef, and Benjamin A. Jayne. Mechanics of wood and wood composites. New York: Van Nostrand Reinhold, 1982. Print.

Bucur, Voichita. Acoustics of wood. 2nd ed. Berlin: Springer, 2006. Print.

"Classical Guitar: Where tradition meets technology.." Classical Guitar: Where tradition meets technology.. N.p., 10 May 2005. Web. 10 May 2012. .

Elliot, Charles. "Attacks and Releases as Factors in Instrument Identification." Journal of Research in Music Education 23 (1975): 35-40. JSTOR. Web. 28 Mar. 2012.

French, Mark. Engineering the guitar theory and practice. New York, NY: Springer, 2009. Print.

"Guitar construction." School of Physics at UNSW, Sydney, Australia. University of South Wales, n.d. Web. 10 May 2012. .

Jansson, Erik. "Acoustics For Guitar and Violin Makers." Acoustics For Guitar and Violin Makers. Version 4. N.p., n.d. Web. 15 Mar. 2012. .

Jansson, Erik. "On Vibration Sensation and Finger Touch in Instrument Playing." Music Perception: An Interdisciplinary Journal 9 (1992): 311-349. JSTOR. Web. 2 Apr. 2012.

Lombardo, Vincenzo. "A Physical Model of the Classical Guitar, Including the Player's Touch." Computer Music Journal 23 (1999): 52-69. JSTOR. Web. 20 Mar. 2012.

Lowery, Harry. A guide to musical acoustics. New York: Dover Publications, 1966. Print.

Maconie, Robin. The science of music. Oxford: Clarendon Press ;, 1997. Print.

Martin, Darryl. "Innovation and the Development of the Modern Six-String Guitar." The Galpin Society Journey 51 (1998): 86-109. JSTOR. Web. 2 Apr. 2012.

Parker, Barry R.. Good vibrations: the physics of music. Baltimore: Johns Hopkins University Press, 2009. Print.

Raichel, Daniel. The Science and Application of Acoustics. New York: Springer, 2006. Print.

Tracey, H.T.. "Musical Wood." International Library of African Music 1 (1949): 17-21. JSTOR. Web. 5 May 2012.

Tsoumis, George T.. Science and technology of wood: structure, properties, utilization. New York: Van Nostrand Reinhold, 1991. Print.

Wegst, Ulrike. "Wood for Sound." American Journal of Botany 93 (2006): 1439-1448. JSTOR. Web. 20 Apr. 2012.

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