Analysis of Electric Guitar Pickups

Transcription

1 Aalysis of Electric Guitar Pickups Fauel T. Ba - Graduate Studet, Pe State Uiversity / Sales Executive, MS North America. 506 Sprigdale St, Suite 0. Hutigto Beach, CA 9649 Nomeclature ε Electromagetic Force Φ Magetic Flux B Magetic Iductio A Area c Trasverse Wave Speed x Displacemet, x Directio y Displacemet, y Directio t Time T Tesio ρ iear Mass Desity j Square Root of ω Agular Frequecy k Wave Number λ Wavelegth f Frequecy egth f f A Pluck ocatio d h Height Mode Number umped Capacitace Z C C c Fudametal Frequecy coil th Harmoic Complex Amplitude of th Solutio Complex Impedace coil load Coil umped Iductace Coil Capacitace oad Capacitace Abstract May guitarists do ot uderstad how toes are geerated by electromagetic pickups o electric guitars. With further egieerig isight, they may become more effective at achievig their desired toe. The creatio of a toe - from a plucked strig to the soud that emerges from the amplifier - requires the uderstadig of several strogly-iteractig acoustical, mechaical, ad electroic systems. These iclude the theory of electromagetic iductio, the desig ad fabricatio of the pickup, ad the locatio of the pickup relative to the bridge, the structural characteristics of the guitar, ad the relatioship of the pickup's output impedace to that of the istrumet cable ad guitar preamplifier. A complete aalysis of the three most commo electromagetic pickups, the Sigle Coil, the Humbucker, ad the P-90, used o the Feder Telecaster(TM) ad Stratocaster(TM) ad Gibso es Paul(TM), provide examples for the approach developed i this paper. INTRODUCTION The electric guitar is oe of the most preemiet cultural icos i America. The electric guitar is heavily resposible for the chages i directio of America society from the 930 s aroud the time of its ivetio, up util preset day. Guitar players youg ad old look to the electric guitar as a meas to greatess, passio ad diversio. Great electric guitar toes are oe of the most coveted ad sought after characteristics of this ifluetial istrumet. History has bestowed may examples of guitar toes upo the listeig commuity, icludig the good, the bad ad the truly bad.

2 For example, Eric Clapto s toe while he was with Joh Mayall ad the Bluesbreakers is ot oly epic, but cosidered to be by may as the ultimate toe. Ideed, may other examples of excellet electric guitar toe exist. As do some very bad oes. Particularly, i the form of the learig player, were coupled with poor toe is poor playig, which ofte makes for tympaic torture. Visit your local music store to experiece this osese. The amazig thig is that there are experieced ad very taleted players that have particularly udesirable toe. It is a geeral cosesus throughout the guitar commuity that Steve Vai, a exceptioal player, has some of the worse toe ever amplified. Frak Zappa, for whom Steve Vai backed up as secod guitarist, said to Steve Your toe souds like a electric ham sadwich. Presumably this was ot a complimet. The field which we seek to study, soud quality of electric guitar pickups, is a highly subjective area, ad presets a umber of hurdles for most electric guitar players. Though a great deal of work has bee doe by people like Zwicker ad Fastl [] ad others to help us quatify ad qualify soud objectively, the field of soud quality has still remaied a mystery to most. Aother problem that may guitarists are faced with is that they just do t really liste to the soud of their guitars. A commo statemet heard at live performaces is, why does he chage guitars after each sog, they all soud the same. Nothig could be further from the truth, as each guitar, each pickup, cotais its ow uique characteristics ad spectral cotet, which distiguish it from the others. May musicias icludig guitarists, do ot uderstad the toes geerated by pickups o a electric guitar; with further isight they will be more effective at achievig their desired toe. HISTORY OF EECTRIC GUITAR & PICKUPS Uderstadig the electric guitar pickup begis by kowig its origis. I this chapter we will discuss the history of the electric guitar ad pickup developmet... Guitar Seekig Amplificatio The guitar s existece may be traced back to aciet times. Though i forms slightly differet tha today s examples, striged istrumets that were strummed or plucked with the right had ad fretted with the left have bee documeted before the 5 th cetury. It was i the Baroque ad Classical periods that the guitar uderwet most of its fial mutatios ad was established as a well recogized classical costructio. The classical style acoustic guitar of this period, a istrumet geeratig musical toes by trasferrig the eergy from the vibratios of six gut strigs to a radiatig soud board, wet o mostly uchaged util the mid-800 s. Aroud 850, steel strigs bega appearig o Spaish style guitars which were vertically held. This added volume ad a brighter soud. But it also added tesio o the eck ad soud board, causig warpig ad shatterig of either or both. Developmets i the iteral bracig for the soud board, called X-bracig, alleviated this problem withi the acoustic guitar. It stregtheed the guitar by arragig the bracig for the soud board i this ew desig, i the shape of a X. I additio, the truss rod was itroduced to help stregthe the eck. The truss rod was a steel rod iside the eck which couteracted the tesio of the strigs pullig agaist it. These desig improvemets set the ew stadard for guitars but they still could t compete i volume with other istrumets typically see i big bads of the early 900 s. Durig the idustrial age, the style of popular music ad the social evets that revolved aroud it, big bad ad dacig became popular. The acoustic guitar was uitelligible over the large brass sectios of these swig bads, ad thus remaied uheard. Cosequetly, the acoustic guitar was demoted to the rhythm sectio, where it was all but a formality. uthiers like Orville Gibso, the bega to experimet with carved, arched soud boards istead of traditioal flat oes to add to the acoustic projectio of the guitars. This helped, but ot eough to be heard over the rest of bad s istrumets. Differet measures were the take to achieve more volume from the guitar. New materials were used ad the desig of the acoustic guitar was chaged. Aroud 97 the resoator guitar was bor of the Natioal Strig Istrumet Compay created by George Beauchamp ad Joh Dopyera. Their creatio was made mostly of hollow metal body with large alumium coe resoators withi the body, uder the strigs. This resoator guitar amplified the soud about 3-5 times louder tha the traditioal acoustic guitar. Some of the drawbacks were the weight of the istrumet ad the soud quality was differet the its predecessor.

3 .. Early Attempts I Electrical Amplificatio I the begiig of the 0 th cetury, the telephoe ad the radio were startig to become everyday household techology. May tikerers had started amplifyig guitar souds with parts from telephoes, like the microphoe i the mouth piece. But whe did the guitar pickup come alog? Who actually iveted the electric guitar? People bega to experimet with amplified istrumets other tha guitars as early as 890. George Breed was a aval officer who filed a patet for a method of ad apparatus for producig musical souds by electricity i 890 []. Aother oe of the earliest developers was loyd oar of the Gibso Guitar Compay, who i 94, developed a pickup to use for the viola ad strig bass. oar s desig was slightly differet ad less effective tha curret desigs. I his desig, the strigs passed vibratios through the bridge to the electrostatic pickup which registered those vibratios ad passed the sigal to a amplifier. Yet, the first marketed electric guitar was from the Stromberg-Voisiet compay i 98 utilizig a similar pickup. The problem with this pickup desig was the sigal was very weak, eve with the help of amplifiers of the time ad was extremely proe to feedback. The eed for a more direct pickup desig led egieers to the pickup desigs we have today, where the electromaget picks up the vibratios from the strigs themselves. This desig is based o the priciple of electromagetic iductio. The same priciple is used i phoographs, electric motors ad geerators [3]. George Beauchamp adapted this priciple to a sigle striged istrumet i 95, but struggled to adapt it to six strigs so that each strig would have a evely powerful sigal. About five years later, i 930 the desig was completed. Beauchamp ad his fried Paul Barth created a pickup based o two horseshoe magets with steel poles added oto oe side of each iteral gap, woud with wire. This allowed the pole placemet to amplify each strig idividually. Oce the pickup was workig as desiged, the two ivetors cotacted a guitar builder by the ame of Harry Watso. Watso built a eck ad body for the first viable electric guitar. This guitar was a Hawaiia style lap guitar ickamed the Fryig Pa. Beauchamp took the Fryig Pa to Adolph Rickebacker, a ower of a tool ad die compay that made steel bodies for Natioal s resoator guitars. Usig the ifluece of Rickebacker, the two created a compay uder Rickebacker s ame, sellig the Fryig Pa to coutless lap steel players. However, it was Adolph Rickebacker that claimed to be the ivetor of the electric guitar..3. Cotiued Improvemets I Pickup Desig Developmets cotiued from the Fryig Pa to the Spaish Electric guitar made by Gibso luthiers. Gibso worked with Alvio Rey, a promiet slide guitarist of the time, to improve the pickup makig it more suitable for Spaish style guitars. They developed a pickup i which a solid bar maget was woud with a pickup coil, istead of idividual pole pieces for each strig. The desig was iitially icorporated i a Hawaiia style guitar, but was quickly adapted to a Spaish style as iteded. This guitar was called the ES-50, stadig for Electric Spaish ad would be the first ormal electric guitar. There were still may issues; the most aoyig was that of feedback. At this poit, the guitar makers were still lookig to the pickup as the culprit. It was oly whe es Paul bega solvig the problems that the desig improved agai. He believed that the solutio was to create a solid body guitar. He tured out to be right. His theory was that the solid guitar would stop feedback caused by the highly acoustic soudboard hearig itself. Paul s first successful solid body guitar was call the og. It was a 4 x 4 piece of pie mouted with simple magetic pickups that Paul made himself. However, whe Paul approached Gibso with cocept of a solidbody, they were skeptical ad thought it too outladish for most musicias to accept. It was i 943 that eo Feder, a radio repair ma, had a workig prototype of a solid body electric that he would ret to players to gather suggestios for improvemet. By 949, Feder released the Esquire, which would be reamed the Broadcaster, ad the agai reamed as the Telecaster. The guitar had all the beefits of es Paul s desig but souded much differet tha the Spaish Electrics, which were preferred i jazz for their warm soud. The Telecaster however was a hit with the Coutry ad Blues players, for the high pitched toes it produced with its sigle coil pickups. Gibso realized they eeded to get ito the solid body electric guitar market ad i 95 they released their ow electric called the es Paul. The pickups Gibso employed for the es Paul varied. Origially, the es

4 Paul was fit with P-90 pickups (described i Chapter 5), which were origially developed i 946. The i 957, Gibso fit the es Paul with Humbuckig pickups. Sice the, the electric guitar has retaied basically the same i desig. THEORY OF EECTRIC GUITAR PICKUP There are a umber of differet guitar pickup desigs available o the market today. The most traditioal is the passive magetic pickup desig employig the physics of electromagetic iductio. This desig represets the majority of the pickups used o electric guitars. Other desigs iclude piezoelectric pickups, typically foud o acoustic guitars, ad optical pickups, curretly foud o some specialized bass guitars. The scope of our study will be limited to the passive magetic variety. All pickups are trasducers that covert a portio of the vibratory eergy of the strig s motio ito oscillatory electrical sigals. They collect, gather or pickup the oscillatio of the guitar strigs. To uderstad the magetic pickup trasducer, oe must have a uderstadig of the priciples of electromagetic iductio. 3.. Itroductio To Electromagetic Iductio There is a distictio betwee permaet magets ad electromagets. The former have two eds, North ad South ad they attract ferromagetic objects typically made of steel or iro. A electromaget has the same effect, except it is temporary; the magetism oly exists whe electric curret is flowig. This is based o the priciple of Ampere [4]; wheever you have a curret travelig through a wire, a magetic field is iduced. By coilig the wire a few times you icrease the stregth of the magetic field iduced, so it behaves like a ordiary permaet bar maget. This pheomeo implies there is a relatio betwee electricity ad magetism. If we ca use electricity to create magetism, ca we do the opposite: use magetism to create electricity? It was this questio that drove Joseph Hery [5] ad later Michael Faraday [6], to their idepedet discoveries of electromagetic iductio i 830 ad 83 respectively. They did so through the followig experimet. A bar was placed across the poles of a electromaget. Wrapped aroud the bar was a isulated coil of wire. Coectig the leads of the coil to a galvaometer, Hery was able to see a mometary deflectio i the galvaometer whe the curret i the electromaget was tured o, eve though there was o electrical coect betwee the coil ad the wires of the electromaget. He had discovered that curret is iduced or geerated i the coil whe the magetic field through it chages. It does t matter if the wire is movig or the field or ay other moveable coductor crossig through the magetic field lies. This is the defiitio of electromagetic iductio. The geeratio of a electric curret i a circuit implies the existece of a electromotive force (emf). A emf is the work per uit charge doe by the source of emf i movig the charge aroud a closed loop. Faraday stated that the iduced emf i a circuit is proportioal to the rate at which the magetic field lies cross the boudary of the circuit. Faraday s aw is expressed i terms of magetic flux, show i equatio. dφ ε dt Where, Φ is equal to the magetic flux, show i equatio. Φ BA B () ( ) Magetic flux is the product of the average magetic iductio B, times the perpedicular area A that it peetrates [7].

5 3.. Electromagetic Iductio Applied to Guitar Pickups The guitar pickup is made of a assembly of permaet magets wrapped with a coil of isulated wire, typically copper. The strigs of a electric guitar are made of magetically permeable material, such as a iro or ickel alloy. The strigs beig i close proximity to the permaet magets of the pickup become magetized. This iduces two magetic poles i the strig directly above the maget. As the strig vibrates, it causes chages i magetic flux which iduces a emf i the pickup coil accordig to Faraday s aw. Because magetic flux chages as a fuctio of time as stated i equatio, the emf geerated is simply a fuctio of strig velocity. This emf is physically the ope circuit voltage that is output from the guitar to the toe cotrols ad the out to the amplifier. The curret produced by the emf is related to the iput impedace of the guitar amplifier. DESIGN & IMPEMENTATION OF EECTRIC GUITAR PICKUP There are may physical desig aspects that affect the performace of pickups such as pickup locatio, pluck locatio, strig height, guitar body type ad costructio, strig type, hardware as well as pickup parameters such as umber of widigs, iductace, impedace, capacitace, toe cotrols, ad cable ad amplifier cosideratios. A thorough examiatio of these follows: 4.. Pickup ocatio The physical locatio of the electric guitar pickup has tremedous impact o the toal properties of the pickup output, i.e. the timbre of soud created. The timbre of a istrumet is defied as the combiatio of qualities of a soud (harmoic or spectral cotet) that distiguishes it from other souds of the same fudametal pitch ad amplitude. The uique harmoic cotet of istrumets is part of the reaso a guitar souds differet from a piao or ay other istrumet. The other determiat is the attack ad decay evelope that characterizes the trasiet behavior of the soud. It is commoly mistake that toe ad timbre are syoymous. Toe ca be thought of as the equalizatio (EQ) that ca be adjusted from the guitar s toe cotrols, a separate EQ device or the toe cotrols o a amplifier. Timbre is the character of the differet souds that pickups geerate prior to modificatio by the toe cotrol circuit. The timbre is related to the pickup s locatio with respect to the strig s harmoic cotet. Most guitars are typically desiged with or 3 pickup locatios depedig o the model. See Figure below. Figure. Pickup locatios o a guitar affect toal characteristics of pickup output.

6 Figure shows a Stratocaster style guitar with the 3-pickup cofiguratio ad associated pickup locatios. The bridge pickup is the pickup located o the body closest to the bridge. The eck pickup is the pickup located o the body just before the eck. Ad the middle positio is located i betwee the eck ad the bridge pickups. Boostig the treble o the output of a eck pickup with a toe cotrol will ot make it soud like the bridge pickup. Similarly, boostig the mids o a strat will ot make it soud like a es Paul! We will explore timbre i more detail, later i this sectio. Regardless of type, it may be geeralized that the closer the pickup is placed to the bridge the more high frequecy cotet is preset, i.e. it souds brighter or cuts more. Coversely, as the pickup locatio is moved closer to the eck, the timbre is characterized as beig deep ad rich. The reaso for this is based o the harmoic cotet that is iheretly preset i the vibratig strigs that the pickup picks up at its various locatios. It is iterestig to ote that oe of these soud like a acoustic guitar, where every compoet of the strig vibratio is coupled to the guitar body through mechaical forces applied by the eds of the strigs through the bridge ad the ut. This icludes logitudial as well as trasverse waves of the fudametal ad every harmoic. O the electric guitar oly the displacemet of trasverse waves alog the axis of the pickup sesitivity at the pickup locatio are sesed. I essece, oly oe specific aspect of a complex mechaical iteractio is captured as a electrical voltage ad set to the iput stage of the amplifier. Whe the strigs of the guitar are plucked, triagle shaped stadig waves o the strig are set up, cosistig of a harmoic superpositio of the fudametal ad higher harmoics. et us the develop the equatio describig this behavior by lookig at the D liear wave equatio for trasverse waves o a strig. The liear oe dimesioal wave equatio assumig small trasverse displacemet as foud i ay reputable acoustics text is as follows. y x c y t () 3 Where the costat c (trasverse wave speed) is defied by T, tesio ad ρ, liear mass desity. c T ρ ( 4) It is reasoable to assume the boudary coditios of the strig to be fixed at the bridge ad the ut. The attachmet of the strig to the guitar body is approximately rigid, ad thus the strigs trasfer relatively little eergy to the body. The reality of this pheomeo is resposible for the immortal words of Nigel Tufel, "liste to that sustai [8]. To fid the ormal mode frequecies of a fixed-fixed stig, we assume the geeral solutio of the followig form: y j( ωt kx) j( ωt + kx) ( x, t) Ae + Be ( 5) I Equatio 5, j equals the square root of -, ω, the agular frequecy, k, wave umber, ad λ, wavelegth, have bee itroduced ad are defied i Equatios 6-8 below. ω πf π k λ ( 6) ( 7)

7 λ c f () 8 We kow that the strig s displacemet at x0 ad x will be zero as see i the Figure below. Figure. Fixed-fixed strig displacemet based o distace. So applyig boudary coditios gives the followig: y y ( 0, t) 0 A + B 0 B A ( 9) jk jk (, t) 0 Ae + Be 0 ( 0) e jk jk [ e ] 0 ( ) A e jk e jsi jk 0 ( ) ( k) 0 ( 3) The frequecies that satisfy the boudary coditios are: k π,,3... λ π f k ω kc c π π ( 5) ( 4) ( 6) These solutios correspod to a iteger umber of half-wavelegths fittig betwee the bridge ad ut, as show i Figures ad 5. Where f is the fudametal frequecy, f is the th harmoic, c is the trasverse strig velocity, is the mode umber ad is the legth of the strig. Recallig from above that B -A, the Eige fuctios (or mode shapes) are:

8 y j( ωt k x) j( ωt + k x) ( x, t) A e + B e ( 7) A A jk x jk x jωt [ e e ] e ( 8) jωt [ jsi( k x) ] e ( 9) Icorporatig the -j ito the A, this leaves us with the well kow expressio for a stadig wave. y jωt ( x, t) A si( k x) e ( 0) Where A is the complex amplitude of the th solutio. As discussed earlier, electromagetic iductio produces a emf that is directly proportioal to the velocity of the strig at the pickup locatio. By takig the time derivative of Equatio 0, we produce the expressio for velocity of a stadig wave i Equatio. v dy dt jωt ( x, t) jω A si( k x) e jω y( x, t) ( ) where: π k ω k c ( ) ( 3) For to ifiity, the complete solutio trasverse displacemet is: y ( x, t) y ( x, t) [ A cos( ω t) + B si( ω t) ] si( k x) ( 4) This result says that a arbitrary iitial displacemet, y(x,0) ca be represeted as a superpositio of the ormal modes of the system. This equatio describes the physical behavior of the etire strig. However, the guitar pickup reads vibratios off a arrow portio of the strig. This has a critical effect o the timbre of the pickups. Figure 3 is a drawig of the strig as foud o a electric guitar. The strig is attached as fixed-fixed, with the bridge beig the left attachmet poit ad the ut beig the right attachmet poit. Three pickups are show i the eck, middle ad bridge positios, as foud o a Stratocaster style electric guitar. The strig is show to be vibratig at the fudametal frequecy. Figure 3. Fixed-fixed vibratig strig i fudametal frequecy ad associated output over bridge, middle ad eck pickup locatios.

9 Sice all parts of the strig oscillate at the same frequecy, the blue stripes represet the output level of the vibratig strig sesed by the idividual pickups at each locatio. The output icreases as the locatio is moved closer to the eck from the bridge for the fudametal ( ) mode. It is importat to remember that the electromagetic pickup output is proportioal to velocity ot displacemet. Therefore, if the strig i Figure 3 is vibratig at a particular frequecy, the ceter of the strig has the highest velocity ad the eds of the strig have zero velocity. As you move away from the bridge ed towards the ceter, the pickup output icreases due to the higher velocity of the strig. For a give displacemet, as frequecy icreases, the output icreases, meaig the pickups have a greater sesitivity to higher frequecies. This is simply because at higher frequecies the strig vibrates faster for a give displacemet amplitude. The pluckig positio affects the amplitudes of the modes. This ca be heard whe the closer to the bridge the strig is plucked, the sharper the ote souds. This is because the higher modes are beig excited more tha the lower modes. I Figure 4 below, a strig with pluckig locatio /d is pictured. Figure 4. Plucked fixed-fixed strig with legth, height h, ad arbitrary pluck distace /d. Figure 4 is a geeral represetatio of a plucked fixed-fixed strig. The associated boudary coditios for iitial displacemet (t 0), are the followig: y ( x,0) dh x d ( d ) h ( x) 0 d x d x ( 5) The Fourier coefficiets for the fixed-fixed strig based o iitial displacemet is show below i Equatio 6. A 0 y ( x,0) si k xdx ( 6) Kowig the boudary coditios of iitial displacemet from Equatio 5, the geeral equatio for the amplitudes (A ) of a strig legth, plucked at locatio /d, at height h is show below i Equatio 7.

10 A d si ( ) 0 dh d h + x kxdx d d ( x) si k xdx ( 7) The solutio to the geeral equatio is show i equatio 8. A hd d ( π ) π si d ( 8) Harmoics that represet the plucked strig decrease i amplitude proportioal to the frequecy squared we ca apply this to a specific case such as at /3. So for pluckig at /3. y ( x,0) 3h x 3 h ( x) 3 0 x x 3 ( 9) A 3 3h si + x kxdx h ( x) si k xdx ( 30) Equatio 30 simplifies to: A 9h π si 3 ( π ) ( 3) For the case of /3, the coefficiets are calculated below i Table. Coefficiet Amplitude Ratio (A/A) A h - A 0.974h /4 A 3 0h - A h /6 A h /5 A 6 0h - A h /49 A h /64 A 9 0h - Table. Harmoic coefficiet amplitudes ad ratios with respect to A. Recall that the pickup output is proportioal to the velocity of the strig.

11 emf ( x) j A si( k x) ( 3) ω Based o Equatio 8, the coefficiets A are proportioal to the reciprocal of the mode umber () squared. A ( 33) For k x <, the sie fuctio ca be approximated by the first term i a Taylor series. ( k x) k x for k x ( 34) si < From Equatio 6, we see that the wave umber, frequecy ad mode umber are proportioal. k ω ( 35) As show i Equatio 3, both ω ad k, are proportioal to for k x <, the velocity is proportioal to. This depedece of the velocity of the th harmoic is cacelled by the depedece of the harmoic amplitude, A. Therefore, for a pickup located a distace x from the bridge such that k x <, the pickup s ope-circuit output voltages will be equal for all of the harmoics of a plucked strig up to the th mode satisfyig k x <. Figure 5 depicts the simplest case of strig vibratio, the fudametal. I reality the strig vibratio is characterized by the fudametal as well as sustaied harmoic frequecies ad some trasiet vibratios. The sustaied harmoic frequecies are of iterest because they defie the timbre of the guitar. I the figure below the same strig is show vibratig at the fudametal ( ), secod ( ), third ( 3), fourth ( 4) ad fifth ( 5) harmoics. Figure 5. Strig vibratio show with the eck pickup (N) located at x /4 as measured from the bridge. The maximum amplitudes of each mode are equal for illustrative purposes. The harmoics exist as compoets of a played ote or idividually forced by mutig the strig lightly with the figer over a ode poit o the strig. The ode poits are those where strig vibratio is at a miimum ad the ati-ode is where vibratio is at a maximum. Together the harmoics add by harmoic superpositio as described i Equatio 4.

12 By lookig at the idividual harmoics we gai further isight to the ature of the emf produced by a electric guitar pickup. The fudametal has a ati-ode directly at the ceter of the strig represetig maximum amplitude ad odes at the eds of the fixed-fixed strig. The secod harmoic has a ode at the ceter of the strig ad ati-odes at /4 ad 3/4 of the strig legth (). I this figure, oe of the ati-odes is directly above the eck pickup, resultig i a higher output tha the other pickup locatios. The third harmoic has two odes at /3 ad /3 the strig legth ad three ati-odes at /6, 3/6, ad 5/6 the strig legth. The middle pickup locatio is directly udereath a ati-ode for the 3rd harmoic ( 3) ad has the highest output, while the eck ad the bridge have lesser outputs. The fourth harmoic has odes at /4, /4 ad 3/4 of the strig legth. This represets a iterestig effect sice the eck pickup is directly udereath a ode at /4 the strig legth. This meas there will be o output at the eck pickup for that frequecy. May electrics are desiged with the eck pickup at oe-quarter of strig legth. The fifth harmoic has odes at /5, /5, 3/5 ad 4/5 the strig legth. Here the red stripe idicates that the displacemet is out-of-phase above the eck pickup. If the eck pickup is combied with other pickups, phase cacellatio of this frequecy will occur, although the cacellatio will oly be complete if the amplitudes of the strig s motio is equal at both locatios, as show. I this case, M ad N cacel ad the total output is due to B. Timbre is determied by the relative levels of each of the differet harmoics, which physically iclude the highest harmoic that a amplifier ca reproduce or the highest harmoic a perso ca hear (which ever comes first)! A higher level of upper harmoics compared to the lower harmoics ad fudametal, produces that brighter, sharper toe as foud at the bridge pickup. This ca be see i Figure 5, whe lookig at each of the harmoics just over the bridge pickup. Physically, there is more upper harmoic cotet, ad less fudametal at the bridge tha at the eck or middle positio for the rather ucommo case where all five harmoics have the same amplitude. As a player frets otes o the fret board, this chages the effective legth of the strig ad alters the frequecy of vibratio to produce differet otes. This also progressively chages the locatios of the odes, which chages the harmoic cotet of the otes. See below i Figure 6 are the effects of the fudametal, secod, third ad fourth harmoic, subject to frettig at the th fret (oe half the distace from bridge to ut). Figure 6. Strigs vibratig while fretted at octave. The exercise of catalogig each of the ode locatios for each strig at each fret is better left to a research studet with spare time ad a computer. The priciples remai the same, though the values of frequecy ad ode locatio chage. 4.. Pickup vs. Strig Height The height of the strigs with respect to the fret board is referred to as the actio. It is a parameter that players chage to suit their playig style ad to achieve a particular soud. O a acoustic guitar with a higher actio the output grows acoustically. A high actio is well suited for rhythm playig, typically characterized by strummig. It is more difficult to play arpeggios with a higher actio. O a electric guitar the opposite is true for output. As the distace from the strigs to the pickups icreases the output decreases. Recall, that the strigs become magetized i the presece of the pickups ad the aligmet of the dipoles i the strig geerates the emf s. This meas that if the strigs are further away, the pickups magetize the strigs less. Also with a greater

13 distace, the pickups sese less of the emf s give off by the strigs durig vibratio Guitar Body ad Costructio Cosideratios I the Pickup ocatio sectio, it was stated that the boudary coditio imposed o the motio of the strigs of a guitar may be treated as fixed-fixed due to the relatively rigid moutig to the guitar body at the bridge ad ut. Thus, very little eergy is trasferred to the body, ad this meas the harmoic cotet of the strigs durig vibratio is ot appreciably chaged by the body of the guitar. This was a fair assumptio for the derivatio of the modes of the strig i Equatio 4. I reality, the guitar body ad eck made of wood, ad usually solid, are ot ifiitely stiff. Due to the guitar itself havig its ow vibratio characteristics ad possibly affectig the respose of the strig vibratio, the soud that is output may vary depedig o the shape, costructio, type of materials used, ad whether the body is solid, semi-hollow or hollow. At this poit it is helpful to defie the differet characteristics of electric guitar toe. Toe ca be broke dow ito time ad frequecy domai compoets called the evelope ad harmoic cotet. The evelope of toe refers to the attack, sustai ad decay of the ote played. The harmoic cotet is the superpositio of the fudametal frequecy alog with ay harmoics sesed by a particular pickup. Guitarists ofte refer to attack to express agle, pressure ad method of the had, figers, plectrum, etc, durig the act of pluckig the strig. This discussio refers to the attack as the chage i the shape of the plucked strig ad the resultig soud, just after the strig has bee released. Essetially, how quickly the soud reaches maximum amplitude. The attack portio of the sigal or ote is determied by the higher harmoics which decay much more quickly tha the lower harmoics ad fudametal. This trasiet portio of the sigal is geerally referred to as the twag of the guitar. Its duratio is measured i millisecods but is a distictive ad importat characteristic of the guitar s soud. The attack portio of the sigal is represeted i the figure below label as sectio A. Figure 7. Time history of a plucked ote showig the attack (A), Sustai (B) ad Decay (C). Sustai is defied as the costat volume portio of the sigal util it begis to decay. I reality, a plucked guitar sigal has zero sustai because it begis to decay immediately after it is geerated. However, there is a portio of the sigal after the attack represeted i Figure 7 as sectio B, where the sigal is early costat called the sustai. I other words, the decay is very gradual, before reachig sectio C which represets a greater decay rate. May guitarist mistakely refer to the sustai of the istrumet to mea the decay rate. Amogst the guitar commuity, a es Paul is kow for havig log sustai, whe techically it has oe. It has a slower decay rate compared to other guitars. The decay rate quatifies how quickly the amplitude of strig vibratio (output of the guitar) returs to zero. From iceptio, the sigal is decayig due to loss of eergy. The decay itself is caused by a umber of mechaisms that together drai the vibratig strig of its eergy. The mechaisms that cause decay are the strigs resistace to bedig (dampig), air resistace slowig the movemet of the strig, ad the trasfer of eergy from the strig to the body of the guitar. I high amplitude or stage volume cases, feedback sustai may be preset. Feedback sustai occurs whe eergy is retured to the strigs from the amplified pickup output. This feedback loop has a iterestig effect by creatig toes that last idefiitely, somethig that is ot possible with a traditioally plucked strig. This feedback mechaism depeds upo the mechaical respose of the guitar body which is coupled to the strigs. Depedig o the style of music the artist is playig, feedback may be desirable. Carlos Sataa uses feedback sustai durig live performaces regularly. Durig soud check (before the show) he determies the locatios o the stage where feedback occurs for differet frequecies. He the marks those poits with tape o the floor to be able to use feedback as eeded durig the performace.

14 The method by which the strig is attached to the guitar ad the tesio are the first two physical parameters affectig toe. The more rigidly the strig is attached to the guitar, the more coupled it is with the guitar s structural respose. The structural respose of a particular guitar ca be foud from a umber of aalysis techiques such as modal aalysis or laser vibrometry. Results of such studies have show that there are may differet atural frequecies ad associated mode shapes for guitars of various shapes. It is ot the itet of this chapter to examie these techiques i detail, but rather to aalyze how the results may affect pickup respose. The cocept of toe may be ituitively described i the followig maer: As the ote is iitiated (attacks) ad decays, the harmoic character chages with time. The resoace or structural respose of the guitar determies what progress the harmoic chages make withi the ote s evelope. The fudametal frequecies of the six strigs o guitar tued to cocert pitch (A 440 Hz) are listed i Table below. Strig Frequecy (Hz) 6th Strig (ow E) 8.4 5th Strig (A) 0.0 4th Strig (D) rd Strig (G) 96.0 d Strig (B) 46.9 st Strig (E) 39.6 Table. Guitar strig atural frequecies. Published research by Da Russell of Ketterig Uiversity [9] shows that the structural characteristics of guitars ca be foud through experimetal modal aalysis techiques. Below i Figure 8, is the plot of the first bedig mode of a solid body guitar. The atural frequecy is 55Hz. Figure 8. Fudametal bedig mode of solid body guitar at 55Hz (Courtesy of D.Russell). Similarly, i Figure 9 the secod mode of vibratio occurs at 60 Hz for this same guitar ad is the secod free-free bedig mode.

15 Figure 9. Secod bedig mode of solid body guitar at 60Hz (Courtesy of D.Russell). The third mode of vibratio is a torsioal mode occurrig at 37Hz. It is most clearly see i the vibratio of the body at opposite corers. See Figure 0 below. Figure 0. First torsioal mode of solid body guitar at 37Hz (Courtesy of D.Russell). Figure represets the fourth mode of vibratio at 47Hz. This is a bedig mode alog the width of the guitar.

16 Figure. Third bedig mode of solid body guitar at 47Hz (Courtesy of D.Russell). I this example the resoat frequecies of the d, 3 rd, ad 4 th modes are well withi the rage of frequecies geerated by the guitar. It should be clear that due to the physical characteristics of the guitar withi the frequecy rage of the otes played that the harmoic respose of the vibratig strigs will be affected. The wood that is utilized i the guitar receives the vibratios from the strig by meas of couplig through the bridge ad ut. It vibrates i respose ad trasmits vibratios back to the strigs. Whe playig a guitar, oe ca physically feel the guitar body vibratios as differet otes are played. It s importat to ote that the guitar will vibrate more at certai frequecies, which meas that the atural resoaces of the body are beig excited ad therefore feedback ito the strig vibratio at various levels depedig o the frequecy beig played. How the vibratios feed back ad forth betwee the strigs ad the guitar body determies how the harmoic cotet chages durig the evelope. Typically, thicker ad deser wood resoate at higher frequecies. This ca be heard by suspedig a es Paul ad a Strat by the eck ad tappig o the back of each. The es Paul has a higher resoace frequecy tha the Strat, aside from the vibratig sprigs that coect the tremolo bridge. The guitar is made of 4 mai parts with differet desities. I order of importace to the modal respose, these are the eck, figerboard, body, ad top. These combied parts of the guitar affect the evelope ad harmoic respose of the guitar. I order of desity from highest to lowest, typical woods used by luthiers are Eboy, Wege, Cocobolo, Rosewoods, Purpleheart, Bocote, Paduak, Hard Maple (flamey or birdseye), Soft Maple (Quilted), Ash, Alder, Mohagay, Koria, Swamp Ash, Cedar, Redwood ad Basswood. Metal compoets such as truss rods ad eck joits also cotribute to the structural respose of the guitar ad are itegral to is costructio. A screwed-i eck referred to as bolt o creates a break i the middle of the guitar, which though firmly attached, lowers the stiffess of the guitar as a whole. Feder guitars are kow for this type of eck. This lowers the resoace of the guitar. O the other extreme, the eck through desig most ofte foud o high ed bass guitars, is such that the eck rus though the etire legth of the body. The two additioal pieces are attached to make up the rest of the body. This is the most solid ad most stiff costructio. The middle of the road solutio is a set eck as foud o most Gibso guitars. The set-eck is firmly set ito the body of the guitar ad secured by adhesive, providig a more rigid coectio tha the screw-i eck. The souds associated with the differet eck joits are a subjective matter, though from a practical stadpoit, the bolt o ecks are much easier to adjust, repair or replace. Semi-hollow ad hollow body electric guitars have uique characteristics that affect the evelope ad harmoic cotet of the sigal. The hollow body electrics are proe to feedback because of the pickup beig mouted directly to the soud board. This meas that whe the stig vibrates the soud board it is vibratig the pickup also. I additio, whe the guitar is ear the amplifier the iteractio is strog ad feedback ca occur. The decay of the sigal is much faster with a hollow body guitar because there is little stiffess ad mass to prevet the eergy from dissipatig through the acoustic radiatio ad mechaical dampig. Semi-hollow guitars

17 are chambered ad typically have a piece of solid wood that rus dow the ceter of the body from the eck to beyod the bridge. This adds stiffess to the pickup mout ad the bridge ad is therefore less proe to feedback ad has a log decay time Strig Type Strigs themselves affect the type of respose the pickup outputs. Heavier gauge strigs are stretched at higher tesio ad have loger decay times sice more eergy is stored i the strig for the same vibratio amplitude. ighter strigs have shorter decay times but have sharper perceived attack. May strigs are woud i ickel ad some i steel. Steel woud strigs have a sharper attack ad therefore soud brighter. Coated guitar strigs have a very thi layer of proprietary material to exted strig life. This adds dampig to the strig which makes the strig soud slightly less bright tha strigs that are t coated Hardware The bridge, ut, tuers, ad tailpiece all determie structural couplig betwee the strig ad the eck ad body of the guitar. The more mass ad cotact area the more couplig there will be preset. The bridge ad achorig poits of the strigs iteract together to trasmit vibratios betwee the guitar ad the strig. As this trasfer occurs, certai frequecies are reiforced. Couplig dictates the amout of trasfer that occurs. For example, a tremolo bridge, as foud o a Strat, trasmits higher harmoics better tha lower oes. A hardtail brass or steel tue-o-matic as foud o a es Paul, trasfers more lower harmoics Performace of Pickups The discussio of pickups util ow addressed implemetatio of the pickup withi the guitar as a mechaical system. et us ow cosider the pickup itself ad its parameters i determiig the toe of a guitar. Toe ad output maily deped o the relatioship betwee iductace, capacitace, magetic stregth ad the efficiecy of the pickup, as well as the relatioship betwee the pickup parameters ad the load see by the pickup due to toe cotrols, cables, effects ad the preamplifier stage of the amp. The pickup may be thought of a trasducer fuctioig primarily as a iductor. As with ay trasducer, the pickup has a frequecy respose that is ot equal for all frequecies. As with other trasducers such as microphoes ad accelerometers, the pickup has a resoace peak at a certai frequecy. This is due to the combiatio of the iductace ad resistace iheret to the pickup ad the iterwidig capacitace of the coil ad the capacitace foud maily withi the cable coectig the guitar to the amplifier, as well as the pickup toe cotrols. As a simplified electrical circuit, the pickup has a lumped iductace, dc resistace R, ad widig capacitace C as show below i Figure. Figure. Electromagetic guitar pickup equivalet circuit diagram.

18 A pickup coil has a dc resistace based o the type of wire used ad the umber of turs. 4 AWG has a resistace of about.6 Ohms/ft ad 43 AWG has a resistace of. Ohms/ft. Pickups have betwee several thousad turs of wire up to 0,000 turs. The dc resistace ad the lumped iductace are i series with each other. Due to the resistaces associated with pickup coils ad the large umber of turs, the tur-to-tur capacitaces build up to a o egligible lumped widig capacitace. The iter-widig capacitace is typically betwee few 0 s -00 pf. The complex impedace of a capacitor is show below i Equatio 36: Z C j ω C j π fc ( 36) Thus, the magitude of the capacitor s impedace is show below i Equatio 37: Z C ω C π fc ~ f ( 37) Whe the frequecy is zero, Z C goes to ifiity, where as whe the frequecy goes to ifiity, Z C goes to zero. Thus, at low frequecies, the lumped iter-widig capacitace of a guitar pickup has little impact. At higher frequecies, the lumped iter-widig capacitace has a icreasigly sigificat effect. As the frequecy iduced by the strigs motio icreases, the pickup capacitace icreasigly shuts or shorts-out the sigal to groud. A exteral load actig o the pickup cosists of resistace from the volume ad toe potetiometer i the guitar, ad ay resistace to groud at the amplifier iput. It is idustry stadard to match the high output impedace of the guitar pickup to a high iput impedace of the preamp stage at aroud MOhm. Also part of the exteral load is the capacitace due to the lead ad shield of the cable which has a sigificat impact o the toe of the pickup. Figure 3 shows circuit diagram with these parameters. Figure 3. Electromagetic pickup ad exteral load circuit diagram. These compoets form a secod order low pass filter which has the frequecy respose as show below i Figure 4.

19 Figure 4. Secod order low pass filter created by loadig of pickup. The respose at low frequecies is liear util about f l. The the respose icreases util f o. The frequecy f o is the frequecy of the resoace peak. Equatio 38 describes the relatioship of f o to iductace ad capacitace. f 0 π coil ( C + C ) coil load ( 38) The respose from f o to f u rolls off at - db per octave as show by the red colored lie. The cutoff frequecy of this secod order low pass filter is desigated by f u. This represets the half power poit where the respose is 3dB dow. This meas that ay toes or harmoics i the rage of the resoat frequecy are amplified. Far below the resoace frequecy the fudametals ad harmoics are reproduced without beig sigificatly altered. Above the resoace frequecy, the harmoics are atteuated by -db/octave. As ca be see, kowig the frequecy f o, as well as the relative amplitude of the resoace peak provides isight ito the pickups trasfer characteristics. The frequecy respose of just the pickup without cable would be relatively flat util a certai frequecy ad the roll off. But, amplifyig the guitar without coectig it to either a cable directly to the amplifier, effects uits, or a cable to a wireless trasmitter, the to the amplifier, is ulikely. But how does this resoace affect the way the guitar souds? The resoace peak of most pickups i combiatio with ormal istrumet or guitar cables lies betwee 000Hz ad 5000Hz. This is the frequecy rage where the huma ear has its highest sesitivity due to the ear caal. At 000Hz the soud is characterized as warm ad mellow, at 3000Hz brilliat or preset, at 4000Hz piercig, ad at 5000Hz more brittle ad thi. The height of the resoat peak also affects the soud; a high peak amplitude produces a powerful ad characteristic soud ad a low peak amplitude produces a weaker, more eve soud. The height of the resoace peak ca rage betwee 0 ad db o most guitars ad is govered by the magetic material i the coil, the exteral resistive load, ad metal pickup cover sometimes foud coverig the pickups. The higher the magetic stregth, the higher the amplitude, the lower the resistive load the lower the amplitude ad without the metal cover the amplitude is higher. Some guitarists prefer this ad remove the metal cover most otably from their es Paul humbuckig pickups to achieve toe with more high frequecy harmoics. The resoace frequecy depeds o the combiatio of the iductace, the widig capacitace ad the cable capacitace (typically pf). By icreasig capacitace the resoace peak is lowered i frequecy ad the amplitude of the peak is icreased. This has two effects; it lowers the high frequecy cotet by lowerig f u ad boosts the mid rage by lowerig f 0. Typically the treble toe cotrol of a guitar is a capacitor coected to a voltage regulator to roll off the highs as desired. Iductace has the opposite effect of capacitors, they affect the low frequecy. So the frequecy resoace ca also be affected by alterig the iductace. By

20 lowerig the iductace the frequecy of resoace is raised as show i Equatio 38, for f 0. This ca be cotrolled by the umber of widigs, the stregth of the core or the pickup coil cofiguratio. Pickups are high impedace devices. The higher the umber of widigs there are, the greater the output of the pickup will be. However, icreasig the umber of widigs also icreases the lumped pickup iterwidig capacitace which atteuates pickup output ad lowers the pickup s resoace frequecy. A pickup with a higher iter-widig capacitace will soud dead (less lively) ad dull (less detail/less shimmer or sparkle), compared to the same pickup with less overall iter-widig capacitace, assumig the same iductace. The lumped iductace is due to the self iductace of the coil ad is ehaced by the magetic permeability of all of the magetic materials used i the pickup. These iclude the permaet magets ad ay magetically permeable pole pieces or booster plates. The stroger the maget the stroger the output will be which meas fewer turs of wire are required for a certai voltage output. There are a few drawbacks to higher maget stregth. First, they are more expesive. Secodly, sice strigs are ferromagetic ad are attracted to magets, a stroger maget may affect the strigs vibratio. This is very bad because it compromises the harmoic itegrity. It physically produces a discordat beat ote whe the strig is plucked. This is to be avoided. SPECIFIC EECTRIC GUITAR PICKUP ANAYSIS There are may electric guitar pickups available o the market today. Our aalysis will focus o the three most commo icludig the sigle coil, P-90, ad humbucker as foud i the most commo electric guitars, the Telecaster, Stratocaster ad es Paul. 5.. Sigle Coil Sigle coil pickups are usually foud o Stratocaster ad Telecaster style electric guitar. They represet the geeral purpose pickup, used i may styles of music icludig coutry, rock, blues, fuk, jazz, R&B ad everythig i betwee. The sigle coil pickup grew i popularity with the Feder Telecaster. Icorporatig two sigle coil pickups, oe at the bridge locatio, oe at the eck locatio, the Telecaster had a strog presece i the coutry music scee. This tred still cotiues today. The toe of a bridge positio telecaster with a sigle coil is most otably characterized to have that twagy, sharp soud. This toe beefits from the higher frequecy harmoics foud ear the bridge, but also because the bridge pickup is mouted o a steel plate. This steel plate is part of the bridge assembly ad ca be see below i Figure 5. Figure 5. Telecaster bridge pickup.

21 I most Telecaster desigs, the strigs pass through the body ad up through the bridge ad over the saddles as see i Figure 5. This icreases decay time of the sigal. Brad Paisley provides us a excellet example of moder coutry Telecaster bridge toe. The sigle coil used i the eck pickup of the Telecaster is a slightly differet desig. It is smaller i size tha the bridge pickup. It has a mellower, fuller toe that cotrasts extremely well with the bridge pickup toe. It is commoly used for lead ad rhythm duties. With distortio, the eck produces a smooth, creamy sustaiig toe ad played clea has a full bodied character. This pickup ca be see below i Figure 6. Figure 6. Telecaster eck pickup. The Telecaster eck pickup souds very similar to a sigle coil o a Stratocaster i the eck positio show i Figure 7. Figure 7. Stratocaster eck pickup.

22 The Stratocaster pickup i the eck positio has a bit more sparkle ad high frequecy cotet. It is characterized as crisp, bright ad clear with a explosive quality. To liste to Stevie Ray Vaugh is to liste to a eck positio strat pickup toe doe properly. Stickig with the Stratocaster model, the guitar offers two other sigle coil pickups as previously discussed; the middle ad bridge pick up. This makes for a very versatile guitar as show i Figure 8. Figure 8. Bridge, middle ad eck Stratocaster pickup locatios. The middle pickup has a similar toe to the eck but less low frequecies ad more high frequecies. The bridge pickup has a sharp ad shrill like quality to it, though soudig distictly differet tha the Telecaster bridge pickup. The uique aspect of the circuit desig withi the Stratocaster is the ability to combie the toe of multiple pickups through the use of a selector switch. The Telecaster has this feature but does t produce a soud quite as sweet as the Stratocaster. The 5-positio selector switch is circled i red i Figure 9. Figure 9. Stratocaster pickup selector switch. It is i positios ad 4 that the famous glassy soud is geerated by combiig either the bridge ad the middle pickup or the eck ad the middle pickups respectively. Mark Kopfler of Dire Straits used positio

23 ad 4 extesively. These are the features that make the Stratocaster the world s best sellig, most popular electric guitar. 5.. P-90 I respose the growig popularity of Feder s sigle coil guitars, Gibso desiged their ow versio of the sigle coil pickup log before it made its well kow humbucker. The P-90 was very popular but quite differet tha the sigle coil pickups desiged by Feder. P-90 s have a large flat coil with adjustable steel screws as pole pieces ad a pair of flat Alico bar magets lyig uder the coil bobbi. This soud ca be classified as a cross betwee a Gibso humbucker ad a Feder sigle coil. It has extremely high widig cout, aroud 0K turs. It has a higher iductace tha other sigle coils, which meas it has high output ad bitig treble respose. The draw back is that of electromagetic backgroud oise, which this pickup is very proe to pickig up. P-90 may be foud o es Pauls, Specials ad Juiors as well as a umber of semi-hollow ad hollow-body Gibso guitars Humbucker A serious problem with the sigle coil guitar pickups is that they iduce a great deal of electromagetic backgroud oise alog with the emf from the strigs. Whe played at ormal volume, the pickup output usually has a high eough sigal-to-oise ratio that the oise is barely heard. The problems arise whe the player is usig lower dyamics or stops playig. The 60Hz oise geerated by all sorts of electroic systems from power lies to fluorescet lights do t stop whe the player stops playig ad cosequetly get iduced by the pickup ad are the amplified. This ca be very oboxious. The humbucker as the ame implies deals with this issue of electromagetic backgroud oise by wirig two sigle coil pickups ext to each other, woud with opposite polarity. This cacels or bucks the hum but has a umber of other impacts o the toe produced. First of all, because there are ow two sigle coil pickups side-by-side respodig to magetic flux chages (see Figure 0), a greater legth of the vibratig strig is read. Figure 0. Humbucker pickup. This results i a soud that is fuller, thicker ad more robust. I effect, the pickup is able to read more of the loger wavelegth vibratios that correspod to lower frequecies icludig the fudametal. Aother effect is that the high frequecy is atteuated whe compared to a sigle coil or P-90 pickup. Part of the reaso for this is due to the pickup covers usually made of brass with a coatig of chrome, as see i Figure.

24 Figure. Humbuckig pickups with chrome pickup covers. This makes for a very smooth ad rich toe, excellet for lead playig with distortio. It also does t suffer from the shrill or cut of sigle coils which may be offesive to the listeer if ot cotrolled. The drawback is it does t cut through the mix as effectively, which requires more volume to be heard. Thus, it is typical to fid a guitar fitted with humbuckers like the Gibso es Paul mated to a high power, air movig amplifier like a Marshall stack. Aother drawback, particularly at the eck positio is that the humbucker may soud muddy. This muddiess occurs whe there are higher levels of low ad mid frequecies which prevet clarity of the idividual otes ad harmoics, i.e. lower resolutio. This effect may be overcome by proper equalizatio. Typically the bridge pickup is favored amogst the es Paul ad humbuckig crowd, especially for lead toes. It has higher frequecy harmoics due to its proximity to the bridge yet it maitais a full rich toe, lush with mid frequecies. The eck pickup has much more low frequecy cotet, ad ca produce a great jazz toe. Although, the eck pickup is also a good lead toe as well, just ask Slash. CONCUSIONS The process of listeig to ad idetifyig the toes geerated by the guitar coupled with a egieerig uderstadig of the productio of those toes will udoubtedly lead a guitarist closer to the toe of their desire as well as help them use those souds i differet musical cotexts more effectively. The priciples of acoustics, mechaics ad electroics, that go ito makig a electric guitar work are ot trivial, but are certaily uderstadable with proper ivestigatio. These priciples are directly applicable to ay guitarist ad ca be implemeted immediately. At the very least, applyig the uderstadig of electric guitar pickups should elimiate oe compoet of the torturous music store experiece. The other compoet (that of techique), will be left to each player to address.