Acoustic Drum Exploration – Basis for Investigation Theodore Argo IV Department of Physics, University of Illinois at Urbana-Champaign 1110 West Green Street, Urbana, Il 61801-3080, USA ABSTRACT A percussionist can alter the harmonic content of a tunable acoustic drum to provide a desired sound. By analysis of different aspects in construction of a drum the specific sound can be implemented. Through a Fast Fourier Transform of electronically acquired audio data an analysis of a drum can be performed at many stages of its construction. By dissecting the drum construction into various layers, a deviation from ideal membrane theory is observed. These deviations form the basis for further investigations into drum acoustics and non-ideal membranes. I. INTRODUCTION Throughout time man has created music. The earliest music was composed of percussive forces on solid objects. Thusly the percussion instruments are considered a simple means of creating musical sounds. The simplest design for a drum consists of a hide stretched over an opening. The tension in the stretched hide, or drum head, is what creates the sound when struck. In this way, the drum has evolved into the modern instrument appearing in the great concert halls and jazz clubs of the present day. Modern drums have greatly evolved from their earliest predecessors. Many of the variables used to create different drum sounds are now controllable and tunable to the specific design of the percussionist or composer. These variables include, but are not limited to the material and construction of shell, sticks, and heads, as well as the adjustment of playing position and tuning of the heads. Each of these variables has a direct influence on the complexity of the sound the drum produces. From the ideal membrane model of a circular drum head each additional change of variable adds yet another layer of complexity to the sound of the radiating head. II. BACKGROUND Past Research Recently, in forums on the internet and conversations worldwide, there has been argument and criticism from many people regarding the way a drum should be built to enhance its tonal characteristics. Many people believe the player is the largest factor and the actual drum plays a relatively small role in the performance. Others claim that the drum has the most significant impact on the tone, reverberation, and other qualities desired by the musicians. Some people have taken the question into their own heads. Thomas D. Rossing of Northern Illinois University has made important discoveries in the field of drum mechanics. He has used many methods to study different drum types and has tried to piece together exactly the way a drum vibrates so as to gain a larger picture of a drum’s qualities. Through modal excitation he has observed the harmonic relationships of many of the vibrational modes of a drum
Transcript
Acoustic Drum Exploration – Basis for Investigation
Theodore Argo IVDepartment of Physics, University of Illinois at Urbana-Champaign
1110 West Green Street, Urbana, Il 61801-3080, USA
ABSTRACTA percussionist can alter the harmonic content of a tunable acoustic drumto provide a desired sound. By analysis of different aspects in constructionof a drum the specific sound can be implemented. Through a Fast FourierTransform of electronically acquired audio data an analysis of a drum canbe performed at many stages of its construction. By dissecting the drumconstruction into various layers, a deviation from ideal membrane theoryis observed. These deviations form the basis for further investigations intodrum acoustics and non-ideal membranes.
I. INTRODUCTION
Throughout time man has createdmusic. The earliest music was composedof percussive forces on solid objects.Thusly the percussion instruments areconsidered a simple means of creatingmusical sounds. The simplest design for adrum consists of a hide stretched over anopening. The tension in the stretchedhide, or drum head, is what creates thesound when struck. In this way, the drumhas evolved into the modern instrumentappearing in the great concert halls andjazz clubs of the present day.
Modern drums have greatlyevolved from their earliest predecessors.Many of the variables used to createdifferent drum sounds are nowcontrollable and tunable to the specificdesign of the percussionist or composer.These variables include, but are notlimited to the material and construction ofshell, sticks, and heads, as well as theadjustment of playing position and tuningof the heads. Each of these variables has adirect influence on the complexity of thesound the drum produces. From the idealmembrane model of a circular drum headeach additional change of variable adds
yet another layer of complexity to thesound of the radiating head.
II. BACKGROUND
Past ResearchRecently, in forums on the
internet and conversations worldwide,there has been argument and criticismfrom many people regarding the way adrum should be built to enhance its tonalcharacteristics. Many people believe theplayer is the largest factor and the actualdrum plays a relatively small role in theperformance. Others claim that the drumhas the most significant impact on thetone, reverberation, and other qualitiesdesired by the musicians.
Some people have taken thequestion into their own heads. Thomas D.Rossing of Northern Illinois Universityhas made important discoveries in thefield of drum mechanics. He has usedmany methods to study different drumtypes and has tried to piece togetherexactly the way a drum vibrates so as togain a larger picture of a drum’s qualities.Through modal excitation he hasobserved the harmonic relationships ofmany of the vibrational modes of a drum
head and has studied deviations from themodel of an ideal circular membrane.
Others have taken a differentapproach. A study at Furman Universityof South Carolina has tested variousheads for the snare drum in hopes ofquantifying the different tonal propertiesof the heads being struck. The result ofthis study is a better understanding of thecharacteristics of the various heads andtheir effect on the sound of the drum.
In effect, scientists and musiciansalike have decided that manycharacteristics of the drums have impact.The question that remains is to whatextent each characteristic has an impacton an elementary drum head model.
Circular Membrane ModelThe model in question is the
mathematical representation of a drumhead when vibrating. When struck in thecenter of the circular area, the idealmembrane exhibits vibrational modesconsistent with mathematical Besselfunctions. These modes are defined by apattern of nodes and antinodes on thevibrating surface. As shown in figure 1,there exist many such vibrational modes,
each with its own pattern.The modes are labeled using a
coordinate system of diameter by circularpairs. For example, the most fundamentalmode, the (0,1) mode, consists of themembrane vibrating with a node at itsboundary but nowhere else; zerodiametric modes are present and onecircular mode is present. The second mostcommon mode is the (1,1) pair consistingof one diametric mode and one circularmode. The labeling system continues asmore of either kind of mode are added.
Each mode also represents acertain frequency based on the amount ofdisplacement of the membrane. Forexample, the (0,1) mode displaces themost and is, therefore, the fundamental.The (1,1) mode has less displacement dueto the node running its diameter and,therefore, has a higher frequency asrepresented by 1.59 times thefundamental. Each mode is similarlylabeled and quantified in figure 1 and isused as a basis for studying drums andother vibrating mediums.
The membrane theory has arequirement for its boundary conditionsas well. The edge of the membrane must
be fixed to a virtually infinite mass so asto force the antinode. If this does notoccur, the wave is not as stable as itpropagates since the edge of themembrane can deform.
The search for understandingthese deviations was continued asdevelopment for the Physics of ElectronicMusical Instruments and Physics ofMusic classes at the University of Illinoisat Urbana-Champaign. Both classes studythe characteristics of instruments andtheir sounds using only electronicinstrumentation available to an averageundergraduate physics lab. Due to theselimitations, many advanced techniquescan not be explored due to lack ofinstrumentation. Therefore, the goal ofthis exploration is the development of asetup by which the deviations from thestandard membrane model can beobserved without use of state of the artelectronics and technology.
III. METHODS
ApparatusTo understand the effects of
variables on a drum, a setup was createdto analyze the sound spectrum of thestruck drum. This included a constantforce beater, a fixed stand, a drum, amicrophone, and a computer systemcapable of taking the waveform data andperforming the necessary calculations.
The general setup, as shown infigure 2, includes most of these elements.The consistent force machine was addedat a later date and is discussedimminently.
Figure 2 – Drum Setup
The setup was designed to be usedfor any instrument desired. Themicrophone picks up the desired soundand sends the waveform data to thecomputer via a LabPC DAQ card whichallows the raw voltage data from themicrophone to be processed into a digitalsignal. The digital signal is then passed toa programmed LabVIEW interface whichrecords, analyzes, and stores the desireddata from an array of useful tools.
Use of drums with this setup iseasily achieved if a few concerns areaddressed. The drum must be sampled ata fast enough rate so that the impulse andreverberating sound can be capturedefficiently. As well, the drum must bestruck with constant force to assureresults which are reproducible andcomparable with other tests.
To solve the first problem,sampling speed, the LabVIEW interfacewas designed in such a way as to allowfor monitoring of the time decay of thewave form and manual adjustment ofsampling time and frequency. The exactsettings are discussed as a part of thecomputer interface.
The second problem is that of aconsistent impulse force with which thedrum is struck. This is solved using afreely rotating device as shown in figure3. The device is composed of a protractorfor measuring the exact displacement of
the stick, a pivot formed of a bar andtube, and a rubber band with which tohold the stick.
Figure 3 – Consistent Force Machine
The pivot is simply used as amechanism for the delivery of the blow.As shown in figure 4, the rubber bandwas affixed to a small copper tube whichwas, in turn, slid over a stationary metalbar. The copper tube was then allowed tofreely rotate about this pivot with littlefriction.
Figure 4 – Stick Pivot
The rubber band was chosen asthe device to hold the stick because of itspliability. A drummer’s hand is not madeof metal and, thusly gives slightly at each
stroke. The rubber band was doubled overmany times to provide a similar give. Aswell, the placement of the stick in therubber band being off center of the pivotwas designed to emulate a drummer’swrist. The stick’s center of mass does notpivot around a single point, but insteadrotates about the pivot of the wrist of thedrummer.
For the tests utilized in this study,the stick was raised to a 45 degree angleabove parallel and let fall to 45 degreesbelow parallel as measured on theprotractor.
One cautionary note: when thestick strikes the drum head the stick willrebound. If the stick strikes the headagain, the pure sound of the strike will betainted. Therefore, a small wire waslooped about the head of the stick in sucha way that the rebound could beprevented. Once the stick had impacted,the wire was held by the tester until thedata was collected to prevent the secondstrike from occurring.
Computer InterfaceThe interface for analysis of the
data was programmed in NationalInstruments’ LabVIEW. The interfacewas constructed to sample the sound,perform a Fast Fourier Transform (FFT)on the waveform, find the peaks in thattransform, and output the findings forlater analysis. Refer to the attacheddiagram and front panel for the specificlayout.
The program receives the inputsignal via the DAQ card. The voltagedata is then windowed and normalized tocreate a more standardized waveform.The data is then sent through a FastFourier Transform function whichanalyses a waveform its harmoniccomponents for frequency and relativeamplitude. These components are output
to a graph for visual confirmation ofproper data. The transform is then sentthrough a subroutine which takes thepeaks above a threshold amplitude andbundles the specific frequency-amplitudepairs into a file for further analysis.
The data was sampled at an arrayfor frequencies to determine the optimalvalue at which all relevant data could bepicked up and a large enough sampletaken. Firstly the FFT had its waveformwindowed to a Hanning window to assistin containment of numerical leakage ofthe FFT spectrum. From analysis ofpreliminary results it was found thatpeaks in the FFT fell into a frequencyrange of 50 hz to 1600 hz. It was decidedthat the range 0-2000 hz was importantfor this data. The sampling frequency wasfinally set at 4400 hz which is slightlymore than double the Nyquist Frequencyfor the sample. The Nyquist Frequency isthe highest important signal frequency.
A large enough sample of thewave had to be obtained to gain anoverall picture of the wave. Therefore,4096 data points were sampled from thewave at 4400 hz giving a sample time ofnearly one second. In this time the wavedecays from the initial strike, but theharmonic content does not change in thisdecay. Ten samples were taken at eachpoint to assure that the data wasconsistent and reproducible. These are thevalues that contribute to the overallaverages as seen in sample data.
When observing the peaks fromthe FFT, a judgment had to be madeconcerning how large a peak had to be tobe considered important. The value wasinitially suggested at 10 percent of thelargest peak, but was quickly reduced to 5percent as there were many harmonics inthis 5 to 10 percent range.
In addition to this interface fordata collection, Microsoft Excel and
another LabVIEW interface were used foranalysis. The data was imported intoExcel an analyzed using basic averagingand statistical (standard deviation)formulae to form a single, cohesive set ofdata. Excel then could produce a reportcontaining average amplitudes andfrequencies, error based on the standarddeviation of the sample, the percent errorcompared with the amplitude, thenormalized amplitude, and thenormalized error. This set of data wasthen fed into a LabVIEW interfacedesigned to give three-dimensional plotsbased on that information. Again, thelayout of data is attached as figures 14and 15 while the graphs are figures 11,12, and 13.
MaterialsFor this phase of the project the
equipment used was minimal. A Gretsch13” X 9” Tom drum was the test drum.The drum was mounted on a standardPearl snare stand. The microphone was aPeavey PVM 45i microphone with windguard and patch cable. The sticks usedwere Vic Firth 5B, 5BN, and GreggBissonette models. The heads on thedrum were Evans Genera G1 and G2models.
IV. RESULTS AND DISCUSSION
Gretsch Drum ShellThe shell is the most fundamental
piece of the drum. The materials for drumshells range widely from metal to varioustypes of wood. The maple Gretsch Tomshell provided a stable base for the testson the other parts of the drum setup. Theshell was not varied in any way duringthis process.
Single HeadsThe Evans Genera G1 drum head
is essentially a sheet of manufacturedplastic mounted to a metal rim. This headproduced the results that were closest tothe ideal membrane model.
Waveforms analyzed from theGenera G1 drum head closely resemblethe ideal membrane model by followingthe modal patterns discussed earlier. Thedrum frequencies radiated from the drumhead fall nearly into the frequencydistribution of the model as shown insample data as figure 5. Not all of themodes were present in sufficient amountsto appear in the final data, but the peaksthat are present represent formal modes.
The other head examined was anEvans Genera G2. This head has adifferent construction than that of the G1.This head has two plastic membranes setinto the wire rim with a thin film of oilbetween them. This dual layer system
causes very different results than thosepredicted by the ideal membrane asshown in figure 6.
SticksWhen looking at sticks there are
many options to consider. The shaft ofthe stick can be made of various types ofwood, most notably hickory and maple.
The head of a standard snare or tom stickis made of either the same type of woodas the shaft or of nylon. Both types ofsticks are in wide use.
The effect of the nylon versuswood head is the notable difference. TheVic Firth 5B stick is a single piece ofhickory whereas the Vic Firth 5BN is ahickory shaft with a nylon tip. Overall,there was little difference between thetwo head types when their sounds areproduced. The only notable difference iswith the presence of the (1,1) mode. Withthe nylon sticks, the (1,1) mode was notfavored as heavily. Instead, the nylonhead tended to induce slightly moreprominent high tones rather than thismode closer to the fundamental.
TensionTo properly play a drum head on a
tom drum, the tension across the head inall directions must be approximately thesame. By varying this tension, the drum’sapparent pitch also changes. To tune adrum properly, an approximate starpattern must be used as demonstrated infigure 7. If this is method is not used, thehead may seat improperly causing thehead to rest unevenly on the drum.
In most cases four or moretensions were studied for each set of tests.The tensions were decreasedincrementally by quarter turns of thetuning rods.
The effect of tuning the drum todifferent pitches caused different modesto be expressed. For example, when at ahigh tension, the Genera G1 headexhibited only a single mode, itsfundamental. As the tuning wasdecreased incrementally, as many as sixmodes were observed at the same strikingposition.
The effect of tuning the drum isconsistent throughout the total data. Asthe tension on the head was lessenedmore modes became apparent.
DistanceMany drummers do not strike
their drum heads in the center. Most optto strike them slightly off center, usuallyby an inch or two. This is anotherdeviation from ideal membranes since theideal membrane model is excited fromthe center for clear modal representation.
Each tuning of the drum wastested at three different positions: thecenter, two inch offset, and four inchoffset. As well, each head was probed at asingle tuning across a narrower range ofdistances, each inch from center to edge.
The distance analysis for the twotest heads produced similar results. As thedistance from the center of the headincreased, more harmonics becamepronounced. The second evidentharmonic was shown to be mostprominent in the middle third of thedistance tests, from 2 to 4 inches offcenter. As well, there was little else thanthe fundamental when struck in themiddle. Higher frequencies became veryapparent at larger distances creating a
sharper, tinnier sound. An example of adistance analysis is attached as figure 15.
This leads to the conclusion that astrong fundamental and first strongharmonic are desirable choices in a drumsound, while higher harmonics are lessdesirable. A drummer’s choice to strike adrum slightly off center is then areflection of these desired characteristics.
Bottom HeadTom drums are usually found with
either one or two heads. The second headcauses very large deviations from thebasic membrane model. Difficulty ariseswhen the second head is attached due tothe individual resonances of that head.Each head on the drum will vibrate atdifferent frequencies causing a verycomplex sound to emerge.
When a second head was added tothe tom, the sound became veryconvoluted. The second head has multipleways in which it can change the sound. Ifthe two heads are tuned to the samefundamental pitch, that pitch will have alarge presence, but the lesser harmonicswill not be exactly the same and interfere,destroying them. As well, if the drums areslightly out of tune, as is popular withsome drummers, many harmonics willsound creating a very rich tone, but hesound will need to be struck harder togain the same volume.
Tuning can be achieved differentways with two heads. If both are thesame, a harmonically consistent sound iscreated no matter the tension. If thebottom head is tuned lower or higher thanthe top head, the sound has many moreharmonics available. The harmonics fromthe upper head are more apparent, so thetuning of the lower head can either addlower or higher harmonics to the mix.
Other ConsiderationsThere are other considerations not
taken into account in this study. Manyvariables exist with the shell itself. Asingle hollow cylinder will have inherentresonances much like any other openpipe. Once the hardware is added to theshell, there will be interruptions in thewalls of the shell, and, thusly, the soundsit produces will differ.
The drum head sits on what isknown as the bearing edge of the shell.This edge is the rim of the drum which isin contact with the actual head. Manydifferent designs for this edge are in wideuse. These include an equilateral triangle,a rounded edge, and 30-60-90 triangle toname a few. Each of these changes howthe drum’s tension is utilized. On arounded edge much more of the head is incontact with the drum causing strongercoupling and more shell vibration. Astrong point for the head to rest on causesless coupling and a more resonant head.The strong point enforces the requiredboundary conditions, where the roundededge does not hold to them as rigidly.
ApplicationThe results from this study can
assist in the construction and restorationof drum sounds. Creation of desired drumsound can be affected by any of thevariables expressed here. As well, peoplewho are not mathematically or physicallyinclined can use the data here as aguideline for understanding and tuning ofdrums.
V. CONCLUSIONS
This study has explored the setupand implementation of a drum analysissystem. The purpose of this study has twoimportant future applications. The first isto create a working data acquisition
system for use in the electronic musicalinstruments lab. Through this systemmany other devices and instruments canbe analyzed for their content andproperties. Secondly, the purpose of thisexploration is to determine the difficultyof a real drum system when compared toan ideal membrane. This comparisonshows the difficulty of modeling real-world simulations and works to sparkideas for doing so.
VI. ACKNOWLEDGMENTS
• Professor Steve Errede, PhysicsDepartment, UIUC for the workspaceand materials.
• Nicole Drummer, PhysicsDepartment, UIUC for drummingknowledge and REU programcoordination.
• The University of Illinois at Urbana-Champaign for hosting this REUprogram and supportingundergraduate research.
• Adam Kempton and Eric Moon forideas, assistance with DAQ setup, andshared workspace.
• The NSF:This material is based upon worksupported in part by the NationalScience Foundation under Grant No.9987906. Any opinions, findings, andconclusions or recommendationsexpressed in this material are those ofthe author and do not necessarily reflectthe views of the National ScienceFoundation.
VII. REFERENCES• Nave, Carl. “Hyperphysics Web
Project”. University of Georgia.http://hyperphysics.phy-astr.gsu.edu/hbase/music/cirmem.html . 2000.
• Rossing, Thomas. “Acoustics ofDrums”. Physics Today. AmericanInstitute of Physics. March 1992.
• Lewis, Ryan and Beckford, John.“Measuring Tonal Characteristics ofVarious Snare Drum Batter Heads”.Furman University.
http://www.furman.edu/~jbeckfor/drumheads/ .
• “Drum Talk”. Drum Center Forum.http://www.drumcenterforum.com/.Continuously Updated.
