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7/27/2019 Acoustical Properties of the Alto Saxophone
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AcousticalPropertiesoftheAltoSaxophone
BenMeyerandCraigRiccardo
UIUCPhysics193POM,Fall2010
HistoryoftheAltoSaxophone
ThealtosaxophonewasinventedbyAdolpheSaxofBelgianin1845. Afterstudyingtheclarinet
andtheflute,Saxdecidedtoattempttoconstructaninstrumentthatwouldcovermoreofthemiddle
rangeofsoundformilitarybands. Hisinitialgoalwastocombinethetoneoftheclarinetwiththe
brassy,brightersoundofthetrumpet. ThealtosaxophonewasfirstusedinFrenchorchestrasand
militarybandsduringthe1800s,butitdidnotgaingreatpopularityuntilthejazzmovementofthe
1920s. Thefirstaltosaxophonewasrelativelysimplecomparedtomodernsaxophones. Notonlywere
therelesskeys,buttheoriginalaltosaxhadtwotothreeoctavekeys,ratherthantheoneoctavekey
associatedwithsaxophonestoday. Theadditionsmadetothesaxophoneovertimemadeiteasierto
playandgavethemusicianmorerange.
MechanicsoftheInstrument
Thealtosaxophoneissimilartotheclarinetinthatitisareedinstrument. Thereed,whichis
usuallymade
of
aspringy
piece
of
cane
and
has
vibrational
tendencies,
is
secured
to
the
mouthpiece
andisforcedtovibratebytheairstreamofthemusician. Thevibrationintheairwithintheinstrument
causesthesaxophonetoresonate.Resonancereferstothecreationoflargeamplitudevibrationsasa
systemwhichvibrateswithacertainfrequencyisactedonbyaperiodicdisturbancewiththesame
frequency. Thismeansthattheinstrumentvibratesatthesamefrequencyastheairflowingthroughit.
Dependingonthekeycombination,differenttoneswillbeproducedasthelengthoftheinstrumentis
shortenedor
lengthened.
The
longer
the
instrument,
the
longer
it
takes
for
the
wave
to
travel
through
it,resultinginalowerfrequency. Lowerfrequenciescorrespondtoalowerpitch,whichisthesubjective
evaluationofthefrequencyofasound,andhigherfrequenciescorrespondtohigherpitch. Thisexplains
whyalowernoteisproducedwhenallofthevalvesonthesaxophoneareclosed. Thefrequencyofthe
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notecanalsobechangedbytheembouchure,ortheshapeofthemusicianslipsaroundthe
mouthpiece.
Asthesoundtravelsthroughtheinstrument,
thewavesorparticlesexperiencecompressionsand
rarefactionsasdemonstratedbythepictureonthe
right. Thesaxophoneissimilartotheclarinetinthatit
isopenononeendandclosedontheother,however,
itactsmoreasaconicaltubeandthereforeplaysall
harmonics,ortheintegermultiplesofthefundamental
frequency,ratherthanjusttheoddharmonics. The
bellofthesaxophonehelpsthesoundwavesradiate
moreintotheairandtraveltotheaudience.TestingtheInstrument
InordertocollectdatatoexaminetheacousticalqualitiesofmyYamahaaltosaxophone,the
instrument
was
placed
in
the
box
and
extremely
small
microphones
were
placed
at
the
mouthpiece
and
bellendoftheinstrument[1]. Themicrophonesmeasuredtheparticlevelocityandparticlepressure
thatwentintotheinstrumentandthatexitedtheinstrumentfromthebellend. Asinewavefunction
generatorwasusedalongwithapiezoelectrictransducer,whichactedasasmallspeaker,toexcitethe
airwithinthecolumnofthealtosaxophone. Thisprocesswasusedwiththreedifferentvalve
combinationssothatwecouldcomparetheinharmoncitiesbetweennotesandofthesaxophonein
general.The
combinations
tested
were
all
valves
up
(C#/Concert
E),
three
valves
closed
(G/Concert
B
flat),andonevalvedown(B/ConcertD). Thesoundpressureandparticlevelocitydatawasalsousedto
calculateacousticalimpedancetoidentifythefrequencyvaluesatwhichdifferentnotescanbeplayed.
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ImageofAltoSaxophoneintheBox:
ImageofPCBasedDataAcquisitionSystem:
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GeneralResults
Impedance:
UsingthisprocesswiththeDAQsystemsupplieduswithalargequantityofdata,suchasthe
complexparticlepressureandcomplexparticlevelocityputintothesaxophone. Themainconcernto
us,however,wastheratioofthetwo,ortheacoustic impedance. Acousticimpedanceisdefinedasthe
soundpressuredividedbytheparticlevelocity,anditisdependentuponfrequency. Impedance,
definedinadifferentway,istheresistancetheinstrumenthastoblowingairthroughit.
Acousticimpedancecanalsobereferredtoasacousticalohms,whichmakessensesinceohms
measureselectricalresistance.Whenplayingthesaxophone,themusicianputspressureintothe
instrumentbyblowingairintothemouthpiece. Thepressuretravelsthroughtheinstrumentasawave
butisreflectedbacktowardsthereedandmouthpiecewhenitreachesthebellendoftheinstrument.
Thisreturnofthepressurewavetothemusicianslipscausesthemouthpiecetovibrate,informingthe
playerabout
which
frequency
they
must
play
to
achieve
the
desired
note.
This
process
helps
to
explain
whyoneoftenfeelsavibrationfromthemouthpiecetotheirlipsastheyplaycertainnotes. Towrapup
thisidea,thegreatertheimpedance,thegreaterthenumberofwavesthatarereflectedbacktowards
themusicianslipstosignalwhatfrequencyshouldbeplayed. Thus,thehighertheimpedance,the
easieritwillbeforamusiciantoplaythatnoteorinotherwords,theplayablenotesontheinstrument
willoccurattheimpedancepeaksormaximumsonthegraphs.
ImpedanceoftheYamahaAltoSaxophone:
Wewillusethefollowinggraph,whichmeasuresthemagnitudeoftheinputimpedanceofthe
saxophoneasavariableoffrequency,inordertomakeconnectionstothedifferentnotesthatcanbe
playedonourspecificaltosaxophone.
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InputImpedanceMaxima&Minima,allvalvesopen(C#5)
The
first
impedance
maximum
that
is
easily
seen
occurs
at
around
400
Hertz.
As
stated
before,
the
maximaoftheimpedancegraphsshouldshowtheplayablenotesontheinstrument. However,the
fundamentalfrequencyorfirstharmonicofthealtosaxophone,orthepedalnote,isextremelydifficult
toplaybecauseitispulleddownsoloworflat. Thesecondimpedancepeak,whichoccursat851.5
Hertz,wouldthenrepresentthelowestplayablenoteontheinstrumentforthefingeringcombination
ofC#5. Thesubsequentpeaksthatoccurathigherfrequenciesrepresenttheoctavesofthisnote.
Therefore,it
seems
to
appear
from
this
graph
and
the
maxima
of
the
impedance
that
there
are
four
playablenoteswhenallthekeysonthealtosaxophoneareup. Thisseemstoexplainourunderstanding
ofhowonoursaxophonesweareabletoplayalowC#belowthestaff,C#inthestaff,ahighC#above
thestaff,andthealtissimonote,eventhoughitisextremelydifficulttoplay,whichcanbeproducedby
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changingtheembouchureorthestreamofair. Thesehighernotesareoftenmoredifficulttoplayon
thealtosaxophone,whichisalsorepresentedbythegraphabovebythelowervaluesoftheimpedance
peaksathigherfrequencies. Thisalsohelpstoexplainwhytheadditionoftheoctavekeywasnecessary
toallowthemusiciantoplaythesehigherpitchednotes.
InputImpedanceMaxima&Minima,1valveclosed(B4)
Similarly,theimpedanceoftheothernotestestedwereexaminedtodeterminethevariousplayable
noteswithonevalveclosed,orB4onthealtosaxophone,andthreevalvesclosed,orG4onthealtosax.
Theabovegraphshowstheimpedancemaxima,andaccordinglytheplayablenoteswiththeB4
fingering,andthefollowinggraphshowsthesamethingfortheG4fingering.
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InputImpedanceMaxima&Minima,3valvesclosed(G4)
TheincreasednumberofimpedancepeaksfortheB4andG4fingeringsasdemonstratedbythegraphs
indicatesthatthereareanincreasednumberofplayablenoteswhenusingthesefingering
combinations. Asasaxophonist,onemaynotactuallyuseallofthesenoteswhenplayingmusic,butby
changingonesembouchuretovarythefrequencyofthenoteplayed,onecouldtheoreticallyproduceall
ofthesepitcheswithbothfingerings. Theoutputimpedance,whichwasalsomeasuredandgraphed,
hasusefulimplicationsinthatitprovidesinformationaboutwhatsoundsorpitchesareheardbythe
audience.
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InharmonicitiesoftheAltoSaxophone
Oneofthemaingoalsintakingallofthisdatawastodeterminetheharmonicvalueofthealto
saxophone. Toachievethis,thegraphsoftheimpedanceforeachnotewereused,andthefrequencyof
thesecondinputimpedancepeak,orthesecondharmonic,wascomparedtotheclosestnoteonthe
piano[2].
Asdepictedbytheinharmonicitygraphabove,theC#5,whichhadasecondharmonicwiththe
frequencyof851.5Hertz,wasclosesttoAb5onthepiano,whichhasafrequencyof830.61Hertz.
Likewise,B4hadasecondharmonicfrequencyof729.5HertzandwascomparedtoGb5witha
frequencyof739.99Hertz. Finally,G4onthealtosax,withameasuredfrequencyof551.5Hertz,was
comparedtotheclosetnoteonthepianoofDb5,withafrequencyof554.37Hertz. Aspredicted,the
firstharmonicofeachnoteispulledextremelylow,sincethepedalnoteisveryflatandrarelyabletobe
played. Thegraphcomparestheharmonicnumberofeachnotetotheinharmonicityvalueincents.
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Centsreferstothelogarithmicunitusedtodivideintervals. Theoctaveisdividedintotwelvedifferent
semitones;therefore,thereare100centsinasemitone. Asemitonecanalsobedefinedasahalfstep.
Usingthisconceptandthedatafromthegraph,wecanstarttomakeconnectionstowhatthismeans
forourspecificinstrument. Forinstance,wecanlookatthethirdharmonicofAb5,orC#onthealto
sax,andnoticethatitisoffbyapproximately90cents,ornearlyafullsemitoneortwelfthofanoctave
sharp. ThefourthharmonicofC#isalsopulledhigh,whichhelpsustounderstandwhywhenplaying
thisspecificsax,thepitchofC#isusuallytoosharpandmustoftenbeadjustedbyusingthe
embouchure. B4onthealtosaxophonealsoappearedtobepulledhigh,withthefourthharmonicbeing
overafullsemitonegreaterthanwhatitshouldbe. Finally,G4,whichisoftenoneoftheeasiernotesto
playonthealtosax,seemedtobelessinharmonic,withtheinharmonicityincentsvaryingslightlylow
andhighforthevariousharmonics. Thismayexplainwhysaxophonistswilloftentunetothisnoteas
well.
Conclusions
Inconclusion,theintendedpurposeofanalyzingthedataobtainedinclasswastodetermine
the
harmonic
content
and
acoustical
properties
of
our
Yamaha
alto
saxophone.
Through
the
data
obtainedbythePCbaseddataacquisitionsystem,wewerenotonlyabletoexaminetheinput
impedancetodeterminethefrequenciesoftheplayablenotesfordifferentkeycombinations,butwe
werealsoabletodeterminetheinharmonicityoftheinstrumentandmakeconnectionstowhatthis
meansintermsofactuallyplayingthesaxophone.
References
[1]Acoustic
Impedance
of
aBb
Trumpet,
David
Pignotti
UIUC
Physics
Senior
Thesis,
2007,
http://online.physics.uiuc.edu/courses/phys193/193_reu.html
[2]CalculatingMusicalInstrumentInharmonicities,Prof.S.Errede,UIUCPhysics193LabHandout,
http://online.physics.uiuc.edu/courses/phys193/193_labs.html