To build a  Monophonic, Modular, Electronic,  Music Synthesiser.

BrianLeach MUSC9002:ComputerMusic2 Project2c)Apreparation/proposalfortheMastersProject(Technology Research)

Lecturer:HughMcCarthy Due:Friday30thMarch2012 Studentnumber:R00043544 17pages.

TobuildaMonophonicModularElectronicMusicSynthesiser.

Introduction Abasicsoundsynthesisercanbemadefromthefollowing5typesofmodules: 1) 2) 3) 4) 5)

Voltage-ControlledOscillator (VCO) Voltage-ControlledAmplifier(VCA) Voltage-ControlledFilter(VCF) EnvelopeGenerator(EG) LowFrequencyOscillator(LFO)

I will discuss the operation of each of these modules and propose an implementation of them in hardware electronics, along with suitable circuit diagrams. Iwillalsoestimatethecostof buildingthemachine. The aim ofthis essay istogaugethefeasibilityofbuildingasynthesiserformyMastersProject (TechnologyResearch).

Overview Themodularnatureofthisprojectmeansthateachmoduleisseparatefromthe othersandalsothattheycanbeinterconnectedinanyconceivablewaytocreate manydifferenttypesofsoundswhenplayedbyakeyboardorothercontroller.I willnowdiscussatypicalmodeofsoundproduction. IfweconsidertheVoltage-ControlledOscillator(VCO)wemustofcoursedefine itsfrequency,aControlVoltage(CV)isusedtodothis.Thisvoltageisdesignated by the key that the user presses on the keyboard. Thus we need a way to transformkeyboardactivityintoControlVoltages.Fornowletsassumethatthe synthesiserisreceivingmidimessages.Acontrolmoduleisnecessarywhichhas a midi input, and a control voltage output. For clarity I will represent control pathswitharedline,andaudiopathswithablueline.

Figure 1. Midi messages being transformed into an audio signal with a definedfrequency.

2

This CVoutput can be connected into the CV input of a VCO. The VCO is now outputtingasignalwithadefinedfrequency.Asyoucanseein Figure1theVCO hasaCVinputandanaudiosignaloutput. ThissignalcanbeputintotheinputoftheVoltage-ControlledAmplifier(VCA) whichmultipliesthesignalbysomenumber≥ 0.Thisnumberisdefinedbythe CVinputoftheVCA.ConsiderthatthisCVcouldbechangingovertime,creating anamplitudeenvelope.ThisenvelopeisdefinedbytheEnvelopeGenerator(EG). TheEGmustreceivedatafromthecontrolmoduletotellitwhentogeneratethe envelope,triggers.

Figure2.AnEnvelopeGeneratoraffectingtheamplitudeoftheaudiosignal viaaVoltage-ControlledAmplifier.

TheEGhas4parametersthataresetbytheuser:Attack,Decay,Sustain,Release (ADSR).

Figure3.AtypicalvoltageenvelopegeneratedbytheEnvelopeGenerator.

3

Ifthesignal iscomplex (has many overtones) then wecan pass itthroughthe VoltageControlledFilter(VCF)toshapethesound.TheVCFwillcutfrequencies above or below some defined frequency. This frequency is defined by the CV inputoftheVCF.Thisfrequencycouldchangeovertime(haveanenvelope)ifwe passtheEGintotheVCF.TheinputoftheVCOcouldalsobeaffectedinthesame way.

Figure4.TheEnvelopeGeneratorcanaffectanyofthemodulesbybeing passedintotheirControlVoltageinput.

NotethattheVCOisnowreceivingtwocontrolvoltages.Thevoltagesneedtobe addedtogetherinamixer.ThesimplestwaytoachievethisistohavetwoCV inputs on the VCO, each one going through an internal resistor. This forms a passive mixer. Any module can receive multiple inputs via a built in passive mixer. Note also that this simple mixercan add control voltagesand/or audio signalsindiscriminatelyasallitisdoingisaddingvoltages. Sowehavetheabilitytovarythepitch,volumeandcharacterofthetonebeing produced. Modules could be replicated so that two oscillators would generate audiosignalsfromthesamecontrolvoltage:

4

Figure5.TwoVoltage-ControlledOscillatorsbeingcontrolled simultaneouslytoproduceadditivesynthesis.

Orthesecondoscillator’soutputcouldbeusedtocontrolanothermodule:

Figure 6. A Voltage-Controlled Oscillator being used to modulate the FrequencybeingproducedbyasecondVoltage-ControlledOscillator.

NotethattheoutputofthesecondVCOisactingasacontrolvoltageandnotas anaudiosignal.Usedinthiswayanoscillatorcanmodulatethecontrolvoltageof anotheroscillatortocreateFrequencyModulation(FM),orifitisaffectingthe

5

VCA,AmplitudeModulation(AM).Ifwewantafixedfrequencyofmodulation, ratherthanonedeterminedbywhichkeywepress,wecanuseaLowFrequency Oscillator(LFO),socalledbecauseitgenerallyoperatesatfrequenciesbelowthe audiblerangealthoughthisisnotnecessarilythecase.Thisoscillatorneedsno controlinputasitsfrequencyissetbyitsownonboardcontrol.

Figure7.ALowFrequencyOscillatormodulatingthecutofffrequencyofa Voltage-ControlledFilteratafixedfrequency.

This outlines just some of the many ways these modules can be connected to generatesound.Iwillnowlookateachmoduleinfurtherdetail.

6

ControlModule This module must sense which key is pressed, when the key is pressed, and whenitisreleased.TheoutputsmusttriggertheEGandalsogivetheVCOthe correctcontrolvoltagetoproducethedesiredfrequency. ControlVoltage Analogue synthesisers generally use control voltages ranging from 0V to 5V. MoogsynthesisersusetheVoltsPerOctavesystemwhichmeansthatanincrease of1Vcorrespondstoadoublingoffrequency 1,oranincreaseofonesemitoneis equalto1/12ofavolt.Hencethenotesandcorrespondingcontrolvoltagesare:

Note

CV

Note

CV

Note

CV

Note

CV

Note

CV

A1

0

A2

1.0000

A3

2.0000

A4

3.0000

A5

4.0000

A♯

0.0833

A♯

1.0833

A♯

2.0833

A♯

3.0833

A♯

4.0833

B

0.1667

B

1.1667

B

2.1667

B

3.1667

B

4.1667

C

0.2500

C

1.2500

C

2.2500

C

3.2500

C

4.2500

C♯

0.3333

C♯

1.3333

C♯

2.3333

C♯

3.3333

C♯

4.3333

D

0.4167

D

1.4167

D

2.4167

D

3.4167

D

D♯

0.5000

D♯

1.5000

D♯

2.5000

D♯

3.5000

D♯

4.5000

E

0.5833

E

1.5833

E

2.5833

E

3.5833

E

4.5833

F

0.6667

F

1.6667

F

2.6667

F

3.6667

F

4.6667

F♯

0.7500

F♯

1.7500

F♯

2.7500

F♯

3.7500

F♯

4.7500

G

0.8333

G

1.8333

G

2.8333

G

3.8333

G

4.8333

G♯

0.9167

G♯

1.9167

G♯

2.9167

G♯

3.9167

G♯

4.9167

A

5.0000

4.4167

Table1.NotesandControlVoltagesintheVoltsPerOctavescheme. Trigger/Gate TheControlModulemustalsosendinformationtotheEGwhichwilltelltheVCA toturnon,allowingthesignalfromtheVCOtobeheardonlywhenakeyisbeing helddown.AcommonwaytoimplementthisiswithanegativeTriggeranda positive Gate1. The Trigger signal is kept high (around 5V) and goes to 0V momentarilywhenakeyispressed.TheGatesignaliskeptat0Vandgoeshigh (5V)forthedurationoftimethatakeyispressed.Thisinformationisenoughto telltheenvelopegeneratortogeneratetheattack,sustainorreleaseportionof theenvelope7(decayhappensimmediatelyafterattackbydefinition).Inpractice the Gate voltage could be the Control Voltage discussed above (or a suitable multiple of it) as the CV 0V when no key is pressed, and >0V when a key is pressed.

7

One way toimplement the control module would betotakeinmidi messages whicharecomprisedofanotenumber(whichkeyispressed),anoteonmessage (whenthe key is pressed)and a note off message (when the key is released). ThisinformationcouldbetransformedtoCVandTrigger/Gateinformation:

Figure8.BlockdiagramofaMiditoControlVoltage/Gateconverter8.

Thisisa complicatedsystemwhichwouldbedifficult tobuildfromscratch,but there are commercially available modules retailing around €200 which are designed to perform exactly this function e.g. the ‘Kenton Modular Solo’ http://www.kentonuk.com/products/items/m-cv/modsolo.shtml. An Arduino couldbeprogrammedtoperformthesefunctionsandpurchasedforaround€50. Another more fundamental way to implement this would be to modify an existing keyboard. Each key could tap into a line of equal resistors in series whichwoulddivide5Vinto61equallyspacedvoltages.Twoadditionalcontacts undereachkeycouldprovidetheTriggerandGate.

8

Figure9.Eachkeyonthekeyboardcouldactuate3switchestogeneratea Gate,TriggerandspecificControlvoltage.

Thegateandcontrolvoltageoutputisselfexplanatory.Thetriggeroutputworks likethis:whennokeyispressedtheswitchesaretotheleftandtheoutputis5V, whenakeyispressedthecorrespondingswitchgoestotheright,thevoltagewill dipmomentarilyto 0Vwhilethecorrespondingcapacitoris charging.Thistime need only be a few milliseconds so a small capacitance will suffice. Once the capacitorischargedtheoutputwillreturnto5V.Whenthekeyisreleasedthe switchreturnstotheleftcontactandthecapacitorisdischarged,allowingthe processtoberepeated. Thiswouldbethecheapestoptionasanoldkeyboardcouldbesalvagedforvery littlemoney.

9

Voltage-ControlledOscillator ThekeytomakingamusicalVCOwasdiscoveredbyRobertMoogandoutlined inhis1964paper‘Voltage-ControlledElectronicMusicModules’.Henoted: “In Technical measurement and control operations, a linear control voltage – frequencyrelationshipisfrequentlyuseful.Intheproductionofmusic,however, constant frequency differences are of little value. The fundamental subjective qualityoffrequencychangeistheinterval,whichisaratiooftwofrequencies.In ordertobemusicallyvaluable,aVCOshouldgenerateafixedfrequencyratiofor agivencontrolvoltagechange.Inmathematicallanguage,thefrequencyshould beanexponentialfunctionofthecontrolvoltage.”2 TheimportanceofhavinganexponentialrelationshipbetweentheCVandthe output frequency is clear if we imagine an LFO modulating the CV feeding an audiooscillator.LetssaytheCVis3V,thiscorrespondstothenoteAat440Hzas describedabove.NowletssaywewanttheLFOtovarythisnoteupanddownby asemitone,henceitsvaluemustchangefrom-0.0833to+0.0833(±1/12V).A linearVCOcouldbecreatedthatwouldproduceaG#(415.3Hz,24.7Hzbelow A440)with a control voltage of2.9167V,but anincrease ofcontrol voltage to 3.0833V would now lead to an increase of 24.7Hz, giving 464.7Hz. The actual valuewewantisA#(466.16Hz),soweseethatourLFOreducesthepitchbya semitonebutfailstoincreasethepitchbythesameamount.Thisvibratoisnot centered on A and thus does not sound as we would expect musically. The introduction of an exponential converter for the control voltage solves this problem and ensures that a linear increase/decrease in CV corresponds to a fractional increase/decreasein frequency,andhence a fixed increase/decrease inpitch. SoourVCOmusthavetheabilitytoacceptmultiplecontrolvoltages,addthem togetherlinearly,andconvertthesumtoanexponentialvaluewhichaffectsthe frequencyofoscillation.

Figure 10. Block diagram of a musical Voltage-Controlled Oscillator with Exponentialconverter.

TheExponentialconverterisofkeyimportanceandwillrequirefurtherresearch tobeunderstoodfullyandimplementedproperly.ThecircuitsuppliedbyMoog inhispapergivesastartingpointforfurtherresearch.HereishisVCOdesign:

10

Figure 11. Circuit Diagram of Robert Moog’s Voltage-controlled oscillator from his 1965 paper. Note the three sections: Adder, Exponential Generator,andRelaxationOscillator(bottom).

11

Voltage-ControlledAmplifier Our perception of loudness follows an exponential relationship similar to that described for perception of pitch: a wave with twice the amplitude is not perceived as twice as loud3. Luckily the VCA is controlled by the envelope generatorwhichgeneratesitsenvelopebycharging/dischargingcapacitors.This process generates exponential voltage increases/decreases9 and hence we can useaVCAthathasalinearCV-to-gainrelationship. AsimpleopampamplifiercircuitcouldbeusedwithalinearVoltageControlled Resistor(VCR)controllingthegain.ItisimportantthattheVCRislinearsothat the signal is not distorted4. Remember that we are amplifying an Alternating CurrentsotheVCAmustbelinearforpositiveandnegativevoltages.Ofcourse some‘distortion’maybedesirable,asthiswillgivethesounditsowncharacter. ItwasthespecifictypeofdistortioninherentinthecircuitsdesignedbyMoog thatmadethemsoundsodesirable5. The VCRs value, and hence the gain of the VCA is controlled by the varying ControlVoltagecomingfromtheEnvelopeGenerator.

Figure 12. A Voltage-Controlled Amplifier utilizing a Voltage-controlled Resistor.

Note that anInverting amplifier must beused because a gain of0 is required whennonoteisbeingplayed.Thegainofthecircuitis G=-VCR/R1 SowhennonoteisbeingplayedthevalueoftheVCRmustbe0andwhenat maximumgainwerequireVCR=R1togiveunitygain. 12

TheVCRcouldbeaFieldEffectTransistor(FET) 4oranLEDpointedataLight DependentResistor.Someexperimentationwillberequiredtoseewhatmethod soundsbest.

Voltage-ControlledFilter TheFiltermodulewilltakeanaudioinputandfilteroutsomefrequencieswhich aredefinedbythecutofffrequencycontrol.Thiswillshapethetoneofthesound beingproducedbytheVCO.Avariablequality(Q)controlcauseresonancejust belowthecutofffrequency.Thisresultsinanamplificationofasmallfrequency bandwhichaddscharactertothefilter.ThemoduleshouldhaveLowPass,High PassandBandPassmodes. Hereisasimplecircuitasastartingpoint.VaryingtheR1andR2simultaneously willchangethecutofffrequency.ReplacingtheseresistorswithVCRswillallow thecutofftobechangedovertimebytheCVprovidedbytheEGorLFO.Having variableresistors,controllablefromthefrontpanel,inserieswiththeVCRswill definetherangeofeffecttheCVhas.

Figure 13. Sample Filter circuit diagram which could be adapted to have Voltagecontrol6.

13

EnvelopeGenerator AsuitablecircuitdiagramfortheEnvelopeGeneratorisgivenbelow

Figure14.EnvelopeGeneratorwithADSRcontrols7.

TheGate/Triggermessagesandcorrespondingoutputareshownbelow

Figure15.Trigger/GatemessagesandcorrespondingEnvelopes7.

TheinputsofthemodulearetheGateandTriggermessages.Theoutputisthe voltageenvelopewhichcanbesentontotheCVinputsofanyothermodule.The amplitudeoftheenvelopecanbesetbytheoutputamplifiersectionandthusthe rangeortheEGcanbechangedbysettingthegainofthisstage.

14

LowFrequencyOscillator The LFO is the simplest module as it requires no control input. It only has a signaloutput.Initsmostsimpleform,thismodulecouldbeasinewavephase shiftoscillatorwhichisacircuitthatIhavebuiltbefore.

Figure16.APhaseShiftOscillator.

The frequency of oscillation can be set using a variable resistor, and the amplitude ofoscillationcan beset bypassing the phaseshiftoscillator output throughanopampamplifiercircuitwithavariableresistorcontrollingitsgain. Othermorecomplicatedcircuitscouldbeusedwhicharecapableofgenerating triangular, saw tooth and square waveforms thus giving more options for the typeofmodulationproduced.TheoutputoftheLFOcanbesenttotheCVinput ofanyothermodule.

PowerSupplyUnit Eachmoduleshouldbecapableofbeingpoweredbya15V1ADCPowersupply. Thisunitcouldbebought,orsalvagedfromoldequipment,as15Vsuppliesare quitecommon.



15

Estimatedcost: Electroniccomponents Control Module €50 VCO Module €10 VCA Module €5 VCF Module €5 EG Module €5 LFO Module €5 PSU €15 Hardware Jack Sockets Knobs PatchLeads Metal Housing

€10 €5 €0(Ihavemanybrokenguitarleadsthatcanbesalvaged) €0 (can be scavenged)

Total

€110

This is probably an over estimation as the bulk of the cost is in the control module, which could be an Arduino borrowed from the college (if midi compatibility is desired), or a modified keyboard which would require an investment of time rather than money. This project could be realized for less than€100,whichisfeasibleforme.

Conclusion I haveoutlinedthe mode ofoperation ofa modular synthesiser and proposed somecircuitdesigns.Whilefurtherresearchisneededtorealiseallthemodules discussed(particularlytheVCO),Ibelievethatitispossibleandaffordablefor me to build a self-contained modular synthesiser for my Masters research project.Thesynthesiserwouldbecomprisedof: 1ControlModule 2Voltage-ControlledOscillators 1Voltage-ControlledAmplifier 1Voltage-ControlledFilter 1EnvelopeGenerator 1LowFrequencyOscillator 1PowerSupplyUnit

16

References [1]Jenkins,Mary. AnalogueSynthesizers.FocalPress,Oxford,2007.p.35 [2] Moog, Robert. Voltage-Controlled Electronic Music Modules,  Journal of the  AudioEngineeringSociety ,Volume13,Number3.NewYork,July1965.p.1. [3]Howard,David&Angus,Jamie. AcousticsandPsychoacoustics,fourthedition. FocalPress,Oxford,2009.p.92. [4]Mayes,Lawrence.TheFieldEffectTransistorasaVoltageControlledResistor , 2002,Viewed30March2012, http://graffiti.virgin.net/ljmayes.mal/comp/vcr.htm [5]Editor:Sinclair,IanR.Chapter20,SoundSynthesisbyJenkins,Mary.  Audio andHiFiHandbook ,3rdedition.Newnes,Oxford,1998.p.362. [6]Steiner,Nyle.Voltagetuneableactivefilterfeatureslow,highandbandpass modes.ElectronicDesign,vol25,SaltLakeCity,December1974.p.1. [7]Jacky,Jonathan.TwoChipgeneratorshapessynthesizer’ssounds.Electronics, Seatle.September1980. [8]Rees,Phillip. LittleMCVMiditoCVconverter .2005.Viewed30March2012. http://www.philrees.co.uk/products/miditocv.htm [9]Mansfield,Michael&O’Sullivan,Colm. UnderstandingPhysics,Chapter15.10. Wiley-Praxis,2008.

Bibliography HorowitzandHill,TheArtofElectronics.CambridgeUniversityPress,1980. Douglas,Alan&Astley,S. TransistorElectronicOrgansfortheAmateur .Pitman Press,Bath.1965. KendallWebsterSessions.Discrete/TransistorCircuitSourcemaster .Wiley.New York,1978. Huelsman, Lawrence. Active and Passive Analogue Filter Design . McGrath-Hill, Newyork,1993.

17