Additive SynthesisAdditive SynthesisAdditive SynthesisAdditive Synthesis• Any periodic waveform can be Any periodic waveform can be

expressed as the sum of one or more expressed as the sum of one or more sine wavessine waves

• [i:44][i:44] If we have two sine If we have two sine waves, where one (3) repeats waves, where one (3) repeats with 3 times the frequency of with 3 times the frequency of the other (1), and we add them the other (1), and we add them together, the sum will be a together, the sum will be a new periodic wave (1+3)new periodic wave (1+3)

Additive SynthesisAdditive SynthesisAdditive SynthesisAdditive Synthesis• [i:45][i:45] Another example, with 5 Another example, with 5

harmonic sine waves:harmonic sine waves:

Additive SynthesisAdditive SynthesisAdditive SynthesisAdditive Synthesis• add a weighted sum of harmonic sine add a weighted sum of harmonic sine

waves — some harmonics are more waves — some harmonics are more important (louder)important (louder)

Additive SynthesisAdditive SynthesisAdditive SynthesisAdditive Synthesis

• har = harmonic numberhar = harmonic number• ff11 = fundamental frequency = fundamental frequency

• harhar = phase of the harmonic = phase of the harmonic• often 0often 0• usually doesn't affect the soundusually doesn't affect the sound

[i:46][i:46] Synthesizing the Synthesizing the Following SpectrumFollowing Spectrum

[i:46][i:46] Synthesizing the Synthesizing the Following SpectrumFollowing Spectrum

Additive Synthesis ExampleAdditive Synthesis ExampleAdditive Synthesis ExampleAdditive Synthesis Example• 10 note statements: 10 note statements:

;; stst durdur ampamp harmharm attkattk decdec

i1i1 11 55 24002400 11 .25.25 .05 .05

i1i1 .. 4.54.5 900900 22 .28.28 .048 .048

i1i1 .. 44 600600 33 .03.03 .047 .047

i1i1 .. 3.53.5 10001000 44 .031.031 .044 .044

i1i1 .. 3.253.25 180180 55 .032.032 .043 .043

i1i1 .. 3.13.1 400400 66 .033.033 .039 .039

i1i1 .. 2.852.85 250250 77 .034.034 .035 .035

i1i1 .. 2.552.55 9090 88 .035.035 .031 .031

i1i1 .. 2.172.17 9090 99 .036.036 .028 .028

i1i1 .. 2.12.1 5555 1010 .037.037 .025 .025

Additive Synthesis ExampleAdditive Synthesis ExampleAdditive Synthesis ExampleAdditive Synthesis Example• OROR — —1 note 1 note

statement statement and 10 and 10 .orc.orc statementsstatements• the peak the peak

amps of the amps of the partials are partials are proportional proportional to the to the amplitude of amplitude of lowest lowest partialpartial: :

iamp1 = 2400iamp1 = 2400

iamp2 = iamp1 * .375iamp2 = iamp1 * .375

iamp3 = iamp1 * .25iamp3 = iamp1 * .25

iamp4 = iamp1 * .4167iamp4 = iamp1 * .4167

iamp5 = iamp1 * .075iamp5 = iamp1 * .075

iamp6 = iamp1 * .1667iamp6 = iamp1 * .1667

iamp7 = iamp1 * .1042iamp7 = iamp1 * .1042

iamp8 = iamp1 * .0375iamp8 = iamp1 * .0375

iamp9 = iamp1 * .0375iamp9 = iamp1 * .0375

iamp10 = iamp1 * .0229iamp10 = iamp1 * .0229

Additive Synthesis InstrumentsAdditive Synthesis InstrumentsAdditive Synthesis InstrumentsAdditive Synthesis Instruments• [i:47][i:47] Tenor instrument design: Tenor instrument design:

• the voice has harmonic partialsthe voice has harmonic partials• additive synthesis — 15 harmonics additive synthesis — 15 harmonics

Additive Synthesis InstrumentsAdditive Synthesis InstrumentsAdditive Synthesis InstrumentsAdditive Synthesis Instruments

• tenor.orc: additive synthesistenor.orc: additive synthesis

instr 11instr 11 ; tenor voice; tenor voice

iduridur = p3= p3 ; duration; duration

iampiamp = p4= p4 ; amplitude; amplitude

ifreqifreq = cpspch(p5)= cpspch(p5) ; frequency; frequency

inorminorm = 1731.8522= 1731.8522 ; normalization; normalization

; sine wave for fundamental and partials; sine wave for fundamental and partials

f1 0 16385 10 1f1 0 16385 10 1

• tenor.sco: one wavetable: tenor.sco: one wavetable:

tenor.orc: Amplitudes and tenor.orc: Amplitudes and Enveloped SignalsEnveloped Signals

tenor.orc: Amplitudes and tenor.orc: Amplitudes and Enveloped SignalsEnveloped Signals

asig1asig1 oscilioscili iamp1, ifreq, iwt1iamp1, ifreq, iwt1

asig2asig2 oscilioscili iamp2, ifreq * 2, iwt1iamp2, ifreq * 2, iwt1

asig3asig3 oscilioscili iamp3, ifreq * 3, iwt1iamp3, ifreq * 3, iwt1

asig4asig4 oscilioscili iamp4, ifreq * 4, iwt1iamp4, ifreq * 4, iwt1

asig5asig5 oscilioscili iamp5, ifreq * 5, iwt1iamp5, ifreq * 5, iwt1

asig6asig6 oscilioscili iamp6, ifreq * 6, iwt1iamp6, ifreq * 6, iwt1

asig7asig7 oscilioscili iamp7, ifreq * 7, iwt1iamp7, ifreq * 7, iwt1

asig8asig8 oscilioscili iamp8, ifreq * 8, iwt1iamp8, ifreq * 8, iwt1

asig9asig9 oscilioscili iamp9, ifreq * 9, iwt1iamp9, ifreq * 9, iwt1

asig10asig10 oscilioscili iamp10, ifreq * 10, iwt1iamp10, ifreq * 10, iwt1

asig11asig11 oscilioscili iamp11, ifreq * 11, iwt1iamp11, ifreq * 11, iwt1

asig12asig12 oscilioscili iamp12, ifreq * 12, iwt1iamp12, ifreq * 12, iwt1

asig13asig13 oscilioscili iamp13, ifreq * 13, iwt1iamp13, ifreq * 13, iwt1

asig14asig14 oscilioscili iamp14, ifreq * 14, iwt1iamp14, ifreq * 14, iwt1

asig15asig15 oscilioscili iamp15, ifreq * 15, iwt1iamp15, ifreq * 15, iwt1

iamp1iamp1 = 3400= 3400

iamp2iamp2 = 2700= 2700

iamp3iamp3 = 6000= 6000

iamp4iamp4 = 6700= 6700

iamp5iamp5 = 3000= 3000

iamp6iamp6 = 4200= 4200

iamp7iamp7 = 600= 600

iamp8iamp8 = 510= 510

iamp9iamp9 = 450= 450

iamp10iamp10 = 350= 350

iamp11iamp11 = 500= 500

iamp12iamp12 = 1600= 1600

iamp13iamp13 = 4800= 4800

iamp14iamp14 = 4200= 4200

iamp15iamp15 = 1250= 1250

tenor.orctenor.orctenor.orctenor.orc

• add the signals: add the signals:

ampenv linseg 0, iattack, 1, isus, 1, idecay, 0, 1, 0ampenv linseg 0, iattack, 1, isus, 1, idecay, 0, 1, 0

asigs = (asig1+ asig2+ asig3+ asig4+ asig5+ asigs = (asig1+ asig2+ asig3+ asig4+ asig5+ asig6+ asig7+ asig8+ asig9+ asig10+ asig11+ asig6+ asig7+ asig8+ asig9+ asig10+ asig11+ asig12+ asig13+ asig14+ asig15)/inormasig12+ asig13+ asig14+ asig15)/inorm

outout asigs * ampenvasigs * ampenv

endinendin

Additive Synthesis AdvantagesAdditive Synthesis AdvantagesAdditive Synthesis AdvantagesAdditive Synthesis Advantages

• Very flexibleVery flexible• Can control each partial individuallyCan control each partial individually• Can represent any harmonic or nearly-Can represent any harmonic or nearly-

harmonic soundharmonic sound• But not good for noisy tones (e.g., drums).But not good for noisy tones (e.g., drums).

• Can be used in combination with Can be used in combination with spectrum analysis to reconstruct spectrum analysis to reconstruct musical instrument tones. musical instrument tones.

Additive Synthesis Additive Synthesis DisadvantagesDisadvantages

Additive Synthesis Additive Synthesis DisadvantagesDisadvantages

• Slow.Slow.• Many instruments require summing Many instruments require summing

40-100 harmonics. Can’t play very 40-100 harmonics. Can’t play very many notes in real-time on current many notes in real-time on current hardware.hardware.

• For example, the hardware may only For example, the hardware may only be able to produce 4-note polyphony be able to produce 4-note polyphony to keep up in real-time.to keep up in real-time.

Additive Synthesis DisadvantagesAdditive Synthesis DisadvantagesAdditive Synthesis DisadvantagesAdditive Synthesis Disadvantages

• Difficult to control group as a wholeDifficult to control group as a whole• Many parameters which are difficult to Many parameters which are difficult to

control:control:• 40-100 amplitude envelopes plus 40-100 40-100 amplitude envelopes plus 40-100

frequency envelopes, where each envelope frequency envelopes, where each envelope consists of about 1000 timepoints.consists of about 1000 timepoints.

SolutionsSolutionsSolutionsSolutions

• Reduce number of parameters Reduce number of parameters somehowsomehow• E.g., simplify envelopes by using E.g., simplify envelopes by using

piecewise linear approximationpiecewise linear approximation