Simple FM InstrumentsSimple FM InstrumentsSimple FM InstrumentsSimple FM Instruments

• John Chowning's FM Designs as John Chowning's FM Designs as shown in Dodge, shown in Dodge, Computer MusicComputer Music• brass-like tonebrass-like tone• clarinet-like toneclarinet-like tone• bell-like tonebell-like tone• wood-drum-like tonewood-drum-like tone• clarbellclarbell

Clarinet and Brass-Like TonesClarinet and Brass-Like TonesClarinet and Brass-Like TonesClarinet and Brass-Like Tones

• fundamental is GCD of carrier and modulator frequencies: 440 Hertzfundamental is GCD of carrier and modulator frequencies: 440 Hertz[iii:8] [iii:9] brass-like tone (Dodge p. 126)

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Clarinet and Brass-Like TonesClarinet and Brass-Like TonesClarinet and Brass-Like TonesClarinet and Brass-Like Tones

• fundamental is GCD: 300 Hertzfundamental is GCD: 300 Hertz[iii:10] [iii:11] clarinet-like tone (pp. 126-127)

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Clarinet and Brass-Like TonesClarinet and Brass-Like TonesClarinet and Brass-Like TonesClarinet and Brass-Like Tones;dodge.orc - use with dodge.sco

instr 1 ; clarinet and brass tonesidur = p3iamp = p4icarfr = p5 ; carrier frequencyimodfr = p6 ; modulator frequencyindex = p7 ; modulation indexiwave = 1 ; wavetable 1 (sine wave)

aenv linseg 0, .1, 1, idur-.3, 1, .2, 0amod oscili index*imodfr, imodfr, iwaveacar oscili iamp, icarfr+amod, iwave

out acar * aenvendin

Bell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like Tones

• fundamental is GCD: 40 Hertzfundamental is GCD: 40 Hertz[iii:12] [iii:13] bell-like tone (Dodge p. 126)

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Bell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like Tones

• fundamental is GCD: 5 Hertzfundamental is GCD: 5 Hertz[iii:14] [iii:15] wood-drum-like tone (Dodge p. 126)

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Bell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like Tones

• fundamental is GCD: 300 Hertzfundamental is GCD: 300 Hertz[iii:16] [iii:17] clarbell — hybrid clarinet and bell

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i2i2 11 2.52.5 1000010000 900900 600600 44

Bell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like Tones

;dodge.orc - use with dodge.sco

instr 2 ; bell and wood-drum tonesidur = p3iamp = p4icarfr = p5 ; carrier frequencyimodfr = p6 ; modulator frequencyimax = p7 ; maximum indexiwave = 1 ; wave table 1

index = imodfr * imax

Bell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like TonesBell and Wood-Drum-Like Tones

; amplitude envelopes for modulator and carrier:ampmod linseg index, .125 * idur, 0, idur * .875, 0; expseg cannot use 0:ampcar expseg .7, .121*idur, 1, idur*.879,.001,1,.001

; modulator and carrier oscillators:amod oscili ampmod, imodfr, iwaveacar oscili ampcar, icarfr+amod, iwave

; expseg cannot use 0:aenv expseg .001,.001,1,idur-.001,.001,1,.001

out acar * iamp * aenvendin

Carrier-Modulator RatioCarrier-Modulator RatioCarrier-Modulator RatioCarrier-Modulator Ratio

CARCAR MODMOD nncc

RATIORATIO

BrassBrass 440440 440440 1/11/1

ClarinetClarinet 900900 600600 3/23/2

BellBell 200200 280280 5/75/7

Wood DrumWood Drum 8080 5555 16/1116/11

Clar-BellClar-Bell 900900 600600 3/23/2

imodfrimodfr == p5p5

icarfricarfr == imodfr * ______imodfr * ______

Formant FM:Formant FM:Generating Harmonic FM SpectraGenerating Harmonic FM Spectra

Formant FM:Formant FM:Generating Harmonic FM SpectraGenerating Harmonic FM Spectra

• A special case of FM with:A special case of FM with:

freqfreqmodmod = freq = freq11

freqfreqcarcar = n = ncc freq freqmodmod = n = ncc freq freq11

• where nwhere ncc is an integer representing the is an integer representing the carrier frequency ratiocarrier frequency ratio usually in the usually in the range: range:

0 <= n0 <= ncc <= 10 <= 10

Formant FMFormant FMFormant FMFormant FM

• fundamental is 100 Hertzfundamental is 100 Hertz

[iii:18] formant fmfreq1 = [iii:19] 100, freqmod=freq1 and freqcar= [iii:20] 5freqmod

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Carrier

Formant FMFormant FMFormant FMFormant FM• "formant" means resonance"formant" means resonance• freqfreqcarcar acts like a resonance with acts like a resonance with

sidebands falling off at harmonics sidebands falling off at harmonics around it.around it.

Formant FMFormant FMFormant FMFormant FM• pitch ambiguity because fundamental is too soft — pitch ambiguity because fundamental is too soft —

moving the formant does not move the fundamental, moving the formant does not move the fundamental, but it changes the pitch we think we hearbut it changes the pitch we think we hear

[iii:21] formant fm freq1 = [iii:22] 100, freqmod=freq1 and freqcar= [iii:23] 8freqmod

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Quasi-Formant FM:Quasi-Formant FM:Quasi-Harmonic FM SpectraQuasi-Harmonic FM Spectra

Quasi-Formant FM:Quasi-Formant FM:Quasi-Harmonic FM SpectraQuasi-Harmonic FM Spectra

• A special case of FM with:A special case of FM with:

freqfreqcarcar = freq = freq11

freqfreqmodmod = n = nmm freq freqcarcar = n = nmm freq freq11

• where nwhere nmm is an integer representing the is an integer representing the modulator frequency ratiomodulator frequency ratio usually in the usually in the range: range:

0 <= n0 <= nmm <= 5 <= 5

Formant FMFormant FMFormant FMFormant FM• a modulator whose frequency is much greater than a modulator whose frequency is much greater than

that of the carrier can give a strange spectrum with that of the carrier can give a strange spectrum with missing harmonicsmissing harmonics

[iii:24] quasi-formant fmfreq1 = [iii:25] 100, freqcar=freq1 and freqmod= [iii:26] 10freqcar

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