Frequency Modulation 2
description
Transcript of Frequency Modulation 2
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)
;; startstart durdur ampamp cfrqcfrq mfrqmfrq indxindx
i1i1 11 1.61.6 1000010000 440440 440440 55
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)
;; startstart durdur ampamp cfrqcfrq mfrqmfrq indxindx
i1i1 11 1.61.6 1000010000 900900 600600 44
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)
;; startstart durdur ampamp cfrqcfrq mfrqmfrq indxindx
i2i2 11 55 1000010000 200200 280280 1010
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)
;; startstart durdur ampamp cfrqcfrq mfrqmfrq indxindx
i2i2 11 .2.2 2000020000 8080 5555 2525
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
;; startstart durdur ampamp cfrqcfrq mfrqmfrq indxindx
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
;; startstart durdur ampamp cfrqcfrq mfrqmfrq indxindx
i1i1 11 1.61.6 1000010000 500500 100100 11
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
;; startstart durdur ampamp cfrqcfrq mfrqmfrq indxindx
i1i1 11 1.61.6 1000010000 800800 100100 11
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
;; startstart durdur ampamp cfrqcfrq mfrqmfrq indxindx
i1i1 11 1.61.6 1000010000 100100 10001000 11