Copyright 2004 Ken Greenebaum Introduction to Interactive Sound Synthesis Lecture 11: Modulation Ken Greenebaum

Copyright 2004 Ken Greenebaum Midterm Material Material from lectures/readings Material from lectures/readings Emphasis on material covered in Emphasis on material covered in in lecture in lecture assignments assignments

Copyright 2004 Ken Greenebaum Midterm Format Multiple choice/fill-in the blank Multiple choice/fill-in the blank Calculations (must show work) Calculations (must show work) Short essay Short essay Simple Coding Simple Coding (closed book, no calculator or computer) (closed book, no calculator or computer)

Copyright 2004 Ken Greenebaum Assignment 4: Mixer Questions? Questions?

Copyright 2004 Ken Greenebaum Assignment 3C: Genetic Collision Who explored this assignment? Who explored this assignment? Who would like to demo? Who would like to demo? What did you learn? What did you learn? What new sounds did you discover? What new sounds did you discover?

Copyright 2004 Ken Greenebaum Genetic searching Will Serve us well when exploring Will Serve us well when exploring Other synthesis algorithms Other synthesis algorithms FM Synthesis is highly unintuitive! FM Synthesis is highly unintuitive!

Copyright 2004 Ken Greenebaum AM Modulation A periodic change in amplitude A periodic change in amplitude Used in Radio broadcast Used in Radio broadcast Violinists’ Tremolo Violinists’ Tremolo

Copyright 2004 Ken Greenebaum AM Modulation Multiply carrier by a modulating signal: Multiply carrier by a modulating signal:

Copyright 2004 Ken Greenebaum AM Modulation If carrier, modulator both pure sine waves If carrier, modulator both pure sine waves Modulated result is comprised of three freqs: Modulated result is comprised of three freqs: Carrier Carrier 2 Sidebands (offset by modulation freq 2 Sidebands (offset by modulation freq

Copyright 2004 Ken Greenebaum AM Modulation If carrier contains multiple partials: If carrier contains multiple partials: 2 Sidebands per partial results 2 Sidebands per partial results

Copyright 2004 Ken Greenebaum AM Sidetones Frequency domain plot: Frequency domain plot:

Copyright 2004 Ken Greenebaum AM Modulation Sidetones What does this tell us about: What does this tell us about: Adding two identical signals together? Adding two identical signals together? Adding two similar signals together? Adding two similar signals together? Beat frequencies Beat frequencies

Copyright 2004 Ken Greenebaum AM Modulation Modulation < 8 Hz Modulation < 8 Hz Tremolo Tremolo Vibraphone, Hammond Organ Vibraphone, Hammond Organ Otherwise > 20 Hz Otherwise > 20 Hz Timbre of sound is changed Timbre of sound is changed Called spectral synthesis Called spectral synthesis

Copyright 2004 Ken Greenebaum FM Synthesis Really: Really: Audio rate frequency modulation Audio rate frequency modulation Developed by John Chowning (Stanford) Developed by John Chowning (Stanford) Early 1970’s Early 1970’s Yamaha DX-7 Synthesizers Yamaha DX-7 Synthesizers

Copyright 2004 Ken Greenebaum FM Synthesis Non-linear system Non-linear system Produces many sidetone Produces many sidetone Rich sounds Rich sounds Inexpensive Inexpensive Difficult to control Difficult to control

Copyright 2004 Ken Greenebaum FM Synthesis Makes these sounds and more: Makes these sounds and more: String instruments String instruments Wind instruments Wind instruments Human voice Human voice Percussion Percussion ‘Spacey’ sounds ‘Spacey’ sounds

Copyright 2004 Ken Greenebaum FM Synthesis Hardware Hardware VCO (Voltage controlled oscillator) VCO (Voltage controlled oscillator) DC in DC in Oscillator out Oscillator out Higher voltage, higher frequency Higher voltage, higher frequency A/C in A/C in Modulated waveform out Modulated waveform out

Copyright 2004 Ken Greenebaum FM Synthesis Output of one VCO controls 2 nd VCO Output of one VCO controls 2 nd VCO Modulator - VCO providing control source Modulator - VCO providing control source Carrier - VCO providing signal Carrier - VCO providing signal y(t) = sin(2πtf c + Δf c cos(2πtf m )) y(t) = sin(2πtf c + Δf c cos(2πtf m ))

Copyright 2004 Ken Greenebaum FM Synthesis Vibrato <20Hz subsonic modulation Vibrato <20Hz subsonic modulation Musicians quickly alter the length of the string Musicians quickly alter the length of the string Degree of vibrato (freq shift) related to Degree of vibrato (freq shift) related to Amplitude of modulating waveform Amplitude of modulating waveform Rate of vibrator related to Rate of vibrator related to Frequency of modulation signal Frequency of modulation signal Modulation signal not in signal path Modulation signal not in signal path It only changes the carrier (the center freq) It only changes the carrier (the center freq)

Copyright 2004 Ken Greenebaum FM Synthesis Sidetones Frequency component generated by the modulation of a signal Frequency component generated by the modulation of a signal Symmetric pairs at frequencies offset from carrier by +/- distance = modulating frequency Symmetric pairs at frequencies offset from carrier by +/- distance = modulating frequency Sidebands ‘steal’ energy from the carrier Sidebands ‘steal’ energy from the carrier

Copyright 2004 Ken Greenebaum Chowning FM Carrier and modulator are pure sinewaves Carrier and modulator are pure sinewaves Linear modulation Linear modulation pushes carrier by equal frequency pushes carrier by equal frequency Not Exponential FM Not Exponential FM pushes carrier by equal musical interval pushes carrier by equal musical interval > Hz up than down > Hz up than down Perceived freq drifts up with increased modulation Perceived freq drifts up with increased modulation

Copyright 2004 Ken Greenebaum Chowning FM Sidetones C f +/- nM f C f +/- nM f Carrier +/- integer multiples of modulation f Carrier +/- integer multiples of modulation f C f, C f + M f, C f - M f, C f + 2M f, C f - 2M f, … C f, C f + M f, C f - M f, C f + 2M f, C f - 2M f, … Frequency domain: Frequency domain:

Copyright 2004 Ken Greenebaum Sidetone Reflection ‘negative’ sidetones reflect ‘negative’ sidetones reflect Just drop the sign Just drop the sign 180° phase change 180° phase change

Copyright 2004 Ken Greenebaum Chowning FM Ratios C:M Ratio C:M Ratio Non-reducible when evenly divisible by only 1 (think fractions 10:4 -> 5:2) Non-reducible when evenly divisible by only 1 (think fractions 10:4 -> 5:2)

Copyright 2004 Ken Greenebaum Chowning FM Ratios Carrier is the fundamental (perceived pitch) Carrier is the fundamental (perceived pitch) M>=2C M>=2C Or Or 1:1 1:1

Copyright 2004 Ken Greenebaum Chowning FM Ratios Lower sidebands ‘fall against’ upper when Lower sidebands ‘fall against’ upper when N:1 Ratios N:1 Ratios 1:1, 2:1, 3:1… 1:1, 2:1, 3:1… Odd N:2 Ratios Odd N:2 Ratios (odd harmonics in upper, lower sidebands) (odd harmonics in upper, lower sidebands) 1:2, 3:2, 5:2… 1:2, 3:2, 5:2… Resulting sidebands not nec. 2f Resulting sidebands not nec. 2f Due to reflections causing phase inversion Due to reflections causing phase inversion

Copyright 2004 Ken Greenebaum Chowning FM Normal Ratios C:M ration in normal form when C:M ration in normal form when Carrier is fundamental in produced spectrum Carrier is fundamental in produced spectrum Normal form when: M > 2C Normal form when: M > 2C Otherwise apply: C = ׀ C - M ׀ Otherwise apply: C = ׀ C - M ׀ Useful for Useful for Predicting sidebands Predicting sidebands But not the phases or amplitudes But not the phases or amplitudes

Copyright 2004 Ken Greenebaum Chowning FM Normal Ratios Example: 8:5 Example: 8:5 C = 8 – 5 C = 8 – 5 3:5 (not normal 5 < 2*3) 3:5 (not normal 5 < 2*3) C = C = Normalized ratio: 2:5 Normalized ratio: 2:5

Copyright 2004 Ken Greenebaum Chowning FM Add M to C Add M to C Generate Sidebands Generate Sidebands Subtract M from C Subtract M from C To Reduce To Reduce

Copyright 2004 Ken Greenebaum Families of C:M ratios Some ratios produce the same sidebands (in different order): Some ratios produce the same sidebands (in different order): 2: : : : : : :5 2:5 Normal Form Normal Form Name of family Name of family

Copyright 2004 Ken Greenebaum Families of C:M ratios Whole family: Whole family: C+nM : M, ׀ C-nM ׀ : M C+nM : M, ׀ C-nM ׀ : M Use each sideband as the carrier in the ratio Use each sideband as the carrier in the ratio (keep same modulation) (keep same modulation)

Copyright 2004 Ken Greenebaum Farey Series Ratios using only values 1-9 Ratios using only values 1-9 Sorted by decreasing C/M Sorted by decreasing C/M 1:1 1:2 4:9 3:7 2:5 3:8 1:3 2:7 1:4 2:9 1:5 1:6 1:7 1:8 1:9 1:1 1:2 4:9 3:7 2:5 3:8 1:3 2:7 1:4 2:9 1:5 1:6 1:7 1:8 1:9

Copyright 2004 Ken Greenebaum Readings: Audio Anecdotes Audio Anecdotes Introduction to the theory of signal detection Introduction to the theory of signal detection

Copyright 2004 Ken Greenebaum Be sure to Work on Mixer Work on Mixer Study for Midterm Study for Midterm

Copyright 2004 Ken Greenebaum Next class: Receiver Operator Characteristic Curve Receiver Operator Characteristic Curve