CTP431- Music and Audio Computing Sound Synthesis Graduate School of Culture Technology KAIST Juhan Nam 1 Musical Sound Synthesis § Modeling the patterns of musical tones and generating them § (Typical) musical tones – Time-wise: amplitude envelope (ADSR) à Waveform – Frequency-wise : harmonic distribution à Spectrogram § How are musical tones different from other sounds (e.g. speech)? 2 Types of Tones § Musical tones have more diverse types – Harmonic: guitar, flute, violin, organ, singing voice (vowel) – Inharmonic: piano, vibraphone – Non-harmonic: drum, percussion, singing voice (consonant) [From Klapuri’s slides] Vibraphone *Inharmonicity in Piano 3 Information in Tones § Musical tones have the main information in “pitch” – Speech Tones have it mainly in “formant (i.e. spectral envelop)” § Examples – Original music : – Reconstruction from timbre features (MFCC) and using white-noise as a source): – Reconstruction from tonal features (Chroma): 4 Pitch Scale and Range § In music, pitch is arranged on a tuning system and the range is much wider 4000 3500 3000 2500 Hz − 2000 frequency 1500 1000 500 0 10 20 30 40 50 time [second] 5 Control of Tones § Musical Instrument Note Number, Velocity, Music Output Duration Synthesizer (+ Expressions) § Speech Speech Phonemes Output Synthesizer (+ Expressions) 6 Overview of Sound Synthesis Techniques § Signal model (analog / digital) – Additive Synthesis – Subtractive Synthesis – Modulation Synthesis: ring modulation, frequency modulation – Distortion Synthesis: non-linear § Sample model (digital) – Sampling Synthesis – Granular Synthesis – Concatenative Synthesis § Physical model (digital) – Digital Waveguide Model 7 Theremin § A sinusoidal tone generator § Two antennas are remotely controlled to adjust pitch and volume Theremin ( by Léon Theremin, 1928) Theremin (Clara Rockmore) https://www.youtube.com/watch?v=pSzTPGlNa5U 9 Additive Synthesis § Synthesize sounds by adding multiple sine oscillators – Also called Fourier synthesis OSC Amp (Env) OSC Amp (Env) + . OSC Amp (Env) 10 Hammond Organ § Drawbars – Control the levels of individual tonewheels 11 Hammond Organ https://www.youtube.com/watch?v=2rqn4bYFUZU 12 Sound Examples § Web Audio Demo – http://femurdesign.com/theremin/ – http://www.venlabsla.com/x/additive/additive.html – http://codepen.io/anon/pen/jPGJMK § Examples (instruments) – Kurzweil K150 • https://soundcloud.com/rosst/sets/kurzweil-k150-fs-additive – Kawai K5, K5000 13 Subtractive Synthesis § Synthesize sounds by filtering wide-band oscillators – Source-Filter model – Examples • Analog Synthesizers: oscillators + resonant lowpass filters • Voice Synthesizers: glottal pulse train + formant filters 20 20 20 10 10 10 0 0 0 −10 −10 −10 −20 −20 −20 −30 −30 −30 Magnitude (dB) Magnitude (dB) Magnitude (dB) −40 −40 −40 −50 −50 −50 −60 −60 −60 5 10 15 20 0 0.5 1 1.5 2 2.5 5 10 15 20 Frequency (kHz) 4 Frequency (kHz) Frequency (kHz) x 10 Source Filter Filtered Source 14 Moog Synthesizers Soft Envelope LFO Control Keyboard Physical Control Wheels Slides Pedal Envelope Parameter Parameter Parameter Audio Path Oscillators Filter Amp Parameter = offset + depth*control (e.g. filter cut-off frequency) (static value) (dynamic value) 15 Oscillators § Classic waveforms 2 1 2 0 0 0 −2 −1 −2 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 20 20 20 0 −6dB/oct 0 −6dB/oct 0 −12dB/oct −20 −20 −20 −40 −40 −40 Magnitude (dB) Magnitude (dB) Magnitude (dB) −60 −60 −60 5 10 15 20 5 10 15 20 5 10 15 20 Frequency (kHz) Frequency (kHz) Frequency (kHz) Sawtooth Square Triangular § Modulation – Pulse width modulation – Hard-sync – More rich harmonics 16 Amp Envelop Generator § Amplitude envelope generation – ADSR curve: attack, decay, sustain and release – Each state has a pair of time and target level Amplitude Attack Decay (dB) Sustain Release Note On Note Off 17 Examples § Web Audio Demos – http://www.google.com/doodles/robert-moogs-78th-birthday – http://webaudiodemos.appspot.com/midi-synth/index.html – http://aikelab.net/websynth/ – http://nicroto.github.io/viktor/ § Example Sounds – SuperSaw – Leads – Pad – MoogBass – 8-Bit sounds: https://www.youtube.com/watch?v=tf0-Rrm9dI0 – TR-808: https://www.youtube.com/watch?v=YeZZk2czG1c 18 Modulation Synthesis § Modulation is originally from communication theory – Carrier: channel signal, e.g., radio or TV channel – Modulator: information signal, e.g., voice, video § Decreasing the frequency of carrier to hearing range can be used to synthesize sound § Types of modulation synthesis – Amplitude modulation (or ring modulation) – Frequency modulation § Modulation is non-linear processing – Generate new sinusoidal components 19 Ring Modulation / Amplitude Modulation § Change the amplitude of one source with another source – Slow change: tremolo – Fast change: generate a new tone Modulator OSC Modulator OSC Carrier OSC x Carrier OSC x + (1 a (t))A cos(2 f t) am (t)Ac cos(2π fct) + m c π c Ring Modulation Amplitude Modulation 20 Ring Modulation / Amplitude Modulation § Frequency domain – Expressed in terms of its sideband frequencies – The sum and difference of the two frequencies are obtained according to trigonometric identity – If the modulator is a non-sinusoidal tone, a mirrored-spectrum with regard to the carrier frequency is obtained carrier sideband sideband am (t) = Am sin(2π fmt)) fc-fm fc fc+fm 21 Examples § Tone generation – SawtoothOsc x SineOsc – https://www.youtube.com/watch?v=yw7_WQmrzuk § Ring modulation is often used as an audio effect – http://webaudio.prototyping.bbc.co.uk/ring-modulator/ 22 Frequency Modulation § Change the frequency of one source with another source – Slow change: vibrato – Fast change: generate a new (and rich) tone – Invented by John Chowning in 1973 à Yamaha DX7 Modulator OSC Ac cos(2π fct + β sin(2π fmt)) frequency Carrier OSC A β = m Index of modulation fm 23 Frequency Modulation § Frequency Domain – Expressed in terms of its sideband frequencies – Their amplitudes are determined by the Bessel function – The sidebands below 0 Hz or above the Nyquist frequency are folded k=−∞ y(t) = Ac ∑ Jk (β)cos(2π( fc + kfm )t) k=−∞ carrier sideband1 sideband1 sideband2 sideband2 sideband3 sideband3 fc-3fm fc-2fm fc-fm fc fc+fm fc+2fm fc+3fm 24 Bessel Function n β k+2n ∞ (−1) ( ) 2 Jk (β) = ∑ n=0 n!(n + k)! 1 Carrier Sideband 1 Sideband 2 Sideband 3 Sideband 4 0.5 J_(k) 0 −0.5 0 50 100 150 200 250 300 350 beta 25 Bessel Function 26 The Effect of Modulation Index 1 1 0 0 Amplitude Amplitude −1 −1 0 500 1000 1500 2000 0 500 1000 1500 2000 Time (Sample) Time (Sample) 20 20 Beta = 0 Beta = 1 0 0 −20 −20 −40 −40 Magnitude (dB) −60 Magnitude (dB) −60 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Frequency (kHz) Frequency (kHz) 1 1 0 0 Amplitude Amplitude −1 −1 0 500 1000 1500 2000 0 500 1000 1500 2000 Time (Sample) Time (Sample) 20 20 Beta = 10 Beta = 20 0 0 −20 −20 −40 −40 Magnitude (dB) −60 Magnitude (dB) −60 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Frequency (kHz) Frequency (kHz) fc = 500, fm = 50 27 Yamaha DX7 (1983) 28 “Algorithms” in DX7 http://www.audiocentralmagazine.com/yamaha-dx-7-riparliamo-di-fm-e-non-solo-seconda-parte/yamaha-dx7-algorithms/ 29 Examples § Web Audio Demo – http://www.taktech.org/takm/WebFMSynth/ § Sound Examples – Bell – Wood – Brass – Electric Piano – Vibraphone 30 Non-linear Synthesis (wave-shaping) § Generate a rich sound spectrum from a sinusoid using non-linear transfer functions (also called “distortion synthesis”) § Examples of transfer function: y = f(x) – y = 1.5x’ – 0.5x’3 – y = x’/(1+|x’|) x’=gx: g correspond to the “gain knob” of the distortion – y = sin(x’) T0(x)=1, T1(x)=x, – Chebyshev polynomial: Tk+1(x) = 2xTk(x)-Tk-1(x) 2 3 T2(x)=2x -1, T2(x)=4x -3x 1 1 1 0 0 Amplitude 0.5 Amplitude −1 0 50 100 150 200 −1 Time (Sample) 0 50 100 150 200 0 Time (Sample) 20 Amplitude 20 0 −0.5 0 −20 −40 −20 −1 Magnitude (dB) −60 −1 −0.5 0 0.5 1 −40 5 10 15 20 Time (Sample) Frequency (kHz) Magnitude (dB) −60 5 10 15 20 Frequency (kHz) 31 Physical Modeling § Modeling Newton’s laws of motion (i.e. � = ��) on musical instruments – Every instrument have a different model § The ideal string '() '() – Wave equation: � = �� à � = � (�: tension, �: linear mass density) '*( '*( * * – General solution: � �, � = � (� − ) + � (� + ) 0 3 5 3 àLeft-going traveling wave and right-going traveling wave 32 Physical Modeling § Waveguide Model – With boundary condition (fixed ends) -1.0 -0.99 § The Karplus-Strong model Delay Line x(n) + Z-M y(n) Noise Burst Lowpass Filter 33 Physical Modeling § The Extended Karplus -Strong model https://ccrma.stanford.edu/~jos/pasp/Extended_Karplus_Strong_Algorithm.html 34 Sample-based Synthesis § The majority of digital sound and music synthesis today is accomplished via the playback of stored waveforms – Media production: sound effects, narration, prompts – Digital devices: ringtone, sound alert – Musical Instruments • Native Instrument Kontakt5: 43+ GB (1000+ instruments) • Synthogy Ivory II Piano: 77GB+ (Steinway D Grand, ….) Foley (filmmaking) Ringtones Synthogy Ivory II Piano 35 Why Don’t We Just Use Samples? § Advantages – Reproduce realistic sounds (needless to say) – Less use of CPU § Limitations – Not flexible: repeat the same sound again, not expressive – Can require a great deal of storage – Need high-quality recording – Limited to real-world sounds § Better ways – Modify samples based on existing sound processing techniques • Much richer spectrum of sounds – Trade-off: CPU, memory and programmability 36 Sample-based Synthesis Off-Line Storing Off-line Recording Processing in table - Sample editing Meta-data: pitch, - Pitch change loudness, action, text - Filter, EQ, envelope - Normalization User Sample Online Audio On-line input Fetching Processing Effect - Pitch, velocity, Read Samples - Pitch Change - Delay-based Timbre from the table - Filter, EQ effects - Speed, strength - Envelope (e.g.