Aerophones in Flatland

Transcription

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2 Aerophones in Flatland Interactive Wave Simulation of Wind Instruments Andrew Allen Nikunj Raghuvanshi

3 Simulation Domain Mouthpiece Spectrogram

4 Wind Instruments Non-linear Feedback Linear mouth reed bore Resonant Cavity Mouthpiece Bore, Toneholes Bell

5 Excitation models: Single Reed (Clarinet) Dalmont, J.P., Gilbert J., and Ollivier, S

6 Excitation models: Lips (Trumpet) Adachi and Sato

7 Excitation models: Air Jet (Flute) de La Cuadra

8 Realtime synthesis: Digital Waveguides SMITH, JULIUS O Physical Audio Signal Processing. jos/pasp/ + (online book, accessed Jan 2014). shift Bell radiation Bell reflection + shift Mouthpiece breath pressure Bore Bell

9 Realtime synthesis: Digital Waveguides Non-linear excitation model + shift Bell radiation Bell reflection + shift Mouthpiece Bore Bell breath = frequency-dependent filter

10 Realtime synthesis: Digital Waveguides Tonehole radiation Tonehole radiation Non-linear excitation model + Tonehole reflection shift Tonehole reflection Bell reflection Bell radiation Mouthpiece + Tonehole shift Bore Tonehole Bell breath = frequency-dependent filter

11 Our approach Borrow and adapt Non-linear excitation model Non-linear excitation model + Tonehole radiation Tonehole reflection 2D wave simulation on GPU shift Tonehole radiation Tonehole reflection Bell reflection Bell radiation Mouthpiece breath pressure + Color = pressure shift Bore Bell

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14 Advantages Signal processing networks require expertise to design and ensure physical plausibility. Geometric manipulation is intuitive. Guaranteed physical plausibility. Lower expertise bar for musical experimentation.

15 Challenges System is driven non-linearly and has perceptually salient transients (note beginnings/ends). Direct time-domain finite-difference solution. Standard finite difference generates artifacts on changing geometry. Need millimeter-scale resolution. Numerical stability requires small time-steps for wave equation. ~3.8mm resolution at 128,000Hz on the GPU.

16 Linear Wave Equation p t + σ p = ρc 2 v β v t + σ v = β 2 p ρ + σ v b (σ = 1 + β σ)

17 Perfectly matched layer (PML) p t + σ p = ρc 2 v β v t + σ v = β 2 p ρ + σ v b σ = 0 (σ = 1 + β σ) σ 0

18 Dynamic Geometry Tone Holes, Valves, Slides, Mutes

19 Abrupt geometric changes: clicks

20 Our formulation (time-varying PML) p t + (1 β + σ)p = ρc2 v β v t + 1 β + σ v = β2 p ρ + (1 β + σ)v b β(x, t) [0,1] introduces smoothly-varying dynamic geometry. v b enforces boundary conditions and input flow from mouthpiece. Handles all phenomena we model.

21 Our formulation (time-varying PML) β v t + 1 β + σ v = β2 p ρ β = 0: Boundary β v p + 1 β + σ v = β2 t ρ + 1 β + σ v b (σ = 0 inside domain) + 1 β + σ v b Smoothly interpolates between Boundary and Air state in every cell β = 1: Air β v p + 1 β + σ v = β2 t ρ + 1 β + σ v b

22 Our formulation: natural transients Off On The transition rate of β controls the smoothness of the transition. Results in a simple conditional-free update equation for the entire domain.

23 Wall losses Off On 2D simulations support transverse resonances Wall loss modeling is required (unlike 1D models)

24 High-amplitude non-linearity Off On Brass instruments have high amplitudes inside the bore. Makes brass sound brighter.

25 GPU Implementation p U Solving Finite Difference uses a 5-point 2D stencil. p L v x v y p v x p R Neighbor pressures and velocities are used to update center pressure. v y p D

26 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. vv y y Four copies of the simulation are stored in one pp large vv x x texture. Ping-pong with R/Ws on one texture. Output pressure written out in block in reserved space on FBO State structure stores: β value (boundary-ness) σ value (PML) Is Excitation? Is Listener? R G B A p v x v y state Per Fragment

27 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. Four copies of the simulation are stored in one large texture. Ping-pong with R/Ws on one texture. Output pressure written out in block in reserved space on FBO Framebuffer Texture R G B A p v x v y state Per Fragment

28 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. Four copies of the simulation are stored in one large texture. Ping-pong with R/Ws on one texture. Output pressure written out in block in reserved space on FBO Framebuffer Texture R G B A p v x v y state Per Fragment

29 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. Four copies of the simulation are stored in one large texture. Ping-pong with R/Ws on one texture. Output pressure written out in block in reserved space on FBO Framebuffer Texture 1 2 t + 1 t 3 4 t 2 t 1 R G B A p v x v y state

30 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. Four copies of the simulation are stored in one large texture. Ping-pong with R/Ws on one texture. Output pressure written out in block in reserved space on FBO Framebuffer Texture 1 2 t t t + 1 t 2 R G B A p v x v y state

31 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. Four copies of the simulation are stored in one large texture. Ping-pong with R/Ws on one texture. Output pressure written out in block in reserved space on FBO Framebuffer Texture 1 2 t 1 t t t + 1 R G B A p v x v y state

32 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. Four copies of the simulation are stored in one large texture. Ping-pong with R/Ws on one texture. Output pressure written out in block in reserved space on FBO Framebuffer Texture 1 2 t 2 t t 1 t R G B A p v x v y state

33 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. Four copies of the simulation are stored in one large texture. Ping-pong with R/Ws on one texture. Output pressure written out in block in reserved space on FBO Framebuffer Texture 1 2 t + 1 t 3 4 t 2 t 1 R G B A p v x v y state

34 GPU Implementation Values for each cell are stored in color channels. Simulation grid is represented as a 2D texture. Four copies of the simulation are stored in one large texture. Ping-pong with R/Ws on one texture. Write output pressure (sound) to reserved space on the FBO. Framebuffer Texture 1 2 t + 1 t 3 4 t 2 t 1 R G B A p v x v y state

35 Clarinet Chalumeau melody Altissimo melody (register key)

36 Saxophone Simple melody Fast Squeaks

37 Flute Robot Performer Wind Controller Interface

38 Bugle & Trumpet (brasses) Lips Overblowing Valve System

39 Trumpet w/o Bell and w/ Mutes Bell On/Off Straight, Cup and Harmon Mute

40 Slide Whistle and Menorah Dynamic Bore Geometry Interlocking Valve System

41 Tuba? and Hybrid Implausible-to-construct Instrument Reed, Lips, Valve, Tonehole, Bell

42 Comparisons to STK (Digital Waveguides) Low note High note

43 Conclusions and Future Work First system for real-time 2D simulation of Aerophones Improving the control of excitation mechanisms Automatic tuning of geometry Generalized excitation model Modeling of larynx/syrinx (speech synthesis/bird song)

44 Thank You! Questions? Special thanks for providing performances Kyle Rowan, clarinetist Paul Hembree, trumpeter