EE2F2 - Music Technology

1. 11. Physical Modelling EE2F2 - Music Technology

2. Introduction • Some ‘expressive instruments don’t sound very convincing when sampled • Examples: wind or bowed stringed instruments • Reasons • When a performer plays a real instrument, every note sounds slightly different – sampled notes all sound the same • Also, the transition between notes is not sudden but gradual • Instead of sampling, physical modelling techniques build a computer simulation of the physical processes of an instrument • The model can then be ‘played’ with an appropriate controller and should sound more realistic

3. Classic Physical Modelling • The science of acoustics is all about how things vibrate • A commonly used numerical technique to model vibrating bodies is finite element analysis • It works by representing complex solid objects by a matrix of discrete points • The problem is quantised • If the density of the points is large enough, vibrations in complex bodies can be simulated by many simple linear equations

4. Vibrating String Example • A taut string can be simulated by a row of small masses connected by ideal springs • If each individual spring is assumed to be always straight, the simulation becomes very simple • The movement of each mass can be calculated using • Hooke’s law for the adjacent springs • Newton’s 2nd law of motion

5. Vibrating String in Action • The sound produced by a vibrating string depends on the velocity of the elements • This can be read directly from the model • Examples: Sum of all elements Single element, mid-string Single element, end of string

6. Planes and Volumes • To simulate a plane (e.g. the skin of a drum), use a 2-dimensional grid of elements • A volume (e.g. a solid bar or an enclosure of air) is a 3-dimensional grid • The equations are the same regardless • All that changes (depending on the material) are: • The mass of the elements • The tension of the springs • The frictional retardation

7. Pros and Cons • Pros • Using finite-element analysis (or similar techniques) any shaped instrument made from any material can be modelled • If the numbers are right, the sound can be indistinguishable from the real thing • Cons • You need a lot of patience to program in all those element positions and parameters • You need a big computer to simulate them in real time • Currently, not technically feasible

8. Functional Physical Modelling • For reasons of user-friendliness and computational demands, there is an urgent need to simplify the classic approach • By way of example, consider the string again. • Given the properties of the string, we can predict known resonant modes: Fundamental 1st Harmonic 2nd Harmonic Sum of Harmonics

9. Functional Modelling Cont. • Any initial pluck displacement (the boundary condition) can be expressed as a sum of weighted sine waves • The weight of each sine wave determines how much that harmonic will be excited • If the behaviour of the harmonics is known beforehand, the behaviour following any initial displacement can be easily predicted by adding them together in the right proportions » + + Fundamental 1st Harmonic 2nd Harmonic

10. Source-Resonator Model Source Resonator • A simplified way of thinking of the plucked string is the source-resonator model • Source: The initial displacement of the string • Resonator: A filter that resonates according to the modes of the string • This model can be applied to a wide range of instruments • NB. Sometimes, the resonator output modifies the source. In these cases feedback is required. Output Feedback (when required)

11. Source-Resonator Model Source Resonator Output Feedback (when required) Fundamental mode Source spectrum Resonator Response Harmonics frequency frequency

12. Source-Resonator Examples • Piano • Source: The hammer displacing the piano string • Resonator: The modes of vibration of the string multiplied by the frequency response of the sound-board • Flute • Source: The noise-like rush of air over the mouthpiece • Resonator: The resonant modes of the pipe • Trumpet • Source: The vibrations of the performers lips • Resonator: The resonant modes of the tube, modified by the effects of the flare at the end • Feedback: In this case, the resonance of the pipe feeds back to the source

13. Sound Examples Bowed Violins Plucked guitar quintet Flute (with ‘overblowing’)

14. Pros and Cons • Pros • Potentially, produces the most realistic synthesised sounds around • Responds in the same way as the real thing • Can be used to synthesise fictional instruments by breaking a few laws of physics! • Cons • Can be very difficult to play (if you’re a rubbish violinist, you’ll also be a rubbish virtual violinist) • Currently, not easy to program – poor user interface

15. Physical Modelling Summary • Very realistic sounds • High computational complexity (especially using classic modelling) • Can be difficult to play

16. Microsoft’s best effort! The Future of Synthesis • Additive Methods • Elaborate additive synthesis techniques allow easy time and pitch stretching and morphing • Could turn out much easier to play than physically modelled instruments • Processor intensive at the moment • Physical Modelling • Modelling environments must be made more friendly • Modelling of fictional instruments • The Human Voice • Speech and music synthesis combined!

17. Music Projects • Current Projects (BEng/MEng) • Microcontroller based MIDI devices • Pitch-to-MIDI conversion • Subtractive synthesiser • Controller pedal • Additive synthesis for data compression • Bass-servo (in conjunction with Linn)

18. Music Projects • Future Projects • More microcontroller based devices • FM synthesis • Wind controller • Signal processing • Effects processing • Automatic transcription • Physical modelling • Analysis and re-synthesis of sounds

19. Course Summary • Recording Technology • Multi-track recording and mixing • Effects • MIDI & Sequencers • Sampling & Synthesis • Subtractive and Additive Synthesis (+FM a bit) • Sampling and Sample+Synthesis • Physical Modelling