1. Physics of Musical Instruments

2. Strings viola da gamba cello guitar harpsichord piano electric guitar

3. Strings vibrate with a frequency depending on its length, weight and tension length tension mass per unit length

4. The length of the part of the string actually vibrating can be changed quickly by the fingers fretless fret

5. The main problem with all string instruments is: How to make a skinny string move a large amount of air (impedance matching) ? Solution: The string moves a board, the board moves the air

6. not useful in a hot day very useful in a hot day

7. Acoustic guitar String vibration body vibration Resonances of the body (and air inside) help transfer the energy from the strings to sound at some frequencies, like the formants in the voice

8. Some resonances free guitar

9. Some resonances

10. Chladni patterns of some resonances

11. Luthiers try to control the frequencies of these resonances using braces

12. Plucking the strings at different points changes the timbre See it yourself at http://www.falstad.com/loadedstring/

13. Violin main difference: bowed, not plucked

14. resonances

15. Helmholtz (air) resonance

16. Loudness when playing different notes

17. Aging of violins: fact or fiction http://www.phys.unsw.edu.au/jw/powerhou setwins.html

18. Piano harpsichord

19. “gravicembalo col piano e forte” (Bartolomeu Cristoforo, 1709) The piano has a hammer instead and it’s possible to control intensity

20. The sound of the piano is loud AND sustained one single string, overtones filtered out change in decay rate

21. vertical mode excited initially by the hammer sounding board “gives” faster dumping horizontal mode not initially present sounding board is rigid slower dumping One reason for the two decay rates

22. Big range in pitch is accomplished by using string of varying thickness thickness length length tension tension Thick string lead to inharmonicities: f, 2f, 3f, 4f, 5f, …, 16f, … f, 2f, 3f, 4f, 5f, …, 16f, … shifted more and more ½ tone higher

23. F F stretching stretching and deforming

24. Consequences for tuning f 2.001f... 2f 4f... beating

25. Consequences for tuning f 2.001f... 2.001f 4.002f... “stretched octave” tuning

26. Soundboard

27. Soundboard

28. Modes of the soundborad: http://www.youtube.com/watch?v=GL5f-EcqPOc

29. Wind instruments oboe flute saxes tuba organ

30. How to generate oscillation (sound) from continuous blowing ? fipple fipple reed reed

31. fipple

32. Simplified, theoretical flute L/2L/2 open end holes closed holes open

33. Simplified, theoretical flute

36. embouchure machinery to open/close tone holes metal Modern Boehm flute

37. semitone mistuning

38. Reeds

39. The reed is like the vocal chords and the strings, NOT ! The resonances of the reed are irrelevant, it vibrates with the frequency of the resonances of the column of air

40. material is irrelevant Boehm fingering

41. flute, recorder clarinet saxophone, oboe

42. basssaxophone