Lecture 4

1. Lecture 4 Acoustics Musical Instruments The Elements of Music

2. Lecture 4 Acoustics … from the Greek akoustikos … which means … “hearing”

3. Acoustics Pythagorean proportions (review) Pythagoras observed relationships between: musical intervals that are naturally “contained” within vibrating objects and simple mathematical proportions

4. Acoustics Pythagorean proportions (review) Pythagoras observed relationships between: musical intervals that are naturally “contained” within vibrating objects and simple mathematical proportions

5. Acoustics Pythagorean proportions (review) Observations: A simple flute “overblows” at the: octave the fifth above that the fourth above that the major third above that the minor third above that

6. Acoustics Pythagorean proportions (review) Observations: A simple flute “overblows” at the: octave the fifth above that the fourth above that the major third above that the minor third above that

7. Acoustics Pythagorean proportions (review) Observations: A simple flute “overblows” at the: octave the fifth above that the major third above that the fourth above that the minor third above that do re mi fa sol la ti do

8. Acoustics Pythagorean proportions (review) Observations: A simple flute “overblows” at the: octave the fifth above that the fourth above that the major third above that the minor third above that octave do re mi fa sol la ti do

9. Acoustics Pythagorean proportions (review) Observations: A simple flute “overblows” at the: octave the fifth above that the fourth above that the major third above that the minor third above that fifth octave do re mi fa sol la ti do

10. Acoustics Pythagorean proportions (review) Observations: A simple flute “overblows” at the: octave the fifth above that the fourth above that the major third above that the minor third above that fourth fifth octave do re mi fa sol la ti do

11. Acoustics Pythagorean proportions (review) Observations: major third A simple flute “overblows” at the: octave the fifth above that the fourth above that the major third above that the minor third above that fourth fifth octave do re mi fa sol la ti do

12. Acoustics Pythagorean proportions (review) Observations: minor third major third A simple flute “overblows” at the: octave the fifth above that the fourth above that the major third above that the minor third above that fourth fifth octave do re mi fa sol la ti do

13. Acoustics Pythagorean proportions (review) Another observation: minor third major third Trumpet-like instruments sound at: octave the fifth above that the fourth above that the major third above that the minor third above that fourth fifth octave do re mi fa sol la ti do

14. Acoustics Pythagorean proportions (review) Yet another observation: minor third major third String “harmonics” sound at: octave the fifth above that the fourth above that the major third above that the minor third above that fourth fifth octave do re mi fa sol la ti do

15. Acoustics Pythagorean proportions (review) Still another observation: minor third major third Cavity “harmonics” sound at: octave the fifth above that the fourth above that the major third above that the minor third above that fourth fifth octave do re mi fa sol la ti do

16. Acoustics Pythagorean proportions (review) Pythagoras used his monochord to produce musical intervals based on the proportions: 1:1 = unison 2:1 = octave 3:2 = fifth 4:3 = fourth

17. Acoustics Pythagorean proportions (review) Followers of Pythagoras extended the process to include musical intervals based on the proportions: • 1:1 = unison • 2:1 = octave • 3:2 = fifth • 4:3 = fourth 5:4 = major third 6:5 = minor third 9:8 = major second 10:9 = major second 16:15 = minor second

18. Acoustics Pythagorean proportions (review) Why should this be so?Why should “natural” vibrations match up so neatly with simple proportions? monochord

19. Acoustics Pythagorean proportions (review) Why should this be so?Why should “natural” vibrations match up so neatly with simple proportions? monochord

20. Acoustics Pythagorean proportions (review) monochord 2 divided by 2 creates: the octave (2:1) 1

21. Acoustics Pythagorean proportions (review) monochord 3 divided by 3 creates: the fifth (3:2) 2

22. Acoustics Pythagorean proportions (review) monochord 3 3 divided by 3 creates: the fifth (3:2) – above the “fundamental” 2 2

23. Acoustics Pythagorean proportions (review) monochord 3 3 divided by 3 creates: the fifth (3:2) – above the “fundamental” the fifth (3:2) above the octave 2 2

24. Acoustics Pythagorean proportions (review) monochord 2 divided by 4 creates: the octave (2:1) above the octave (the “double octave”) 1

25. Acoustics Pythagorean proportions (review) monochord 5 divided by 5 creates: the fourth (5:4) ??????? 4

26. Acoustics Pythagorean proportions (review) monochord 5 5 divided by 10 creates: the fourth (5:4) above the “double octave” 4 4

27. Acoustics Pythagorean proportions (review) The vibrating object … … vibrates simultaneously at all these “divisions.”

28. Acoustics Pythagorean proportions (review) The vibrating object … … vibrates simultaneously at all these “divisions.”

29. Acoustics Pythagorean proportions (review) The “small” vibrations contained within the single “large” vibration are called … partials overtones harmonics

30. Acoustics Pythagorean proportions (review) The “partial” vibrations, or “overtones,” occur in all vibrating objects.But they will be heard as “tones” only if: the “object” is consistent in material, density, and tension the energy that triggers the vibration is steady

31. Acoustics Pythagorean proportions (review) The “partial” vibrations, or “overtones,” occur in all vibrating objects.But they will be heard as “tones” only if: the “object” is consistent in material, density, and tension the energy that triggers the vibration is steady

32. Acoustics Pythagorean proportions (review) The “partial” vibrations, or “overtones,” occur in all vibrating objects.But they will be heard as “tones” only if: Otherwise, the mix of vibrations will be heard as “noise.” • the “object” is consistent in material, density, and tension • the energy that triggers the vibration is steady

33. Acoustics Pythagorean proportions (review) Among the “vibrating objects” that might produce audible overtones are: automobile, motorcycle and airplane engines the body of an automobile as it moves on a highway the “squeaky” brakes of a car or truck the air contained within a room electrical power lines water moving through pipes musical instruments

34. Musical Instruments “instrument” … from the Latin instrumentum, meaning “tool” n. 1. A means by which something is done; agency. 2a. One used to accomplish some purpose. b. a person used and controlled by another; dupe. 3. A mechanical implement. 4. A device for recording or measuring … . 5. A device for producing music. 6. A legal document. American Heritage Dictionary

35. Musical Instruments “instrument” … from the Latin instrumentum, meaning “tool” n. 1. A means by which something is done; agency. 2a. One used to accomplish some purpose. b. a person used and controlled by another; dupe. 3. A mechanical implement. 4. A device for recording or measuring … . 5. A device for producing music. 6. A legal document. American Heritage Dictionary

36. Musical Instruments three basic types: wind instruments string instruments percussion instruments

37. Musical Instruments wind instruments three basic types: • string instruments • percussion instruments air column activated by: buzzing lips vibrating reeds movement of wind across a sharp edge

38. Musical Instruments string instruments three basic types: • wind instruments • string instruments • percussion instruments string set in motion by: bowing plucking or strumming striking wind

39. Musical Instruments percussion instruments three basic types: • wind instruments • string instruments • percussion instruments materials set in vibrational motion by: striking rubbing plucking shaking

40. Musical Instruments •buzzing lips• vibrating reeds• movement of wind across a sharp edge Wind instruments activated by: trumpet trombone French horn tuba bugle

41. Musical Instruments •buzzing lips• vibrating reeds• movement of wind across a sharp edge Wind instruments activated by: commonly known as “brass” instruments • trumpet • trombone • French horn • tuba • bugle

42. Musical Instruments •buzzing lips• vibrating reeds• movement of wind across a sharp edge Wind instruments activated by: conch shell shofar didjeridoo garden hose • trumpet • trombone • French horn • tuba • bugle

43. Musical Instruments The basic sound of these instruments is determined by: Wind instruments activated by: • buzzing lips• vibrating reeds• movement of wind across a sharp edge shape of the air column the amount of “noise” that is part of the blowing process

44. Musical Instruments The pitch of these instruments is determined by: Wind instruments activated by: • buzzing lips• vibrating reeds• movement of wind across a sharp edge the tension of the vibrating lips the length of the air column

45. Musical Instruments • buzzing lips•vibrating reeds• movement of wind across a sharp edge Wind instruments activated by: clarinet saxophone oboe bassoon

46. Musical Instruments • buzzing lips•vibrating reeds• movement of wind across a sharp edge Wind instruments activated by: single reed • clarinet • saxophone • oboe • bassoon

47. Musical Instruments • buzzing lips•vibrating reeds• movement of wind across a sharp edge Wind instruments activated by: double reed • clarinet • saxophone • oboe • bassoon

48. Musical Instruments • buzzing lips•vibrating reeds• movement of wind across a sharp edge Wind instruments activated by: some organ pipes harmonica a blade of grass • clarinet • saxophone • oboe • bassoon

49. Musical Instruments The basic sound of these instruments is determined by: Wind instruments activated by: • buzzing lips•vibrating reeds• movement of wind across a sharp edge the nature of the reed (“closed” or “open”) the amount of “noise” featured in the blowing process the shape of the air column (conical or cylindrical) the “overtones” contained in the vibrating air column

50. Musical Instruments The pitch of these instruments is determined by: Wind instruments activated by: • buzzing lips•vibrating reeds• movement of wind across a sharp edge the length of the air column the activation of “overtones” NOTE: a “closed” cone produces all the overtones, but a “closed” cylinder producesonly the odd-numbered overtones.