Fundamentals of Music Instrument Acoustics

1. Alexis Baskind Fundamentals of Musical Instrument Acoustics Alexis Baskind, https://alexisbaskind.net

2. Alexis Baskind Fundamentals of Music Instrument Acoustics Course series Fundamentals of acoustics for sound engineers and music producers Level undergraduate (Bachelor) Language English Revision January 2020 To cite this course Alexis Baskind, Fundamentals of Music Instrument Acoustics, course material, license: Creative Commons BY-NC-SA. Full interactive version of this course with sound and video material, as well as more courses and material on https://alexisbaskind.net/teaching. Except where otherwise noted, content of this course material is licensed under a Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License. Fundamentals of Music Instrument Acoustics

3. Alexis Baskind Outline 1. General Considerations about instrumental acoustics 2. Woodwinds 3. Brass Instruments 4. Strings 5. Percussions Fundamentals of Music Instrument Acoustics

4. Alexis Baskind Functions of the different parts of a musical instrument Exciter Strings: Finger, pick, bow Winds: air pressure Piano: hammer Percussions: stick, mallets … Oscillator Strings, Piano: string Brass: air column+lips Woodwinds: air column+reed Drums: plate, skin Marimba, Vibraphone: bars … Resonator Strings: body + neck Piano: soundboard, body Winds: tube, bell (and mute) Drums: shell Marimba, Vibraphone: resonators … Sound (radiation) The radiation pattern (=directivity) is a function of the frequency and of the note (key, string) being played Fundamentals of Music Instrument Acoustics

6. Alexis Baskind Woodwinds • A Woodwind instrument is a wind instrument where the sound is produced by interaction between a resonant tube and the vibration of: – The interaction of a column of air and a sharp edge (flute, recorder) – a reed (clarinet, saxophone, oboe, bassoon…) • The source of energy in a woodwind instrument is the player’s breath. Fundamentals of Music Instrument Acoustics

7. Alexis Baskind Woodwinds – Principle of reed instruments Basic model for a reed instrument: • The air pressure makes the reed open • The column of air travel through the pipe (“bore”) back and forth, thus creating a resonance • This resonance forces the reed to vibrate at the corresponding frequency (Source: Julius O. Smith III) Fundamentals of Music Instrument Acoustics

8. Alexis Baskind Woodwinds – Principle of reed instruments Fundamentals of Music Instrument Acoustics

9. Alexis Baskind Woodwinds – Reeds and airjets There are three kinds of rinds for woodwinds: • Clarinets and Saxophones use a single reed • Oboes and bassoons use a double reed: both parts of the reed vibrate • For flutes and recorders, there is no physical reed, but an airjet (interaction between the column of air from the mouth and the sound wave) (Source: Joe Wolfe) Fundamentals of Music Instrument Acoustics

10. Alexis Baskind Woodwinds – Reeds • The reed opens because of the air pressure, and then oscillates • If the pressure increases, the reed closes again from time to time, thus producing higher harmonics Oscillation High pressure = the reed closes during a part of the cycle => clipping Fundamentals of Music Instrument Acoustics

11. Alexis Baskind Woodwinds – Airjets Here are four pictures of a modelized recorder’s mouthpiece: The airjet oscillates at the resonant frequency, and behaves like an actual reed (it’s also called an air reed) The principle is similar for flutes (Source: Claire Ségoufin) Recorders Flutes Fundamentals of Music Instrument Acoustics

12. Alexis Baskind Woodwinds – Clarinet bores • The model for the bore of a clarinet (with all keys closed) is a cylindrical pipe, closed at one end (reed) and open to the other end (bell) (Source: Joe Wolfe) Fundamentals of Music Instrument Acoustics

13. Alexis Baskind Woodwinds – Cylindrical bores (closed) • The model for the bore of a clarinet (with all keys closed) is a cylindrical pipe, closed at one end (reed) and open to the other end (bell) • The wavelength of the lowest note (all keys being closed) equals four times the length of the bore • When the sound wave reaches the open end (the bell), its phase is inverted • The corresponding overtone spectrum has theoretically only odd harmonics (1,3,5,7…) • For the clarinet, in practice, the first even harmonics (2,4,6,8…) are often way softer than the first odd harmonics. This is not true any more for higher overtones Fundamentals of Music Instrument Acoustics

14. Alexis Baskind Example: Overtone Spectrum of a Clarinet • E3 (Fundamental frequency: 162 Hz) played on a B-Clarinet • The first odd harmonics are way louder than the first even harmonics • The spectrum contains a significant amount of air noise • For a given fingering, only notes corresponding to the odd harmonics can be played by overblowing Fundamentals of Music Instrument Acoustics

15. Alexis Baskind Woodwinds – Cylindrical bores (open) • The model for the bore of a flute or a recorder (with all keys closed) is a cylindrical pipe, open at both ends • The wavelength of the lowest note (all keys being closed) equals twice the length of the bore • When the sound wave reaches any open end, its phase is inverted • The corresponding overtone spectrum contains theoretically all harmonics, but in practice, the fundamental is always more powerful than any of the other harmonics (except for higher dynamics) Fundamentals of Music Instrument Acoustics

16. Alexis Baskind Example: Overtone Spectrum of a Flute • Example for a A#4 (Fundamental frequency: 463 Hz) • The fundamental is always louder than the overtones • The spectrum contains a significant amount of air noise • For a given fingering, all notes of the harmonic series can be played by overblowing Fundamentals of Music Instrument Acoustics

17. Alexis Baskind Woodwinds – Conical bores • For saxophones, oboes and bassoons, the bore is a conical pipe, also closed at one end (reed) and open to the other end (bell) • The wavelength of the lowest note (all keys being closed) equals four times the length of the bore • When the sound wave reaches the open end (the bell), its phase is inverted • The corresponding overtone spectrum contains theoretically odd and even harmonics (contrary to the clarinet) • The amount of higher overtones depends on the air pressure and on the stiffness of the reed: the harder the reed, the brighter the sound Fundamentals of Music Instrument Acoustics

18. Alexis Baskind Woodwinds – Modes for different bores • A mode is a simple vibration that produces a single frequency (i.e. a single overtone) • The vibration in cylindrical (open and half-closed) and conical bores can be decomposed into modes, as shown below: Fundamental: F 1st overtone: 2F 2nd overtone: 3F 3rd overtone: 4F Etc… Fundamentals of Music Instrument Acoustics

19. Alexis Baskind Formants Regions for some woodwinds Instrument Formant 1 (Hz) Formant 2 (Hz) Flute 800 Oboe 1400 3000 English Horn 930 2300 B-Clarinet 1500-1700 3700-4300 Bassoon 440-500 1220-1280 • As shown in the course on overtone spectrum, those modes are thus boosted or attenuated in the instrument as a function of its natural resonances: the formants • Most woodwinds, except the flute which has only one strong resonance, may have up to four formants. Here are some examples: Fundamentals of Music Instrument Acoustics

20. Alexis Baskind Example: Overtone Spectrum of a Saxophone Example for a C#4 (Fundamental frequency: 276 Hz) played on an alto saxophone for three dynamics (pp, mf and ff) • The level of the lowest overtones almost does not change with dynamics • The spectrum contains a significant amount of air noise • For a given fingering, all notes of the harmonic series can be played by overblowing Fundamentals of Music Instrument Acoustics

21. Alexis Baskind Woodwinds: role of the keys • The keys aim at opening holes in the bore, thus making it shorter • Example for the soprano saxophone: • Thus theoretically, the sound should radiate only from the first opened hole • In practice for the saxophone, this is only true for the low frequencies. Higher frequencies still propagate until the bell (see later for radiation patterns) All keys closed: lowest note =Ab2 (196 Hz) Fingering for G3 (392 Hz) Fundamentals of Music Instrument Acoustics

22. Alexis Baskind Woodwinds: role of the bell • The bell helps the instrument to radiate into the air • However, this is only strong at high frequencies • Therefore, the bell acts as a high-pass filter. This means that the lowest frequencies are less radiated than high frequencies, which allows the resulting sound to be more similar over the whole range • But it makes the lowest notes more difficult to play • The bell has another role for the clarinet: it shifts the higher harmonics/note down (up to more than a semitone for the higher notes) Fundamentals of Music Instrument Acoustics

23. Alexis Baskind Woodwinds: Radiation Patterns • The sound is radiated from all the opened holes • This means in practice that there is one radiation pattern for each fingering ! • This makes the woodwinds hard to record, as there is no ideal position for a unique microphone: it may sound good for one fingering, but very bad for another one • Most of time, two microphones are used and mixed Fundamentals of Music Instrument Acoustics

24. Alexis Baskind Some Radiation Patterns for a tenor saxophone All holes opened (B2, 246 Hz) Source: Eric Boyer Fundamentals of Music Instrument Acoustics

25. Alexis Baskind Some Radiation Patterns for a tenor saxophone All holes closed (Ab1, 104 Hz) Source: Eric Boyer Fundamentals of Music Instrument Acoustics

26. Alexis Baskind Some Radiation Patterns for a tenor saxophone Half holes closed (F2, 175 Hz) Source: Eric Boyer Fundamentals of Music Instrument Acoustics

27. Alexis Baskind Average Radiation Patterns for Oboe, Bassoon and B-Clarinet Source: J. Meyer Fundamentals of Music Instrument Acoustics

28. Alexis Baskind Radiation Patterns for a B-clarinet with a reflecting floor Source: Jürgen Meyer Fundamentals of Music Instrument Acoustics

29. Alexis Baskind Radiation Patterns for three notes of an oboe Source: J. Meyer Fundamentals of Music Instrument Acoustics

31. Alexis Baskind Brass • A Brass instrument is a wind instrument where the sound is produced by interaction between the vibration of the lips and a resonant tube • The source of energy in a brass instrument is also the player’s breath • Examples of brass instruments: – Trumpet, Trombone, cornet – Horn, Tuba – Cornetto, Serpent – Didgeridoo (!) Fundamentals of Music Instrument Acoustics

32. Alexis Baskind Principle of Brass Instruments • Brass instruments are made of: – The mouthpiece, which is in airtight contact with the lips – The bore – The bell (Source: Joe Wolfe) Fundamentals of Music Instrument Acoustics

33. Alexis Baskind Principle of Brass Instruments (Source: IWK - Music acoustic Vienna / Matthias Bertsch) Fundamentals of Music Instrument Acoustics

34. Alexis Baskind Principle of Brass Instruments • Contrary to woodwinds, most brass instruments do not have holes (exception: keyed brass instruments, such as the cornett or the serpent) • Thus, the variation of the pitch is produced: - By the modification of the tube’s length (slide for the trombone, valves for the trumpet or the horn) - By selecting the overtones (by lip and breath tuning) (Source: Joe Wolfe) Fundamentals of Music Instrument Acoustics

35. Alexis Baskind Bores of brass instruments • The bore may be cylindrical (trumpet, trombone, baritone horn) or conical (alto horn, horn, tuba, cornet, flugelhorn…) • A cylindrical bore has theoretically only modes with odd harmonics (see previous part) • So how can the whole harmonic series can be played ? (Source: Joe Wolfe) Fundamentals of Music Instrument Acoustics

36. Alexis Baskind Role of the bell • The bell shifts the lowest frequencies up: it seems to be the opposite effect than for a clarinet but actually not: the bell is not added to the tube like for a clarinet (thus making it longer) but it replaces a part of the tube (Source: Joe Wolfe) Cylindrical tube, no mouthpiece, no bell Cylindrical tube, no mouthpiece, with bell Fundamentals of Music Instrument Acoustics

37. Alexis Baskind Role of the bell • The mouthpiece limits the rise of the highest frequencies: because of it the shortest wavelength “see” a longer tube • The resulting overtone spectrum is as follows (Source: Joe Wolfe) Cylindrical tube with mouthpiece and bell • It’s almost a complete harmonics series, except the fundamental (the “pedal”), which is not a resonance of the instrument and is very hard to play • The lowest resonance of the instrument is not a member of the series and cannot be played Fundamentals of Music Instrument Acoustics

38. Alexis Baskind Brassiness • The brassiness for louder dynamics is due to two reasons: 1. As for woodwinds, the vibration of the lips differs with level: - At lower volumes, the lips oscillate but cannot close completely - At higher volumes, the lips are closed during a part of the cycle: this non- linear clipping effect creates high frequencies Stroboscopic view of the lips vibrating in a tuba (Source: IWK - Music acoustic Vienna / Matthias Bertsch) Fundamentals of Music Instrument Acoustics

39. Alexis Baskind Brassiness • The brassiness for louder dynamics is due to two reasons: 2. The sound pressure may be so high inside the instrument that it creates a small shock wave: the air cannot be considered as linear anymore, and part of the power is transferred from low frequencies to high frequencies Example: crescendo with bass trombone 10 Hz 100 Hz 1 kHz 10 kHz 0 dB -60 dB -120 dB frequency (log scale) level Fundamentals of Music Instrument Acoustics

40. Alexis Baskind < 450 Hz (omnidirectional) • Low frequencies radiate in all directions 650 Hz Radiation pattern of a trombone Example: angular width of the regions of main radiation (between -3 dB and 0 dB relative to the maximum level in the band) for a trombone for various frequency zones 500 Hz 1 kHz Between 2 and 5 kHz Between 7 and 10 kHz (highly directional) • Except for the 650 Hz zone (the first formant), directivity increases with frequency Fundamentals of Music Instrument Acoustics

41. Alexis Baskind Radiation pattern of a trumpet The trumpet has a similar radiation pattern than the trombone, but shifted up in frequency: the limit for omnidirectional radiation is around 500 Hz (source: J. Meyer) Fundamentals of Music Instrument Acoustics

42. Alexis Baskind Radiation pattern: trumpet 10 Hz 100 Hz 1 kHz 10 kHz 0 dB -60 dB -120 dB frequency (log scale) level Example: trumpet miked with a TLM-103: 1 – on-axis Fundamentals of Music Instrument Acoustics

43. Alexis Baskind Radiation pattern: trumpet Example: trumpet miked with a TLM-103: 2 – 90° off-axis 10 Hz 100 Hz 1 kHz 10 kHz 0 dB -60 dB -120 dB frequency (log scale) level Fundamentals of Music Instrument Acoustics

44. Alexis Baskind Radiation pattern: horn Fundamentals of Music Instrument Acoustics

46. Alexis Baskind Strings The string instruments can be divided in three main categories, depending of the main playing technique for each of them: • Plucked strings: guitar, harp, hapsichord, banjo, sitar, oud… => the string is plucked with a plectrum or a finger • Bowed strings: violin, viola, cello, double bass… • Struck strings: piano, clavichord, cimbalum, berimbau… => The string is struck with a hammer => Of course this classification is not perfect: a guitar can be bowed, a double bass is often plucked, a piano can be plucked as well… Fundamentals of Music Instrument Acoustics

47. Alexis Baskind Principle of string instruments • Below is a very basic model for most string instruments: • The vibration of the string is transmitted to the soundboard through its attachments (bridge, nut or capo bar) • Therefore, the soundboard vibrates as well • The cavity inside the body resonates at certain frequencies and amplify them Body = resonator string soundboard bridgeNut (violin, guitar) or capo bar (piano) Fundamentals of Music Instrument Acoustics

48. Alexis Baskind Vibration of a string • The basic model for a string vibration is the standing wave • Careful: this standing wave is not of the same type as the sound standing wave between two walls (course on “Interactions”): – in the case of the string, the movement of the string is forced to zero on both sides – In the case of two walls, the amplitude of the sound pressure on both walls is not necessarily zero (but the velocity is zero) Fundamentals of Music Instrument Acoustics

49. Alexis Baskind Vibration of a string • All oscillations for which the wavelength is a multiple of twice the length of the string are possible standing waves: 1st harmonics 2nd harmonics 3rd harmonics 4th harmonics Etc… Fundamentals of Music Instrument Acoustics

50. Alexis Baskind Vibration of a string • The standing wave only describes one single frequency = one mode. The actual vibration of a string is more complex: Example: vibration of double bass strings shown in slow motion Fundamentals of Music Instrument Acoustics

51. Alexis Baskind Vibration of a string Basic vibration pattern for a plucked string Example: oscillation of a rope (similar to a string but at lower frequencies) shown in slow motion Fundamentals of Music Instrument Acoustics

52. Alexis Baskind Vibration of a string Basic vibration pattern for a bowed string Example: oscillation of bowed string for a violin, shown in slow motion Fundamentals of Music Instrument Acoustics

53. Alexis Baskind Vibration of a string • The vibration of a string is the superimposition of sinusoidal modes which frequencies form the complete harmonic series frequency (linear scale) level F 2F 3F 4F • The fundamental frequency “F” depends on the length, the diameter and the tension of the string • Each mode corresponds to one overtone Fundamentals of Music Instrument Acoustics

54. Alexis Baskind The whole body also has vibration modes example: some measured vibration modes (exaggerated) for the body of a guitar Mode 1: “bending” mode (≈60 Hz) Source: Dan Russell (the red plate represents the motion of air in the soundhole) Fundamentals of Music Instrument Acoustics

55. Alexis Baskind The whole body also has vibration modes example: some measured vibration modes (exaggerated) for the body of a guitar Mode 2: “breathing” mode (≈100 Hz), synchronized with the Helmoltz resonance (see later) Source: Dan Russell (the red plate represents the motion of air in the soundhole) Fundamentals of Music Instrument Acoustics

56. Alexis Baskind The whole body also has vibration modes example: some measured vibration modes (exaggerated) for the body of a guitar Mode 3 (≈190Hz) Mode 4 (≈200Hz) Mode 5 (≈220Hz) Mode 6 (≈230Hz) Mode 7 (≈260Hz) Mode 8 (≈315Hz) Mode 9 (≈380Hz) Mode 10 (≈480Hz) Mode 11 (≈750Hz) Source: Dan Russell Fundamentals of Music Instrument Acoustics

57. Alexis Baskind The whole body also has vibration modes • The geometry of the body is carefully designed to fine- tune the modes in amplitude and frequency • For instances, guitar top plates (as well as soundboards on piano) have braces on the back Source: Neville H. Fletcher, Thomas D. Rossing, The Physics of Musical Instruments Fundamentals of Music Instrument Acoustics

58. Alexis Baskind The whole body also has vibration modes frequency (linear) level • Those vibrations entail resonances (= formants) in the overtone spectrum which are characteristic of the instrument • The formants are independent of the pitch example: some measured vibration modes (exaggerated) of the top and back of a violin 457 Hz 545 Hz 723 Hz 850 Hz Fundamentals of Music Instrument Acoustics

59. Alexis Baskind First vibration modes for the soundboard of a piano Fundamentals of Music Instrument Acoustics

60. Alexis Baskind The Role of the Soundholes • The soundholes (in guitar, violins…) aim at creating a Helmholtz Resonance to amplify the low range of the instrument Guitar: the Helmholtz resonance of the soundhole is around 100 Hz (between G3 and G#3), slightly below the open note of the second last string Violin: the Helmholtz resonance of the f- holes is around 300 Hz (D3), corresponding to the open note of the second last string Fundamentals of Music Instrument Acoustics

61. Alexis Baskind Radiation Pattern of a guitar Source: Neville H. Fletcher, Thomas D. Rossing, The Physics of Musical Instruments • The radiation is omnidirectional at low frequencies, but this is more complex at higher frequencies Fundamentals of Music Instrument Acoustics

62. Alexis Baskind Radiation Pattern of a guitar Source: Rolf Bader Fundamentals of Music Instrument Acoustics

63. Alexis Baskind Radiation Pattern of a grand piano – vertical plane Source: Jürgen Meyer Note: this is a far- field radiation pattern: it does not apply to near- field Fundamentals of Music Instrument Acoustics

64. Alexis Baskind Radiation Pattern of a grand piano – horizontal plane Source: Jürgen Meyer Note: this is a far- field radiation pattern: it does not apply to near- field From outside to inside: - 1000 Hz - 2000 Hz - 4000 Hz - 8000 Hz (the keyboard is below) Lid open Lid closed Lid removed Fundamentals of Music Instrument Acoustics

65. Alexis Baskind Radiation Pattern of a violin – vertical plane Source: Jürgen Meyer Fundamentals of Music Instrument Acoustics

66. Alexis Baskind Radiation Pattern of a violin – horizontal plane Source: Jürgen Meyer Fundamentals of Music Instrument Acoustics

68. Alexis Baskind Percussions • Percussion Instruments are a very wide family • The main vibrating elements used in western drums are: – Membranes (i.e. heads): toms, snare drum, bass drum, djembe, tabla… => The vibration of the membrane is emphasized by a resonator – Plates: cymbals for example Cymbals are in the family of idiophones, which are instruments that produce sound through their entire body – Other idiophones: bells, marimbas/xylophones, vibraphones, triangles, gongs… – Tubes: tubular bell for example Fundamentals of Music Instrument Acoustics

69. Alexis Baskind Percussions • Most percussions have an inharmonic overtone spectrum • However, some percussion instruments may have a definite pitch, if the spectrum is quasi harmonic, or if the strongest tonal component is way louder than the others – Some percussion instruments with a definite pitch: Marimba, vibraphone, glockenspiel, crotale, tubular bells, gong… – Some percussion instruments without a definite pitch: Cymbals, tamtam • Officially, bass drums, toms and snare are considered as unpitched instruments. However a more or less clear pitch can be obtained by tuning the head Fundamentals of Music Instrument Acoustics

70. Alexis Baskind Vibration of a cymbal Example: vibration of a cymbal hit with a stick, shown in slow motion Fundamentals of Music Instrument Acoustics

71. Alexis Baskind Modes of a circular membrane (similar to cymbals) • The vibration of the head/cymbal is the superimposition of modes which frequencies are not in harmonic series frequency level • Here again, each mode corresponds to one overtone Fundamentals of Music Instrument Acoustics

72. Alexis Baskind Vibration of a snare drum Example: vibration of a snare drum hit with a stick, recorded in high-speed (3000fps) and shown in slow motion Fundamentals of Music Instrument Acoustics

73. Alexis Baskind Radiation of a snare drum Because of the coupling between both heads, the radiation patterns for a snare drum are more complicated than in the case of a single head (source: Thomas D. Rossing) Fundamentals of Music Instrument Acoustics

74. Alexis Baskind Radiation of a snare drum 182 Hz 330 Hz 278 Hz 341 Hz Side view Because of the coupling between both heads, the radiation patterns for a snare drum are more complicated than in the case of a single head (source: Thomas D. Rossing) Fundamentals of Music Instrument Acoustics

75. Alexis Baskind Radiation of a snare drum 278 Hz 341 Hz Top view Fundamentals of Music Instrument Acoustics

76. Alexis Baskind Conclusion • Understanding the basic mechanical and acoustical principles of the instruments is of major importance to be able to record them • Remember that two different instruments will never sound the same ! The figures given in this course are just given as examples. One has to adapt to each situation, there is no one golden rule to obtain the best sound of a given instrument • The overall sound results from a complex interaction between the instrument and the room, as a function of the radiation pattern => The acoustical quality of the room, as well as the position of the instrument, plays a fundamental role in the resulting sound Fundamentals of Music Instrument Acoustics

77. Alexis Baskind To go further… Neville H. Fletcher, Thomas D. Rossing, The Physics of Musical Instruments, Springer-Verlag Jürgen Meyer, Akustik und musikalische Aufführungspraxis - Leitfaden für Akustiker, Tonmeister, Musiker, Instrumentenbauer und Architekten, PPV Medien GmbH Fundamentals of Music Instrument Acoustics

Fundamentals of Music Instrument Acoustics

You are reading a preview.

Check these out next

Fundamentals of Music Instrument Acoustics

More Related Content

Slideshows for you (20)

Similar to Fundamentals of Music Instrument Acoustics (20)

Recently uploaded (20)

Fundamentals of Music Instrument Acoustics