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0 100 200 300 400 500 600 700 800 90010

Trombone Impedance

Frequency (Hz)

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17.8mm

37.8mm

25.3mm

22.3mm

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0 100 200 300 400 500 600 700 800 900 10000

Frequency (Hz)

Transparent MouthpieceDenis Wick 6BS Mouthpiece

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0 100 200 300 400 500 600 700 800 900 10000

Frequency (Hz)

Trombone with transparent mouthpiece and adapter pieceTrombone with Denis Wick 6BS mouthpiece and no adapter

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ARTIFICIAL

TROMBONE

PHOTODIODE

LOUDSPEAKER

WATER TUBES

MICROPHONES

MIRROR

MANOMETER

LENSES

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0 200 400 600 800 1000 1200 1400 1600 1800 20000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

−pi/2

Frequency (Hz)

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Side View

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0 ./1023%(' 02 '

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10−4

10−3

10−2

Frequency Response of the Artificial Lips

50 100 150 200 250 300 350 400 450−180

Frequency (Hz)

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Trombone

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0 ./1023%(' 0

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0 ./1023%(' 02 '

0 200 400 600 800 10000

Frequency (Hz)

Trombone with 6BS Mouthpiece

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0 ./1023%(' 0

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Optical Rail

Mirror

Photodiode

PolarisingFilter

Oscilloscope1/4" Microphone

Loudspeaker

Audio Amplifier

Trombone

Manometer

Probe Microphone

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0 ./1023%(' 02 '

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0 10 20 30 40 50150

Slide Extension (cm)

Experimental Threshold Playing Frequencies

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Sound Desk

Optical Rail

Mirror

Photodiode

PolarisingFilter

Oscilloscope

Probe MicrophoneTrombone

Microphone

Water outlet

PumpAir

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300 300 800 800

Volume (ml)

1st Partial2nd Partial3rd Partial4th Partial5th Partial6th Partial

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0 ./1023%(' 02 ' 02' ''%

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300 320 340 360 380 400 420 4401500

Cavity Volume (ml)

High NoteLow Note

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300 320 340 360 380 400 420 440 460 48084

Cavity Volume(ml)

Playing Frequency as a function of cavity volumePlaying Frequency as a function of blowing pressure

low medium high Blowing Pressure

' !# % 02

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0 5 10 150

4Data Set 2

0 5 100

4Data Set 3

0 5 100

8Data Set 4

0 5 10 150

15Data Set 6

0 5 100

15Data Set 5

Time (ms)

Opening AreaOpening Height

Thresh. Thresh. 177Hz 268Hz 177Hz

Max. Max. 262Hz 173Hz

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10−0.9

Height (mm)

10−0.3

10−0.6

Data Set 2 Data Set 3 Data Set 4

Data Set 5 Data Set 6

Thresh. Thresh. Med.

Max. Max.

177Hz 177Hz 268Hz

262Hz 173Hz

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0 0.5 10

z (mm)

Data Sets 9 & 10

0 0.5 10

z (mm)

Data Sets 11 & 12

Amp. = Max

Freq = 167Hz

Amp. = Threshold

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0 5 10 15−1

−0.5

Time (ms)

Data Set 9

0 5 10 15−1

−0.5

1Data Set 8

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PhotodiodeArtificial Mouth

Transparent Mouthpiece

Optical Rail

4938 1/4" Microphone4192 Probe Microphone

Polarising Filter

OFV−3001 Controller

Computer

Vibrometer Position 3

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0 100 200 300 400 500 600 700 800

−pi/2

Frequency (Hz)

DiodePosition 1Position 2Position 3Playing Frequency

122 145

173 334

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0 10 20 30 40 50150

Slide Extension (cm)

Threshold Playing Frequencies

(c)(b)

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& *$ 87 : !# "L!(# ,(

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1110

Length (m)

Two Mass ModelInstrument Resonance Outward Lip Resonance Inward Lip Resonance Inward One−Mass Model Outward One−Mass Model

K$! / !E 8M *I!#(#L!A "$!"K!#(( 9( "$!";!(" .0 ( . L!(# I& *$'!7>","*;LF "$!"%;!"( .0 " (N4,"!#) :"!)I!" ,(!7>","* A ! ,( G80)( "$!"N2G!#(( .0 "6 .M*I,"!#" :"!

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,&,&,,&,&,,&,&,,&,&,,&,&,-&-&--&-&--&-&--&-&--&-&-

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K$! 1/C .0 (<E:, !$ &&!#&! =& ! (!C,O,"E .0 "6, 87 &( 9H!"&!"">F 8! #%& *(!##.D&

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67#98! % ! 82 %42: 8 - % %52:3 "! ! 8 %4"2 ;?/ 1!$! %5+3 2

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$ # $ ': 2 ;" % 1!= 2 8 ! " 82 8 !$" 8/ ' % ;?"!# " 8 342>2 + 8 )J 2 8 3 # 3 82 %52: 2 =$1! !$# % " N/ ! % ; # 3 8/ %42 8! $# 2 L 1! % " %52 2 $'.8 % ! 82 8?! " !

8 / ' 89/,$1!$# 3 ! % % 8 3>%4.) 1!# % '.8/ %42 ! 2 / % ;# 3 ! $1!$ 2: ! 2 /% ! 3 8 1; %4 8

% $ %42 ! 2 ;?8!$! < 8 ;?8!$! @ 1!$ %5) 2> # $1! # 3 !! 2 8<@

98 % 2 12 # 3 ! % ; 3 @98 ; 2:% 2 ! "%4343 82 2 ! & 8;? 35- 2 1! 2: 8 , 8)7! % !% ! ! 2 %4 '# 98 ! + (98 )>%42 #/ 2 "! "! 2: 8 "! ! 2 ! 13 8 35-82/1 8 + 2 %5 8 @ 8 2 # 8 @ !# % ) %5 ' 98 8 1 % !# % !8!$! 2 1% 8/ % 9=; 2 %52: ! 2 /1! ,;?8! !$1!

50 100 150 200 250 300 350 400 4500

50 100 150 200 250 300 350 400 450

Frequency (Hz)

mass 1mass 2

% ':# % ;# 3 !$ $1! 2: !$ %4 "6>#/ - 2 ;?8 %42 % ! 3 8 ";? 2 %4/%5)>%4 #8 3 2:%5 ;?8! !$1! 2 34% ; 2 3 $ ! ! 8 2 I 0212 # 3 2:%5 ;?8! !$1!! 0 %5+% !H 02 $1! 2: 8 1! 982 8 8 3 ! 2 + ! " % !@98//1 8$ 13 18 3*- %5 8 8 2 # 8 !# % ) %4 ' 98 8 " % !# % ! $1! %5 1!$ "! 2: !$ # ) 1!

% !, "! 2: !$ #/ ) % !,!# %4343 8= 1; 2 ) 2 ; 2 !$ 2:+ ! 1 ) ! 1 % ;? 8 3535- !$1 ':#$5< ! 1 % ;? 8 3 $1! 2: !$ # ) 1! !# 2 8 8 ; 2 12 ; 3 ! !# # #$ % ##1 8)7!8 + 2) + 342 8 + " =; 8 %4 $1! 2 8 1!

2 ) " / ! " % ;? 8 3 /% 67#=#! 2 2:+ 8 %4 8/ 8 ! 2 %5 ':#$*< % % ! " 182 " 8! ':#/ 2 $ " 8! 1! % ' 2 ; 8 ! #$/ 8 8 2 2 %4 ' + " 1 / 35% ! 8 2 @ %4/%5)>%4 #8 3 % ! 3 8 ";? ! 2 2:%4 0; 8!$! "! %4 35% 2: !$167# 35- 8 % $ 12 ;98 % ! 2: + " 1 02 82 8! ! % ! 2 8 2 % 82 ! 8 % ! ! % ; # 3 82 "! 2: ! # ) "2 # 35 + "2 ;98

10−4

10−3

10−2

Frequency Response of the Artificial Lips

50 100 150 200 250 300 350 400 450−180

Frequency (Hz)

% ':# $167# "- "! 2: !$ 2 81 - % 8 3 12: ':# 8/ %42 ) 1 % 8 3 34%5 1!! 2 "!# 8 +%435% ! %5 ' 2 # 8 8 / %4 8 ! % ) %4 ' 1! 2: 8 1! 8/ < 8 @7@ "! %5) 3*- % ! '# % ! 8 " 182 2 ':#$ 5< 2 ! 1 % ;? 8 3 ; 8!$# ";? ! 2 2:%5 /% ! 3 8 1; ! 2 8 % 1% 8 3 ; 2 # 2 / ! 1 % ;? 8 3 ; 8 ! #$1; ! 2 =8$ 8 2 2 /%4 ' "2 # 34 + "2 ;?8 2 /167# %*) 8 3 # %42: %4 =! % ; # 3 82 %42: 82 8

2 ;98 % ! 2: 2 ! " % ;? 8 343*- 2:+ 8 %4 2:%5 % ! 3 8 ";? ! % ! 3 1! !?8 #/ 82 2 3 2 % 67#"! "2 ;# 8/ %42 8 3 ; 2> 3 % ! 8 % ' 3*- ! % ; 34% " "! 82 %52: 2 - ! % 8 3 ! - ! 1; 2 ; 8 %5 ! % ; 34% 82 %42: ! % ! 1 "! 82 %52: 2 / 34% /! % 8$ 8 % ! %4+ # ! - ! "; 8 ! 8 98 % 2 2%4 ;?8! !$1! % !,;?8 1! % $ "2 ;?8 % ! 2: ! + " 1 % ! 3 8 ";? 2 /1! ! - ; + 2:35% % % 1! % R $ 8 3 - ! % 8 3 ! - !# 1; % # 3 2 ) 1 ! " % ;? ! " 2 $;? #! %4 'I 3 8! " 2 3 1 )>%4+ 2 ;? " / 1!$ %5 ! %42: 2 )>%4 8 2 ! ! %5+3 ! 2 # 2 82 8 2 "! 12 ;?98 % ! 2: ! % ! %5343 + /% ! #! !$ 3 82 1 %5 % ! ! %42:

8 ; %5%4 '% "2 ;?/# 82 %42: 8 3 ; 2> 3 2 G 8 2 % 82 8 18 2 2 %5 ' # %52: % !(8 ; # ! % ; 3 " 12 ;?98 % ! 2: 2 ;?8 ,2 16 2/2 % ! 8$ 8 2 2 %4 ' # %52: 1 ! 2 + 9 2 K 2: "': " 2 1 2 ; ; 2> 3 #! ?%5 ! %52: *<,8$ 8 2 2 %5 ' 8 !8 ! ! #/;? 2 + $ 8 ':# 3 8 % 8 %4 8 8 ) 8 % 8 +3 ) % ' % 1 ! 2:3 35- 2: / % !$ 3 8 1; 2 / ; 8!$! ! 8 ;? 8!$! #; %42: ! 8 #!$ 1$ ! ".982)3 % ' 2 352: ':" 1 / ! 2:/ % ! 3 8 ";? 2 8,! %4 ' 3 ; 8!$! + # 821 2: % !$ 3 8 1; 2 + 2 ?; 8 ! ! "!%4 ; 2> 3 8 8 8 2 2 %5 ' % ! " 8 2: % ! 3 8 ";? 2 % ) 1=; 8 ! ! % ! 342 "=824 % ;? 2 ;?18! #$1; % ! 8 + 1! %5+ +7-! 8 ->%4 '

@ ; %5

" % !% %5 2 34% 2 /%4 ' 8 ; %4 % !F 3 1!$! " ; %4 % ; #; 2 / % ! 3 8 ";? ! 8 / % '# !# 2 !/ "! 2: !$ 2 % ! # %52: %4 $167# "- 2 ;?8 %5

1!$ 2 ! 13 18 3*- !# 2 ! 8 ; 2 12 ; 3 ! ! $# # .98 /$1!$ 2: ! 1! 2 / % ! 3 8 ";? ! 2 2:%5 ?;?8! !$1! $1!$ 2 02 187! 8 + 2) / "! 2: 8 $167# 1% 1! 2 ;?8!$! 1! % ! ! % ; %53 8A 2 2 ! ! " %4 ! 1 % ; 8 3 "! 2: !$ ;?18! #$1; ':#$ *< "! 87! 8 + ! 3 8 %4 +.- "2: ! %4 " %4 '/ + "98 )>%42 # 2 35% ?; 2> 3 % %5 1 8 2 # 1 2:%5 ; 8 ! ! "! 8 2 ! "%4353 82 %4 '2 # 2 8! ! %5 ')/ ! % ;? 3 8!$ 2 ! %4 #! 2%4 8 3 ; 2 %52: 8 ! 8 /8;? 3 % I/ 2:%4 ;?8!$! 1! 2 ! 1%5343 82 %5 ' 8/ / ! 8; "67# - 8 8 % 8 ! 2 #0 2 98 ! %

50 100 150 200 250 300 350 400 450 5000

Inner MassOuter MassArea

50 100 150 200 250 300 350 400 450 500−200

−150

−100

% ':# 1!$ 2: ! 2 8 18 2 2 /%4 ' # %42: 2 35% ; 2> 3 ' 1 34%5 8 +3 # 35%4 "! ! 2 "! 2: !$ 2 % !$ 3 8 1; 2 4 02 2:%4 0; 8!$! "! ! " ':#/ % '" 02 187! 2 ; / 9 '1 / %4 2 /2: 34%5 8 / % '> # %52: 342 " 02 "! 2: 8 "! 2 $; 8 98 % 2 2 # 8 8 %4 8 !# % %5 ' "! 2: 8 "!2: 8 /2 " P % ' # %42: %4353 89 2 $; 2 8 % 8 ) ':#$*< % 8 # 8; 8 3 1 %52 % % !8 3 82 2 / %4%*)>%4 #98 3 ! %4 #! 2%4 8 3; 2 %52: !

98 ! 2 8 18 2 2 %4 ' # %42: !# 2 !C982KA 02 ; 8 %5 $1! 2 8 1! 2 $; 8 2 # 8 !# % %4 ' 8 %5 8 ! % %4 ' 98 % 8!,! " %4 ! 1 % ; 8 3!# # % 1! < < 7#!/ )>%4 % ! ! 2: '398/ 8$ 8 2 2 %5 ' # %42:?%4 ; 2> 3 #/! /1 + "98 ) "! %4 8 ! % ; %53 8 8! %52: 2 8 8 !

0 200 400 600 800 1000

−pi/2

Frequency (Hz)

0 200 400 600 800 100010

Frequency (Hz)

0 200 400 600 800 1000 1200 1400−1

Sample Number

% ':# 5< 22 # 2 98! ! %5 8 ) "! +3 #8 / $ 35%4 "! 8$0!$# 1 2 !$ /?$1! # 3 %5 ' 8 ) 2 ; +3 8 35%4 98! % H/ $167# "- 2 2 % ' %4 8 3 ! %4 8 ) 1!2 2 %5 ' ;?18! #$ ! 1 % ;? 8 3535-

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% !$ 8! 2: 8 +/3 2 12 ;98$ /% ! 3 8 1; ! 2 2:%5 ;?8! !$1! 8 3 # 3 82 <

0 100 200 300 400 500 600 700 800R

0 100 200 300 400 500 600 700 800

−pi/2

Frequency (Hz)

DiodePosition 1Position 2Position 3Playing Frequency

122 145

173 334

% ':# 5<< 1! 2: !$ 2 2 %5 ' 8$ 8 %52 ! % ' 8 3 8 / 2:%5 % !$ 3 8 ; ! , ) "# % 8 3 34%4 ! 2 !%$1! 2:34 3 8 ->%4 ' $167# "- @ /) "# % 8 3 +3 8 35%4 "! !# 2 "! 2: 8 "! %4 % %4 2 %4 ' 8 18 1!$ 2 ! - 1! 2: 8 1! 8 5 2 # 8 !# % %5 ' 1! 2: 8 1! 82 .@ <@:@ 8 < 8 / %4 8 ! % %4 ' 1! 2: 8 82 @ < % ! '# % ! 8 $1 82 2 ':#/ *< %4 ! % ; # 3 82 %42: ! % / ;?18! #$ % ! 3 8 ";? ! 2 2:%5 ! 2: 34% !$# 8 ; 8!$# % /

98# % # 3 8 ; 8!$# ";? !I 8 %4 2 ! % %42: @

' 1 35%4 8 + ?8/ 2 % ;?82 8 ! 8 ;?18! #/ 1; 2 % !$ 3 8 1; %4 /) "# % 8 3/% %42: 2 2: 2 34% 167# %*) 8 3 2 2: 2:%5 =;?8!$! %5/ ; 2 3 $ 35%4 %5 '# ! % ; %53 8 % - + " % ! # ) 8 82 2:+ 8 %4 2 2:%4 ;?8!$! % ! 67# % !# % %4 ' 8 # % # 3 8 3*- "! 2 02 ;?8 %5 "! 2: 8 "! 82 < 8 @ >< % 2 # 8 ! % %4 ' 98! @ 8 % 8 ! %4 ! " % ;? 8 3 #/ ) ;?82 "! % H/! % ; # 3 82 82 8 8 % %52:

/ 3 8 2 8 .- ! % ' % 8 1!$ 2 ! 8 + 2 ) F;?8 %5 $1!$ 2: ! 1! %4 ! 1 % ; 8 3)>%4+ 2 ;" " 8/ 8 !$#':':"!# !J982J1!$ "! 2: 8 "! ! " %4 /%42> ! % ' 8 3 /+3 # 34%4 %4 ':#$ 5<< 8 %4/ 1 2 34%5 8 2 ; 8 1!$# 3 %4 ' 2 ; /8$ 8 2 2 /%4 ' # %42 2 # # 82 3*- / - ! % 8 3 "2: !# 8 %5 ! 2 02 %5 ' % 8 % 1% 8 3 ; 2 # ;?18 82 % 8! /2 2 !$! %4+/3 2 ; 8!$# ) "# % 8 3% ! 3 8 ";? 2 %4 1 98 2 34% ! #/ 8 % 02 # 35 12 $ 1!$ 2 2; 2 %52: 2 ; 8!$! < %4 % %52:

342 "6>#/ - 34% 1! 2: 8 1! !$1 %4 ! 1 % ; 8 3535-2:+ !$1 ) 8 18 2 2 %5 ' $1! 2: !$ '# 5< 8$ 8 3 ! 2 $1!$ %4 )>%4+ 2 ;" 1 ; 8 ! #$1; ! %5 ':#/ *<:< / % / 1!$ %5 ; 8 ! #$1; ! 2 % ! 3 8 ";? %4 % $ %422 35% 8 3 2 ! % %52: !,< 8 ! 2 +.- ; 8' 8 8 - 34352 35%4 "! %5 ':#/ 5<:< !$#':':"!# ! 982 "! $1! 2: 8 1! 8$! 2:3 35- $ 3 8/ 2 ; 2 %42:2 /34% %5 % ! /% %42: % ! 02 # 35 + 167# %*) 8 3 2 % ! 3 8 ";? %4 % $ %42%4 ; 2 3 "! 8 + 2) 2 ) 1 "! $1! 2 8 1! 2 2 8 8 %4 ':#$ + 8#!$ =; 2> 3 8 !/ 2 %5+% 2 ; ; 2)>%5 ' 1 35- %4 % ! % $ %42

% '# ?!# 2 ! / % ; 2 ;?8 %4 8 ) 2 $;?! 2 8 18 2 34% 2 /%4 ' 2 8 #; + 1 2 % " 2 "! $ "2 #! %4 ' I % ' ! 1 8;1 8 1!$ 8 ) 2 $;?!J8 ) 82 # "! /1 1 ) 352"% - ! # 3*- 98 '1! % ! 8 + " 2> # / 352 2 %5 ' 82 $! % %4 ' + (98 )>%42 #/ 2 / 35% ; 2> 3 1$/ 8 ) 2 ; 2 =8 18 2 2 %4 ' 8 + !$1 2 0 %4+% % ! 12: %4 # % % "! 1$/ % !$ 3 8 1; 2 2: ; 8!$! + "2 ;?"! 342 1 98 2 " % ! % ! ! 2 %5

':#/ *<@

1300 1320 1340 1360 1380 14001.5

Sample Number

2 ) % ':# *<@ /%4 ' 8 8 8 ) 2 ; / 2> # +7-

2 #! ; 2 3 /% ! 12 %4 # % % "! 2 # " - % !$ 3 8 1; 2 2: ; 8 ! ! + 12 ;1! 3 "! !98 /2 1

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2 1 2 %5.) 1! % '.82 ")"! ? 1! 2: 8 1! 1$ #/ 2 ; 2 %42 %5/ % %52: ; 2> 3 8 ! 8 80 2 8 35342 2 ,; 2 %42 %4 % ! % ;? ! %52: ,; 2 !# 127) % 8 - 2 /2:%4 '@ % ! 8!L 2 98 ':/ "2 2 %4 82 ! - ! "; 282 !# 2 %4 ':# *< % #! %4 ') "2 2 %4 82 "! 8 2 "! %4+ / ! - !# 1; % ! %4.):235) 8 % %42 2 "2: 23 98 8;" " ! 8 % " "! @ %*) !$ %5 ' 12 !# 8 ! 8 8; %4 ' 8 2 ! 2

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air flow

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6>#82 %52: ! H 2 8 8 2 8 3 # 3 82 % !$ 3 8 1; %5 "% # 3 8 "2 2 %4 8/ 1! 2 18 2:%4 ; 8!$! % #! %5 ' 8 %4 ! 8 2 8 8 ' %5) " ,167#98/ %42 2 ; 2 %52: 2 % ! ' %5) +7-

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100 200 300 400 500 600 700 800 900 10000

100 200 300 400 500 600 700 800 900 1000

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2 ! 8 ;? 3 1! 8 ) " 8' %5 ' 8 ! /2: #! %4 '3/ $! 2: % 8 3 8 ) 1 8' %4 ' ;" 2> 2)>%5 +.- ! 2 8$ % ! 8 ;? 3 1! 2) 1 3 8 %4 ' +.- % !;" 2 % '> "2: %5+ # %42: 2 8 ! 8 ;? 3 5 2 8 !3 8 ) 1 8': +7- 8

! 2: % 8 3535- 8 - %5 ' # ) % ,8A % ;? 12: ! 8 167#98 3 2 #; + 1 2 8 ) " 8':"! 8 ; # 3 % 34% +.- 5 % ; + " 1 ! 8 ;? 3 % '':1$! @ 2 8 2 ) " 3 8

5< % ! ;?18 ?98/8 %*)>%4 '! % ' 8 3 /1 A $167# "- "2 ;? 2: ! 1 !$ 18

2 # 2 ) 1 8 342: '. % ; 02 # 35 2 + 8 2 % 82 / #! %4 ' 8 167# "- ! 1" % ! ; 8 !982I ! % ' 8 33 '2 ; #/!# + !# 2 # 2 #' 82I ! 2: % 8 3 % '> %4 ' 12 1% + 1352 ! = 2 # % - 2 G/ 2:3 3 ' 2 ! 11 2 ) 1 ! %5 5 8 ) " 8' %5 ' 8 3 ' 2 % ; % ! 8 35% 2 + 2 " ! % ' 8 3 8 / "! 2: !$ ! % ' 8 3 "67#98 343*- "! # 3 %5 ' 127)2:3 #0 %42 % !# 8 +.- % ! 8 ) 1 8' %5 ';" 2 ! 1 %5 ; 8 % "!# 8/ %42?2 $ # + 8 >' 2 # / 2:% !$ 2: " 2342>2 82E %4/%5)>%4 #8 3 2 2: 2 /1! =! % ' 8 3 ! 2 #' /=8 ) 1 8' %4 ';" 2>2 1! 1 2 + "2: ! %4 " 2 8?! 8 ;? 3 " %52 2 <,! 12:/ 8 8 ) 1 8' %4 ' 2 ) "@ ! 8 ;? 3 1! 8 @ ! 12:/ ! 1% 82 %42: ! % ' 8 3 %5343 98 ) 8 )>% 8/ %42 2 2 ; ! 8 2 9% ! < ?!$ 12 ! % ' 8 3 02 # 35 98 ) 8 < ) % 82 %52: % ! #; + " 8 + # +.- %413 # %4 ' ; 2 8 ) 1 8 ':1! %4 ! %4 8 ! %4 'P?! 8; 3 1 %42> 2 18! %5 'H=! "% 8/ %42 ! % ' 8 3& #/ 82 %42:

0 200 400 600 800 10000

Frequency (Hz)

Trombone with 6BS Mouthpiece

0 200 400 600 800 10000

Frequency (Hz)

Trombone with Transparent Mouthpiece

0 200 400 600 800 10000

Frequency (Hz)

Trombone with 6BS Mouthpiece and Adapter

0 200 400 600 800 10000

Frequency (Hz)

Trombone with Transparent Mouthpiece and Adapter

% ':# *< /# % ; 8 ; 8!$# ";? ! 2 2 ; + 2: % ) 8 %42 #!; 2 #/ % 12 ':# 82 %52: !

2: ':# 8/ %42 1! % %42: 2 ; + 2: % /% ! % ; 2 #0 % 2 ; + 2: % /% ! % ; 2 #0 % =8 8 8 1 % 2 ; + 2: % 3 8 !$98 ; 2 # % 2 ; + 2: % 3 8 !$98 ; 2 # % =8 / 8 8 " %

8 +3 *< "! % %42: 2 ) 8 %42 #! "2: ':#/ 82 %42: ! 2 2 ; + 2: 8 ; 2 # % "! 2: '# 82 %42: 9 167# "- ; 8 #98 35% - 8 2 2 @ << <

2 < @ 2 @ @ 2 .@

2 @ < K <@ 2 < /< < 2 @< @ K @>< 2 @ K /< .@

2 @ < K < 2 < < 2 @ @ 2 @ K

2 @ < < 2 < < < 2 @ @ 2 @ @ @

8 +3 @ ; 8 82 8 2 E ) 8 %42 #!E 2 ; + 2 "2: '# 82 %42: ! 8 343 % 8 # / ! 34%5 2 #0 % 9 "67# - ; 8 #98 34% - 8 2 8 !$98$ K.@ 8 !$98$ % 8 " < % 8 " .@ /< K.@ 8 +3 ;? 8 8/ 8 2 ?/L 02 ; 2 # % "! #! + 2 % 8 % 2 #0/ 8 8 1 %

0 200 400 600 800 10000

Frequency (Hz)

Denis Wick 6BS Mouthpiece

0 200 400 600 800 10000

Frequency (Hz)

Transparent Mouthpiece

0 200 400 600 800 10000

Frequency (Hz)

Denis Wick 6BS Mouthpiece with Adapter

0 200 400 600 800 10000

Frequency (Hz)

Transparent Mouthpiece with Adapter

% ':# @ # % ; 8 =;?18! #/ 1; ! 2 E/ ; 2 # % "!#!$ % 8 % 2 #E,8 80 1 %

50 100 150 200 250 300

−pi/2

Frequency (Hz)

% ':#/ *< 98 % 8 3 "6>#/ - $1!$ 2: ! 2 ,8# % "% 8 3 34% 1

50 100 150 200 250 300

−pi/2

Frequency (Hz)

% ':#/ @ 98 % 8 3 "6>#/ - $1!$ 2: ! 2 ,8# % "% 8 3 34% 1

50 100 150 200 250 300 350 400

−pi/2

Frequency (Hz)

% ':#/ 98 % 8 3 "6>#/ - $1!$ 2: ! 2 ,8# % "% 8 3 34% 1

100 150 200 250 300 350 400

−pi/2

Frequency (Hz)

% ':#/ 98 % 8 3 "6>#/ - $1!$ 2: ! 2 ,8# % "% 8 3 34% 1

50 100 150 200 250 300 350 400 450

10−3

10−2

50 100 150 200 250 300 350 400 450

−pi/2

Frequency (Hz)

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Investigation of the Lip Reed Using Computational Modelling and ...

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