Objective and subjective study of trumpets Jean-François PETIOT IRCCyN (UMR CNRS) : Ecole Centrale de Nantes, France
et al. Emilie POIRSON Joël GILBERT UK Musical Acoustics Network Conference September 21st, 2006
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Outline
Context and background •
The trumpet’s leadpipe
Methodology Subjective study • Objective study • Data analysis - Correlations • Design of a leadpipe - Optimization •
Conclusions - Perspectives
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General context
[Pratt and Bowsher]
• Study of the perceived quality of brass instruments
Physical measurements (e.g. impedance)
Perceived quality
Ze (jω ) =
Amplitude (dB)
10
10
10
d'entrée Pe (jωImpédance ) Pe (jωZe ) Ze (jω ) = Ue (jω ) Ue (jω )
BACH IFJN
8
7
6
0
200
400
600
800
1000
1200
1400
Fréquence (Hz)
Quality : aptitude of a product to satisfy the user’s needs, explicit or implicit [NF]. musical
acoustical
financial
aesthetical ergonomical
The « ideal » instrument does’nt exist. Only compromises between differents dimensions of the perceived quality can be made 21st september, 2006
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Research objectives •
Study the influence of the bore’s geometry of brass instruments on the perceived quality - Focus on the “intonation”
•
“optimise” the design of an instrument according to a given dimension of the perceived quality (target)
Experimental approach • “Parameterized” instrument •
Control the “variability” of the instrument
• Panel of musicians “experts ” • control the subjective response (reliability)
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The trumpet leadpipe bell mouthpiece
Resonator
leadpipe
The inner shape of the leadpipe has a great influence on the sound quality of the trumpet (intonation, timbre, response,…) 21st september, 2006
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Methodology [PhD Poirson] Product space
Objective study
Subjective study Panel of Experts
Sensory analysis
Objective measurement
Sensory profiling
Objective variables
Acoustics
Correlations data analysis
Design Optimisation
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Setting-up of the product space Parameterized trumpet leadpipe (r2, r3, r4) Part 2
Part 1 r1
r2
r3
Tuning slide
r4
Several hundred of possible instruments
Manufacturing with NC machine [ECN]
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Part 4
Part 3
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Shapes of the parameterized parts Codage des pièces constituives des branches
A B C D E
Diamètre Entrée d1 9,28 9,28 9,28 9,28 9,28
Diamètre Sortie d2 9,28 9,4 10 10,9 11,65
F
9,4
11
1
G H I
10 10 10
10,1 11 11,4
1 1 1
J
10,1
11,4
1
K
10,9
11
1
L M N O
11 11 11 11
11 11,4 11,65 12
1 1 1 1
P Q
11,4 11,4
11,4 11,65
1 1
R
11,65
11,65
3
S
12
11,65
1
Code
Several hundred of combinations
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Qté 3 1 1 1 1
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Example of inner shapes
AAAE
DKOS
8
8
6
6
4
4
2
2 0
0 -2 0
50
100
150
200
250
-2 0
-4
-4
-6
-6
-8
-8
50
100
200
150
200
250
CHMQ
IFJN 8
8
6
6
4
4
2
2 0
0 -2 0
150
50
100
150
200
250
-2 0
-4
-4
-6
-6
-8
-8
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50
100
250
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Subjective study How to be sure that the assessment of the musician is reliable ? ⇒ Sensory analysis • Definition of sensory attributes • Training of a panel of experts • Statistical study of the significativity of the results
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Subjective study panel of experts • 10 professional musicians • Setting up of the sensory profiling (attributes)
brainstorming Free-verbalisation task on instruments of various quality Attribute Intonation
Definition Relative position of the notes Difference of height note E (fingering Test note E 0) and note E (fingering 12) Ability of the instrument to be centered Centering on a note Ability of the instrument to play Response immediately Width of the Dynamic range Low register Medium register Width of the Dynamic range Width of the Dynamic range High register Tone of the instrument Timbre
Range out of tune / in tune
Procedure arpeggio
similar / different
play notes E(0)-E(12)
bad / good
attack of the note G4
bad / good
Detached notes
limited/ big limited/ big limited/ big dark / bright
dynamics pp, mf, ff dynamics pp, mf, ff dynamics pp, mf, ff comparison/reference
attribute : relevant, accurate, discriminating, independent 21st september, 2006
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Training sessions • « blind » tests • task: • 4 different leadpipes, in 3 replications • Same trumpet (Bach Vernon)
• evaluation of the repetability, the ability to
perceive differences, of the experts • one-way and two-ways ANOVA (product effect ;
product/subject/interaction effects)
Sensory profile
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example of results Typical assessement chart of an expert (training) Intonation
Branches AAAE
DKOS
IFJN
CHMQ
Val. 3,1 3 3 6 8,7 6,3 9,2 6,2 5,9 8,2 8,8 8,2
average
test E(0) et E(12) Rg
3,033
4
7,000
3
7,100
2
8,400
1
Val. 2,5 5,4 5,9 4,2 7,4 9 8,4 5,8 6,2 8,3 8,5 7
average
Rg
4,600
4
6,867
2
6,800
3
7,933
1
Val. 4,2 6 7,2 4 7,4 7,8 7,5 6,6 7,8 7,6 8 6,7
average
Rg
5,800
4
6,400
3
7,300
2
7,433
1
Val. 6,2 6,2 6,2 5,4 7,6 7,2 7,6 6,3 7,2 8,1 8,2 7,5
average
Rg
6,200
4
6,733
3
7,033
2
7,933
1
« bad » repeatability
Good repeatability 21st september, 2006
Response
Centering
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Repeatability/discriminating Good repeatability, but not discriminating
Poor repeatability, but discriminating
Instrument A 21st september, 2006
Instrument B J-F PETIOT
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Two-ways ANOVA (product- expert) Example of results: training session
Intonation Test E Centering Response
=significant effect
Low
Medium
High
Timbre
Product effect Expert effect Interaction
No effect of the leadpipe Pb of repeatability « Interaction » effect « expert » effect
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Evaluation session • 12 instruments, 2 replications
Assessment of the intonation fingering (0)
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Average intonation scores
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Subjective score of Code intonation I 7.2 ABFN 8.8 ACHN 9.5 ADKN 8.9 BFLN 8.6 BFOS 8.2 CGJQ 7.5 CHMQ 6.6 CHNR 6.1 CIPQ 7.7 DKLN 5.1 DKNR 6.9 DKOS
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Objective study Measurement of the input impedance Zin [BIAS – ITEMM, Le Mans] pin(t) uin(t)
Zin (jω) =
Pin (jω) Uin (jω)
Pe (jωInput ) impedance Pe (Zin jω ) Ze (jω )= Ze (jω )= Ue (jω ) Ue (jω ) Amplitude Zin (dB)
10
10
10
BACH IFJN
8
7
6
0
200
400
600
800
1000
1200
1400
Frequency (Hz) 21st september, 2006
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Objective variables extracted from Zin Resonance frequencies of the impedance Zin
resonance frequencies of Zin (Hz) Code ABFN ACHN ADKN BFLN BFOS CGJQ CHMQ CHNR CIPQ DKLN DKNR DKOS
f2
f3
f4
f5
f6
f7
f8
f9
f10
230.5 230 229.5 229.5 229 229.5 228.5 229 228.5 227.5 227.5 228
343.5 344.5 345.5 346 347 345.5 346 347.5 346.5 344.5 345.5 346.5
454.5 457 460 460.5 463 460 463 465 464.5 463.5 465 465.5
574 575.5 576.5 577.5 575 577.5 579 580.5 581 582.5 581.5 581.5
691 690 687.5 687.5 685 690 687.5 689 687 690 688.5 688.5
801.5 801 796.5 796.5 799.5 799 796 798.5 796 791.5 794 795.5
901.5 904.5 906 907 908.5 903 905 908 907 901.5 902 903.5
1019 1022 1024 1025.5 1021.5 1021 1023 1025.5 1025.5 1025.5 1022.5 1022.5
1144 1144 1143 1144 1140 1145 1144 1147.5 1146.5 1150 1146.5 1146.5
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Link between the subjective/objective data
subjective study
objective study
Intonation scores
Objective variables
?
Subjective score of Code intonation I 7.2 ABFN 8.8 ACHN 9.5 ADKN 8.9 BFLN 8.6 BFOS 8.2 CGJQ 7.5 CHMQ 6.6 CHNR 6.1 CIPQ 7.7 DKLN 5.1 DKNR 6.9 DKOS
resonance frequencies of Zin (Hz) Code ABFN ACHN ADKN BFLN BFOS CGJQ CHMQ CHNR CIPQ DKLN DKNR DKOS
f2
f3
f4
f5
f6
f7
f8
f9
f10
230.5 230 229.5 229.5 229 229.5 228.5 229 228.5 227.5 227.5 228
343.5 344.5 345.5 346 347 345.5 346 347.5 346.5 344.5 345.5 346.5
454.5 457 460 460.5 463 460 463 465 464.5 463.5 465 465.5
574 575.5 576.5 577.5 575 577.5 579 580.5 581 582.5 581.5 581.5
691 690 687.5 687.5 685 690 687.5 689 687 690 688.5 688.5
801.5 801 796.5 796.5 799.5 799 796 798.5 796 791.5 794 795.5
901.5 904.5 906 907 908.5 903 905 908 907 901.5 902 903.5
1019 1022 1024 1025.5 1021.5 1021 1023 1025.5 1025.5 1025.5 1022.5 1022.5
1144 1144 1143 1144 1140 1145 1144 1147.5 1146.5 1150 1146.5 1146.5
⇒ propose assumptions to interpret the intonation scores by objective variables 21st september, 2006
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Assumption 1
the intonation is mainly conditioned by the following frequency ratio
relation musical intervals / frequency ratio
f3 / f2
: fifth
f4 / f2
: octave
f5/ f4
: third
f6 / f4 f8/ f4
: fifth : octave
5 explanatory variables 21st september, 2006
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Principal component analysis
The five explanatory variables are correlated ⇒ Reduction of the dimensionality by Principal
Component Analysis (PCA) Factors
Variables
F1
f3/f2 f4/f2 f5/f4 f6/f4 f8/f4 1,49 1,97 1,26 1,52 1,98
1,22
-0,19
ACHN
0,80
-0,09
ADKN
0,23
0,06
BFLN
0,18
0,02
BFOS
-0,47
0,46
CGJQ
0,28
-0,11
CHMQ
-0,30
0,00
1,5
ADKN
1,51
BFLN
1,51 2,01 1,25 1,49 1,97
BFOS
1,52 2,02 1,24 1,48 1,96
CGJQ
1,51
CHMQ
1,51 2,03 1,25 1,48 1,95
CHNR
1,52 2,03 1,25 1,48 1,95
CHNR
-0,47
0,06
CIPQ
1,52 2,03 1,25 1,48 1,95
CIPQ
-0,45
-0,03
DKLN
1,51 2,04 1,26 1,49 1,94
DKLN
-0,27
-0,39
DKNR
1,52 2,04 1,25 1,48 1,94
DKNR
-0,62
-0,18
DKOS
1,52 2,04 1,25 1,48 1,94
DKOS
-0,66
-0,10
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1,99 1,26 1,51 1,98
ABFN
ACHN
2
2
1,25 1,49 1,97
1,26
1,5
1,96
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PCA Trumpets
Trumpets
ABFN
F2
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Factorial plane (F1 F2) ⇒ 98% of variance on the factorial plane (F1, F2)
0.8 0.6
f8/f4
F2 – inertia : 14%
BFOS
0
f3/f2 f4/f2
CHNR CIPQ CHMQ DKOS DKNR
ADKN BFLN CGJQ
ACHN f6/f4
ABFN
DKLN
f5/f4 -0.8 F1 – inertia : 84% -1
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0.5
1
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Assumption 2
linear model between the intonation score Ii and the factors F1 F2
Ii = a.F1i + b.F2i + c.(F1i2 + F2i2) + d
•
Ideal point model (extremum of the paraboloid)
calculation of the coefficients a, b, c, d by least square method (regularized regression) - Significant regression (F-test) - Determination coeff.
R2
= 0.7
⇒
Assumptions are relevant
• determination of the coordinates of the « ideal » point -a/2c « Maximum » of intonation « ideal » -b/2c 21st september, 2006
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Results
Position of the “ideal” point (target)
0.8 Target 0.6
f8/f4
F2 – inertia : 14%
BFOS
0 f3/f2 f4/f2
CHNR CIPQ CHMQ DKOS DKNR
ADKN BFLN CGJQ
ACHN f6/f4
ABFN
DKLN
f5/f4 -0.8 F1 – inertia : 84% -1 21st september, 2006
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0.5
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Calculation of the initial variables of the “target” ⇒ Inversion of the coordinate transformation relations of
the PCA
F = X.U
F: matrix (n×p) of the factorial scores X: matrix (n×p) of the initial data U: matrix (p×p) of the eigen vectors Solution
Target
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ft3/ ft2
ft4/ ft2
ft5/ ft4
ft6/ ft4
ft8/ ft4
1,52
2,03
1,24
1,49
1,98
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Optimisation ⇒ Design of the leadpipe corresponding to the “target” by
optimisation method
Multicriteria optimization problem ⎧ e1 = f3 − ft3 f2 ft 2 ⎪ ⎪ e2 = f6 − ft 6 f4 ft 4 minimize ⎪⎪ ⎨ e3 = f4f2 − ft 4 ft 2 x = [r2, r3, r4 ]⎪ f8 ft8 ⎪ e4 = f4 − ft 4 ⎪ e5 = f5 − ft5 ⎪⎩ f4 ft 4 Part 2
Part 1 r1
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r2
Design variables : r2, r3, r4 of the leadpipe
Part 4
Part 3 r3
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Tuning slide
r4
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Results ⇒ Selection of 5 solutions of the PARETO set (not-
dominated)
S1 S2 S3 S4 S5 DKOS
r2 (mm) 4.3 4.6 4.6 4.6 4.6 5.5
r3 (mm) 5.4 5.3 5.3 5.4 5.5 5.5
r4 (mm) 6 5.9 6 5.7 5.8 6
Si dominates Sj if Si is better than Sj on all the objectives and strictly better on at least one objective
Coming soon … ⇒ Manufacturing of an “optimal” leadpipe and test with
the experts ⇒ Exploitations of the results for other attributes 21st september, 2006
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Conclusions
Illustration of a user-centered methodology for the design of brass instruments
Application to the sensory profiling technique to the assessment of musical instruments •
The sensory profiling technique is relevant for certain attributes
•
Importance of the training of the experts
•
Difficult to have an homogeneous panel for some attributes (response, centering)
Implementation of optimisation method to solve a design problem
Perspectives
Taken into account users’ preferences
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Reference
J-F. Petiot, E. Poirson, J. Gilbert. « User-centred design via sensory analysis techniques and optimisation procedures: application to musical instrument design ». proceedings of ICED 2005, International Conference on Engineering Design, August 15-18, 2005, Melbourne, Australia.
Thanks to …
Philippe COURCOUX, professor, ENITIAA Nantes, Our 10 Experts : J-C.BAULIN, Ch.BELZ, L.BOILLEREAUX, P.BOSSEAU, Ph.CORCUFF, S.GRIMAULT, J-J.METZ, Y.NEVEU, P.PINEAU, S.SCOUBART, Jacques GEFFRIAUD and Patrick BARON, École Centrale de Nantes, Brasswind & Woodwind (C. CHAUVIN).
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Objective and subjective study of trumpets Jean-François PETIOT IRCCyN (UMR CNRS) : Ecole Centrale de Nantes, France
UK Musical Acoustics Network Conference September 21st, 2006
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