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E N G A G I N G T H E W O R L D
Automatic Calibration of Modified FM Synthesis
to Harmonic Sounds using Genetic Algorithms
...
Replicating sounds of musical instruments
• Problem frequently addressed in Computer
Music
• Various synthesis techniques ...
Issues / Limitations
• Parametric Synthesis techniques
• Selecting suitable controls and synthesis
parameters can be unint...
Automatic calibration
• Genetic algorithms
• Neural networks
• Cellular automata
• Particle Swarm Optimization
• etc.
4
Scope of our research
• Genetic algorithms (GA)
• Modified FM synthesis
• Musical harmonic sounds
5
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
FM synthesis
Classic	
  FM	
  synthesis:
Chowning	
  
(AES	
  Journal	
  1973)
Modified	
  FM	
  synthesis:
Lazzarini,	
  V...
Synthesis Model
9
Synthesis Model
9
Synthesis Model
9
Synthesis Model
9
Synthesis Model
9
Synthesis Model
Insure	
  the	
  harmonicity	
  of	
  the	
  sound
Scale	
  spectum	
  on	
  the	
  target	
  sound	
  spe...
Parameters to optimize
k1 I1 k2 I2 ... kN IN
Param. Bounds Type Use
k [0,10] Integer
I [0,20] Double
10
Input parameters
• number of carriers
• harmonic target sound
11
Genetic Algorithm
12
Image	
  from	
  www.genePc-­‐programming.com
Initialization
13
PopulaPon	
  size	
  =	
  100
Initialization
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN ...
Evaluation
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k...
Evaluation
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k...
Evaluation
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k...
Evaluation
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k...
E N G A G I N G T H E W O R L D
Fitness function
Analysis parameters
Analysis window size 10	
  ms
Overlapping 5	
  ms
Zero padding factor 4
Spectral resolution 20	
  Hz
16
Target	
  Sound
Fitness function
17
Target	
  Sound
Fitness function
17
Target	
  spectrum
A
Hz
18
Target	
  spectrum
A
Hz
18
Target	
  spectrum
A
Hz
Target	
  vector
18
k1 I1 k2 I2 k3 I3
19
k1 I1 k2 I2 k3 I3
19
k1 I1 k2 I2 k3 I3
Hz
A
19
k1 I1 k2 I2 k3 I3
Hz
A
19
k1 I1 k2 I2 k3 I3
Hz
A
19
k1 I1 k2 I2 k3 I3
Hz
A
19
k1 I1 k2 I2 k3 I3
Hz
A
Hz
A
19
k1 I1 k2 I2 k3 I3
Hz
A
Hz
A
19
k1 I1 k2 I2 k3 I3
Hz
A
Hz
A
19
20
System	
  of	
  equaPons	
  to	
  solve
Unknown
Least	
  Squares	
  ApproximaPons
Fitness	
  Func:on	
  +=	
  approximaPon...
Target	
  Sound
22
Target	
  Sound
22
Target	
  Sound
22
1st	
  Carrier	
  envelop	
  
3st	
  Carrier	
  envelop	
  
2st	
  Carrier	
  envelop	
  
Synthesized	
  sound:
23
Fitness...
Termination
criteria
• Reach 300
generations
• Weighted change in
the fitness < 1.E-10
over 50 generations
24
GeneraPon	
  0:	
  Size	
  =	
  100
2	
  elites	
  
children
0.8	
  x	
  98	
  =	
  78	
  children	
  
by	
  crossover
98-...
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ...
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ...
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ...
Crossover
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
k1 I1 k2 I2 ... kN IN
Parents
Children
Crossov...
Gaussian Mutation Operator
k1 I1 k2 I2 ... kN IN
Add	
  a	
  random	
  number	
  from	
  a	
  gaussian	
  
distribuPon
28
Termination
criteria
• Reach 300
generations
• Weighted change in
the fitness < 1.E-10
over 50 generations
29
Evaluations
1.Musical Instrument Sounds (University of
Iowa Electronic Music Studios)
2.Comparison between ClassicFM and M...
Insure	
  the	
  harmonicity	
  of	
  the	
  sound
Scale	
  spectum	
  on	
  the	
  target	
  spectrum
31
Musical Instrument Sounds
• AltoSax
• Bass
• Bassoon
• Clarinet
• Cello
• Flute
• Violin
32
• Horn
• Oboe
• Piano
• Tenor ...
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
Best	
  fitness	
  score 368 1...
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
Best	
  fitness	
  score 368 1...
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
Best	
  fitness	
  score 368 1...
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
Best	
  fitness	
  score 368 1...
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
Best	
  fitness	
  score 368 1...
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
Best	
  fitness	
  score 368 1...
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
Best	
  fitness	
  score 368 1...
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
Best	
  fitness	
  score 368 1...
Flute - Harmonic 1 34
Flute - Harmonic 4 35
Flute - Harmonic 6 36
Flute - Harmonic 9 37
Results Clarinet - ModFM
38
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
B...
Results Clarinet - ModFM
38
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
B...
Results Clarinet - ModFM
38
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
B...
Results Clarinet - ModFM
38
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
B...
Results Clarinet - ModFM
38
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
B...
Results Clarinet - ModFM
38
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
B...
Results Clarinet - ModFM
38
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
B...
Results Clarinet - ModFM
38
Target
Number	
  of	
  carriersNumber	
  of	
  carriersNumber	
  of	
  carriers
Target
2 4 6
B...
39
Clarinet Spectra
20.8
8.50
3.9
Fitness
Stats ClassicFM - ModFM
40
ParametersParameters
ClassicFMClassicFM ModFMModFM
mean SD mean SD
Fitness
Gen.	
  to	
  conv.
...
Trumpet - 6 carriers 41
Trumpet - 6 carriers 41
Trumpet - 6 carriers 41
Trumpet - 6 carriers 41
Trumpet - 6 carriers 41
Trumpet - 6 carriers 41
Trumpet - 6 carriers 41
Stats Evolution 42
Contributions
• Apply GA to a new FM synthesis technique
• Automatize completely the process
• Refine the parameters of the...
Future work - GA
• Remove constraints:
–Non harmonic sounds
–Remove constraint on the synthesis method
–Other fitness funct...
Future work - GP
• Go further!
• Evolve not only the
parameters but also
the synthesis model
45
http://www.metacreation.net/mume2012/
46Chair
Philippe	
  Pasquier
Co-­‐Chairs
Arne	
  Eigenfeldt,	
  Olivier	
  Brown
E N G A G I N G T H E W O R L D
Thank you !
Matthieu Macret - Philippe Pasquier - Tamara Smyth
mmacret@sfu.ca - pasquier@s...
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Automatic Calibration of Modified FM Synthesis to Harmonic Sounds using Genetic Algorithms

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Automatic Calibration of Modified FM Synthesis to Harmonic Sounds using Genetic Algorithms

  1. 1. E N G A G I N G T H E W O R L D Automatic Calibration of Modified FM Synthesis to Harmonic Sounds using Genetic Algorithms Matthieu Macret - Philippe Pasquier - Tamara Smyth
  2. 2. Replicating sounds of musical instruments • Problem frequently addressed in Computer Music • Various synthesis techniques developed over the past century (Additive, FM, granular...) 2
  3. 3. Issues / Limitations • Parametric Synthesis techniques • Selecting suitable controls and synthesis parameters can be unintuitive, manual and time consuming 3
  4. 4. Automatic calibration • Genetic algorithms • Neural networks • Cellular automata • Particle Swarm Optimization • etc. 4
  5. 5. Scope of our research • Genetic algorithms (GA) • Modified FM synthesis • Musical harmonic sounds 5
  6. 6. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 6
  7. 7. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 7
  8. 8. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 7
  9. 9. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 7
  10. 10. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 7
  11. 11. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 7
  12. 12. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 7
  13. 13. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 7
  14. 14. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 8
  15. 15. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 8
  16. 16. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 8
  17. 17. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 8
  18. 18. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 8
  19. 19. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 8
  20. 20. FM synthesis Classic  FM  synthesis: Chowning   (AES  Journal  1973) Modified  FM  synthesis: Lazzarini,  V.  and  Timoney   (AES  Journal  2010) 8
  21. 21. Synthesis Model 9
  22. 22. Synthesis Model 9
  23. 23. Synthesis Model 9
  24. 24. Synthesis Model 9
  25. 25. Synthesis Model 9
  26. 26. Synthesis Model Insure  the  harmonicity  of  the  sound Scale  spectum  on  the  target  sound  spectrum 9
  27. 27. Parameters to optimize k1 I1 k2 I2 ... kN IN Param. Bounds Type Use k [0,10] Integer I [0,20] Double 10
  28. 28. Input parameters • number of carriers • harmonic target sound 11
  29. 29. Genetic Algorithm 12 Image  from  www.genePc-­‐programming.com
  30. 30. Initialization 13 PopulaPon  size  =  100
  31. 31. Initialization k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN INk1 I1 k2 I2 ... kN IN 13 PopulaPon  size  =  100
  32. 32. Evaluation k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN INk1 I1 k2 I2 ... kN IN 14
  33. 33. Evaluation k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN INk1 I1 k2 I2 ... kN IN 14
  34. 34. Evaluation k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN INk1 I1 k2 I2 ... kN IN 14
  35. 35. Evaluation k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN INk1 I1 k2 I2 ... kN IN 6 3 1 2 4 2 7 6 4 14
  36. 36. E N G A G I N G T H E W O R L D Fitness function
  37. 37. Analysis parameters Analysis window size 10  ms Overlapping 5  ms Zero padding factor 4 Spectral resolution 20  Hz 16
  38. 38. Target  Sound Fitness function 17
  39. 39. Target  Sound Fitness function 17
  40. 40. Target  spectrum A Hz 18
  41. 41. Target  spectrum A Hz 18
  42. 42. Target  spectrum A Hz Target  vector 18
  43. 43. k1 I1 k2 I2 k3 I3 19
  44. 44. k1 I1 k2 I2 k3 I3 19
  45. 45. k1 I1 k2 I2 k3 I3 Hz A 19
  46. 46. k1 I1 k2 I2 k3 I3 Hz A 19
  47. 47. k1 I1 k2 I2 k3 I3 Hz A 19
  48. 48. k1 I1 k2 I2 k3 I3 Hz A 19
  49. 49. k1 I1 k2 I2 k3 I3 Hz A Hz A 19
  50. 50. k1 I1 k2 I2 k3 I3 Hz A Hz A 19
  51. 51. k1 I1 k2 I2 k3 I3 Hz A Hz A 19
  52. 52. 20
  53. 53. System  of  equaPons  to  solve Unknown Least  Squares  ApproximaPons Fitness  Func:on  +=  approximaPon  error 21
  54. 54. Target  Sound 22
  55. 55. Target  Sound 22
  56. 56. Target  Sound 22
  57. 57. 1st  Carrier  envelop   3st  Carrier  envelop   2st  Carrier  envelop   Synthesized  sound: 23 Fitness  Func:on  =  sum(approximaPon  errors)
  58. 58. Termination criteria • Reach 300 generations • Weighted change in the fitness < 1.E-10 over 50 generations 24
  59. 59. GeneraPon  0:  Size  =  100 2  elites   children 0.8  x  98  =  78  children   by  crossover 98-­‐78  =  20  children   by  mutaPon GeneraPon  1:  Size  =  100 25 Generating the next population
  60. 60. k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN INk1 I1 k2 I2 ... kN IN 6 3 1 2 4 2 7 6 4 26 Binary selection tournament
  61. 61. k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN INk1 I1 k2 I2 ... kN IN 6 3 1 2 4 2 7 6 4 26 Binary selection tournament
  62. 62. k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN INk1 I1 k2 I2 ... kN IN 6 3 1 2 4 2 7 6 4 26 Binary selection tournament
  63. 63. Crossover k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN k1 I1 k2 I2 ... kN IN Parents Children Crossover  point 27
  64. 64. Gaussian Mutation Operator k1 I1 k2 I2 ... kN IN Add  a  random  number  from  a  gaussian   distribuPon 28
  65. 65. Termination criteria • Reach 300 generations • Weighted change in the fitness < 1.E-10 over 50 generations 29
  66. 66. Evaluations 1.Musical Instrument Sounds (University of Iowa Electronic Music Studios) 2.Comparison between ClassicFM and ModFM 30
  67. 67. Insure  the  harmonicity  of  the  sound Scale  spectum  on  the  target  spectrum 31
  68. 68. Musical Instrument Sounds • AltoSax • Bass • Bassoon • Clarinet • Cello • Flute • Violin 32 • Horn • Oboe • Piano • Tenor Trombone • Trumpet • Tuba • Viola
  69. 69. Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 368 180 121 nb  Gen  to  converge 69 138 58 Results Flute - ModFM 33
  70. 70. Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 368 180 121 nb  Gen  to  converge 69 138 58 Results Flute - ModFM 33
  71. 71. Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 368 180 121 nb  Gen  to  converge 69 138 58 Results Flute - ModFM 33
  72. 72. Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 368 180 121 nb  Gen  to  converge 69 138 58 Results Flute - ModFM 33
  73. 73. Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 368 180 121 nb  Gen  to  converge 69 138 58 Results Flute - ModFM 33
  74. 74. Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 368 180 121 nb  Gen  to  converge 69 138 58 Results Flute - ModFM 33
  75. 75. Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 368 180 121 nb  Gen  to  converge 69 138 58 Results Flute - ModFM 33
  76. 76. Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 368 180 121 nb  Gen  to  converge 69 138 58 Results Flute - ModFM 33
  77. 77. Flute - Harmonic 1 34
  78. 78. Flute - Harmonic 4 35
  79. 79. Flute - Harmonic 6 36
  80. 80. Flute - Harmonic 9 37
  81. 81. Results Clarinet - ModFM 38 Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 20.8 8.50 3.9 nb  Gen  to  converge 71 64 75
  82. 82. Results Clarinet - ModFM 38 Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 20.8 8.50 3.9 nb  Gen  to  converge 71 64 75
  83. 83. Results Clarinet - ModFM 38 Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 20.8 8.50 3.9 nb  Gen  to  converge 71 64 75
  84. 84. Results Clarinet - ModFM 38 Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 20.8 8.50 3.9 nb  Gen  to  converge 71 64 75
  85. 85. Results Clarinet - ModFM 38 Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 20.8 8.50 3.9 nb  Gen  to  converge 71 64 75
  86. 86. Results Clarinet - ModFM 38 Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 20.8 8.50 3.9 nb  Gen  to  converge 71 64 75
  87. 87. Results Clarinet - ModFM 38 Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 20.8 8.50 3.9 nb  Gen  to  converge 71 64 75
  88. 88. Results Clarinet - ModFM 38 Target Number  of  carriersNumber  of  carriersNumber  of  carriers Target 2 4 6 Best  fitness  score 20.8 8.50 3.9 nb  Gen  to  converge 71 64 75
  89. 89. 39 Clarinet Spectra 20.8 8.50 3.9 Fitness
  90. 90. Stats ClassicFM - ModFM 40 ParametersParameters ClassicFMClassicFM ModFMModFM mean SD mean SD Fitness Gen.  to  conv. 51.94 77.96 52.60 87.52 99.24 69.24 87.60 42.57
  91. 91. Trumpet - 6 carriers 41
  92. 92. Trumpet - 6 carriers 41
  93. 93. Trumpet - 6 carriers 41
  94. 94. Trumpet - 6 carriers 41
  95. 95. Trumpet - 6 carriers 41
  96. 96. Trumpet - 6 carriers 41
  97. 97. Trumpet - 6 carriers 41
  98. 98. Stats Evolution 42
  99. 99. Contributions • Apply GA to a new FM synthesis technique • Automatize completely the process • Refine the parameters of the GA • Evaluation on a large set of sounds • Comparison between ClassicFM and ModFM 43
  100. 100. Future work - GA • Remove constraints: –Non harmonic sounds –Remove constraint on the synthesis method –Other fitness function 44
  101. 101. Future work - GP • Go further! • Evolve not only the parameters but also the synthesis model 45
  102. 102. http://www.metacreation.net/mume2012/ 46Chair Philippe  Pasquier Co-­‐Chairs Arne  Eigenfeldt,  Olivier  Brown
  103. 103. E N G A G I N G T H E W O R L D Thank you ! Matthieu Macret - Philippe Pasquier - Tamara Smyth mmacret@sfu.ca - pasquier@sfu.ca - tamaras@sfu.ca

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