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Carnegie Mellon
Learning Musicianship for Automatic Accompaniment
Gus (Guangyu) Xia Roger Dannenberg School of Computer Science Carnegie Mellon University
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Introduction: Musical background
2
Interaction
Expression Rehearsal
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Introduction: Technical background
3
Interaction Musicianship Score following and automatic
accompaniment
Expressive Performance
Expressive Interactive Performance
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Introduction: Problem definition
4
¢ How to interpret the music based on the expression of human musicians?
¢ How to distill models from rehearsals? ¢ What are the limits of validity of the learned models? ¢ How many rehearsals are needed?
For interactive music performance, how can we build artificial performers that automatically improve their ability to sense and coordinate with human musicians’ expression with rehearsal experience?
We start from piano duets, focusing on expressive timing and expressive dynamics.
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Outline
¢ Introduction ¢ Data Collection ¢ Methods ¢ Demos ¢ Conclusion & Future Work
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Current Data Collection
¢ Musicians: § 10 music master students play duet pieces in 5 pairs.
¢ Music pieces: § 3 pieces of music are selected, Danny boy, Serenade
(by Schubert), and Ashokan Farewell. § Each pair performs every piece of music 7 times.
¢ Recording settings: § Recorded by electronic pianos with MIDI output.
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Outline
¢ Introduction ¢ Data Collection ¢ Methods ¢ Demos ¢ Conclusion & Future Work
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Method Overview ¢ From “local” to “general”
§ Local: low-dimensional feature space, only apply to certain notes
§ General: high-dimensional feature space, apply to the whole piece of music
¢ Base line:
Reference time
Rea
l tim
e
Score Following Automatic Accompaniment
Reference time
Rea
l tim
e
next note’s reference time
predicted next note’s performance time
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Method (1): Note-specific approach
¢ Idea: § Expressive timings of the notes are linearly correlated. § Predict the expressive timing of 2nd piano by the
expressive timing of 1st piano.
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¢ Model:
! = [!! , !! ,… , !!]!
! = !! ,!! ,… ,!! !
!! = !!!! + !!!!!!"#$(!!)!!!
!!!!
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Result: Note-specific approach
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0 10 20 30 40 50 600
0.05
0.1
0.15
0.2
0.25
Score time (sec)
Tim
e re
sidu
al (s
ec)
BLNote−8Note−34
Mean Absolute Error: BL: 0.098 Note-8: 0.087 Note-34: 0.060
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Method (2): Rhythm-specific approach
¢ Idea: § Notes with same score rhythm context share parameters. § Introduces an extra dummy variable to encode the score
rhythm context of each note .
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¢ Model:
! = [!! , !! ,… , !!]!
! = !! ,!! ,… ,!! !
!! = !!!!!"!!(!!,!) + !!!!!"!!(!!,!)!!"#$(!!)!!!
!!!!
!
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Result: Rhythm-specific approach
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Mean Absolute Error: BL: 0.098 Rhythm-4: 0.084 Rhythm-8: 0.067
0 10 20 30 40 50 600
0.05
0.1
0.15
0.2
0.25
Score time (sec)
Tim
e re
sidu
al (s
ec)
BLRhythm−4Rhythm−8
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Method (3): General feature approach
¢ Idea: § Make the model more general. § Predict the expressive timing by considering more
than score rhythm context .
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¢ Model: ! = !!!
! = !! ,!! ,… ,!! !
! = !! ,!! ,… ,!! !
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Regularization: Group Lasso
¢ Idea: § Reduces the burden for training. § Discover the dominant features that could predict the
expressive timings.
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¢ Solve:
min!∈!!
! − !" !! + ! !! !! !
!
!!!!
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Result: General feature approach
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Mean Absolute Error: (ONLY 4 training pieces!) BL: 0.098 LR: 0.072 Glasso: 0.059
0 10 20 30 40 50 600
0.05
0.1
0.15
0.2
0.25
Score time (sec)
Tim
e re
sidu
al (s
ec)
BLLRGlasso
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Method (4): LDS approach
¢ Idea: § Add another regularization by adjacent notes. § Lower dimensional hidden mental states that
control the expressive timings.
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¢ Model:
zt zt+1 zt-‐1
ut-‐1 ut ut+1
yt-‐1 yt yt+1
… …
!! = !!!!! + !!! + !! !!!!!!!~!(0,!)!!! = !!! + !!! + !! !!!!!!!!~!(0,!)!
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Result: LDS (horizontal regularization)
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Mean Absolute Error: (ONLY 4 training pieces!) BL: 0.085 LR: 0.072 LDS: 0.067
0 10 20 30 40 50 600
0.05
0.1
0.15
0.2
0.25
Score time (sec)
Tim
e re
sidu
al (s
ec)
BLLRLDS
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A Global View
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BL Note−4 Rhythm−4 Glasso−4 Note−8 Rhythm−8 Glasso−8 Note−34 Rhythm−34Glasso−340
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Methods and training size
Tim
e re
sidu
al(s
ec)
SerenadeDanny boyAshokan Farewell
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Outline
¢ Introduction ¢ Data Collection ¢ Methods ¢ Demos ¢ Conclusion & Future Work
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Some Initial Audio Demo ¢ Base Line:
¢ Note-specific approach: 34 training examples
¢ General feature approach, group lasso: 4 training
examples
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Future Work
¢ Cross-piece models ¢ Performer-specific models ¢ Online learning and decoding ¢ Plugin with music robots
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Conclusion
¢ An artificial performer for interactive performance ¢ Learn musicianship from rehearsal experience ¢ A combination of expressive performance and
automatic accompaniment ¢ Much better prediction just based on 4 rehearsals
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Q&A
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Spectral Learning(1): Oblique projections
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zt zt+1 zt-‐1
ut-‐1 ut ut+1
yt-‐1 yt yt+1
… …
!(!!) = [!!! !!!! !!!!] !!!!!!!
!
¢ We don’t know the future. ¢ Partially explain future observations based on the
history !! ≝ [!!! !!!! !0] !
!!!!0!
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Spectral Learning(2): state estimation
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zt zt+1 zt-‐1
ut-‐1 ut ut+1
yt-‐1 yt yt+1
… … !! = !!!! ≝!!"!!!!!⋮! !!! !
!! = !Σ!! = (!Σ!!)(Σ
!!!!!)!
¢ States estimation by SVD
¢ Moreover, enforce a bottleneck by throwing out near-zero singular values and corresponding columns in U and V.
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Spectral Learning(3): Estimate parameter
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¢ Based on estimated hidden states, the parameters could be estimated from the following equation:
zt zt+1 zt-‐1
ut-‐1 ut ut+1
yt-‐1 yt yt+1
… …
!!!! = !!! + !!! + !! !!!!!!~!(0,!)!
!! = !!! + !!! + !! !!!!!~!(0,!)!
!!!!!! = ! !
! !!!!! + !!
!! !
