2014 IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP)TIMBRE REPLACEMENT OF HARMONIC AND DRUM COMPONENTS
FOR MUSIC AUDIO SIGNALS
Tomohiko Nakamura†‡ , Hirokazu Kameoka† , Kazuyoshi Yoshii‡ and Masataka Goto‡†

Graduate School of Information Science and Technology, The University of Tokyo‡
National Institute of Advanced Industrial Science and Technology{nakamura,kameoka}@hil.t.u-tokyo.ac.jp,{k.yoshii,m.goto}@aist.go.jp

ABSTRACTThis paper presents a system that allows users to customize an audio
signal of polyphonic music (input), without using musical scores,by replacing the frequency characteristics of harmonic sounds andthe timbres of drum sounds with those of another audio signal ofpolyphonic music (reference). To develop the system, we first use amethod that can separate the amplitude spectra of the input and reference signals into harmonic and percussive spectra. We characterizefrequency characteristics of the harmonic spectra by two envelopes
tracing spectral dips and peaks roughly, and the input harmonic spectra are modified such that their envelopes become similar to those of
the reference harmonic spectra. The input and reference percussive
spectrograms are further decomposed into those of individual drum
instruments, and we replace the timbres of those drum instrumentsin the input piece with those in the reference piece. Through thesubjective experiment, we show that our system can replace drum
timbres and frequency characteristics adequately.
Index Terms— Music signal processing, Harmonic percussive
source separation, Nonnegative matrix factorization.
1. INTRODUCTION
Customizing existing musical pieces according to users’ preferences
is a challenging task in music signal processing. We would sometimes like to replace the timbres of instruments and audio texturesof a musical piece with those of another musical piece. Professional
audio engineers are able to perform such operations in the music
production process by using eﬀect units such as equalizers [1–5] thatchange the frequency characteristics of audio signals. However, sophisticated audio engineering skills are required for handling such
equalizers eﬀectively. It is therefore important to develop a new system that we can use intuitively without special skills.
Several highly functional systems have recently been proposed for
intuitively customizing the audio signals of existing musical pieces.
Itoyama et al. [6], for example, proposed an instrument equalizer
that can change the volume of individual musical instruments independently. Yasuraoka et al. [7] developed a system that can replace
the timbres and phrases of some instrument with users’ own performances. Note that these methods are based on score-informed source
separation techniques that require score information about the musical pieces (MIDI files). Yoshii et al. [8], on the other hand, developed a drum instrument equalizer called Drumix that can change
the volume of bass and snare drums and replace their timbres andpatterns with others prepared in advance. To achieve this, audio signals of bass and snare drums are separated from polyphonic audio
signals without using musical scores. In this system, however, only
the drum component can be changed or replaced. In addition, users
would often need to prepare isolated drum sounds (called reference)with which they want to replace original drum sounds. Here we areconcerned with developing an easier-to-handle system that only requires the users to specify a diﬀerent musical piece as a reference.
This study was supported in part by the JST OngaCREST project.

978-1-4799-2893-4/14/$31.00 ©2014 IEEE

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In this paper, we propose a system that allows users to customize
a musical piece (called input), without using musical scores, by replacing the timbres of drum instruments and the frequency characteristics of pitched instruments including vocals with those of anothermusic piece (reference). We consider the problems of customizing the drum sounds and the pitched instruments separately, because
they have diﬀerent eﬀects on audio textures. As illustrated in Fig. 1,
the audio signals of the input and reference pieces are separated
into harmonic and percussive components, respectively, by usinga harmonic percussive source separation (HPSS) method [9] basedon spectral anisotropy. The system then (1) analyzes the frequency
characteristics of the spectra of the harmonic component (hereafter
harmonic spectra) of the input piece and (2) adapts those characteristics to the frequency characteristics of the reference harmonic
spectra. Moreover, (a) the spectrograms of the percussive components (hereafter percussive spectrograms) of the input and reference
pieces are further decomposed into individual drum instruments suchas bass and snare drums, and (b) the drum timbres of the input piece
are replaced with those of the reference piece. In the following, we
describe a replacement method of frequency characteristics for harmonic spectra and a replacement method of drum timbres for percussive spectrograms.

2. FREQUENCY CHARACTERISTICS REPLACEMENT

The goal is to modify the frequency characteristics of the harmonic
spectra obtained with HPSS from an input piece by referring to thoseof a reference piece. The frequency characteristics of a musical piece
are closely related to the timbres of the musical instruments used inthat piece. If score information is available, a music audio signal
could be separated into individual instrument parts [6, 7]. However,blind source separation is still diﬃcult when score information is notavailable. We therefore take a diﬀerent approach to avoid the needfor perfect separation.
We here modify the input amplitude spectrum using two envelopes, named bottom and top envelopes, which trace the dips andpeaks of the spectrum roughly as illustrated in Fig. 2. The bottom
envelope expresses a flat and wide-band component in the spectrum,and the top envelope represents a spiky component in the spectrum.
We can assume that the flat component corresponds to the spectrumof vocal consonants and attack sounds of musical instruments, while
the spike component corresponds to the harmonic structures of musical instruments. Thus, individually modifying these envelopes allows us to approximately change the frequency characteristics of themusical instruments. The modified amplitude spectra are converted
into an audio signal using the phases of the input harmonic spectra.

Acoustic signalof input piece

Spectrogram of
harmonic component(1) Analysis of bottom
and top envelopes
Harmonic spectra
and bottom and top envelopes

Spectrogram of
percussive component(1) Analysis ofbottom/top envelopes

Spectrogram of
percussive component(a) Source
separation by NMF

Bottom and top
envelopes

NMF results andpercussive spectrogram(2) Synthesis of harmonic spectra

reference piece

Spectrogram of
harmonic component(a) Source separation by nonnegative matrix factorization (NMF)

Synthesized acoustic signalof percussive component

spectrumtop envelope
0-20
How to replace
drum timbres

bottom envelope

10

-10

NMF results andpercussive spectrogram(b) Synthesis of percussive spectrogram

Synthesized acoustic signalof harmonic component

20

Acoustic signal of

HPSS

Amplitude [dB]

Harmonic percussive source
separation (HPSS)

0

2000

4000

6000

Frequency [Hz]

8000

User

Proposed system

Acoustic signal ofsynthesized piece

Fig. 1. System outline for replacing drum timbres and frequency characteristics of the harmonic component. Red and blue modules relate to harmonic and percussive components of input and reference pieces.

Fig. 2.
Bottom (green) andtop (red) envelopes of a spectrum(blue). The envelopes trace dipsand peaks of a spectrum roughly.

2.1. Mathematical model for bottom and top envelopes
We describe each envelope using a Gaussian mixture model (GMM)
as a function of the frequency ω:∑[
k fnyq )]
1
1 (
exp −
ω−
Ψ(ω; a) :=ak ψk (ω), ψk (ω) := √
2
2
2σ
K
2πσ
k
(1)
K
where a := {ak }k=1
, and fnyq stands for a Nyquist frequency. ak ≥0 denotes the power of the k-th Gaussian ψk (ω) with the averagek fnyq /K and the variance σ2 .
We first estimate a for the bottom envelopes of the input and reference pieces respectively by fitting Ψ(ω; a) to their harmonic spectra,
and also estimate a for the top envelopes (see Sec. 2.3). We thendesign a filter that converts the input envelopes so that their time averages and variances equal those of the reference envelopes. Finally,by using the converted version of the input envelopes, we convert the
input amplitude spectra.

Threshold-based ruleGain for top
envelopes

Gain for bottom
envelopes

ProposedruleFig. 3. The proposed (red curve) and threshold-based (blue lines)
conversion rules of an input spectral element into a synthesized one
in the log-spectral domain. The horizontal and vertical axes are an
amplitude spectral elements of input and synthesized pieces.

2.2. Spectral synthesis via bottom and top envelopes
We consider converting the input piece so that the bottom and top
envelopes of the converted version become similar to those of thereference piece. Let us define the averages and variances in timeof the envelopes of the input and reference harmonic spectra as µ(l)ωand Vω(l) for l = in, ref, respectively. Assuming that the envelopes
follow normal distributions, the distributions of the converted input
envelopes approach those of the reference envelopes by minimizinga measure between the distributions. As one such measure, we canuse the Kullback-Leibler divergence, and derive the gains as
√
(ref)
(in)
(in) 2(ref)(ref) 2+ (µ(in)µ(in)ω µωω µω ) − 4{Vω + (µω ) }Vω
gω =
. (2)
2
2{Vω(in) + (µ(in)ω ) }Next, we show the conversion rule for the harmonic amplitude
spectrum (S ω(in) ) of the input piece by using the gains for the bottom
and top envelopes in the log-spectral domain. When modifying thebottom envelope, we want to modify only the flat component (andkeep the spiky component fixed). On the other hand, when modifying the top envelope, we want to modify only the spiky component(and keep the flat component fixed). To do this, we multiply thespectral components above or near the top envelope by gtop,ω (thegain factor for the top envelope), and multiply the spectral components below or near the bottom envelope by gbot,ω (the gain factor forthe bottom envelope). One such rule is a threshold-based rule whichmeans that we divide the set of spectral components into two sets,
one consisting of the components above or near the top envelope
and the other consisting of the components below or near the bottom
envelope. We multiply the former and latter sets by gtop,ω and gbot,ω ,7521

respectively. Fig. 3 illustrates the rule where S ω(synth) is a synthesized
amplitude spectrum and a threshold θ := {ln(Ψ(ω; abot )Ψ(ω; atop ))}/2
is the midpoint of the bottom and top envelopes (Ψ(ω; abot ) andΨ(ω; atop )) of the input piece in the log-spectral domain. However,
the rule changes spectral elements near θ with discontinuity. To
avoid the discontinuity, we use the relaxed rule as shown in Fig. 3:)
gtop,ω (ln S ω(in) − θfgbot,ω ρ ln(Ψ(ω; atop )/Ψ(ω; abot ))(3){
10 (x → −∞)f (x) :==
(4)
1 (x → ∞)1 + exp(−x)
where ρ > 0. Note that (3) is equivalent to the threshold-based rule
when ρ → 0.
ln S ω(synth) = ln gbot,ω S ω(in) + ln

2.3. Estimation of bottom and top envelopes
2.3.1. Estimation of bottom envelopes
When estimating the bottom envelope Ψ(ω; a), we can use the
Itakura-Saito divergence (IS divergence) [10] as a cost function. The
estimation requires a cost function that is lower for the spectral dips
than for the spectral peaks. The IS divergence meets the requirement
as illustrated in Fig. 4. Let S ω be an amplitude spectrum. The costfunction is described as∑
Jbot (a) :=DIS (Ψ(ω; a)||S ω ),(5)
ωDIS (Ψ(ω; a)||S ω ) :=Ψ(ω; a)Ψ(ω; a)
− ln
−1
Sω
Sω

(6)

K,W
where λ = {λk (ω)}k=1,ω=1
is a series of auxiliary variables such that∑∀ω, k λk (ω) = 1, λk (ω) ≥ 0. The auxiliary function is obtained by
Jensen’s inequality based on the concavity of the logarithmic func+tion in the second term of (5). By solving ∂Jbot(a, λ)/∂ak = 0 and+the equality condition of Jbot (a) = Jbot(a, λ), we can obtain∑λk (ω)ak ψk (ω)
ak ← ∑ ω, λk (ω) ← ∑
.
(8)
ψ
(ω)/S
k
ω
ω
k′ ak′ ψk′ (ω)

2.3.2. Estimation of top envelopes
The estimation of the top envelope Ψ(ω; a) requires a cost functionthat is higher for the spectral dips than for the spectral peaks. This is
the opposite requirement for that in Sec. 2.3.1. The IS divergence isasymmetric as shown in Fig. 4, thus exchanging Ψ(ω; a) with S ω of(6) leads to the opposite property to (6), and DIS (S ω ||Ψ(ω; a)) meetsthe requirement. Suppose that the bottom envelope Ψ(ω; abot ) was
estimated. The cost function is defined as∑
Jtop (a) := P(a; abot ) +DIS (S ω ||Ψ(ω; a))
(9)
∑

ω

where P(a; abot ) := k ηk abot,k /ak is a penalty term for the closenessbetween the bottom and top envelopes, and ηk ≥ 0 is the weight ofabot,k /ak . Direct minimization of Jtop (a) is also diﬃcult because the
IS divergence in the second term of (9) includes non-linear terms as
described in (6).
Here we can define the auxiliary function of Jtop (a) as∑ { ∑ (νk (ω))2 S ω+
Jtop(a, ν, h) :=P(a; abot ) ++ ln h(ω)
ak ψk (ω)ωk)
} (10)
1 (∑ak ψk (ω) − h(ω) − ln S ω − 1+h(ω) kK,Wwhere ν = {νk (ω)}k=1,ω=1
and h = {h(ω)}W
ω=1 are series of auxiliary∑
variables such that ∀ω, k νk (ω) = 1, νk (ω) ≥ 0, h(ω) > 0. Thisinequality is derived from the following two inequalities for the nonlinear terms:
∑ ν2
1
1
k
∑
≤
, ln x ≤ ln h + (x − h).
(11)
x
x
h
k
k k
k
∑
where ∀k, νk ≥ 0 and h > 0 are auxiliary variables such that k∑νk =1. The first inequality is obtained by Jensen’s inequality for 1/ k xk
and the second inequality is a first-order Taylor-series approximation+of ln x around h. By solving ∂Jtop(a, ν, h)/∂ak = 0 and the equality+
condition of Jtop (a) = Jtop (a, ν, h), update rules can be derived as{ ηk abot,k + ∑ω (νk (ω))2 S ω /ψk (ω) }1/2
∑
,
(12)
ak ←
ω ψk (ω)/h(ω)∑
ak ψk (ω)νk (ω) ← ∑, h(ω) ←ak ψk (ω).
(13)
k′ ak′ ψk′ (ω)k(12) does not guarantee ak ≥ abot,k , and we set ak = abot,k whenak < abot,k .

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Peak

Error

where DIS (·||·) is the IS divergence. Minimizing Jbot (a) directly is
diﬃcult, because of the non-linearity of the second term of (5).
We can use the auxiliary function method [11]. Given a cost function J, we introduce an auxiliary variable λ and an auxiliary function J + (x, λ) such that J(x) ≤ J + (x, λ). We can then monotonicallydecrease J(x) indirectly by minimizing J + (x, λ) with respect to x
and λ iteratively.
The auxiliary function of Jbot (a) can be defined as∑ { ∑ ( ak ψk (ω)}
ak ψk (ω) )+Jbot(a, λ) :=− λk (ω) ln
−1
(7)
Sω
λk (ω)S ω
ω
k

18
16
14
12
10
8
6
4
2
0

Dip

For top envelope

For bottom envelope

-3

-2

-1

0

1

2

3

Fig. 4. The Itakura-Saito divergence for bottom and top envelopes.
3. DRUM TIMBRE REPLACEMENT
To replace drum timbres, we first decompose the percussive amplitude spectrograms into approximately those of individual drum instruments. The decomposition can be achieved by nonnegative matrix factorization (NMF) [12] and Wiener filtering. We call a component of the decomposed spectrograms a basis spectrogram. NMF
approximates the amplitude spectrograms by a product of two nonnegative matrices, one of which is a basis matrix. Each column of thebasis matrix corresponds to the amplitude spectrum of an individual
drum sound, and the corresponding row of the activation matrix represents its temporal activity. The users are then allowed to specify
which drum sounds (bases) in the input piece they want to replacewith which drum sounds in the reference piece. According to thischoice, the chosen drum timbres of the input piece are replaced withthose of the reference piece for each basis.
3.1. Equalizing method
One simple method for replacing drum timbres, called the equalizing(EQ) method, is to apply gains to a basis spectrogram of the input
piece such that the drum timbre of the input basis becomes similar tothat of the reference basis. The input and reference bases represents
the timbral characteristics of their drum sounds, and we use the gainthat equalize the input and reference bases for each frequency bin.
Let us define the complex basis spectrogram of the input piece and(in)its basis as Yω,tand Hω(in) . Using the corresponding reference basis(synth)(ref)forHω , we can obtain the synthesized complex spectrogram Yω,t(synth)(in)(in) (ref)the basis as Yω,t = Yω,t Hω /Hω for ω ∈ [1, W] and t ∈ [1, T ].
This method only requires applying gains to the input basis spectrograms uniformly in time. However, when there is a large diﬀerence between the timbres of the specified drum sounds, the method
often amplifies low-energy frequency elements excessively, and so
the resulting converted version would sound very noisy and themethod fails to replace the drum timbres adequately.
3.2. Copy and paste method
To avoid the problem of the EQ method, we directly use basis spectrograms of the reference piece. The reference basis spectra include
the drum timbre which we want, and by appropriately copying andpasting the reference basis spectra, we can obtain the percussive
spectrogram with the reference drum timbres and the input temporal
activities. We call the method the copy and paste (CP) method.
This method requires how to copy and paste the reference basis
spectra with keeping the input temporal activities and how to reducenoise occured by this method. Features should be less sensitive tothe drum timbres but reflect temporal activities. As the features, theNMF activations are available. Furthermore, there are three requirements related to the noise reduction. Noise occurs when previously
remote high-energy spectra are placed adjacent to each other. To

Ot,τ := αD(Ũt(in) ||Ũτ(ref) ) + βPτ
(15)where τ is a time index of the reference piece, α > 0 and β > 0
are the weights of D(Ũt(in) ||Ũτ(ref) ) and Pτ , and Ũt(l) := Ut(l) / maxt {Ut(l) }for l = in, ref. The first term of (15) indicates the generalized Idivergence between the two normalized activations. Pτ represents
the degree to which the reference basis spectrum at the τ-th frame
includes non-percussive components: the term becomes larger as thenumber of non-percussive components in the spectrum (requirement(iii)). Cτ′ ,τ is the transition cost from the τ′ -th frame to the τ-th frameof the reference piece:{1(τ = τ′ + 1)′
Cτ ,τ =
.
(16)
(ref)
(ref)
c + γ(Ũτ′ + Ũτ ) (τ , τ′ + 1)
The constant c expresses a cost for all other transitions except for astraight one. We set c > 1 and this ensures that a straight transition
occurs more frequently than the others (requirement (i)). The second
term of (16) for τ , τ′ + 1 indicates that transitions to remote frames
tend to occur when the activations are low (requirement (ii)), and+ Ũτ(ref) . We can obtain the alignment
γ > 0 is the weight of Ũτ(ref)′as an optimal path that minimizes the cumulative cost by the Viterbi
algorithm [13].
The input basis spectra may include the non-percussive components because of imperfect source separation. In this case, the input
basis spectra which may include the non-percussive components are
replaced with the reference basis spectra by the CP method, and the
input basis spectra loses the input non-percussive components. To
recover the components, we make an extra processing. The components tend to have low energy, and they would probably be includedin the input percussive spectra with low energy. We replace syn(synth)thesized percussive spectra {Yω,t}ω with the corresponding input∑ (in)(in)is lower than a threshold ϵ.
percussive spectra {Yω,t }ω when ω Yω,t
4. EXPERIMENTAL EVALUATION
4.1. Experimental condition
We conducted an experiment to evaluate the performance of the system subjectively. We prepared three audio signals of musical pieces(10 s for each piece) from the RWC popular music and music genre
databases [14] as input and reference pieces, and they were downsampled from 44.1 to 22.05 kHz. Then, we synthesized six pairs1of these musical audio signals. The signals of the input and reference pieces were converted into spectrograms with the short time
Fourier transform (STFT) with a 512-sample Hanning window and a
256-sample frame shift, and the synthesized spectrograms were converted into audio signals by the inverse STFT with the same window
and frame shift. The parameters of the frequency characteristics replacement were set at σ = 240 Hz and (K, ρ, ηk ) = (30, 0.2, 100/k)
for k ∈ [1, K].
∑ Then, the parameter ak of the envelope model was initialized by ω S ω /K for k ∈ [1, K], all frames and all pieces. For the
NMF of the percussive spectrograms, we set the number of bases at
4, and used the generalized I-divergence. The CP method was compared with the EQ method, and one of the authors chose which drum
1 Some synthesized sounds are available at http://hil.t.u-tokyo.
ac.jp/˜nakamura/demo/TimbreReplacement.html.

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Separated percussive spectrogramof the reference piece for a basis
Time of the reference piece [frame]

suppress the noise, (i) time-continuous segments should be used and(ii) the segment boundaries should be established when the activation is low. Since unsupervised source separation is still a challenging problem, the basis spectra may include a non-percussive component due to imperfect source separation, and (iii) the use of basis
spectra that include non-percussive components should be avoided.
The problem can be formulated as an alignment problem. The
requirements of (i), (ii), and (iii) are described as cost functions, andthe cumulative cost It (τ) can be written recursively as{Ot,τ
(t = 1),(14)
It (τ) :=Ot,τ + maxτ′ {Cτ′ ,τ + It−1 (τ′ )} (t > 1)

Activation of the reference
percussive spectrogram for a basis
Viterbi path =How to copy & paste
Copy & paste
Synthesized percussive
spectrogram for a basis
Time of the target piece [frame] Activation of the target percussive

spectrogram for a basis

Fig. 5. Outline of the copy and paste method.
sounds in the input piece were replaced with which drum sounds inthe reference piece. The parameters for the drum timbre replacement were set at (M, α, β, γ, c, ϵ) = (4, 0.5, 3, 10, 3, 100). A negativelog posterior, which was computed by the L2-regularized L1-loss
support vector classifier (SVC) [15], was used as Pτ , and the SVC
was trained to distinguish between percussive and non-percussive
instruments, using the RWC instrument database [14].
We asked 9 subjects how adequately they felt that (1) the drum
timbres of the input piece were replaced with those of the reference
piece and (2) the timbres of the input harmonic components were replaced with those of the reference piece. The subjects were allowed
to listen to the input, reference, and synthesized pieces as well as
their harmonic and percussive components as many times as they
liked. They then evaluated (1) and (2) for each synthesized piece ona scale of 1 to 5. 1 point means that the timbres were not replaced
and 5 points indicates that the timbres were replaced perfectly.
4.2. Result and discussion
The average scores of (1) with standard errors were 2.37 ± 0.15 and2.83 ± 0.15 for the EQ and the CP methods. The CP method result
was provided prior to that provided by the EQ method, in particular when the drum timbres were very diﬀerent as we mentioned inSec. 3. The average score of (2) with standard errors was 2.5 ± 0.1.
The results show that the subjects perceived the replaced drum timbres and frequency characteristics, and that the system works well.
We asked the subjects to comment about the synthesized pieces.
One subject said that he wanted to control the degree to which drum
timbres and frequency characteristics were converted. This opinion
indicates that it is important to enables users to adjust the conversions. Additionally, another subject mentioned that replacing vocal
timbres separately would change the moods of the musical pieces
more drastically. We plan to replace vocal timbres by using an extension of HPSS [16] for vocal extraction.
5. CONCLUSION
We have described a system that can replace the drum timbres andfrequency characteristics of harmonic components in polyphonic audio signals without using musical scores. We have proposed analgorithm that can modify a harmonic amplitude spectrum via its
bottom and top envelopes. We have also discussed two methods
for replacing drum timbres. The EQ method applies gains to basis spectrograms by the proportions of the NMF bases of the input
percussive spectrograms and those of the reference percussive spectrograms. The CP method copies and pastes the basis spectra of areference piece, according to NMF activations of the input and reference pieces. Through the subjective experiment, we confirmed thatthe system can replace drum timbres and frequency characteristics
adequately.

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