CONCURRENT ESTIMATION OF SINGING VOICE F0 AND PHONEMES BY USING
SPECTRAL ENVELOPES ESTIMATED FROM POLYPHONIC MUSIC
Hiromasa Fujihara and Masataka Goto
National Institute of Advanced Industrial Science and Technology (AIST)
ABSTRACTThe scarcity of available multi-track recordings constitutes a severe
constraint on the training of probabilistic models for voice extraction from polyphonic music. We propose a novel training method toestimate a spectral envelope of a singing voice that makes it possible to train the models from a polyphonic music without segregating a singing voice. We implement this method as an extension to
the existing W-PST method, which concurrently estimates singing
voice fundamental frequency (F0) and phoneme from polyphonicmusic. The novel training method is based on random samplingfrom probabilistic distributions. We conducted experiments on concurrent F0 and phoneme estimation and confirm the effectiveness of
our method.
Index Terms— Singing voice, Phoneme recognition, F0 estimation, Spectral envelope estimation.
1. INTRODUCTION
We aim to develop a computer that has the ability to distinguishsinging voices in the same manner that humans do. When a human hears singing voices that are mixed with other sounds, he or
she has an innate ability to distinguish singing voices from such
mixed sounds. The current ability of computers to recognize thereal world auditory scene is still inadequate when compared to human ability. In this paper, we focus on the fundamental frequency(F0) and phoneme (utterance content) as important elements of thesinging voice. Computational recognition of F0 and phonemes is important from an industrial standpoint, since the fruits of this research
are applicable in many important areas, including metadata description for music content, content-based music information retrieval,and sophisticated music playback interfaces.
We previously proposed a method for estimating phonemefrom singing voice polyphonic music, called W-PST (Weightedcomposition of Probabilistic Spectral Template) method [1]. Thismethod stochastically models a mixture of a singing voice and other
instrumental sounds without segregating the singing voice. It canalso estimate a reliable spectral envelope by estimating it from theharmonic structure of many voices with various F0s. This method
can be considered a new framework for recognizing a singing voicein polyphonic music because it is designed to concurrently recognize not only a phoneme but also other elements of a singing voice,including a singer’s name and gender.
However, this method had a major technical issue; a monophonic singing voice, which is not always available, is required
to train the models. Therefore, the scope of application of themethod was limited. Moreover, although we proposed a frameworkthat could concurrently estimate phonemes and F0, we evaluatedonly phoneme estimation tasks where the correct F0 was given inadvance.
This work was supported by CrestMuse, CREST, JST.

978-1-4577-0539-7/11/$26.00 ©2011 IEEE365

We propose a training method that—in contrast to existing
approaches—requires no separate singing voice recording, but instead trains a probabilistic model directly from polyphonic mixes of
vocal music. Hence, all recordings of vocal music become available
as potential training data. The original W-PST method approximatedthe mixture of sounds from a singing voice and other instruments byusing the first-order Taylor expansion. However, the equation obtained by the method was too complicated to train the models. Thus,
we developed a new approximative optimization method based ona random sampling from probabilistic distribution and enabled WPST to estimate the spectral envelope of a clean singing voice fromthe polyphonic music. Moreover, in this paper, we evaluated our
method using concurrent F0 and phoneme estimation tasks.
A great deal of research has been conducted on lyrics orphoneme recognition in the polyphonic singing voice [2, 3, 4, 5],
and vocal F0 estimation [6, 7, 8, 9, 10]; however, to our knowledge, no studies have concurrently estimated both F0 and phoneme.
The approaches of these studies differ from ours in that they either
ignored the influence of accompaniment sound or segregated thesinging voice from other instruments.
The rest of this paper is organized as follows. In the next section,
the original W-PST method is described. Section 3 explains how theoriginal W-PST method was extended. In Section 4, we describe theconcurrent estimation of F0 and phoneme experiments, which was
not in our previous paper[1]. In Section 5, we draw conclusions andpoint out future directions.
2. W-PST METHODThis section gives an overview of the W-PST method [1]. Thismethod consists of the following: (i) modeling of the singing voiceaccompanied by the other instruments based on templates of spectral envelope of singing voice, and (ii) estimation of the models that
represent the templates of the spectral envelope. Section 2.1 and 2.2
explain (i) and (ii), respectively.
2.1. Modeling of a Singing Voice in a Polyphonic Music
W-PST method expresses the observed spectrum of a singing
voices “as is” without segregation by stochastically modeling thegeneration process of the spectrogram of a singing voice with accompaniment sounds.
2.1.1. Probabilistic spectral template
We assume a spectrum of polyphonic sound mixture, y(f ), is
generated from the probabilistic variables Yf . We call these variables the probabilistic spectral template. Here, f represents a frequency in log scale, and y represents a spectral power in log scale.
We then assume that Yf can be expressed by two different probabilistic spectral templates, Yv,fand Yn,f , and a function H(f ; f0 ),which depends on a frequency f , as the following equation (Figs. 1
and 2),ICASSP 2011

Log-Pow er

where uf and σf2 are defined by (5) and (7), respectively.
To calculate Eq. (9), we need to optimize the parameter θ =(gv , gn , f0 ) using the quasi-Newton method based on the BFGS(Broyden-Fletcher-Goldfarb-Shanno) method, which is a class ofhill-climbing optimization techniques.

gv

Log-Pow er

Log-Pow er

4000

Log-Pow er

500 1000 2000
Frequency (H z)(a)Vocalspectraltemplate Yv , f

gn
500 1000 2000
Frequency (H z)

500 1000 2000
Frequency (H z)

4000(b)N ois
espectraltemplateYn , f

500 1000 2000
Frequency (H z)

4000

(c)
Probabili
sticspectral
template Y f

4000(d)O bserved spectrum y ( f )Fig. 1. Generation process of the observed spectrum [1]. The probability values are indicated by darkness.

500 1000 2000
Frequency (H z)

Log-Pow er+

Log-Pow er

Log-Pow er

f0

500 1000 2000
Frequency (H z)

4000

4000

500 1000 2000
Frequency (H z)

4000

(a)
Vocalenvelop
etemplateY 'v , f (b)Excit
Vocalspectraltemplate Yv , fatio
n Functi
on H ( f ; f 0 ) (c)Fig. 2. Example of vocal spectral template [1], which is generated
from the vocal envelope template and the excitation function.
Yf =log(exp(Yv,f + gv ) + exp(Yn,f + gn )),
Yv,f =Yv,f+ H(f ; f0 ),X
2
N (f ; log f0 + log h, σH).
H(f ; f0 )=

(1)
(2)
(3)

h


Here, Yv,frepresents a spectrum of a vocal, which is called the vocal
spectral template, and Yn,f represents that of the other instrumental
sounds, which is called the noise spectral template. H(f ; f0 ) represents a spectrum of a vocal cord vibration of pitch f0 , which iscalled an excitation function. gv and gn represent the gain parameters. By changing them, the S/N ratio of the vocal and noise spectral
templates can be controlled. Note that we assume the additivity ofthe power spectrum is in the linear scale and the source-filter model.

We assume that Yv,fand Yn,f follow the Gaussian distribu
2∼ N (y; μv,f , σv,f),tion (in log scale) and are represented by Yv,f
2
2
Yn,f ∼ N (y; μn,f , σn,f ), where N (y; μ, σ ) represents the Gaussian distribution with mean μ and variance σ 2 .
Since the probabilistic spectral template expressed in (1) is difficult to calculate, we approximate Yf using a Gaussian distribution
based on the first-order Taylor expansion as follows,
Yf ∼N (y; μf , σf2 )(4)
μf =log(exp (μv,f + gv ) + exp (μn,f + gn ))(5)μv,f =μv,f + H(f ; f0 )
(6)
2 2
2 2
+
g
))
σ
+
(exp
(μ
+
g
))
σ
(exp
(μ
v
n
v,f
n,f
v,f
n,f
. (7)
σf2 =
(exp (μv,f + gv ) + exp (μn,f + gn ))22.1.2. Phoneme recognition and F0 estimation
To recognize a phoneme using this model, first, an individual
template, θvp , for each phoneme p has to be prepared. Given theF0 of the singing voice f0 and the observed spectra y(f ), we canestimate a pair of the phoneme and the F0, {î, fˆ0 }, involved in the
spectra by the following equation:X{î, fˆ0 }=argmax max
log pf (y(f ); θi,v , θn , f0 , gv , gn ) (8)i,f0

gv ,gn≈argmax max
i,f0

gv ,gnf

X

log N (y(f ); uf (θi,v , θn , f0 , gv , gn ),f

σf2 (θi,v , θn , f0 , gv , gn ))

(9)

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2.2. Estimation of Spectral Templates from a MonophonicSinging Voice
We estimate a spectral envelope that is represented by Yv,fin
Eq. (1) from a monophonic singing voice. The spectral envelope ofthe singing voice cannot be directly observed; what we can observe
is a harmonic structure that is considered to be points sampled fromthe original spectral envelope. Thus, in general, it is difficult to estimate the original spectral envelope from a single harmonic structure.
We overcome this difficulty and estimate a reliable spectral envelope
using many harmonic structures with various F0s. Moreover, since
we estimate the spectral envelope as a set of probabilistic distributions, the estimated envelope is robust against the fluctuation of thesinging voice and the difference in conditions between the training
and testing data.

Since volumes could differ from frame to frame, we need ascheme to normalize such volume differences when we estimate theenvelope from many harmonic structures. We consider the volumeof each frame as an unknown parameter, and estimate it concurrently
with the parameters of the model for estimating the spectral envelope.
2.2.1. Mixture of experts
For a spectral template model, we use the mixture of experts(MoE) model [11] based on the linear regression model. This model2
represents μv,f and σv,fof a spectral template asX2
Gm (f |ψm , μm , σm)(am f + bm )(10)
μv,f =
2
=
σv,f

i
X

2 2 2
Gi (f |ψm , μm , σm
) βm ,(11)i2where Gm (f |ψm , μm , σm
) is the output of the gating network, andwe use a normalized Gaussian function [12] defined by2)
ψm N (f |μm , σm
2
Gm (f |ψm , μm , σm
)= P
.
(12)
2


ψ
N
(f
|μ
m , σm )m m
2
2, am , b m , βm
} isHere, {ψm , μm , σm
Pa set of unknown parameters,
where ψm satisfies ψm ≥ 0 and m ψm = 1. These parameters can be estimated using the expectation-maximization (EM) algorithm.

2.2.2. Iterative parameter estimation
When we observe harmonic structures si (i = 1, . . . , I), which
consist of the log power of the h-th harmonic component, yi,h , andits frequency, fi,h , denoted bysi = {(fi,1 , yi,1 ), . . . (fi,h , yi,h ), . . . (fi,Hi , yi,Hi )},(13)
the target likelihood function to be maximized is defined by
Hi
I X
X
L=
log N (yi,h + ki ; μv,fi,h , σv,fi,h ),(14)i=1 h=1

where ki represents the offset parameter, which normalizes the volume of the harmonic structure. Since it is difficult to estimate bothki and the parameters of MoE at the same time, we update themsequentially. As for the noise spectral envelope, we can estimate
the parameter in the same manner by considering the spectrum assi (i = 1, . . . , I).

3. ESTIMATION OF SPECTRAL TEMPLATES FROM ASINGING VOICE IN A POLYPHONIC MUSICIn this section, we describe a new method to expand the WPST method so that the template can be estimated from polyphonicsinging voices. We concurrently estimate the parameters of the voice
envelope template and noise spectral template.
In Section 2.1.1, we approximate the sum of log-normal distribution using the first-order Taylor expansion. However, the obtained
equations, Eq. (4)!A(7), have become so complex that it is difficult
to use these approximated equations to estimate the parameters of
the templates. Our approach to estimate them is to strictly calculate the sum of log-normal distribution and estimate the parameters
based on an approximative algorithm.

dom values (Ui,1,f , · · · , Ui,r,f , · · · , Ui,R,f ), which have the nor2
mal distribution N (U ; μn,f + gi,n , σn,f) and lies within the interval(−∞, yi (f )). The objective function L can be approximated as
Z X
I
R
X
L≈
log
πi,r,fi=1

r=1

N (log(exp(yi (f )) − exp(Ui,r,f ))2; μv,f,i + gi,v , σv,f)exp(yi (f ))
πi,r,f =(exp(yi (f )) − exp(Ui,r,f )) Cyi (f ),i,f R
Z y2
N (U ; μn,f + gi,n , σn,f)dUCy,i,f =

(20)
(21)
(22)

−∞

It should be noted that πi,r,f and log(exp(yi (f )) − exp(Ui,r,f ))become constants if gi,n and θn are constants, and we can thus esti3.1. Basic formulation of an objective function
mate gi,v and θv by using Eq. (20). Similar to Eq. (18), gi,n and θn
The observed spectra are represented as y1 (f ), · · · , yi (f ), · · · , yI (f )can be updated in by considering gi,v and θv as consonants.
and the parameters of the voice envelope template and the noise
3.3. An EM-like method to optimize a logarithm of a sum
spectral template to be estimated are written as22θv = {ψv,m , μv,m , σv,m
, av,m , bv,m , βv,m},(15)However, Eq. (20) is the shape of logarithm of a sum, which is22, an,m , bn,m , βn,m},(16)
θn = {ψn,m , μn,m , σn,mknown to be difficult to maximize directly. Thus, we maximize Eq.
(20) by an iterative method resembling the EM algorithm. Hereafter,
respectively. The mean parameter of the vocal spectral template isparameters to be estimated are denoted as λ = {gi,v , θv } for concalculated as μv,f,i = μv,f + H(f ; f0 (i)) by adding the excitavenience and λ represents the updated parameters in the previous
tion function. Note that we assume the F0 sequence of the observed
iteration. First, we introduce new variables asspectrum, f0 (0), · · · , f0 (i), · · · , f0 (I), is given.
πi,r,f ψi,r,f
The objective function to be maximized is written as
zi,r,f = PR
(23)

Z X
I


r =1 πi,r ,f ψi, r , fL=log pi,f (y; θv , θn , gi,v , gi,n )df(17)
ψi,r,f =N (log(exp(yi (f )) − exp(Ui,r,f ))2
i=1; μv,f,i + gi,v , σv,f)(24)
„Z yi (f )
Z X
I


and write zi,r,f calculated by using λ as zi,r,f. L can be maximizedlog
N (log(exp(yi (f )) − exp(U ))=by iterating the following two steps: (i) estimate λ that maximizes a−∞i=1
new objective function Q1 (λ|λ ),22; μv,f,i + gi,v , σv,f )N (U ; μn,f + gi,n , σn,f )
Z X
R
I X
«

exp(yi (f ))Q1 (λ|λ )=zi,r,flog πi,r,f
dU df
(18)
exp(yi (f )) − exp(U )i=1 r=1
Z yi (f )Z X
IN (log(exp(yi (f )) − exp(Ui,r,f ));2log(
N (log(exp(yi (f )) − exp(U ))=μv,f,i + gi,v , σv,f
)df
(25)
−∞
i=1
and
(ii)
calculate
z
using
the
estimated
λ.
i,r,f
2
2
)N (U ; μv,f,i + gi,v , σv,f)
; μn,f + gi,n , σn,fSince the term πi,r,f in Eq. (25) is irrelevant to the maximization
exp(yi (f ))of Q1 (λ|λ ), we can use new objective function Q2 (λ|λ ),dU )df(19)
exp(yi (f )) − exp(U )
Z X
I X
R


where pi,f (y; θv , θn , gi,v , gi,n ) represents a probabilistic density
Qzi,r,f2 (λ|λ )=function of composed spectral template1 . Note that gi,v and gi,n are
i=1 r=1
the parameters used to normalize the volume of each frame, which
log N (log(exp(yi (f )) − exp(Ui,r,f ))2
is similar to ki in Section 2.2.2 . Practically, the integral in the above; μv,f,i + gi,v , σv,f
)df
(26)

equation is substituted in sum operations in the discrete frequency
instead of Q1 (λ|λ ). Finally, since Q2 follows the same form as Eq.
scale because continuous wavelet transform is calculate in discrete(14) in Sec 2.2.2, we can maximize Q2 by using the EM algorithm
time. Here, the parameters to be estimated are {gi,v , gi,n , θv , θn }.
in the same manner as the template estimation from a monophonicsinging voice.
3.2. Approximative parameter estimation based on a random
sampling
Since it is difficult to estimate all the parameters at the sametime, we estimate them successively and iteratively. We first estimate gi,v and θv based on Eq. (18) considering gi,n and θn as
constants and we then estimate gi,n and θn based on Eq. (19) considering gi,v and θv as constants. When we consider gi,n and θn
as constants, Eq. (18) can be interpreted as an expectation operation. Thus, we approximate the expectation using the sum operation by sampling the probabilistic variable U that follows truncated normal distribution. To be more precise, we obtain R ran1 We added an index of the observed spectrum i because the shape of the
PDFs are different from frame to frame here.

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4. EXPERIMENTS
We conducted experiments on phoneme recognition using 10
Japanese songs performed by 6 singers (3 male, 3 female), takenfrom the “RWC Music Database: Popular Music” (RWC-MDB-P2001) [13]. The target phonemes were all 5 Japanese vowels; /a/, /i/,/u/, /e/, and /o/. We conducted a 6 fold cross validation; that is, when
we evaluated a song of a specific singer, the vocal and noise templates (we call them phoneme model) were trained using songs fromthe other 5 singers. We used a manually annotated phoneme label
and F0 annotation of the songs for both training data and groundtruth. Accuracy for both phoneme estimation and F0 estimation isdefined as the ratio of the number of frames that are correctly esti-

Extended W-PST
Phoneme
F0
70.2
55.4
57.4
71.6
44.0
43.2
63.5
77.3
58.0
81.0
68.5
85.0
63.0
80.1
65.4
79.6
68.5
86.4
42.0
82.5
60.1
74.2

LogPow er

LogPow er

Baseline
W-PST
Song∗
PhonemeF0
Phoneme
F0
No. 4
31.1
62.6
73.5
58.9
No. 11
56.5
65.6
57.6
71.5
No. 9
47.5
65.5
43.4
43.3
62.8
76.8
63.9
77.6
No. 12
No. 6
51.5
69.2
60.4
80.8
69.5
71.6
68.5
86.3
No. 2
No. 16
62.7
78.2
65.4
82.6
No. 7
60.0
73.8
67.2
82.7
No. 18
64.1
73.5
70.2
87.6
44.1
79.1
42.3
82.0
No. 14
Average
55.0
71.6
61.2
75.3
∗
Song number of RWC-MDB-P-2001[13].

LogPow er

Table 1.
Experimental results for concurrent estimation ofphonemes and F0 (%).

500
2000
1000
Frequency (H z)

40007000(a)A etm plateesti
m ated from am onophonicsingingvoiceusinga m ethoddescribedin Sec2.2.

500
2000
1000
Frequency (H z)

40007000(b) A tem plateesti
m atedfr
om a polyphonicm usic
usingourm ethod

500
2000
1000
Frequency (H z)

40007000(c) A tem plateesti
m atefrom apolyphonicm usicusinga
m ethoddescribedin Sec2.2.

Fig. 3. An example of spectral estimation from a singing voice of apolyphonic music. This example represents an envelope of phoneme/i/ in song No. 7 in the RWC-MDB-P-2001 [13].

mated to the total number of frames. Only frames that involve thetarget 5 vowels were used for calculating the accuracy.
We tested our method under the following 3 conditions.
(i) Baseline Use the F0 estimation method called PreFEst [14] andthe feature extraction method used in [15]; segregate the singing
voice based on the harmonic structure before extracting MFCCs,
ΔMFCCs, and ΔPower and recognize them using the GMMs.
(ii) W-PST Use the method described in [1].
(iii) Extended W-PST Use the W-PST method with the new template estimation algorithm from polyphonic singing voices proposedin this paper.
In condition (i) , we used the Short Time Fourier Transform forspectrum analysis and we set the number of mixtures of GMMs andthe number of dimensions of MFCCs to 12 and 32, respectively. The
data used for training GMMs were also segregated. In conditions (ii)and (iii), we used the wavelet transform with the Gabor wavelet forspectrum analysis, and set the number of mixtures of the MoE to 10.
In condition (ii), the vocal templates were trained using the vocalonly tracks of the songs, and the noise template was trained usinga karaoke (without vocal) track of the songs based on the harmonic
structures. In condition (iii), the vocal and noise templates weretrained using polyphonic tracks of the songs.
The results are summarized in Table 1. We can see that the original W-PST method (ii) increased the average accuracy by 6.2 points
for phoneme estimation and 3.7 points for F0 estimation compared
to baseline method (i). We confirmed that the W-PST method canestimate F0 and phonemes better than the conventional method. We
can also see that the extended W-PST method (iii), though not as
accurate as the original W-PST method, is still more accurate thanbaseline method (i) by 5.1 points for phoneme estimation and 2.6
points for F0 estimation. These results show that our method worked
well even if monophonic singing voices are not available for training
data.
Fig. 3 shows examples of a spectrum estimated from a monophonic singing voice using our previous method described in 2.2.2(Fig. 3 (a)), and a spectrum estimated from a singing voice in a polyphonic music using a method proposed in this paper (Fig. 3 (b)), anda spectrum estimated from a singing voice segregated from a polyphonic music in using the accompaniment sound reduction method
proposed in [15] (Fig. 3 (c)). We can see the spectrum proposed by
the proposed method (b) is closer to the spectrum of optimal case(a) than the spectrum directly estimated from a polyphonic music
without dealing with the accompaniment sound (c).
5. CONCLUSION
We described how to expand a method called W-PST [1] that
concurrently estimates the F0 and phonemes of a polyphonic singing
voice. Since the original W-PST method could train models only

from monophonic singing voices, we made it possible to train models from polyphonic singing voices by developing a method for estimating spectral envelopes from polyphonic singing voices. We
conducted concurrent F0 and phoneme estimation experiments andfound that our method indicated improved performance comparedto the conventional method. In the future, we plan to extend thismethod to deal with consonant phonemes and vocal activity detection. Future plan also includes integration with temporal modelingmethods such as the hidden Markov models (HMMs).
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