MUSICAL TYPICALITY: HOW MANY SIMILAR SONGS EXIST?
Tomoyasu Nakano1 Daichi Mochihashi2 Kazuyoshi Yoshii3 Masataka Goto1
1
National Institute of Advanced Industrial Science and Technology (AIST), Japan
2
The Institute of Statistical Mathematics, Japan
3
Kyoto University, Japan1
2{t.nakano, m.goto}[at]aist.go.jp
daichi[at]ism.ac.jp
3
yoshii[at]kuis.kyoto-u.ac.jp
ABSTRACT
We propose a method for estimating the musical “typicality” of a song from an information theoretic perspective.
While musical similarity compares just two songs, musical typicality quantiﬁes how many of the songs in a set are
similar. It can be used not only to express the uniquenessof a song but also to recommend one that is representativeof a set. Building on the type theory in information theory (Cover & Thomas 2006), we use a Bayesian generativemodel of musical features and compute the typicality of asong as the sum of the probabilities of the songs that share
the type of the given song. To evaluate estimated results,
we focused on vocal timbre which can be evaluated quantitatively by using the singer’s gender. Estimated typicality
is evaluated against the Pearson correlation coefﬁcient between the computed typicality and the ratio of the numberof male singers to female singers of a song-set. Our resultshows that the proposed measure works more effectively toestimate musical typicality than the previous model based
simply on generative probabilities.
1 INTRODUCTION
The amount of digital content that can be accessed has
been increasing and will continue to do so in the future.
This is desirable with regard to the diversity of the content,
but is making it harder for listeners to select from this content. Furthermore, since the amount of similar content isalso increasing, creators will be more concerned with theoriginality of their creations. All kinds of works are inﬂuenced by some existing content, and it is difﬁcult to avoid
an unconscious creation of content partly similar in some
way to other content.
This paper focuses on musical typicality which reﬂects
the number of songs having high similarity with the target song as shown in Figure 1. This deﬁnition of musical typicality is based on central tendency, which in cognitive psychology is one of the determinants of typicality [2]. Musical typicality can be used to recommend aunique or representative song for a set of songs such as
those in a particular genre or personal collection, those on
c Tomoyasu Nakano, Daichi Mochihashi, Kazuyoshi

Yoshii, Masataka Goto. Licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). Attribution: Tomoyasu
Nakano, Daichi Mochihashi, Kazuyoshi Yoshii, Masataka Goto. “Musical Typicality: How Many Similar Songs Exist?”, 17th International
Society for Music Information Retrieval Conference, 2016.

song asong asong bﬁ

ﬁ
ﬁ

musicalsimilarity

lowmusicaltypicality

high

ﬁ

song bsong set Aﬁ ﬁ ﬁ ﬁ ﬁ
ﬁ ﬁ ﬁ ﬁ ﬁlowe.g., a particular genre
a personal collectiona specific playlist

Figure 1. Musical similarity and typicality.
Generative modeling

ﬁ
ﬁ
ﬁ

...
feature vectors

1 2 3 1 ... 5

generative model
generative model
generative model

vector quantization

song models(LDA)

1 2 3 1 ... 5

calculate
probability

vector quantization

Previous approachsong-setmodel

Typicality estimationﬁ...
feature vectors

song-setmodel

song model (LDA)
calculate
probability

2 2 1 1 ... 2
topic sequence

type

Proposed approach(topic distribution)

Figure 2. Estimation of music typicality represented by adiscrete sequence based on the type theory. Both the previous and the proposed approach are illustrated.
a speciﬁc playlist, or those released in a given year or adecade. And it can help listeners to understand the relationship between a song and such a song set. However,human ability with regard to typicality is limited. Judging similarity between two songs is a relatively simple task
but is time-consuming, so judging the similarities of a million songs is impossible. Consequently, despite the comingof an era in which people other than professional creators
can enjoy creating and sharing works, the monotonic increase in content means that there is a growing risk thatone’s work will be denounced as being similar to someone else’s. This could make it difﬁcult for people to freely
create and share content. The musical typicality proposedin this paper can help create an environment in which specialists and general users alike can know the answers to thequestions “How often does this occur?” and “How many
similar songs are there?”.
Much previous work has focused on musical similarity
because it is a central concept of MIR and is also important for purposes other than retrieval. For example, the use

Previous approach

2/3
1/3

0 0 0 0 0 0 song a
generative probability highProposed approach

01
type

0 1 0 1 0 0 song b
1 0 0 0 1 0 song c
typicality highFigure 3. Examples of a song having high generative probability and songs having high typicality.
of similarity to automatically classify musical pieces (intogenres, music styles, etc.) has been studied [10, 13], as has
its use for music auto-tagging [17]. Each of these applications, however, is different from musical typicality: musical similarity is usually deﬁned by comparing two songs,
music classification is deﬁned by classifying a given song
into one out of a set of categories (category models, centroids, etc.), and music auto-tagging is deﬁned by comparing a given song to a set of tags (tag models, the closest
neighbors, etc.).
Nakano et al. proposed a method for estimating musical typicality by using a generative model trained fromthe song set (Figure 2) [16] and showed its application tovisualizing relationships between songs in a playlist [14].
Their method estimates acoustic features of the target songat each frame and represents the typicality of the target
song represented as an average probability of each frameof the song calculated using the song-set model. However,
we posit that the generative probability is not truely appropriate to represent typicality.
The method we propose here, in contrast, introduces thetype from information theory for improving estimated musical typicality by a bag-of-features approach [16]. In thiscontext, the type is same meaning with the unigram distribution. We ﬁrst model musical features of songs by using
a vector quantization method and latent Dirichlet allocation (LDA) [4]. We then estimate a song-set model fromthe song models. Finally, we compute the typicality of thetarget song by calculating the probability of a type of themusical sequence (quantized acoustic features) calculatedusing the song-set model (Figure 2).

think about the sum of the probabilities of songs that are
similar to the song to measure the typicality.
2.1 Type and the Typicality
Let us formalize our ideas from the viewpoint of information theory [5–7]. Let x = {x1 , x2 , · · · , xn } be a sequenceof length n whose alphabet x comes from a set X . We
assume that x comes from a stationary memoryless information source, i.e. we can drop the order of symbols in x
and regard x as a bag of words. Next, we introduce somedeﬁnitions:Deﬁnition 1 (type). Let N (x|x) be the number of times
that x ∈ X appeared in sequence x. The type Px of thesequence x is an empirical probability distribution of symbols in x:




1

Px =
N (x|x)  x ∈ X .
(1)n
We denote the space of all Px as Pn .
Deﬁnition 2. Let P ∈ Pn . A set of sequences of length nthat share the same type P is called a type class T n of P :T n (P ) = {x ∈ X n | Px = P } .

(2)

Now let us denote the probability of a sequence x froman memoryless information whose symbol probabilities
are Q(x):p(x) = Qn (x) =nQ(xi ) .

(3)

i=1

Given these deﬁnitions, the following simple theorems follow:
Theorem 1. The probability of a sequence x having type
P from a stationary memoryless information source Q isexpressed as follows:Qn (x) = exp −n(H(P ) + D(P ||Q))(4)
Here, H(P ) and D(P ||Q) are an entropy of P and
Kullback-Leibler divergence of P from Q, respectively.

P (x) log P (x)(5)
H(P ) = −x∈X

D(P ||Q) =P (x) log

x∈X

P (x)
Q(x)

(6)

Proof.
2 METHOD
The key concept of the method in this paper is the type ofa sequence on which we consider the typicality of a given
music. Previous work have mentioned/used simple generative probabilities to compute musical similarity [1] or
typicality [16] of a music and for singer identiﬁcation [8].
However, simple generative probability will not conformto our notion of typicality. Imagine the simplest example
in Figure 3: here, each song consists of alphabets of {0, 1}
and the stationary information source has a probability distribution on alphabets Q(0) = 2/3, Q(1) = 1/3.
Clearly, while the song “a” has the highest probabilityof generation, we can see that the sequences like “b” and“c” will occur more typically. This means that we should

Qn (x) =

n

i=1

=



Q(xi ) =

Q(x)N (x|x) =x

exp nP (x) log Q(x)x= exp −n −Q(x)nP (x)

x



(7)

P (x) log Q(x)(8)

x= exp −n H(P ) + D(P ||Q)

.



(9)

Theorem 2 (lower and upper bounds). For any type P ∈Pn ,1
exp{nH(P )}(n + 1)|X |−1(10)≤ |T n (P )| ≤ exp{nH(P )}.

Using the theorems above, the following important theorem can be proved.
Theorem 3. For any type P ∈ Pn and any probability
distribution Q,.
Qn (T n (P )) = exp{−nD(P ||Q)},(11).
where an = bn if limn→∞ (1/n) log(an /bn ) = 0.
Proof. Using (4) and (10),Qn (T n (P )) =x∈T n (P ) Q
n

n

(x)

= |T (P )| exp(−n(H(P ) + D(P ||Q))).
= exp(nH(P )) · exp(−n(H(P ) + D(P ||Q)))= exp{−nD(P ||Q)} .



(12)

This theorem says that the sum of the probabilities ofsequences that share the same type P is given by an exponential of Kullback-Leibler divergence from the information source Q. While the equation (11) is usually used in
information theory to formalize that such a probability exponentially decays with the length n, here we do not carefor n but for the form of the function. Thus, we normalize(11) for a unit observation like the well-known perplexity,
yielding the deﬁnition of typicality as follows:
Deﬁnition 3 (Typicality).
Typicality(P |Q) = exp{−D(P ||Q)}(13)

where P is the type of a musical sequence and Q is a generative model of its musical features.
2.2 Generative modeling and TypeF0 is used to estimate the ΔF0 and the LPMCCs of the
vocal. To estimate the LPMCCs, the vocal sound is resynthesized by using a sinusoidal model based on the estimated vocal F0 and the harmonic structure estimated fromthe audio signal. At each frame the ΔF0 and the LPMCCs
are combined as a feature vector.
Then reliable frames (frames little inﬂuenced by accompaniment sound) are selected by using a vocal GMM
and a non-vocal GMM (see [8] for details). Feature vectors of only the reliable frames are used in the following
processes (model training and probability estimation).
2.2.2 Quantization
Vector quantization is applied using the k-means algorithm
to convert acoustic feature vectors of each element to asymbolic time series representation. In that algorithm thevectors are normalized by subtracting the mean and dividing by the standard deviation, and then the normalized vectors are quantized by prototype vectors (centroids) trained
previously. Hereafter, we call the quantized symbolic timeseries acoustic words.
2.2.3 Probabilistic generative model: song model
The observed data we consider for LDA are D independentsongs X = {X 1 , ..., X D }. A song X d is Nd acoustic
words X d = {xd,1 , ..., xd,Nd }. The size of the acoustic words vocabulary equals to the number of clusters of
the k-means algorithm, V . We consider a K-dimensional
multinomial of latent topic proportions θd for each X d ,and write θ = (θ1 , · · · , θD ).
Introducing latent topic assignments Z d={z d,1 , ..., z d,Nd } for X d and collectively write
Z = {Z 1 , ..., Z D }, the full joint distribution of our
LDA model is given by

To evaluate the typicality estimation method, we computethe type of each song by modeling them in a way basedon our previous work [16]. From polyphonic musical audio signals including a singing voice and sounds of various
musical instruments, we ﬁrst extract vocal timbre. We thenmodel the timbre of songs by using a vector-quantization
method and latent Dirichlet allocation (LDA) [4]. Finally,a song-set model Q is estimated by integrating all songmodels (Figure 2).
In addition, we use the expectation of Dirichlet topic
distribution as a type P because the hyperparameter of theposterior Dirichlet distribution can be interpreted as thenumber of observations of the corresponding topic. In theother words, the P indicates mixing weights of the multiple topics.

where φ indicates the emission distribution of each topic.
The ﬁrst two terms are likelihood functions, and the othertwo are prior distributions. The likelihood functions aredeﬁned as
Kxd,n,v
Nd 
V
D 

 z
d,n,k
p(X|Z, φ) =
φk,v
(15)

2.2.1 Extracting acoustic features: Vocal timbre

We endow θ and φ conjugate Dirichlet priors:

We use the mel-frequency cepstral coefﬁcients of the LPC
spectrum of the vocal (LPMCCs) and the ΔF0 of the vocal to represent vocal timbre because they are effective for
identifying singers [8, 15]. In particular, the LPMCCs represent the characteristics of the singing voice well, since
singer identiﬁcation accuracy is greater when using LPMCCs than when using the standard mel-frequency cepstral
coefﬁcients (MFCCs) [8].
We ﬁrst use Goto’s PreFEst [11] to estimate the F0 of
the predominant melody from an audio signal and then thep(X, Z, θ, φ) = p(X|Z, φ)p(Z|θ)p(θ)p(φ)

d=1 n=1 v=1

andp(Z|θ) =

(14)

k=1

Nd 
D 
V


z

d,n,k
θd,k
.

(16)

d=1 n=1 v=1p(θ) =

D

Dir(θd |α0 ) ∝d=1p(φ) =

K

k=1

K
D 


α0 −1
θd,k

(17)

β0 −1
φk,v
.

(18)

d=1 k=1

Dir(φk |β0 ) ∝VK 
k=1 v=1

where p(θ) and p(φ) are products of Dirichlet distributionsand α0 , β0 are their prior hyperparameters.
Finally, we obtain a type of each song X d as an expectation of the Dirichlet posterior distribution of θd .

Dir(6,2,2)

Dir(6,2,6)

Dir(18,10,10)

Dir(6,6,2)

Dir(7,1,1)

Dir(5.4, 2.9, 2.8)

Dir(1,1,7)

Dir(9,9,9)

Proposed method

Previous approachDir(1,7,1)

Dir(0.92, 0.89, 0.97)

Proposed method

Previous approach

Figure 4. Song-set model estimation of previous approach and a model estimated by our proposed method.
2.3 Typicality over a set of Songs=

Given the type of each song, we wish to compute the typicality of a song as compared to a set of other songs. In Section 2.1, we deﬁned the typicality of a sequence of type P
from an information source having distribution Q. Therefore, we need some way to estimate Q from the set of songs(i.e. types) beforehand. Actually, we do not have to estimate a single Q but compute an expectation around it:
Typicality(P |Θ) = E[exp(−D(P ||θ))]θ∼Dir(α)(19)

where Θ = {θ1 , · · · , θn } is a set of types of other songs
and Dir(α) is a prior Dirichlet distribution from which
each θi ∈ Θ is deemed to be generated.
In the previous work [16], we estimated the hyperparameter α by just summing the topic distributions
θ1 , · · · , θn . As shown in Figure 4, however, this could leadto an undesirable result and we employ a Bayesian formula
to estimate α. This derivation is based on the following
Dirichlet and Gamma distributions:αk )  αk −1Γ(Dir(θ|α) =  kθk(20)k Γ(αk )kGa(α|a, b) =ba a−1 −bα
e
α
Γ(a)

(21)

Therefore,p(α|Θ) ∝ p(Θ|α)p(α)
 Γ(αka−1 e−bαk ·
∝

(22)
 α
α
)
k
k
θk k , (23)k Γ(αk )jkkwhich leads top(αk |αk−1 , Θ) ∝ αka−1 e−bαk · Γ(jk α k ) αkθk . (24)Γ(αk )

Because we cannot expand Γ( k αk )/Γ(αk ), we make afollowing approximation with n being a nearest integer toj=k αk [18]:Γ(αk + j=k αj )Γ( k αk )Γ(αk +n)=Γ(αk )
Γ(αk )
Γ(αk )= αk (αk + 1) · · · (αk + n − 1)
=

n−1

i=0

αk (αk + i)

(25)

n−1




(αk )yi (i)1−yi .

(28)

i=0 y∈{0,1}

Therefore, introducing auxiliary variablesαkyi ∼ Bernoulli,
αk + i(29)

we can make a following Gamma proposal for αk :p(αk |αk−1 , Θ)(30)

 αka−1 e−bαk ·
=

a+
αk

eαk log θjk ·j n−1i=0 yji −1

j= Ga(a +

 n−1

j

· e−αk (b−yji , b −



i=0


 n−1

j


y

αkji (31)i=0

j log θjk )log θjk ).

(32)
(33)

j

Because this is just a proposal, we further correct the bias
using a Metropolis-Hastings algorithm with the exact likelihood formula (24).
2.4 Computing the Expectation
Once we obtain α from Θ, we can compute the expectation(19) analytically. Denoting P = (p1 , · · · , pK ) and writing
E[] as ,
Typicality(P |Θ) = exp(−D(P ||θ)) θ∼Dir(α)
(34)


K

θk
pk log= exp
pk
k=1
θ∼Dir(α)
1=pk log θkexp
exp( k pk log pk )kθ∼Dir(α)
K p= exp(H(P ))
θk k
.
(35)
k=1

θ∼Dir(α)

Here, the second term is

K
 p
Γ(
k
θk
= 
k=1

θ∼Dir(α)

k αk )k Γ(αk )

(26)

Γ(
= 

(27)

Γ(
= 

k αk )k Γ(αk ) θkαk −1 · p
θkk dθk kθkαk +pk −1 dθ

 k
α
)
k k
k Γ(αk +pk )k Γ(αk ) Γ(k αk +pk )

=

1
k αk

 Γ(αk +pk )k

Γ(αk ).

(36)

Therefore, from (35) we ﬁnally obtainexp(H(P ))  Γ(αk +pk ). (37)
Typicality(P |Θ) =Γ(αk )k αk
k

3 EXPERIMENTS
The proposed methods were tested in an experiment evaluating the estimated typicality. To evaluate estimated results, we focused on vocal timbre which can be evaluatedquantitatively by using the singer’s gender.
3.1 Dataset
The song set used for the LDA-model-training and typicality estimation comprised 3,278 Japanese popular songs1
that appeared on a popular music chart in Japan (http://www.oricon.co.jp/) and were placed in the top
twenty on weekly charts appearing between 2000 and2008. Here we refer to this song set as the JPOP MDB.
The song set used for GMM training and k-means training to extract the acoustic features consisted of 100 popular songs from the RWC Music Database (RWC-MDB-P2001) [9]. These 80 songs in Japanese and 20 in English
reﬂect styles of the Japanese popular songs (J-Pop) andWestern popular songs in or before 2001. Here we refer
this song set as the RWC MDB.
3.2 Experimental Settings
Conditions and parameters of the methods described in the
METHODS section are described here in detail. Someconditions and each parameter value were based on previous work [15, 16].

3.2.4 Training the generative models
Training song models and song-set models of the vocal
timbre by LDA, we used all of the 3,278 original recordings of the JPOP MDB.
The number of topics, K, was set to 100, and the model
parameters of LDA were trained using the collapsed Gibbs
sampler [12]. The hyperparameters of the Dirichlet distributions for topics and words were initially set to 1 and 0.1,
respectively.
3.3 Four typicality measures
We evaluated the following four typicality computing conditions.
T1: computing the Euclidean distanceT2: computing the generative probability [16]T3: computing the KL-divergence, equation (13)
T4: computing the KL-divergence, equation (37)
As a baseline method, under the T1 condition, one simple method used to estimate the typicality of vocal timbre
calculated the Euclidean distance between mean feature
vectors of a song and a song-set. Each mean vector was
calculated from each song, using the reliable vocal frames,
and was normalized by subtracting the mean and dividing
by the standard deviation of all mean vectors.
Under the T2 condition, one typicality between a song
and a set of songs is obtained by calculating a generative probability [16] of song P calculated using a song-set
model of song Q. This typicality pg (P |Q) is deﬁned asfollows:log pg (P |Q) =NP
1 log p(xP,n | E[θ Q ], E[φ]), (38)NP n=1p(xP,n | E[θ Q ], E[φ]) =K
(E[θQ,k ] · E[φk,v ]) ,

(39)

k=1

3.2.1 Typicality estimation
The number of iterations of the Bayesian song-set model
estimation described in Subsection 2.3 was 1000.
3.2.2 Extracting acoustic features
For vocal timbre features, we targeted monaural 16-kHz
digital recordings and extracted ΔF0 and 12th-order LPMCCs every 10 ms. To estimate the features, the vocal sound
was re-synthesized by using a sinusoidal model. The ΔF0
was calculated every ﬁve frames (50 ms).
The feature vectors were extracted from each song, using as reliable vocal frames the top 15% of the featureframes. Using the 100 songs of the RWC MDB, a vocal
GMM and a non-vocal GMM were trained by variational
Bayesian inference [3].
3.2.3 Quantization
To quantize the vocal features, we set the number of clusters of the k-means algorithm to 100 and used the 100
songs of the RWC MDB to train the centroids.
1 Note that some are Western popular songs and English in them .

where E[·] is the expectation of a Dirichlet distribution,
NP is the number of frames, and v is the corresponding
index (the word id) of the K-dimensional 1-of-K observation vector xb,n .
The other two typicalities, under the T3 and T4 conditions, are calculated Typicality(P, Q) by using equations(13) and (37), respectively.
3.4 Experiment: musical typicality estimation
We evaluated the four typicality computing conditions (T1T4) in combination with the following three song-set modeling conditions.
M1: computing a mean vector
M2: summing the Dirichlet hyperparameters [16]M3: Bayesian estimation of the hyperparameters described in Subsection 2.3
We computed typicalities under ﬁve evaluation conditions
T1+M1, T2+M2, T3+M2, T3+M3, and T4+M3.
Our typicality evaluation experiment used ﬁve hundred
songs by a hundred singers (50 male and 50 female), eachsinger sung ﬁve songs. The songs are taken from the JPOPMDB and each of the songs included only one vocal. To

Evaluatedconditions
T1+M1
T2+M2
T3+M2
T3+M3
T4+M3

First selection
ρm
ρf
ρmf
.855 .866 .855
.924 .930 .860
.921 .927 .861
.940 .961 .931
.936 .973 .942

Second selection
ρm
ρf
ρmf
.775 .821 .798
.905 .921 .866
.912 .921 .871
.910 .961 .926
.844 .973 .896

Third selection
ρm
ρf
ρmf
.935 .835 .882
.953 .918 .879
.951 .919 .880
.962 .955 .944
.968 .962 .952

Fourth selection
ρm
ρf
ρmf
.870 .876 .872
.925 .938 .875
.924 .935 .876
.936 .967 .934
.930 .976 .936

Fifth selection
ρm
ρf
ρmf
.914 .842 .876
.945 .910 .864
.944 .907 .865
.952 .950 .933
.970 .949 .939

Table 1. Pearson correlation coefﬁcients of a hundred songs under the ﬁve evaluated conditions (“T4+M3” is the proposed
method) and the underline means the highest value. The songs are randomly selected ﬁve times from ﬁve hundred songs.
Typicality
49:1

2
1.8
1.6
1.4

ratio
T1+M1 (male:female)

1:49
49:1

T2+M2
(previous method) 1:49

0.02
0.01

49:1

0.6

T3+M2

0.4
0.2

1:49
49:1

0.6

T3+M3

0.4
0.2

1:49
49:1

0.3

T4+M3
(proposed method) 1:49

0.2

better than the baseline method based on the Euclidean distance of mean vectors (T1+M1) and the previous method
based on computing the generative probabilities (T2+M2).
The results also show that estimated musical typicality byusing the proposed method can reﬂect the ratio between
the number of songs belonging to a class (e.g., male singer)
and the number of songs belonging to another class (e.g.,
female singer).

0.1

4 CONCLUSION

Typicality (scaling, range in [0, 1] for each song)
49:1

1

ratio
T1+M1 (male:female)

1:49
49:1

0
1

49:1

0
1

1:49
49:1

0
1

1:49
49:1

0
1

T2+M2
(previous method) 1:49
T3+M2
T3+M3
T4+M3
(proposed method) 1:49

050 male vocalists(50 songs)

50 female vocalists(50 songs)

Figure 5. Estimated typicalities (ﬁrst selection) and thosescaled values for each of the ﬁve evaluation conditions.
estimate musical typicality, a hundred songs by different
singers are randomly selected ﬁve times. Then, to integrateor estimate song-set models, ﬁfty songs are randomly selected from the songs with different ratios of the number ofmale singers to female singers (1 : 49, 2 : 48, ..., 49 : 1).
When a model with a high proportion of female songs isused, the typicality of songs sung by females is higher than
the typicality of songs sung by males (and vice versa).
Estimated typicality was evaluated against the Pearson
product-moment correlation coefﬁcient between the computed typicality the ratio of the number of male singers tofemale singers with respect to song-set modeling. Before
computing the coefﬁcients, the typicality for each song wasscaled to have values from 0 to 1 for evaluating smoothtransition. Let ρm , ρf , and ρmf denote the coefﬁcients under a set of songs consist of 50 songs by male singers, 50
songs by female singers, and all 100 songs, respectively.
The estimated typicalities and those scaled values areshown in Figure 5 for each of the ﬁve evaluation conditions. The Pearson’s correlation coefﬁcients are listed
in Table 1. The results show that the proposed method
achieved the highest value of the correlation coefﬁcient(T4+M3). This means that the proposed method works

We proposed a method for estimating musical typicality
based on the type theory. Although this method is used forquantized acoustic features for vocal timbre in this paper,
it can be used for other discrete sequence representationsof music, such as quantized other acoustic features (e.g.,
MFCCs to represent musical timbre/genre), lyrics and musical score. It can also be used with probabilistic representation instead of estimating musical similarities of all possible song-pairs by using a model trained from each song,for integrating or collaboration with other probabilistic approach as a uniﬁed framework.
Our deﬁnition of musical typicality was based on thecentral tendency [2] which is only the deﬁnition to be computed from the audio data; this is the reason to adopt it. In
future work we expect to deal with two other deﬁnitions
in cognitive psychology are frequency of instantiation andideals. The frequency of instantiation is a perspective onsocial recognition, that is, things with a lot of exposure on
media or in advertisements are typical, and ideals focuseson an ideal condition of the category, that is, things that areclose to an ideal condition are typical.
Musical typicality can be used not only for musiclistening support interface such as retrieving an uniquenesssong or visualizing typicalities, but also to do this by developing a music-creation support interface enabling high/low
typicality elements (e.g., timbre and lyrics) to be used toincrease originality or visualize typicality in order to avoid
unwarranted accusations of plagiarism. We also want topromote a proactive approach to encountering and appreciating content by developing music-appreciation support
technology that enables people to encounter new content
in ways based on its typicality to other content.
5 ACKNOWLEDGMENT
This paper utilized the RWC Music Database (Popular Music). This work was supported in part by CREST, JST.

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