Audio-Based Automatic Generationof a Piano Reduction Score
by Considering the Musical Structure
Hirofumi Takamori1(B) , Takayuki Nakatsuka1(B) , Satoru Fukayama2(B) ,Masataka Goto2(B) , and Shigeo Morishima3(B)1Department of Pure and Applied Physics, Waseda University, Tokyo, Japan{tkmrkc1290,t59nakatsuka}@gmail.com
2
National Institute of Advanced Industrial Science and Technology (AIST),
Ibaraki, Japan{s.fukayama,m.goto}@aist.go.jp
3
Waseda Research Institute for Science and Engineering, Tokyo, Japanshigeo@waseda.jp

Abstract. This study describes a method that automatically generates
a piano reduction score from the audio recordings of popular music whileconsidering the musical structure. The generated score comprises bothright- and left-hand piano parts, which reﬂect the melodies, chords, andrhythms extracted from the original audio signals. Generating such a
reduction score from an audio recording is challenging because automatic music transcription is still considered to be ineﬃcient when the
input contains sounds from various instruments. Reﬂecting the longterm correlation structure behind similar repetitive bars is also challenging; further, previous methods have independently generated eachbar. Our approach addresses the aforementioned issues by integratingmusical analysis, especially structural analysis, with music generation.
Our method extracts rhythmic features as well as melodies and chords
from the input audio recording and reﬂects them in the score. To consider
the long-term correlation between bars, we use similarity matrices, created for several acoustical features, as constraints. We further conduct
a multivariate regression analysis to determine the acoustical featuresthat represent the most valuable constraints for generating a musicalstructure. We have generated piano scores using our method and haveobserved that we can produce scores that diﬀerently balance between
the ability to achieve rhythmic characteristics and the ability to obtainmusical structures.
Keywords: Piano reduction · Multivariate regression analysis
Musical structure · Acoustic feature · Self-similarity matrix

Supported by JST ACCEL, Japan (grant no. JPMJAC1602).
c Springer Nature Switzerland AG 2019

I. Kompatsiaris et al. (Eds.): MMM 2019, LNCS 11296, pp. 169–181, 2019.
https://doi.org/10.1007/978-3-030-05716-9_14

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Introduction

One way to enjoy music is by playing an instrument yourself, which brings a different joy as compared to merely listening to music. The piano is the instrumentthat can simultaneously play multiple roles, including the melody line, harmony,and rhythm. For genres such as popular music, comprising a main vocal melody
and an accompaniment played using various instruments, the piano is a suitable
instrument for an individual to play his or her favorite songs. Herein, we focus
on generating a piano reduction score for popular music.
Piano scores for several popular songs have been written by professional musicarrangers. However, it is often necessary for a player to create a piano score fromscratch because there is no guarantees that the desired song will be available asa piano score. Creating a piano reduction requires carefully working out how allparts of the original music can be expressed using a playable piano score. To
address this issue, our method automatically generates a piano reduction score.
It considers the audio signals from a pop song as the input and outputs a score
suitable a piano.
The goal of this study is to automatically generate piano scores from audio
signals. To achieve this goal, we adopt the approach proposed in paper [1]. The
previous approach generates piano scores for each bar based on musical elements;
melody, rhythm, chords, and number of notes. These elements are obtained fromoriginal scores. However, directly adopting this score-based method in audiobased applications is problematic since audio-based feature extraction is notalways accurate, and it causes a lack of overall coherence. Hence, structuralconsiderations are necessary for audio-based piano reduction.
In this study, we present a piano reduction method while considering thestructure of the music. Our piano reduction method follows three stages: (a)analysis of the musical structure; (b) determination of the structure of the audio
signal; and (c) score composition. Figure 1 shows the schematic of the proposed
method. The main contribution of our study is twofold: First, we have generated
piano scores that reﬂect both the rhythmic and structural features of the input
audio signals. Second, we have determined self-similarity matrices (SSMs) for
seven diﬀerent acoustical features, which represent the structure of the piano
performance. As the limitations of our method, we treat only popular songs inquadruple time, and the minimum resolution of generating the score is limited
to a semiquaver note.

2

Related Work

Several studies have attempted to generate piano scores from original scores
involving the usage of multiple instruments. Fujita et al. [2] generated a pianoscore from an ensemble score by extracting the melody and bass part and using
them to develop the piano reduction. Chiu et al. [3] have considered ﬁve roles ofthe piano in music, which are the lead, foundation, rhythm, pad, and ﬁll that wereoriginally proposed by Owsinski [4]. By analyzing an original score, Chiu et al.

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171

Fig. 1. Overview of our proposed method. (a) Using multivariate regression analysis,
we analyze the correlation between the SSMs of the acoustical features and the SSMof the left-hand part of a manually arranged score. (b) We determine the SSM fora sample song using partial regression coeﬃcients obtained in (a). (c) We generatea piano score with both the right- and left-hand parts using the extracted musicalelements and structural feature estimated as SSM in (b).

associated each phrase in the score with a weighted importance value. They proposed a phrase-selection algorithm that maximized the importance value whileconsidering the score’s playability. Nakamura et al. [5] generated a piano reduction from an ensemble score using a ﬁngering model. They focused both on thepreservation of the sounds and on playability as constraints, where playability
can be separately controlled by the respective diﬃculty parameters observed incase of the right- and left-hand parts. A common thread in these previous studies
has been the reduction and selection of notes from an original score using either
the original notes directly or through octave shifts. These are valid approaches
that preserve the original impression of the music without generating any
dissonance.
Methods exist that do not completely transcribe a score from an audio signal, but that can extract musical elements from an audio signal to generate an
arrangement. For example, Percival et al. [6] have presented Song2Quartet, a system for generating string-quartet versions of popular music from audio recordings
without requiring pitch determinations for all parts. This method can extract
musical elements from an original piece, including the melodies, rhythms, chords,
and number of notes. We emphasize the consideration of the constraints involvedin piano reduction.

3

Piano Reduction of Popular Music

Melody, harmony, rhythm, timbre, and texture are deemed essential elements ofmusic [7], and play important roles in musical expression. To preserve the original

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song’s impression, focusing on these elements is essential. Since expressing thetimbre of diﬀerent instruments using only the piano is diﬃcult, we focus onpreserving the remaining elements, including melody, harmony, rhythm, andtexture, in the piano reduction. In particular, we note the following points:– The melody is always the highest pitch.
– Each chord in the output score matches with the original one.
– The output score represents the original rhythm.
– The output score exhibits a contrast between the verse and the chorus.
A previous study [1] established the value of the aforementioned requirements. Along with the aforementioned requirements, we consider a long-termcorrelation structure that is observed especially in the piano scores of popular
music. Popular music generally contains structures, such as a verse, a chorus,
and a bridge, and some of these musical sections are repeated in a single song[8]. Hence, it is important to reﬂect these repetitive structures in the generated piano scores. Thus, we impose an additional requirement to express the
structural features of popular music as follows:– The left-hand part should exhibit similar accompaniment patterns within thesame section.
In this study, we perform piano reduction by considering the ﬁve aforementioned requirements.

4

Analysis of the Structure of the MusicIn this section, we explain the analysis stage illustrated in Fig. 1(a) and outlined in Fig. 2. We have initially prepared a dataset containing 27 popular songs
that include both the audio data and the corresponding piano scores. These
audio data are acquired from the Internet, and these piano scores are manually
produced.1,2,3
4.1

Feature Extraction

As acoustic features, we use chromagrams, Mel-frequency cepstrum coeﬃcients(MFCCs), onsets, root-mean-square (RMS) energy, spectral centroid, spectral
ﬂatness, and zero-crossing rates (ZCRs). The audio signals are monaural andtheir sampling frequencies are 44.1 kHz. The window length during analysis is1024, with an overlap of 256. We also set the number of channels of the Melscale ﬁlter bank at 20, and we use the 12 low dimensions. Especially for onsets
detection, the methodology is inspired by Böck et al. [10].
1

Bokaro Kamikyoku Daishugo Best 30, Depuro MP, Japan (2016).
Jokyu Piano Grade Bokaro Meikyoku Piano Solo Concert, Depuro MP, Japan (2015).
3
Print Score, https://www.print-gakufu.com/.
2

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173

Fig. 2. Overview of the analysis of the musical structure. (a-1) Feature extraction
from an audio recording and a score. We use Songle [9] to acquire the beats data. (a-2)
Multivariate regression analysis of all songs in the dataset. The quantity, A, represents
a matrix whose complete list of entries are 1. The quantity, S(·), represents the SSM of
acoustic features or of a piano feature, and ai represents a partial regression coeﬃcient.

In this study, we extract the aforementioned seven features for each bar.
Songle [9], a web service for active music listening, is used to get the start timeof each bar in a song. This allows us to work out how the times (frames) of
the audio signal correspond to the bars. Each feature of the mth bar can be
represented as follows: chrm ∈ R12×16 for the chromagram, mfccm ∈ R12×16
for the MFCCs, onsetm ∈ Z1×16 for the onsets, rmsm ∈ R1×16 for the RMS
energy, centm ∈ R1×16 for the spectral centroid, ﬂatm ∈ R1×16 for the spectral
ﬂatness, and zcrm ∈ R1×16 for the ZCR, respectively. Row-wise represents thetime direction of a bar which is divided into segments with length of 16th note.
For example, the ﬁrst column represents the one-dimensional feature for the ﬁrst
16th note in a bar. Acoustic features, excluding the onsetm , are projected onto
each segment with length of a 16th note by considering the mean between thecurrent and subsequent beats. The j th column value of onsetm is set to unity
if there is a peak between the current and subsequent beats or is set to zero if
there is none.
Considering the features of a piano score, we extract the positions and numbers of the notes from the left-hand part and described them for each bar. We
denote the mth bar’s feature of a piano score by pianom ∈ Z1×16 . Row-wiseagain represents the time direction. The values of the j th column of pianom are
the numbers of notes positioned at the j th beat.
4.2

Multivariate Regression Analysis of the Self-Similarity Matrices

SSMs are calculated for both acoustic features and the features of a piano scoreby the procedures described in Sec. 4.1. The SSM indicates the structural similarity between the bars included in a song. For the feature sequence of a song,f = {f1 , f2 , · · · , fM }, the SSM, S(f ) ∈ RM ×M , can be deﬁned as follows:174

H. Takamori et al.

⎞
1 s12 . . . s1M⎜ s21 1 . . . s2M ⎟⎟⎜S(f ) = [sij ] = ⎜ .
.. . . .. ⎟
⎝ ..
. . ⎠
.
sM 1 sM 2 . . . 1⎛(1)where sij represents the similarity between a feature’s ith bar, fi , and the j thbar, fj . The similarity, sij , can be given as follows:
1
1 + dij
dij = ||fi − fj ||
sij =

(2)
(3)

where dij represents the distance between fi and fj , which can be obtained bycomputing the Frobenius norm. The values of sij lie in the range (0, 1], wheresij = 1 indicates that the two features being compared are identical. Conversely,
sij exhibits a low value if the two features being compared are unidentical.
We further perform multivariate regression analysis on the SSM. We assign
the explanation variable, X, and the objective variable, Y, as follows:
Xf = {S(f )1 , S(f )2 , · · · , S(f )N }Ypiano = {S(piano)1 , S(piano)2 , · · · , S(piano)N },where f represents a sequence of each acoustic feature. The quantity, S(·)n ,represents the SSM of the dataset’s nth song. We denote the formula to perform
multivariate regression analysis as follows:afγ Xfγ = Ypiano(4)
a0 A +
γ

where a0 represents the intercept and af denotes the acoustic features’ partial
regression coeﬃcient. The quantity, A, denotes a list of the matrices whose
complete list of entries include 1, and it is introduced to match the matrix
dimensions. The subscript, fγ , represents one of the seven acoustic features usedin this study. Eq. (4) is schematically depicted in Fig. 2(a-2). According to Eq.
(4), we determine the intercept a0 and the partial regression coeﬃcients af .

5

Structural Segmentation

In this section, we explain the approach used to determine the structure of a
piano score from the audio signals (Fig. 1(b)). The structure of a piano scoreis determined by segmenting SSM, which is estimated from acoustic featuresby using Eq. (4) with the partial regression coeﬃcient obtained by multivariate
regression described in Sect. 4.2. To segment a song into several musical sections,
we adopt novelty detection [11]. We perform novelty detection by identifying thepeaks of the novelty scores, obtained by multiplying the checkerboard kernel, C,
along the SSM’s diagonal.
1 −1
C=
(5)
−1 1

Audio-Based Automatic Generation of a Piano Reduction Score

175

In our methodology, we calculate ﬁve kinds of novelty scores having checkerboard kernel sizes of (2×2), (4×4), (6×6), (8×8), and (10×10), respectively. We
further consider the mean of the ﬁve novelty scores and normalize them to [0, 1]
range. Additionally, we perform peak detection for the novelty scores by introducing a second-order diﬀerential threshold, th = 0.00, −0.05, −0.07, −0.10,−0.15. The peak position is set to one at which the ﬁrst-order diﬀerentiation
turns from positive to negative and at which the second-order diﬀerentiation isless than th. We further obtain the musical structures’ boundaries according to
the peaks of the novelty scores. The musical structure is represented by lists ofbars that mark the boundaries between various segments. Bars located between
the acquired boundaries are considered to belong to the same segment.

6

Score Composition from Audio Signals

In this section, we explain the architecture for generating a piano score fromthe audio signals (Fig. 1(c)). First, we focus on the accompaniment database
constructed beforehand. Further, we discuss the extraction of musical elementsfrom the audio signals. We obtain the chorus, chord, and melody using Songle[9], while rhythm is obtained by detecting the onsets of spectral ﬂux. Finally, we
generate a piano score for both left- and right-hand parts based on the extracted
elements.
6.1

Accompaniment Database

We construct the accompaniment database, DB, based on the existing pianoscores [1]. The accompaniment database comprises accompaniment matrices.
An accompaniment matrix represents a bar of the left-hand part as an 88 × 16
matrix, where 88 is the number of piano keys and 16 is set to match the lengthof a semiquaver. The matrix is generated after being transposed so that the root
becomes C. In case of the matrix elements, the note value is stored in the places
at which the note exists; zero is stored if there is no note. This allows the system
to record the relative pitch transition and the rhythm of the original piano score.
In this study, DBn ∈ Z88×16 denotes the nth accompaniment matrix; it contains
the 16-dimensional vector, DBRn , that represents the rhythm. When a non-zerovalue is stored in the j th column of DBn , the value 1 is stored in the j th elementof DBRn . If only zeros are stored in the j th column of DB, the value zero isalso stored in the j th element of DBRn .
6.2

Extraction of Musical Elements from Audio Signals

We extract musical elements, including the melody M, chord Cd, chorus Cr,
and rhythm R. We acquire M, Cd, and Cr from Songle [9], while we extract R
by onset detection of the spectral ﬂux, as described in Sect. 4.1. We obtain thefollowing analysis results for each element from Songle Widget 4 :4

http://widget.songle.jp/.

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Beat: index, start time, position
Chord: index, start time, duration, chord name
Melody: index, start time, duration, MIDI note number
Chorus: index, start time, duration
The index denotes the number of beats, chords, or notes of melody observed
from the beginning of a song; start time represents the time at which each
event starts; the position speciﬁes the number of beats in each bar; duration
denotes the length of the event; chord name shows the root note and the chord
type; and the MIDI note number is the value that indicates the pitch. Fromthese information, the melody and the chords can be described for each bar,and we also obtain the bar number, which is in the chorus section. For M, Cd,
Cr and R, the subscript, m, indicates the mth bar of the score. The quantity,
Mm ∈ Z88×16 , provides the pitch, note values, and position in the score for eachbar. The number of rows corresponds to the number of keys on the keyboard,
whereas the number of columns corresponds to the time resolution (16th note).
The chord notes are represented in Cdm for each beat as a set of MIDI notenumbers. For Crm , the value is set to unity if the mth bar is in the chorus and is
set to zero otherwise. The rhythm, R ∈ Z1×16 , is acquired in the same manneras the onset, as explained in Sect. 4.1.
6.3

Generation of the Right-Hand PartWe allocate the melody, M, to the right-hand part, RH, as follows:
RHm =Add(Mm , Rm , Cdm ) Crm = 1
otherwise
Mm(6)

The quantity, RHm ∈ Z88×16 , represents the mth bar of RH. If the mth bar
is in a chorus section, Addm attaches additional chord notes to each note in the
melody, Mm , where a component of the rhythm, Rm , is unity. The chord notes
at each beat are obtained from Cdm and are considered to be lower in pitch
than the melody and more than four semitones away.
6.4

Generation of the Left-Hand Part

The left-hand part, LH, of the piano score can be generated by selecting fromthe accompaniment database, DB. First, we select an accompaniment for which
the rhythm is similar to that of the audio signal, R, for each bar. This accompaniment list is deﬁned as LH , which represents the accompaniment list byconsidering only the rhythm. Further, we reﬂect the features of the musicalstructure, as determined in Sec. 5. We reduce the kinds of accompaniments thatappeared in the same musical section so that they exhibit similar rhythmic patterns. The result of this reduction is designated as LH. The mth bar of LH
is denoted by LHm . We deﬁne the parameter, λ, to be the number of kinds ofAudio-Based Automatic Generation of a Piano Reduction Score

177

accompaniments in the same musical section. This process is described by thefollowing formula:
LH = F uncS(LH , λ, th)LHm = argmin CostR(DB, Rm )
CostR(DB, Rm ) =||DBRn − Rm ||

(7)
(8)
(9)

n

Here, F uncS(·) reduces the kinds of accompaniments by changing the accompaniment patterns with a low appearance frequency to form accompanimentswith a high appearance frequency. This reduction continues until the number ofkinds of accompaniments became less than λ for each musical section. The value,
λ = 1, indicates that only one kind of accompaniment is selected in each musicalsection, and λ = ∞ indicates that the musical structure is not considered. LH isa candidate accompaniment list selected on the basis of CostR(·), where CostR
is introduced to select accompaniments with high similarities in audio rhythms.
Finally, to ensure that the sound of LHm reﬂects Cdm we shift LHm to thenearest chord notes for each bar.

7

Results and Evaluation

As the result of the multivariate regression analysis described in Sect. 4, thepartial regression coeﬃcients and t-values of them are presented in Table 1.
Table 1. The result of multivariate regression analysis.
a0
coefs

achr

amf ccaonsetacent

af latarms

azcr−0.0373 0.4439 −0.0329 0.1403 0.2224 0.3153 0.0494 −0.1175

t-value −8.974

74.50−8.863

74.88

111.3

87.47

27.87

−34.95Here, a0 represents the intercept and af represents each acoustic feature’s
partial regression coeﬃcient. The t-value in linear regression analysis is commonly considered to be a value that indicates the similarity of the explanation value with the objective value. The t-value can be derived by dividing acoeﬃcient with its standard error. A large absolute t-value indicates that the
explanation value exhibits large eﬀectiveness in determining the objective. We
2. The
also calculate p-values and an adjusted coeﬃcient of determination Radj
p-value represents the probable signiﬁcance of the explanation value. Generally,an explanation value is eﬀective when the p-value is lower than 0.05. The results2
isof all the p-values of the coeﬃcients are lower than the order of 10−18 . Radj
an indicator of multivariate regression analysis’ accuracy, and can be deﬁned asfollows:
2
≡1−
Radj

 2
i (yi − yi ) /(N − p − 1)2i (yi − y i ) /(N − 1)

(10)

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where y is the true data; y is the mean of y; y  is the predicted data; N is the
sample size; and p is the number of explanation values. Unity is achieved when
there is no residual relative to the predicted data, and unity decreases as the2in our model was 0.1590.
residual increases. The obtained Radj
We output the piano score for each of the 27 popular songs included in
the dataset. To verify the eﬀectiveness of our method, we conduct leave-oneout cross-validation for the SSMs of all the songs in the dataset. Each SSM is
calculated from a left-hand part of each score.
First, we select one song as test data and generate a piano score of this songusing the partial regression coeﬃcients derived from the remaining 26 songs.
Finally, we obtain the residuals by calculating the Frobenius norm of the diﬀerence between the SSM of the generated and manually created piano scores. We
calculate the residuals for each of the seven diﬀerent values of λ, which denotes
the number of types of accompaniments in one musical section, and for ﬁve
diﬀerent block thresholds, th. Table 2 presents the result of this cross-validation.
Table 2. The result of leave-one-out cross-validation. (×10−3 )threshold th The number of kinds of accompaniments λ
1
2
3
4
5
6
∞
0.00

3.550

3.630

3.674

3.685

3.714

3.730

3.760

−0.05

3.535

3.612

3.684

3.708

3.738

3.742

3.760

−0.07

3.277

3.357 3.452

3.522

3.591

3.647

3.760

−0.10

3.257 3.451

3.413 3.430 3.460 3.506 3.760

−0.15

3.311

3.538

3.503

3.535

3.564

3.560

3.760

All the values are normalized by dividing with the size of the matrix. We
calculate the residuals for all songs in the dataset and estimate the mean value.
The values represent how closely the generated scores’ accompaniments resemble those of manually-produced scores in their structure. Figure 3 depicts thevariation of the SSM structure with λ for the cases in which th = −0.07, −0.10.
We selected three songs5,6,7 where the SSMs of these songs clearly changed bytrying diﬀerent values for λ. We also test our method using one song from the
RWC Music Database [12] (RWC-MDB-P-2001 No. 7).88

Discussion

Table 1 shows that the t-values of the spectral centroid, spectral ﬂatness, onset,
and chromagram exhibit comparably high values, indicating that these acoustic
5

Mosaic Roll (DECO*27), https://www.nicovideo.jp/watch/sm11398357.
Ghost Rule (DECO*27), https://www.nicovideo.jp/watch/sm27965309.
7
Irohauta (Ginsaku), https://piapro.jp/t/0D18/20100223020519.
8
The generated results is available at https://youtu.be/Yx9c0LnEyyE.
6

Audio-Based Automatic Generation of a Piano Reduction Score

179

Fig. 3. Comparison of the SSMs with the ground truth about three songs.

features eﬀectively determine the structure of the piano performance. The spectral centroid, spectral ﬂatness, and chromagram are features related to the pitchof the sound and harmony. Hence, the registers, melodies, and chords are deemed
important for structural determination. The onset is a rhythmic feature; hence,focusing on the sounds that correspond to beats or rhythm is also important.
Conversely, the t-values for MFCC, RMS, and ZCR exhibit comparably low
values, indicating that the features related to timbre and texture are not as eﬀective as the aforementioned harmonic and rhythmic features. Obviously, timbre
and texture change during a song. However, repetitive structures of these features are not as well-correlated with the structure of the piano performance. In
this study, the left-hand part of the piano score represents the structure of the
piano score. We conclude that the timbre and texture of the sounds are expressedin the piano score by other elements such as musical symbols and the number ofnotes. Hence, the structure of the piano score generated by our method is not
suﬃcient to express the structure of timbre and texture, resulting in low t-values
for MFCC, RMS, and ZCR.
2
2
is below unity, which is the maximum value of Radj
. Several possible
Radjvariations of piano scores exist for a given song depending on the arranger. There2
inevitably exhibits low values owing to these ﬂuctuations. However, afore, Radj
determination of the musical structure from the acoustic features is possible to2exhibits a positive value.
some extent because Radj
Table 2 shows that the SSMs of the generated piano scores exhibit low residuals when λ is small and when th is −0.07 and −0.10. This indicates that segmenting the music with moderate roughness and selecting fewer kinds of accompaniments in the segmented sections produces results closer to the ground truth.
However, in a piano score by an arranger, several kinds of accompaniments are

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H. Takamori et al.

often included in the same section. For instance, several kinds of accompaniments may be alternatively observed, or distinguishing accompaniment appears
just before the next phrase. Therefore, it is important to consider short-term
structure and to focus on musical transitions, in order to ensure that the generated result is close to the original piano score.

9

Conclusions and Future Work

Herein, we have proposed method of a piano reduction from audio signals byconsidering the structure of the music. We output several patterns of piano scoresand calculated the SSMs to verify the relation between the musical structures of
the audio signals and the piano scores. The results of the multivariate regression
analysis show that spectral centroid, spectral ﬂatness, onset, and chromagram
were valuable features for determining the musical structure. The results also
show that giving consideration to music structure ensures that the generated
piano structure will be close to one written by an arranger. In future studies, we
aim to augment the music database and reselect acoustic features that are morevaluable for generating a piano reduction score.

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