Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016

deepGTTM-I: Local Boundaries Analyzer based on A
Deep Learning Technique
Masatoshi Hamanaka1 Keiji Hirata2, and Satoshi Tojo3
Kyoto University,
hamanaka@kuhp.kyoto-u.ac.jp,
2
Future University Hakodate,hirata@fun.ac.jp,
3
JAIST,
tojo@jaist.ac.jp,
1

http://gttm.jp/
Abstract. This paper describes a method that enables us to detect the local
boundaries of a generative theory of tonal music (GTTM). Although systems thatenable us to automatically acquire local boundaries have been proposed such as afull automatic time-span tree analyzer (FATTA) or σGTTM, musicologists have tocorrect the boundaries because of numerous errors. In light of this, we propose anovel method called deepGTTM-I for detecting the local boundaries of GTTM byusing a deep learning technique. The experimental results demonstrated that
deepGTTM-I outperformed the previous analyzers for GTTM in an F-measure ofdetecting local boundaries.
Keywords: A generative theory of tonal music (GTTM), local groupingboundary, deep learning.

1

Introduction

We propose a method of automatically acquiring local grouping boundaries based ona generative theory of tonal music (GTTM) [1]. GTTM is composed of four modules,
each of which assigns a separate structural description to a listener’s understanding ofa piece of music. These four modules output a grouping structure, metrical structure,
time-span tree, and prolongational tree. As the acquisition of local groupingboundaries is the first step in GTTM, an extremely accurate analyzer makes it
possible to improve the performance of all the later analyzers.
We previously constructed several analyzers or methods that enabled us to acquire
local grouping boundaries such as: an automatic time-span tree analyzer (ATTA) [5],a fully automatic time-span tree analyzer (FATTA) [6], a GTTM analyzer by using
statistical learning (σGTTM) [7], and a GTTM analyzer based on clustering andstatistical learning (σGTTMII) [8]. However, the performance of these analyzers or
methods was inadequate in that musicologists had to correct the boundaries becauseof numerous errors.
We propose deepGTTM-I in which we attempted to use deep learning [9] to
improve the performance of acquiring local grouping boundaries to detect them.

8Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
2

Masatoshi Hamanaka, Keiji Hirata, and Satoshi Tojo

Unsupervised training in the deep learning of deep layered networks called pretraining helps supervised training, which is called fine-tuning [10].
Our goal was to develop a GTTM analyzer that enabled us to output the results
obtained from analysis that were the same as those obtained by musicologists basedon deep learning by learning the results of analysis obtained by musicologists. We
had to consider three issues in constructing a GTTM analyzer based on deep learning.
Multi-task Learning
A model or network in a simple learning task estimates the label from an input
feature vector. However, local grouping boundaries can be found in many notetransitions. Therefore, we consider a single learning task as estimating whether
one note transition can be a boundary or not. Then, a problem in detecting localgrouping boundaries can be solved by using multi-task learning.
Subsection 4.3 explains multi-task learning by using deep learning.



Large scale training data
Large scale training data are needed to train a deep layered network. Labels are
not needed in pre-training the network. Therefore, we collected 15,000 pieces ofmusic formatted in musicXML from Web pages that were introduced in theMusicXML page of MakeMusic Inc. [11]. We needed labeled data to fine-tune
the network. Although we had 300 pieces with labels in the GTTM database [12],this number was too small to enable the network to learn.
Subsection 4.1 explains how we collected the data and how we got the network
to learn effectively with a small dataset.



GTTM rules
GTTM consists of multiple rules and a note transition that is applied to manyrules tends to be a local grouping boundary in the analysis of local groupingboundaries. As a result of analysis by musicologists, 300 pieces in the GTTM
database were not only labeled with local grouping boundaries, but also labeledwith applied positions of grouping preference rules. Therefore, the applied
positions of grouping preference rules were helpful clues in detecting localgrouping boundaries.
Subsection 4.3 explains how the network learned with the grouping preference
rules.

The results obtained from an experiment demonstrated that multi-task learning using
the deep learning technique outperformed the previous GTTM analyzers in groupingboundaries.
The paper is organized as follows. Section 2 describes related work and Section 3
explains our method called deepGTTM-I. Section 4 explains how we evaluated theperformance of deepGTTM-I and Section 5 concludes with a summary and an
overview of future work.

9Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
deepGTTM-I

2

3

Related work

We consider GTTM to be the most promising of the many theories that have been
proposed [2–4], in terms of its ability to formalize musical knowledge, because
GTTM captures the aspects of musical phenomena based on the Gestalt occurring inmusic and is presented with relatively rigid rules. We have been constructing both
systems of analysis and application of GTTM for more than a decade (Fig. 1) [13].
The horizontal axis in Fig. 1 indicates years. Above the timeline are analyzers or
methods that we developed.
2.1

System of Analysis for GTTM based on Full Parameterization

We first constructed a grouping structure analyzer and metrical structure analyzer(Figs. 1a and b). We developed an ATTA (Fig. 1c) [5] by integrating a grouping
structure analyzer and a metrical analyzer. We extended the GTTM by full
externalization and parameterization and proposed a machine-executable extension of
the GTTM, exGTTM. We implemented the exGTTM on a computer that we call
ATTA The ATTA had 46 adjusted parameters to control the strength of each rule.
The ATTA we developed enabled us to control the priority of rules, which enabled us
to obtain extremely accurate groupings and metrical structures. However, we neededmusical knowledge like that which musicologists have to properly tune the parameters.
FATTA [6] (Fig. 1d) did not have to tune the parameters because it automaticallycalculated the stability of structures and optimized the parameters so that thestructures would be stable. FATTA achieved excellent analysis results for metricalstructures, but results for grouping structures and time-span trees were unacceptable.
We constructed an interactive GTTM analyzer [14] (Fig. 1e) that enabled seamlesschanges in the automatic analysis and manual editing processes because it wasdifficult to construct an analyzer that could output analysis results in the same way asmusicologists. The interactive GTTM analyzer is still used to collect GTTM analysis
data and everyone can download and use it for free [15].
However, all these systems or methods [5, 6, 14, 15] had problems. ATTA neededmusical knowledge to tune the parameters. FATTA performed poorly.
2.2

System of Analysis for GTTM based on statistical learning

σGTTM [7] (Fig. 1f) enabled us to automatically detect local grouping boundaries
by using a decision tree. Although σGTTM performed better than FATTA, it wasworse than ATTA after the ATTA parameters had been tuned.
σGTTMII [8] (Fig. 1g) had clustering steps for learning the decision tree and it
outperformed ATTA if we could manually select the best decision tree. Although
σGTTMII performed the best in detecting grouping boundaries, it was difficult toselect the proper decision tree without musical knowledge.
σGTTMIII [16] (Fig. 1h) enabled us to automatically analyze time-span trees bylearning with a time-span tree of 300 pieces from the GTTM database [12] based on
probabilistic context-free grammar (PCFG). σGTTMIII performed the best in

10

11

Fig. 1. Related work on analysis and application systems for GTTM.
DTSRPR5 + DGPR72DTSRPR5

Reproducing music [19]

TA

0

1

B2nb1

2008

0

1

B
0

1

TA TB

TC

TD

（3）Combining two melodies

LB

TC
LA
（2）Melody
division reduction

TB

TD

Melody B

Melody D

TD

B3nd

The kind of GPR,B

1, B3na1 , B3nb1 , B3nc1 , B3nd1 ,2009

B3nc1

0

0

1

B

1

0

B3nc

Violin I

Basso

Viola

Violin II

Allegro       




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                                  Time-span
XML(Polyphony)                             Time-span tree
analyzer       




 

 

 

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 

            










    Time-spanXML(homophony)..
.

MetricalXML.
Metricalstructure analyzer

Manual analysis..
.

.
Grouping
structure analyzer

MusicXML by musicologists(homophony)        Manual arrangementby musicologists

 



                            



..
..

HarmonicXML

Harmonic
analyzer

GroupingXML

2011

2012

2014

HD

2016
ShakeGuitar

2015(h) σGTTMIII
based on PCFG [16](i) pGTTM based on PCFG [17]Composing system

2013

Polyphonic Music Time-Span Tree

0

2010

n
3d

PTTA
MusicXML(Polyphony) Part
dividerMusicXML(monophony)

PATTA：Polyphonic MusicTime-Span Tree Analyzer

Melody extrapolation [22] ShakeGuitar

Target Attribute b
If a local grouping boundary is
between notes, b = 1, otherwise b = 0.

B2na1 , B2nb1 , B3na1 , B3nb1 , B3nc1 , B3nd1

B

n 1
2b

B2na , B2nb , B3na , B3nb , B3nc , B3nd ,
n 1
2a

0

The position between notesb0

Conditional Attribute

B2na

B

Melodymorphing [21] Melody
expectation

2007

TSRPR5の適用

タイムスパン木・拍節構造の
安定度

GPR7の
適用

DGPR7

（1）Linking the common information of melodies

Melody E

Melody A

Melody C

TC

2006

No

Yes

TSRPR1,3,4,8,9の適用

ヘッドが2つ以上

次の階層

Yes

1

b0

B2nb

…

Rendering [18]Summryzation [20]2005

Ditime-span

現在の構造(ヘッドの強さ)No

拍点が2つ以上b 1
End Node

n 1
2a

1

…

2004

No

MPR1,2,3,4,5の適用 [time]

MPR10の適用、構造の選択

m4
m5

次の階層 m  1
m 2
の候補
m3

Time-spanXML

次の階層のヘッドの選択

Dilow-level(拍点の強さ)Yes

GPR1, 2, 3, 4, 5, 6 の適用
グループ中に局所的境界がある

現在の構造

MetricalXML

ヘッドの強さの算出

タイムスパン木
分析器

次の階層の
拍節構造の選択

局所的な拍点の強さの算出

拍節構造分析器

GroupingXML

高次の境界の検出[time]

Splitting Test

0

…

2003

タイムスパン木
分析器の調節可能な
パラメータ

局所的境界

トップダウンによる分割

n 1
3c

…

最適化

Bi

0

…

拍節構造分析器
の調節可能な
パラメータ

MusicXML

局所的境界の検出 (境界の深さ) GPR1, 2, 3, 6 の適用

グルーピング構造
分析器

ATTA: タイムスパン木分析器

B2nb

B2na

…

最適化

グルーピング構造
分析器の調節可能な
パラメータ

最適化

パラメータ最適化部

FATTA: 完全自動タイムスパン木分析器

1

1

…
…

(a) Grouping structure analyzer(b) Metrical structure analyzer(f) σGTTM [7](g) σGTTMⅡ [8]4(d)FATTA：Full
Automatic Time-span
Tree Analyzer [6](c)ATTA：Automatic Time-span Tree Analyzer [5](e) Interactive GTTM Analyzer [15]Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
Masatoshi Hamanaka, Keiji Hirata, and Satoshi Tojo

Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
deepGTTM-I

5acquiring time-span trees. pGTTM [17] (Fig. 1i) also used PCFG and we used it toattempt unsupervised learning. The main advantages of σGTTMIII and pGTTM werethat the systems could learn the contexts in difference hierarchies of the structures(e.g., beats were important in the leaves of time-span trees, or chords were importantnear the roots of the trees.).
However, all these systems or methods [7, 8, 16, 17] had problems with detecting
local grouping boundaries. σGTTM III and the pGTTM were focused on acquiring
time-span trees and could not acquire local grouping boundaries.σGTTM II neededmusical knowledge to select the decision tree. As σGTTM and the σGTTM II used
rules that musicologists applied, they could not work as standalone analyzers. For
example, information on parallel phrases is needed when detecting local groupingboundaries because parallel phrases create parallel structures in GTTM. However,σGTTM and σGTTM II do not have processes for acquiring parallel phrases.
We introduced deep learning to analyzing GTTM to solve these problems.
2.3

Application System by Using Analysis Results of GTTM

There are applications that we constructed under the time-line in Fig. 1 to use theresults from analysis of GTTM. The time-span and prolongational trees provide
performance rendering [18] and music reproduction [19] and provide a summarizationof the music. This summarization can be used as a representation of a search,
resulting in music retrieval systems [20]. It can also be used for melody morphing,which generates an intermediate melody between two melodies in systematic order[21, 22].
These systems presently need a time-span tree analyzed by musicologists because
our analyzers do not perform optimally.
2.4

Melody Segmentation

As conventional methods of melody segmentation such as the Grouper of theMelisma Music Analyzer by Temperley [23] and the local boundary detection model(LBDM) by Cambouropoulos [24] require the user to make manual adjustments to theparameters, they are not completely automatic. Although Temperley [25] has also
employed a probabilistic model, it has not been applied to melody segmentation. The
unsupervised learning model (IDyOM) proposed by Pearce et al. makes no use of therules of music theory with regard to melodic phrases, and it has performed as well asGrouper and LBDM [26]. However, as deepGTTM-I statistically and collectively
learns all the rules for the grouping structure analysis of GTTM, we expect that
deepGTTM-I will perform better than a model that only uses statistical learning.

12Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
6

Masatoshi Hamanaka, Keiji Hirata, and Satoshi Tojo

3

GTTM and Its Implementation Problems

Figure 2 Shows local grouping boundaries, a grouping structure, a metrical structure,a timespan tree, and a prolongational tree (Fig. 2). The detection of local groupingboundaries in the grouping structure corresponds to melody segmentation.

Prolongation tree

Time-span tree

Metrical structureGrouping structure
Local grouping boundary

Fig. 2. Local grouping boundaries, grouping structure, metrical structure, time-spantree, and prolongational tree.
3.1

Grouping Preference Rules

The grouping structure is intended to formalize the intuitive belief that tonal music isorganized into groups that are in turn composed of subgroups. These groups arepresented graphically as several levels of arcs below a music staff. There are two
types of rules for grouping in GTTM, i.e., grouping well-formedness rules (GWFRs)
and grouping preference rules (GPRs). GWFRs are necessary conditions for theassignment of a grouping structure and restrictions on these structures. When morethan one structure can satisfy the well-formedness rules of grouping, GPRs indicate
the superiority of one structure over another. The GPRs consist of seven rules: GPR1
(alternative form), GPR2 (proximity), GPR3 (change), GPR4 (intensification), GPR5
(symmetry), GPR6 (parallelism), and GPR7 (time-span and prolongational stability).
GPR2 has two cases: (a) (slur/rest) and (b) (attack-point). GPR3 has four cases: (a)(register), (b) (dynamics), (c) (articulation), and (d) (length).
3.2

Conflict Between Rules

Because there is no strict order for applying GPRs, a conflict between rules often
occurs when applying GPRs, which results in ambiguities in analysis. Figure 3
outlines a simple example of the conflict between GPR2b (attack-point) and GPR3a(register). GPR2b states that a relatively greater interval of time between attack points

13

Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
deepGTTM-I

7

initiates a grouping boundary. GPR3a states that a relatively greater difference inpitch between smaller neighboring intervals initiates a grouping boundary. Because
GPR1 (alternative form) strongly prefers that note 3 alone does not form a group, aboundary cannot be perceived at both 2-3 and 3-4.

3a2bCandidate 1
Candidate 2
Violate GPR1
Fig. 3. Simple example of conflict between rules.
3.3

Ambiguity in defining GPR4, 5, and 6

GTTM does not resolve much of the ambiguity that exists in applying GPR4, 5, and 6.
For example, GPR6 (Parallelism) does not define the decision criteria for construing
whether two or more segments are parallel or not. The same problems occur with
GPR4（Intensification）and GPR5 (Symmetry).

4
deepGTTM-I: local grouping boundary analyzer based on
deep learning
We introduced deep learning to analyze the structure of GTTM and solve theproblems described in Subsections 3.2 and 3.3. There were two main advantages of
introducing deep learning.


Learning rules applications
We constructed a deep layered network that could output whether each rule wasapplicable or not on each note transition by learning the relationship between thescores and positions of applied grouping preference rules with the deep learningtechnique.
Previous analysis systems based on GTTM were constructed by a humanresearcher or programmer. As described in Subsection 3.3, some rules in GTTM
are very ambiguous and the implementations of these rules might differ
depending on the person.
However, deepGTTM-I is a learning based system where the quality of theanalyzer depends on the training data and trained network.



Learning priority of rules
σGTTM and σGTTMII do not work well because they only determine thepriority of rules from applied rules because the priority of rules depends on the14Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
8

Masatoshi Hamanaka, Keiji Hirata, and Satoshi Tojo

context of a piece. The input of the network in deepGTTM-I, on the other hand,is the score and it learns the priority of the rules as the weight and bias of the
network based on the context of the score.
This section describes how we detected the local grouping boundaries by using deeplearning.
4.1

Datasets for training

Three types of datasets were used to train the network, i.e., a non-labeled dataset for
pre-training, a half labeled dataset, and a labeled dataset for fine-tuning.
(a) Non-labeled dataset. The network in pre-training learned the features of themusic. A large scale dataset with no labels was needed. Therefore, we collected,
15,000 pieces of music formatted in musicXML from Web pages that were introducedon the musicXML page of MakeMusic Inc. [11] (Fig. 3a). The musicXMLs were
downloaded in three steps.
1) Web autopilot script made a list of urls that probably downloaded musicXMLs infive links from the musicXML page of MakeMusic Inc.
2) The files in the url list were downloaded after urls had been omitted that wereclearly not musicXML.
3) All the downloaded files were opened using the script, and files that were notmusicXML were deleted.
(b) Half Labeled Dataset. The network in fine-tuning learned with the labeleddataset. We had 300 pieces with a labeled dataset in the GTTM database, which
included musicXML with positions of local grouping boundaries, and positions towhich the grouping preference rules were applied. However, 300 pieces wereinsufficient for deep learning.
Consequently, we constructed a half labeled dataset. We automatically added thelabels of six applied rules of GPR2a, 2b, 3a, 3b, 3c, and 3d, because these rules could
be uniquely applied as a score. We used ATTA to add labels to these rules (Fig. 3b).
(c) Labeled dataset. We artificially increased the labeled dataset, because 300 pieces
in the GTTM database were insufficient for training a deep layered network. First, wetransposed the pieces for all 12 keys. Then, we changed the length of note values to
two times, four times, eight times, a half time, a quarter time, and an eighth time.
Thus, the total labeled dataset had 25,200 (= 300x12x7) pieces (Fig. 3c).

15

Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
deepGTTM-I

9

Web autopilot 15,000 pieces (musicXML)

ATTA- MusicXML- Applied rules- MusicXML（a) Non-labeleddataset（b) Half labeleddatasetGTTM database- MusicXML- Applied rules- Local grouping boundaries（c) Labeleddataset300 pieces
x 12 keys
x 7 kinds of anote value

Fig. 4. Non-labeled dataset, half labeled dataset, and labeled dataset.
4.2

Deep Belief Network

We used a deep belief network (DBN) to detect the local grouping boundaries (Fig. 5).
Figure 5 outlines the structure for the DBN we used. The input of DBN was the onset
time, offset time, pitch, and velocity of note sequences from musicXML. The output
of DBN formed multi-tasking learning, which had 11 outputs, such as 10 kinds ofgrouping preference rules (GPR2a, 2b, 3a, 3b, 3c, 4, 5, 6, and 7) and local grouping
4.3

Multidimensional multi-task learning

The DBN that we introduced in Subsection 4.2 was a very complex network. The
fine-tuning of local grouping boundaries was a multi-task learning itself. The finetuning of each grouping preference rule also involved multi-task learning. Therefore,
the fine-tuning of grouping preference rules involved multidimensional multi-task
learning.
Multi-task learning. The processing flow for the multi-task learning of a grouping
preference rule or local grouping boundaries involved four steps.
Step 1: The order of the pieces of training data was randomly shuffled and a piece
was selected from top to bottom.
Step 2: The note transition of the selected piece was randomly shuffled and a notetransition was selected from top to bottom.
Step 3: Back propagation from output to input was carried out in which the notetransition had a boundary or the rule was applied (=1) or not (=0).
Step 4: The next note transition was repeated or the next piece in steps 2 and 1.
Multidimensional multi-task learning. The processing flow for themultidimensional multi-task learning of grouping preference rules involved threesteps.
Step 1: The order of grouping preference rules was randomly shuffled and a rule wasselected from top to bottom.
Step 2: Multi-task learning of the selected grouping preference rule was carried out.
Step 3: The next rules in step 1 were repeated.

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Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 201610

Masatoshi Hamanaka, Keiji Hirata, and Satoshi Tojo

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Onset time
Offset time
Pitch
Velocity

HiddenLayer n -1

GPR6

・・・

HiddenLayer nBoundary
GPR2a

・・・・・

Fig. 5. Deep belief network for detect local grouping boundaries.

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Proc. of the 12th International Symposium on CMMR, São Paolo, Brazil, July 5-8, 2016
deepGTTM-I

5

11

Experimental Results

We evaluated the performance of deepGTTM-I by using 100 pieces from the GTTM
database where the remaining 200 pieces were used to train the network. Table 1
summarizes the results for a network that had 11 layers with 3000 units.
Table 1.

Performance of ATTA, σGTTM, σGTTMII, and deepGTTM-I.

ATTA with manual editing of parameters
σGTTM
σGTTMII with manual selection of decision tree
deepGTTM-I

Precision P
0.737
0.467
0.684
0.784

Recall R
F measure
0.441
0.552
0.736
0.571
0.916
0.783
0.814
0.799

The results indicate deepGTTM-I outperformed the previous analyzers in the Fmeasure. ATTA had adjustable parameters and σGTTMII could select the decision
tree. The performance of ATTA and σGTTMII changed depending on the parametersor decision trees. Table 1 indicates the best performance was achieved by manual
editing. However, as σGTTM and deepGTTM-I had no parameters for editing,deepGTTM-I performed extremely robustly.

6

Conclusion

We developed a local grouping boundaries analyzer called deepGTTM-I that was
based on deep learning. We proposed multidimensional multi-task learning that
efficiently learned local grouping boundaries and grouping preference rules by
sharing the network. We prepared three kinds of datasets to learn the network, such as
non-labeled, half labeled, and labeled datasets because labeled datasets were very
limited and some labels of GPR2 and 3 could automatically acquire the previous
analyzer of GTTM. After a network that had 11 layers with 3000 units had been
trained, deepGTTM-I outperformed the previously developed analyzers for localgrouping boundaries in the F measure.
This work was the first step in implementing GTTM by using deep learning. We
plan to implement a complete analysis of GTTM by using deep learning. We also plan
to analyze the network after local grouping boundaries are learned.

Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 25700036, 16H01744,
23500145.

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Masatoshi Hamanaka, Keiji Hirata, and Satoshi Tojo

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