ATTA: IMPLEMENTING GTTM ON A COMPUTER
Masatoshi Hamanaka
University of Tsukuba
hamanaka@iit.tsukuba.ac.jp

Keiji Hirata
NTT Communication Sience
Laboratories

ABSTRACT
We have been discussing the design principle for theimplementation of GTTM and presented the semiautomatic generation techniques of grouping structure,
metrical structure, and time-span tree, and the searching
method for the optimal parameter value assignments. InISMIR2007, we organize a tutorial session on thetechniques for implementing music theory GTTM forsummarizing our work and report it to relevant participantsof the conference. Since the time of the tutorial session is
not enough, we demonstrate a working automatic timespan tree analyzer ATTA in a demo session. ATTA is anintegration of our work done so far; by looking at theATTA demonstration or using ATTA, people will be able
to understand the techniques for implementing GTTM aswell as GTTM itself in more detail.
1.

INTRODUCTION

Music theory, in particular for a piece written as a score,gives us a methodology for analyzing and understandinga piece, and it explains deep structure, musicalknowledge, experience, and skills in a comprehensive
way. We believe that implementing such a music
theory on a computer would bring great benefits to theMIR research. Since analysis results by a music theory
can be considered as the expressions of the musicalsemantics of a piece, there is a possibility that musicalsemantic computing at a symbol level can be made more
precise and consistent. Therefore, the advances inmusical semantic computing will be beneficial to those
who are working on various kinds of music applications.
Formalizing and mechanizing music theories is one ofthe primary concerns in computational musicology, andthe researchers in the field are recently paying more
attention to the elaborating music theories throughexperiences of implementing a working system basedon the theories. Furthermore, since the analyzer basedon our techniques may be helpful for educational use inmusic courses for understanding and composing music.
We believe that the generative theory of tonal music(GTTM) [1] is the most promising theory formechanizing and developing a support system, thanks tothree of its features. The first feature is that it uses rules
to describe musical insight and knowledge obtained byinvestigating the musical structures and relations
occurring in a piece of music. The second feature is that
GTTM is designed to consistently represent multiple
aspects of music in a single framework. The thirdfeature is that GTTM has been developed based on theconcept of reduction. We argue that the proper way oftaking into account deep structures is to adopt theconcept of reduction [2, 3].
© 2007 Austrian Computer Society (OCG).

Satoshi Tojo
Japan Advanced Institute ofScience and Technology
2.

EXGTTMTo get music theory GTTM to operate on a computer,however, we must overcome some widely recognizedfundamental difficulties. One is giving an ambiguous
concept a firm definition, and the other is supplementing thelack of necessary concepts (externalization). Here, note that
we distinguish two kinds of ambiguity in music analysis: one
involves the musical understanding of humans, and the otherconcerns the representation of a music theory.
In our approach, we extend GTTM by full externalizationand parameterization and propose a machine-excutable
extension of GTTM, exGTTM. This externalization inmechanizing GTTM includes introducing an algorithm
for generating a hierarchical structure of the time-spantree in the mixed manner of top-down and bottom-up.
Such an algorithm has not been presented for GTTM. The
parameterization includes introducing a parameter
controlling the priorities of rules to avoid a conflictamong the rules as well as parameters for controlling theshape of the hierarchical time-span tree.
The significance of full externalization andparameterization is twofold: precise controllability andcoverage of the correct results. Whenever we find a correct
result that exGTTM cannot generate, we introduce newparameters for exGTTM and give them proper values sothat it can generate the correct result. In this way, werepeatedly externalize and introduce new parameters until
we can obtain all of the results that humans consider
correct. In total, we have introduced 15 parameters forgrouping-structure analysis, 18 for metrical-structure
analysis, and 13 for time-span reduction. We think that full
externalization and parameterization is an importantintermediate step toward a fully automatic GTTM analyzer.
Based on the above consideration, we have presented
the semi-automatic generation techniques of groupingstructure [4], metrical structure [5], and time-span tree[6], and the searching method for the optimal parametervalue assignments [7].
3.

ATTA

We developed a working automatic time-span tree
analyzer, called ATTA, which realizes exGTTM.
Figure 1 is the overview of the ATTA, which consists ofa grouping structure analyzer, a metrical structure
analyzer, and a time-span tree analyzer. The features of
ATTA contain: an XML-based data structure,
programming in Perl, and a Java-based GUI (Figure 2).
4.

ANALISYS RESULTS BY ATTA

Figure 3 shows the analysis results of two pieces, which

=====Figure 1. Processing flow of ATTA.

REFERENCES

Time-span tree

[1] Lerdahl, F. and Jackendoff, R. A Generative
Theory of Tonal Music, The MIT Press,
Cambridge, 1983.

Grouping structure[2] Selfridge-Field,
E.
''ConceptualandRepresentational Issues in Melodic Comparison'',Computing in Musicology 11, The MIT Press,
pp. 3-64, 1998.

Metrical structure

Figure 2. ATTA: automatic time-span tree analyzer.

[3] Hirata, K. and Aoyagi, T. ''Computational
Music Representation on the Generative
Theory of Tonal Music and the Deductive
Object-Oriented Database'', Computer Music
Journal, Vol. 27, No. 3, pp. 73-89, 2003.

are generated with the same parameter values,
Beethoven’s Turkish March, and English Traditional,
Green Sleeves. The numbers shown around thebranches of the trees in the figure indicate the rulenumbers that hold. By comparing the two pieces, weinterestingly find the similarity between the two, where
the same rules hold. At present, the parameters areconfigured by hand, because the optimal values of theparameters depend on a piece of music.
5.

[4] Hamanaka, M., Hirata, K. and Tojo, S. ''Automatic
Generation of Grouping Structure Based on The
GTTM'', In Proc. of ICMC 2004, pp.141-144, 2004.

[5] Hamanaka, M., Hirata, K. and Tojo, S. ''Automatic
Generation of Metrical Structure Based On GTTM'',CONCLUSION

In Proc. of ICMC 2005, pp.53-56, 2005.

We briefly present a machine-executable extention ofGTTM, exGTTM, and a working automatic time-span tree
analyzer, ATTA, which realizes exGTTM. We would liketo contribute to the MIR research through mechanizing amusic theory. In the demo session of ISMIR2007, welook forward to demonstrating ATTA and discussing thetechniques for implementing GTTM.

[6] Hamanaka, M., Hirata, K. and Tojo, S. ''ATTA:
Automatic Time-Span Analyzer Based On Extended
GTTM'', In Proc. of ISMIR 2005, pp.358-365, 2005.

[7] Oka, Y., Hamanaka, M., Hirata, K. and Tojo, S.
''Optimal Parameter Set Acquisition for exGTTM'',In Proc. of Music-AI 2007, 2007.
1(a) Beethoven, Turkish March

1111, 3b1, 3b1, 3b1, 3b13b11, 3b1, 3b11, 3b1

13b1

111, 3b1

13b1
111, 3b1

11, 3b(b) English Traditional, Grenn Sleeves

3b1111111, 3b1, 3b1, 3b1

11111

Figure 3. Analysis results of two pieces having the same parameter sets.