33rd Physics Congress of the SamahangPisika ng Pilipinas University of Northern Philippines, Vigan City

3 - 6 June 2015 1

Characterization of Filipino folk songs using a network approach

Ma. Christina Jamerlan∗1, Ranzivelle Marianne Roxas-Villanueva2 and Giovanni Tapang1 1National Institute of Physics, University of the Philippines, Diliman, Quezon City

2Institute of Mathematical Sciences and Physics, University of the Philippines, Los Baños, Laguna ∗Corresponding author: mjamerlan@nip.upd.edu.ph

Abstract We use music networks to characterize 300 Filipino folk songs. Adjacent notes in

Filipino folk songs tend to cluster together in short repetitive patterns resulting in

lower densities compared to those of random networks. It was found that Filipino folk

songs are not small-world networks.

Keywords: 43.80.Ka Sound production by animals; 64.60.aq Networks;

89.75.Fb Structures and Organization in complex systems; 89.75.Kd Patterns

1. Introduction In complex systems research, the use of network attributes as bases for network comparison is a common and

reliable method [1]. This technique has been applied to the comparison of writing styles and word meanings in texts

[2–4]. Complex networks have several properties that are used to create a profile for comparison with other

networks.

Universal features have been identified in different types of music [5]. These findings led to the creation of an

algorithm for generating artificial music that is appealing in certain standards [5]. Musical genre classification using

complex networks has been done using network motifs (recurring melodic patterns) found in Western musical pieces

[6]. Statistical distributions of melodic events have been used in ethnomusicology to classify and predict similarities

between musical pieces [7].

Complex networks have also been used to characterize musical compositions. Previous studies have identified

universal features in different types of music [5]. However, no such studies have been done for Filipino music. In

this study, we characterize Filipino folk songs based on a set of network parameters to verify the existence of

patterns. This method extends to other dynamical systems that can be represented as complex networks.

2. Methodology The complex networks were constructed using Python. The network components were extracted from MIDI files

of Filipino folk songs. The MIDI files were generated from transcribed musical scores of Filipino folk songs

obtained from the UP College of Music Library [8–10].

Using a program called MID2TXT [11], the MIDI files were converted into text files for event extraction. This

was done using a batch processing program written in GNU BASH. From the text files, the note numbers

corresponding to the pitch and the duration of the notes were obtained. The notes were used as the nodes of the

network. Links were created between successive notes played in the MIDI file (repeated notes were represented as

self-loops), and these became the edges of the network. The duration between the two notes in the folk song

correspond to the weights of these edges.

The NetworkX software package [12] of Python was used to create the networks and compute the parameters. A

list of network attributes, namely: number of nodes, number of edges, average clustering coefficient, density, and

average shortest path length was generated for each of the networks.

The clustering coefficient cu, refers to the measure of the degree of clustering toward a node in the network. For

weighted graphs, it is mathematically defined as

(1)

where uvw , uww and vww are the normalized weights of the network edges, and deg(u) is the degree or the number

of edges connected to the node u [12].

For directed graphs, the network density d is defined by

33rd Physics Congress of the SamahangPisika ng Pilipinas University of Northern Philippines, Vigan City

3 - 6 June 2015 2

(2)

where n is the number of nodes and m is the number of edges in the network [12].

The average shortest path a of a network is defined by the equation

(3)

where d(s,t) is the shortest distance between nodes s and t which are part of the set of nodes V in the network, and n

is the number of nodes [12].

Small-world networks exhibit a higher clustering coefficient than their equivalent random networks, but share a low

average path length [13]. In order to determine if the Filipino folk song networks are small-world, they were

compared to their equivalent random graphs (with the same corresponding number of nodes and edges) in terms of

their average clustering coefficients and average shortest paths.

3. Results and Discussion

Figure 1: The music network of the Filipino folk song “Bahay Kubo” with the node sizes

indicating the degree centrality, and the width of the edges representing the duration

between notes. The nodes are labeled with the note number which corresponds to their pitch

in the musical scale.

Figure 2: The density (left) and the average clustering coefficient (right) vs. node count plotted for all 300 networks and their

random network equivalents. A lower average clustering coefficient compared to those of their random network equivalents

indicates that the networks are not small-world.

A sample network is shown in Figure 1. The network attributes of the 300 Filipino folk song networks show a

decrease in graph density and average clustering coefficient with increased node count as shown in Figure 2.

Adjacent notes, therefore, have a high tendency to cluster together and create short repetitive patterns rather than a

long sequence of distinct notes.

33rd Physics Congress of the SamahangPisika ng Pilipinas University of Northern Philippines, Vigan City

3 - 6 June 2015 3

Among the 300 folk songs, “Dulawi” had the lowest average shortest path length (1.00), while “An Loro” had

the highest (2.50). The average shortest path length is a measure of the efficiency of information or mass transport in

a network. A lower value implies that only some notes in the folk song are well connected, and therefore create short

repetitive patterns or “sub-songs” within the whole song.

Network measures showed that Filipino folk songs are not small-world networks. An average clustering

coefficient of 0.26±0.18 for all 300 networks is significantly lower than the average clustering coefficients of their

random equivalents, 0.55±0.20, based on the results of a two-sample t-test. The best fit curve to the boundary

between the average clustering coefficients of Filipino folk songs and their equivalent random networks follows the

equation y = -0.414 ln(x) + 1.3293 as shown in Figure 2. A two-sample t-test showed that the average path length of

the Filipino folk song networks is 1.73±0.25, which is significantly higher than that of the random networks,

1.49±0.23.

4. Conclusion and Recommendations We have shown that music network properties may be used to compare and characterize Filipino folk songs.

From the plot of the network density against the average shortest path, we conclude that the structures of the Filipino

folk song networks are less dense compared to random networks of the same node count. This indicates that

repetitive sub-songs or patterns exist in Filipino folk songs.

The study has limitations in terms of musicality. The characterization of Filipino folk song networks is based on

the melodic contour alone. Accents on pitches, phrasing, syllabication, and vocal styles are not considered. Encoding

musical score sheets as MIDI files to ensure the accuracy of the conversion process proved to be a very tedious

procedure. For future studies, we recommend the automation of the musical score digitization process.

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