MIREX 2013 SYMBOLIC MELODIC SIMILARITY:
Melodic Similarity based on Extension Implication-Realization Model
Sakurako Yazawa, Yuhei Hasegawa, Kohei Kanamori and Masatoshi Hamanaka
University of Tsukuba
sakurako@music.iit.tsukuba.ac.jp, yuhei@music.iit.tsukuba.ac.jp,
kohei@music.iit.tsukuba.ac.jp , hamanaka@iit.tsukuba.ac.jp

ABSTRACT
We propose the method that Implication-Realization
Model (IRM) for adaptation to the similarity calculation
method and will be that submitted to the MIREX 2013
Symbolic Melodic Similarity. Current symbolic melodic
similarity calculation methods using the original IRM
cannot differentiate the interval direction of a note sequence. Our extension eliminates the ambiguity of thedefinition of the pitch change definition when analyzing
music based on the IRM. Experimental results show that
our method outperformed the baseline performance,
which uses the original IRM, when calculating melodic
similarity.
1. INTRODUCTION
The goal of this research was to calculate melodic similarity based on music theory. Toward this goal, we havebeen developing an extension of the ImplicationRealization Model (IRM) [1,2] that adapted for the similarity calculation method and an extension IRM parser.
The IRM we used was the music theory proposed by Eugene Narmour, and which can be expressed into a symbol
sequence by using rests, pitch, and rhythm that, constite
the music.
Various music similarity calculation methods havebeen proposed, which can be classified into "not based onmusic theory" and "based on music theory". Current similarity calculation methods based on music theory uses a
melodic structure called a symbol, which is defined in theoriginal IRM [6]. However, they are less accurate interms of similarity calculation for the definition in which
the pitch direction is not very strong in the symbols because they use the original IRM.
Therefor, when the IRM expresses two melodies assame symbols development, so listeners feel the difference of pitch directions. For example, the same symbol is
assigned if the tones that behave like pitch, called"down-up" or "up- down", appeared in the music, and welistening to the melody completely differently.
To solve this problem, we extended the definition of theinterval direction new order by using eight original symbols with ten extension symbols with our extended IRM.
In the following sections, we explain the basic conceptof our Extension IRM parser and calculation method inSections 2 and 3, respectively. We explain the experimental results and conclusions in Sections 4 and 5, respectively.
2. EXTENSION IRM PARSER
We have been developing the Extension IRM parser,
which enables a user to input music into a system throughoutputting 18 types of symbols that have been expanded.
The input is midi format music and output is a symbol
sequence abstraction of a melody on the basis of the IRM.
Figure. 1 shows the processing flow of our Extension
IRM parser.
Our Extension IRM parser follows two steps as melody
abstraction,
1. Melody separator
2. Original or Extension Symbolizers.
A user enters midi format music into the Melody separator, which outputs a bracket. A bracket is input data tothe Original or Extension Symbolizers.
The abstraction of music using the IRM enables expression of the symbol sequence that uses information constituting the music pitch, rhythm, rests and so on. The
bracket is an important structure to abstract music. A
bracket consists of units that enclose the sound of threeconsecutive melodies in a break, in and rest part, and notevalue rapidly changes before and after.
The Melody separator applies a bracket in two steps.
First, the Melody separator creates a large notes column
group to detect the location where the bracket is interrupted. Then the Melody separator applies the bracket ofthree tones from the beginning to the end of the group.
In the Original and Extension symbolizers, three tones
enclosed by brackets are adapted to the symbol. There are
two important points to generate the symbol. The firstpoint is the pitch of the current two to three consecutive
notes. The second point is the interval direction.
The Original symbolizer in our Extension IRM parser
applies symbols to each bracket. For example, the symbol
called "IR" applies feature from same interval direction,
large interval and small interval.
The Extension IRM symbolizer analyzes a symbol with
our proposing extension symbols a total of 18 types. We
extend the original 8 symbols to 18 symbols, as shown
Fig.2.

Fig 1.Processing flow of Extension IRM parser

Fig 2.Original and extension symbols

3. CALCLATING SIMILARITY
Similarity calculation based on the IRM is conducted using
pattern matching of symbols sequences. We use N-gram as
the pattern matching method such sequences.
Figure. 3 shows the calculation similarity method thatconsists of three steps. First, to abstract comparison andquery melodies from a symbol sequence, we input twomelodies to our Extension IRM parser. Then we determine
the degree of similarity using the N-gram of symbol sequences from the comparison and query melodies.
For calculating the degree of similarity, we use the expression in Fig.3
For calculating the degree of similarity, we use following
expression (1).

S(query, comparison) =n(1)
max(a, b)

Where S: value of similarity(0≦S≦1), n: matching element count, a: element count of query melody, b: element
count of comparison melody.
in p u t
q u ery	 m id i

in p u t
co m p ariso n 	 m id i

Exten sion 	 IRM 	 p arser

5. CONCLUSIONS
We have developed an Extension IRM parser for similarity calculation based on the IRM with extended symbols. From our experimental results, our extended IRM
was found to be useful for calculating melodic similarity.
To further increase the precision of similarity calculation, we plan to use another structure called "chain structure", which is represents the relationship of symbols defined in the IRM.
6. REFERENCES[1] Eugene Narmour, “The Analysis and Cognition ofBasic Melodic Structures ” , the university ofChicago press, 1990.

Exten sion 	 IRM 	 p arsero u tp u t	 	 	 	 sym b o lso u tp u t	 	 	 	 sym b o lsIPu	 S	 V Rd 	 IPu	 M 	 R u	 IRd 	 V Rd 	 MV Ru	 S	 P u	 IPu	 M 	 R u	 IRd 	 ID d 	 M[IP u 	 S	 V R d 	 IP u ][V R u 	 S	 V R d 	 IP u ][S	 V R d 	 IP u 	 M ]was the query to the song?”, and ranked on a 5-bradescale; 1) quite similar, 2) similar, 3) neutral, 4) not similar,
and 5) quite different. The top five songs edited foursongs and the query. The other five songs were evaluatedas relatively similar to the query.
From our preliminary experimental results, our proposed
extended IRM determined to be useful for calculating
melodic similarity.

[2][S	 P u 	 IP u 	 M ][V R d 	 IP u 	 M 	 R u ][P u 	 IP u 	 M 	 R u ][IP u 	 M 	 R u 	 IR d ][IP u 	 M 	 R u 	 IR d ][M 	 R u 	 IR d 	 V R d ][M 	 R u 	 IR d 	 ID d ][R u 	 IR d 	 V R d 	 M ][IR d 	 V R d 	 M ][IR d 	 ID d 	 M ][V R d 	 M ][ID d 	 M ]

[M ]

[M ]

Fig 3.Calculation sample

4. EXPERIMENTAL RESULT
We now describe the results from evaluating the performance of calculation similarity methods and extensions todetermine their usefulness.
We randomly selected one song from five thousands data sets of Essen as a query. We then added four newsongs to the retrieval target data by manually editing thesongs as follows; “one note deleted”, “one note inserted”,"one interval en-larged", "one interval compressed".
The four new songs we edited were included in the top
ten songs of the output from searching similar songs.
When calculating similarity by using N-gram, we change
the number of N from one to ten. As a result, using fouras N was suitable for similarity calculation based on theIRM using N-gram.
We compared the basic IRM parser and our Extension
IRM parser. From the top ten similarity results, the basic
IRM parser output-ted only two songs for editing, whichsuggests that the current extension of IRM may be useful.
We also investigated the subjective similarity by withfive participants who listened to the top ten retrieval results of the query. A participant listed to all query andsong pairs in random order without duplication. Everytime he/she listened to it, he/she was asked "how similar

Eugene Narmour, “The Analysis and Cognition ofMelodic Complexity” The university of Chicago
Press, 1992.

[3] Julian Urbano, Juan Llor´ens, Jorge Morato andSonia S´ anchez-Cuadrado, "MIREX 2012 Symbolic
Melodic Similarity: Hybrid Sequence Alignment
with Geometric Representations", MIREX 2012
Symbolic Melodic Similarity Results, 2012
[4] Fred Lerdahl, Ray Jackendoff: "A Generative
Theory of Tonal Music", The MIT Press, 1983.
[5]

Satoshi Tojo, Keiji Hirata, "Distance and Similarityof Time-span Trees”, Journal of Information
Processing, Vol. 21 No. 2 pp. 256-263, 2013.

[6] Maarten Grachten, Josep Lluis Arcos and Ramon
Lopez de Mantaras："Melody Retrieval using theImplication/Realization Model", MIREX 2012
Symbolic Melodic Similarity Results, 2005
[7] Sakurako Yazawa, Hiroko Terasawa, KeijiHirata,Satoshi Tojo, Masatoshi Hamanaka,"
Identifying the basic structures of ImplicationRealization Model in a melody ",IPSJ specialinterest group on music and computer, 2010-MUS87, No.1, Oct.2010(in Japanese).
[8] Sakurako Yazawa, Hiroko Terasawa, Keiji Hirata,
Satoshi Tojo, Masatoshi Hamanaka," Analysis thechain structures of Implication-Realization Model ina melody ", IPSJ special interest group on music andcomputer, 2012-MUS94SLP90, No.34, Feb.2012 (inJapanese).