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Classification of Three Composers' Popular Songs Using Feature Vectors Based on the Musical Score Information

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Classification of Three Composers' Popular Songs Using Feature Vectors Based on the Musical Score Information

Sachiko DEGUCHI, Shohei MlKAMOTO* and Yoshinobu KUROSE

Abstract: This paper describes the extraction of features from three composers' songs and the classification of the songs by applying the NN rule with several feature vectors. The features are extracted from the score database that was built by inputting the musical score information. This research uses several 3-dimensional feature vectors that consist of the features of 5-note patterns, notes in a musical scale, intervals in a scale, and 3-note patterns in a scale. Each axis of the feature space represents the feature of each composer. The classification result indicates that the features of pitch transitions in a scale are more effective than those without a scale. This research also uses several 9-dimensional feature vectors that are the combinations of the features used in the 3-dimensional vectors. The classification result indicates that the combinations of the features of pitch transitions in a scale and those without a scale are effective. Next, this research examines the combinations of composers. The result shows that the correct classification ratio depends on the combination of composers. A prototype system to recommend songs has been made by applying the feature space studied in this research.

Keywords: feature vector, n-gram, NN rule, music classification, musical score, scale, composer, recommendation system

1. Introduction

Since there are large amounts of music resources today, classification methods are getting more important. Many methods are proposed based on the acoustic data, however, the analysis of melodies is not sufficient. On the other hand, there have been many researches on the analysis of melodies based on the musical score information, and several statistical methods are appliedl ) 2). N-gram is applied in several works3) 4), and HMM is also applied in several works5), but these works are not using the information about musical scales sufficiently. Since music is based on the structure of

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scale, statistical method should be applied on the scale. The authors have analyzed pitch transitions in a musical scale as well as pitch transitions without a musical scale. The authors have extracted features from three composers' popular songs, and then applied those features to the classification of popular songs using the NN rule6).

2. Score Database

The authors have built the musical score database of four composers of Japanese popular music: Hirai, Makihara, Sakurai and Kusano; 24 pieces for each composer. We have input the pitches

Cluster of Electronic Engineering and Information Science, Graduate School of Systems Engineering, Kinki University

* currently Fujitsu Ten Technology Limited

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and durations of notes in the voice parts of scores using the Humdrum kern format7) for 48 pieces. We have also input the score information by using a scanner and OCR software8) for other 48 pieces, and we have corrected the input errors and converted the Music XML data into Humdrum kern data.

3. Feature Extraction

This section describes the feature extraction from three composers' songs -- Hirai, Makihara, and Sakurai's songs.

3.1. N-note Patterns

Table 1. Top 20 of 5-note patterns

Hirai Makihara Sakurai

% count oattem % count oatlem % count oattem 1.24 137 0000 3.34 408 0000 0.83 97 0000 0.80 88 -1 1 -1 1 0.89 109 0002 0.63 74 -2 -1 1 2 0.70 77 -2 2 -2 2 0.61 74 2 2 1 -1 0.49 57 -1 -2 -2 2 0.61 67 1 -1 1 -1 0.59 72 21 -1 -2 0.46 54 -1 -2 -2 0 0.56 62 2 -2 2 -2 0.57 70 -2 -2 0 0 0.45 53 2 2 1 2 0.53 58 2000 0.57 69 2000 0.45 53 -2 -2 -1 1 0.52 57 2 1 -3 2 0.56 68 1 -1 -2 -2 0.45 53 2 -2 2 -2 0.48 53 0002 0.53 65 000 -2 0.38 45 -2 -2 2 2 0.47 52 1 -3 2 1 0.48 59 002 2 0.37 43 1 1 2 2 0.46 51 -2 -2 -1 1 0.44 54 00 -2 -1 0.36 42 2 1 22 0.45 50 -1 1 -1 -2 0.43 53 0200 0.35 41 00 -1 0 0.44 49 -33 -3 3 0.42 51 -3 -2 -2 0 0.32 38 -2 2 2 2 0.43 47 -3 2 1 -3 0.41 50 -2 -2 0 2 0.32 37 -1 -2 2 1 0.43 47 -2 -2 00 0.41 50 02 2 1 0.32 37 -2 2 -2 2 0.42 46 -2 2 -2 -2 0.40 49 0007 0.32 37 2 -2 -1 1 0.40 44 3 '-3 3 -3 0.40 49 -2000 0.30 35 22-2 2 0.37 41 000 -2 0.39 48 -1 -2 -2 0 0.30 35 1 2 -2-1 0.37 41 1 -1 -2 -2 0.38 46 000 -1 0.30 35 00 -2 0 0.36 40 0-2 -1 1 0.37 45 0700 0.29 34 -2 -2 0 2 0.35 39 00 -2 -1 0.37 45 0 -2 -1 -2 0.29 34 -1 1 2 2

The authors have converted pitch information of the Humdrum kern data into MIDI note numbers, where middle C is represented as 60 and a half step is represented as 1. Next, we have extracted n-note melodic patterns (n-grams, n = 3, 4, 5, 6, 7) from the numerical pitch data. Each melodic pattern is represented as a sequence of musical interval, where a musical interval is represented as the difference between two pitches. For example, from the pitch sequence (60 62 60 62 62), 3-note melodic patterns (2 -2), (-2 2) and (2 0) are extracted, where 2 represents a whole step. We count the number of occurrences of each pattern and calculate the ratio.

We also analyze 4-note, 5-note, 6-note, and 7-note melodic patterns in the same way.

The result shows that the feature of each composer appears in 5-note patterns. Table 1 shows the top 20 of 5-note patterns. We have extracted the feature of each composer as follows.

Hirai: the ratio of patterns (n -n n -n) and (-n n -n n),

where n=l, 2, 3, .... We call this feature 5-note-H.

Makihara: the ratio of patterns (0 0 0 n) and (n 0 0 0), where n=O, ± 1, ±2, .... We call this feature 5-note-M.

Sakurai: the ratio of patterns (n m -m -n) and (-n -m m n), where n=l, 2, 3, ... , m=l, 2, 3, .... We call this feature 5-note-S.

3.2. Distribution and Transitions of Notes in a Musical Scale

This section describes the analysis of the distribution and transitions of notes in a musical scale. The authors have transposed the numerical pitch data (note numbers) of each composer's pieces into C major. For example, a number 7 is subtracted from each note number of the songs in G major (because the difference between the pitch C and pitch G is 7). All pieces analyzed in this research are written in the major key. Next, we have extracted notes, intervals, and 3-note patterns from the transposed data. We count the number of occurrences of each note, interval and 3-note pattern, and then calculate the ratio.

(1) Notes in a Scale

Table 2. Notes in a scale

1 st 2nd 3rd 4th 5th 6th 7th

Hirai [%) 21.50 14.56 18.21 10.83 12.21 11.45 9.08

Makihara [%) 25.78 16.75 18.29 6.30 13.89 12.49 5.60

Sakurai [%) 25.39 14.20 1603 10.85 13.49 9.57 8.75

Table 2 shows the distribution of notes in a musical scale. The most frequently used note in a musical scale is the 1st note (tonic), however, the ratio of the 1st note of Hirai's songs is lower than other composers' ratios. We have extracted the feature of each composer as follows.

Hirai: the ratio of the 1st note in a scale. We call this feature I-note-scale-H.

Makihara: the ratio of the 4th note in a scale. We call this feature I-note-scale-M.

Sakurai: the ratio of the 7th note in a scale. We have first extracted the ratio of the 6th note, but it appears that the ratio of the 7th note is more effective for the classification. We call this feature I-note-scale-S.

(2) Intervals in a Scale

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Table 3. Interval (2) in a scale Hirai Makihara Sakurai

% count % count % count 1 st 3.84 429 5.36 664 6.24 748 2nd 3.89 435 4.53 562 3.88 465 4th 1.87 209 0.64 79 2.24 268 5rh 2.47 276 1.78 221 1.99 239 6th 2.35 263 1.82 225 1.86 223

Table 3 shows an example of intervals in a musical scale. The ratio of 'interval (2) from the 1st note' of Sakurai is higher than the other composers' ratios, where 'interval (2) from the 1st note' means the pitch transition from the 1st note to the 2nd note in a scale. We have extracted the feature of each composer as follows.

Hirai: the sum of the ratios of interval (1) from the 3rd note and interval (-2) from the 6th note. We call this feature 2-note-scale-H.

Makihara: the sum of the ratios of interval (0) from the 1st note and interval (0) from the 5th note. We call this feature 2-note-scale-M.

Sakurai: the sum of the ratios of interval (2) from the 1st note and interval (2) from the 4th note. We call this feature 2-note-scale-S.

(3) 3-note Patterns in a Scale

Table 4. 3-note pattern (0 0) in a scale Hirai Makihara Sakurai

% count % count % count 1 st 2.25 250 4.48 552 1.41 167 2nd 0.70 78 1.35 166 0.22 26 3rd 1.34 149 1.86 229 0.56 66 4th 0.50 55 0.56 69 0.63 75 5rh 1.36 151 2.44 300 1.33 158 6th 0.73 81 2.23 275 0.42 50 7th 0.12 13 0.05 6 0.15 18

Table 4 shows an example of 3-note patterns in a musical scale. The ratio of 'pattern (0 0) from the 1st note' of Makihara is higher than the other composers' ratios. We have extracted the feature of each composer as follows.

Hirai: the sum of the ratios of pattern (-1 1) from the 4th note and pattern (2 -2) from the 5th note.

We call this feature 3-note-scale-H.

Makihara: the sum of the ratios of pattern (0 0) from the 1st note and pattern (2 2) from the 1st note.

We call this feature 3-note-scale-M

Sakurai: the sum of the ratios of pattern (-1 1) from the 1st note and pattern (1 2) from the 7th note. We call this feature 3-note-scale-S.

4. Classification of Songs

4.1. Evaluation of Features

The authors evaluate the features described in the previous section by applying the NN (Nearest Neighbor) rule. Axes of the feature space are usually fixed, however, we use the feature space with the axes that represent composers' features.

We compare several 3'dimensional, 9-dimensional, and 12-dimensional feature spaces.

In this section we classify the songs of three composers: Hirai, Makihara and Sakurai. First we calculate the prototype (mean feature vector) of each composer's 24 pieces for each composer's class.

Next we classify all 72 pieces of three composers.

We calculate the Euclidean distances between the feature vector of each piece and the prototypes of three composers' classes, and then classify the piece as the nearest class. We calculate the correct classification ratio, i.e., the ratio of Hirai / Makihara / Sakurai's pieces that are classified as Hirai / Makihara / Sakurai's class respectively.

4.1.1. 3-dimensional Feature Vector

We classify three composers' pieces using four kinds of 3-dimensional feature vectors as follows.

(1) Feature Vector of 5-note Patterns

We use three features extracted in section 3.1., i.e., (5-note-H, 5-note'M, 5-note-S). We calculate three features for each piece, and then determine the nearest class for the piece. Table 5 shows the confusion matrix of this classification. The correct classification ratios are as follows.

Hirai: 50.0%, Makihara: 58.3%, Sakurai: 66.7%

Average: 58.3%

Hirai Makihara

Sakurai Average

Table 5. Worst classification result (3d vector of 5-note patterns)

Hirai(credicted) Makihara( redicted) SakuraKoredictecO Accuracy[%]

12 7 5 50.0

2 14 8 58.3

5 3 16 66.7

58.3

(2) Feature Vector of Notes in a Scale

We use three features extracted in section 3.2.(1), i.e., (l-note-scale-H, 1-note'scale-M, 1-note-scale-S).

The correct classification ratios are as follows.

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Hirai: 66.7%, Makihara: 79.2%, Sakurai: 58.3%

Average: 68.1%

(3) Feature Vector of Intervals in a Scale

We use three features extracted in section 3.2.(2), i.e., (2-note-scale-H, 2-note-scale-M, 2-note-scale-S).

The correct classification ratios are as follows.

Hirai: 70.8%, Makihara: 70.8%, Sakurai: 66.7%

Average: 69.4%

(4) Feature Vector of 3-note Patterns in a Scale

We use three features extracted in section 3.2.(3), i.e., (3-note-scale-H, 3-note-scale-M, 3-note-scale-S).

The correct classification ratios are as follows.

Hirai: 45.8%, Makihara: 66.7%, Sakurai: 66.7%

Average: 59.7%

4.1.2. 9-dimensional Feature Vector

We classify three composers' pieces using four kinds of 9-dimensional feature vectors.

(1) Feature Vector of 5-note Patterns, Notes in a Scale and Intervals in a Scale

We use nine features as follows:

(5-note-H, 5-note-M, 5-note-S,

I-note-scale-H, I-note-scale-M, I-note-scale-S, 2-note-scale-H, 2-note-scale-M, 2-note-scale-S). We calculate normalized nine features for each piece, and then determine the nearest class for the piece.

The correct classification ratios are as follows.

Hirai: 66.7%, Makihara: 62.5%, Sakurai: 75.0%

Average: 68.1%

(2) Feature Vector of Notes in a Scale, Intervals in a Scale and 3-note Patterns in a Scale

We use nine features as follows:

(l-note-scale-H, I-note-scale-M, I-note-scale-S, 2-note-scale-H, 2-note-scale-M, 2-note-scale-S, 3-note-scale-H, 3-note-scale-M, 3-note-scale-S). The correct classification ratios are as follows.

Hirai: 70.8%, Makihara: 79.2%, Sakurai: 70.8%

Average: 73.6%

(3) Feature Vector of 5-note Patterns, Intervals in a Scale and 3-note Patterns in a Scale

We use nine features as follows:

(5-note-H, 5-note-M, 5-note-S,

2-note-scale-H, 2-note-scale-M, 2-note-scale-S, 3-note-scale-H, 3-note-scale-M, 3-note-scale-S). The

correct classification ratios are as follows.

Hirai: 75.0%, Makihara: 66.7%, Sakurai: 79.2%

Average: 73.6%

(4) Feature Vector of 5-note Patterns, Notes in a Scale and 3-note Patterns in a Scale

We use nine features as follows:

(5-note-H, 5-note-M, 5-note-S,

I-note-scale-H, I-note-scale-M, I-note-scale-S, 3-note-scale-H, 3-note-scale-M, 3-note-scale-S). The correct classification ratios are as follows.

Hirai: 75.0%, Makihara: 70.8%, Sakurai: 79.2%

Average: 75.0%

This result (the average of the ratios) is highest in the classifications. The confusion matrix of this classification is shown in table 6.

Table 6. Best classification result (9d vector of 5-note patterns, notes in a scale

and 3-note patterns in a scale)

Hirai(DI'"edicted) Makihara(predicted) SakuraiCoredicted Accuracvr"bl

Hirai 18 3 3 75.0

Makihara 3 17 4 70.8

Sakurai 3 2 19 79.2

Averaf!.e 75.0

4.1.3. 12-dimensional Feature Vector

We classify three composers' pieces using a 12-dimensional feature vector. We use twelve features as follows: (5-note-H, 5-note-M, 5-note-S, I-note-scale-H, I-note-scale-M, I-note-scale-S, 2-note-scale-H, 2-note-scale-M, 2-note-scale-S, 3-note-scale-H, 3-note-scale-M, 3-note-scale-S). We calculate normalized twelve features for each piece, and then determine the nearest class for the piece.

The correct classification ratios are as follows.

Hirai: 75.0%, Makihara: 70.8%, Sakurai: 75.0%

Average: 73.6%

4.1.4. Comparison of Feature Vectors

The results of section 4.1.1 show that the classification using the features of intervals in a scale is best and that the classification using the features of 5-note patterns is worst in the classifications using 3-dimensional feature vectors.

However, the results of sections 4.1.2 and 4.1.3 show that the classification using the combination of features of 5-note patterns, notes in a scale and 3-note patterns in a scale is best in the classifications using 9-dimensional feature vectors and is also better than the classification using a 12-dimensional feature vector. These results

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indicate the following:

The features of pitch transitions in a scale are more effective than those without a scale.

The combinations of the features of pitch transitions in a scale and those without a scale are effective.

We have also compared these classifications with the classifications using feature spaces of fixed axes.

The result shows that the feature space with the axes tuned for the composers is more effective than the feature space with the fixed axes. For example, we have classified the songs by using the 3-dimensional feature vector of notes in a scale: (1st note, 2nd note, 3rd note). The correct classification ratios are as follows.

Hirai:58.3%, Makihara:41. 7%, Sakurai:54.2%

Average: 51.4%

This result is lower than the result of classification using the feature vector (1st note, 4th note, 7th note), which is described in section 4.1.1.(2).

4.2. Combination of Composers

This section describes the classification depending on the combination of composers. We choose three composers from four composers (Hirai, Makihara, Sakurai, Kusano) and classify those three composers' songs. We use 9 features of 5-note patterns, notes in a scale and 3-note patterns in a scale for the classification in this section.

4.2.1. Feature Extraction of the 4th Composer

We have extracted the features of Kusano as follows.

5-notte Patterns: the ratio of patterns (2 0 n m), (n 2 Om), and (n m 2 0), where n=O, 1, 2, 00., m=O, 1,2'00' . We call this feature 5-note-K.

Notes in a scale: the ratio of the 5th note in a scale.

We call this feature 1-note-scale-K.

3-note Patterns in a scale: the sum of the ratios of pattern (0 0) from the 2nd note and pattern (0 0) from the 7th note. We call this feature 3-note-scale-K.

4.2.2. Classification of Three Composers' Songs

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Hirai, Makihara and Sakurai

We use nine features of three composers: H, M, S.

This classification is described in section 4.1.2.(4).

The correct classification ratios are as follows.

Hirai: 75.0%, Makihara: 70.8%, Sakurai: 79.2%

Average: 75.0%

(2) Makihara, Sakurai and Kusano

We use nine features of three composers: M, S, K.

We use the features (5-note-M, 5-note-S, 5-note-K, 1-note-scale-M, 1-note-scale-S, 1-note-scale-K, 3-note-scale-M, 3-note-scale-S, 3-note-scale-K). The correct classification ratios are as follows.

Makihara: 79.2%, Sakurai: 83.3%, Kusano:

58.3%

Average: 73.6%

(3) Sakurai, Kusano and Hirai

We use nine features of three composers: S, K, H.

The correct classification ratios are as follows.

Sakurai: 70.8%, Kusano: 66.7%, Hirai: 70.8%

Average: 69.4%

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Kusano, Hirai and Makihara

We use nine features of three composers: K, H, M.

The correct classification ratios are as follows.

Kusano: 41. 7%, Hirai: 79.2%, Makihara: 62.5%

Average: 61.1%

The result shows that the classification of Hirai, Makihara and Sakurai's songs is best -- the average of the ratios is highest. This result also shows that Kusano's features are not effective for the classification of his songs and other composers' songs.

5. Prototype Recommendation System

The result of our research shows that some composers' songs can be classified at the ratio of 70% using their features. This result indicates that we can build a recommendation system based on the composers' features.

We have made a prototype system to recommend songs applying the feature space described in section 4.1.2.(4), which is composed of Hirai, Makihara and Sakurai's features of 5-note patterns, notes in a scale and 3-note patterns in a scale. This system recommends other composers' songs which are classified as Hirai / Makihara / Sakurai's class to the users who like Hirai / Makihara / Sakurai's songs respectively.

We use Kusano's 24 songs for the recommendation. Seven songs are recommended to

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who like Hirai's songs, eight songs are recommended to who like Makihara's songs, and nine songs are recommended to who like Sakurai's songs.

6. Conclusions

The authors have extracted features from three composers' songs described in musical scores. We have classified these songs by applying the NN rule with several 3-dimensional feature vectors, which consist of the features of 5-note patterns, notes in a musical scale, intervals in a scale, and 3-note patterns in a scale. Each axis of the feature space represents the feature of each composer. The result indicates that the features of pitch transitions in a scale are more effective than those without a scale.

We have also classified the songs by applying the NN rule with several g'dimensional feature vectors, which are the combinations of the features used in the 3'dimensional vectors. The result indicates that the combinations of the features of pitch transitions in a scale and those without a scale are effective.

Next, the authors have examined the combinations of composers for the classification four combinations of three composers selected from four composers. The result shows that the correct classification ratio depends on the combination of composers. We have made a prototype system to recommend songs applying the feature space studied in this research.

In this research we have used the features of pitch information to evaluate how they are effective

for the classification. In the next step of our research, we will extract the features of durations and apply them to the classification. We will also add other composers' songs to evaluate the prototype system for recommendation.

References

1) D. Huron, "The Melodic Arch in Western Folksongs", Computing In Musicology, vol. 10, pp.3-23, the MIT Press, 1996.

2) C. McKay, I. Fujinaga, "Automatic Genre Classification Using Large High-level Musical Feature Sets", Proc. of 5th ISMIR, 2004.

3) S. Doraisamy, S. Rueger, "A Polyphonic Music Retrieval System Using N-Grams", Proc. of 5th ISMIR, 2004.

4) J. S. Downie, "Evaluating a Simple Approach to Music Information Retrieval: Conceiving Melodic N-gram as Text", The University of Western Ontario, 1999.

5) W. Chai, "Melody as a Significant Musical Feature in Repertory Classification", Computing in Musicology, voLl3, pp.51-72, the MIT Press, 2004.

6) S. Deguchi, S. Mikamoto, T. Kosako, Y. Kurose,

"Melodic Analysis and Classification of Three Composers' Songs in Japanese Popular Music", Proc.

of the Spring Meeting of The Japanese Society for Music Perception and Cognition, pp.59-64, 2008.

7) D. Huron, The Humdrum Toolkit Reference Manual, CCARH, Stanford University, 1994.

8) http://www.kawai.co.jp/cmusic/products/sm/

Table  1.  Top 20 of 5-note patterns
Table  3.  Interval (2) in a scale  Hirai  Makihara  Sakurai
Table 6.  Best classification result  (9d vector of 5-note patterns,  notes in  a scale

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