COMPARING RNN PARAMETERS FOR MELODIC SIMILARITY
Tian Cheng, Satoru Fukayama, Masataka Goto
National Institute of Advanced Industrial Science and Technology (AIST), Japan{tian.cheng, s.fukayama, m.goto}@aist.go.jp

ABSTRACT
Melodic similarity is an important task in the Music Information Retrieval (MIR) domain, with promising applications including query by example, music recommendation and visualisation. Most current approaches computethe similarity between two melodic sequences by comparing their local features (distance between pitches, intervals,etc.) or by comparing the sequences after aligning them.
In order to find a better feature representing global characteristics of a melody, we propose to represent the melodic
sequence of each musical piece by the parameters of a generative Recurrent Neural Network (RNN) trained on its sequence. Because the trained RNN can generate the identical melodic sequence of each piece, we can expect that the
RNN parameters contain the temporal information within
the melody. In our experiment, we first train an RNN on
all melodic sequences, and then use it as an initialisation
to train an individual RNN on each melodic sequence. The
similarity between two melodies is computed by using the
distance between their individual RNN parameters. Experimental results showed that the proposed RNN-basedsimilarity outperformed the baseline similarity obtained bydirectly comparing melodic sequences.
1. INTRODUCTION
Melodic similarity is a task to analyse the similarity between melodies, which has been used for music retrieval,recommendation, visualisation and so on. To compute thesimilarity, a melody is always represented by a sequenceof monophonic, musical fragments/events (MIDI event,
pitch, etc.). Current approaches usually compare two
melodic sequences using the string edit distance [8, 9, 17],geometric measures [19] and N-Gram based measures[5, 27]. Alignment-based methods are applied when two
melodic sequences are of different lengths [15, 23], or
when events of two sequences are not corresponding toeach other one by one [2]. Not only melodic sequence
but also melody slopes on continuous melody contours
are aligned for comparing melodic similarity [28]. Readers can refer to [25] for state-of-the-art melodic similarc Tian Cheng, Satoru Fukayama, Masataka Goto. Licensed under a Creative Commons Attribution 4.0 International License(CC BY 4.0). Attribution: Tian Cheng, Satoru Fukayama, Masataka
Goto. “Comparing RNN parameters for melodic similarity”, 19th International Society for Music Information Retrieval Conference, Paris,
France, 2018.

ity methods. The existing methods focus on local features
extracted from melodic sequences, such as distances between pitches or between subsets of melodic sequence (NGram). In addition alignment is needed when two melodic
sequences are not comparable directly.
In order to deal with these drawbacks, we propose totrain a generative Recurrent Neural Network (RNN) on a
melodic sequence, and use the RNN parameters to represent the melodic sequence. The proposed feature (RNN
parameters) projects a melodic sequence to a point in theparameter space, having two characteristics described asfollows. Firstly, the feature is independent to the length of
the input melodic sequence because every sequence is represented by its RNN parameters of the same dimension.
Secondly, because the RNN can generate an identical sequence, we can expect that the RNN parameters containthe global, temporal information of the melody.
In our experiment, we first train an RNN on all melodic
sequences from 80 popular songs as an initialisation. With
the initialisation, RNNs are trained on individual melodic
sequences. All the networks are trained in tensorflow. We
compute the similarity between two melodic sequences by
the Cosine similarity of their RNN parameters. The results
show that the similarity based on RNN parameters outperforms the baseline similarity obtained by comparing the
melodic sequences directly. To the best of our knowledge,
this is the first study that uses parameters of generative
RNNs for the purpose of computing melodic similarity.
2. RELATED WORKIn this section, we introduce related work on RNNbased melody generation models, and briefly introduce researches on word and sentence embedding for understanding semantic meanings in natural language processing.
2.1 RNN-based melody generation models
We discuss several state-of-the-art RNN-based melody
generation models. The RNN-based generative models areusually applied with Long Short Term Memory (LSTM)
units in order to model a long time dependence, such as
Melody RNN in Magenta [1] and folk-rnn [22]. Magenta [1] uses 2-layer RNNs with 64 or 128 LSTM units
per layer, while folk-rnn [22] uses a deeper network (RNN
with 3 hidden layers of 512 LSTM units for each layer).
The RNNs generate melody by predicting the next
melodic event based on its previous N events:[xt−N , ..., xt−1 ] → xt ,

763

764

Proceedings of the 19th ISMIR Conference, Paris, France, September 23-27, 2018
ModelsRepresentation

Architecture

Magenta [1]MIDI event

2-layer RNN (LSTM)

Folk-rnn [22]abc notation

3-layer RNN (LSTM)

Hierarchical
RNN [26]

bar profile, beatprofile and note

3 RNNs (2-layer LSTM)
for bar, beat and note

Table 1: Brief summary of RNN-based melody generation
models.
where xt denotes the melodic event in time t. The melodic
event can be represented in many forms, for example MIDI
events [1], abc notation [22] and so on, as shown in Table 1.
With quantised time steps (in sixteenth notes, for example),a melody can be represented as a sequence of pitches 1 or
MIDI events (pitch onset, offset, and no event) [1].
Rhythm information can also be modelled for melody
generation. One simple way is to concatenate beat information with the melodic event for each frame to feed into
the network [1]. There are also several hierarchical RNNs
proposed with rhythm information. In [4], each note isrepresented by its pitch and duration, and 2 RNNs (rhythm
and melody RNNs) are trained for duration and pitch, respectively. The rhythm network receives the current pitchand duration as inputs, and outputs the duration of thenext note. The melody network receives the current pitch
and generated upcoming duration as inputs to generate thepitch of the next note. [26] trains 3 RNNs for bar, beat, andnote, respectively. The first RNN generated bar profiles.
Generated bar profiles are fed into the second network to
generate beats, and then bar and beat profiles are fed into
the third network to generate notes.
Studies of generative RNN models always list generated examples [1, 22] as results, or conduct a listening testfor evaluation [26]. We believe that the generative RNN
actually learns something ‘musical’ and can be used formusic analysis. In this paper we extend the utility of thegenerative RNN to represent a melody and evaluate it in a
melodic similarity task.
2.2 Word embedding and sentence embedding
In natural language processing, word embedding and sentence embedding work on representing semantic meanings
of words and sentences. There are two successful wordembedding models introduced in [13, 14]: word representations are learnt in order to predict surrounding words or
to predict the current word by its content. In these ways,
the meaning of a word is related to its context. With theembedded words, a representative vector for a sentence (asequence of words) can be learned at the same time of parsing the sentence [21] or can be trained in a weakly supervised way on the click-through data by making sentence
vectors with similar meanings close to each other [18]. Inspired by word embeding, [11] learns to represent a paragraph by predicting words in the paragraph using previous
words and a paragraph vector. The same paragraph vector
1 https://brangerbriz.com/blog/

using-machine-learning-to-create-new-melodies/is shared when predicting words in the paragraph and thenis used to represent the paragraph.
We believe that word embedding may correspond tochord embedding [3, 12] in understanding music; and sentence embedding may correspond to representing a sequence of chords (also an interesting topic to investigate).
In general, the musical meaning (of a sequence of pitches
or chords) is less intuitive than the textual meaning (of aword or a sentence). Thus, it is more difficult to learn agood representation for a musical sequence. In this paper
we work on representing a melody (a sequence of pitches).
We train an RNN model to predict the current pitch by its
previous pitches in a melody and represent the melody by
the RNN parameters. To the best of our knowledge, thisis the first work to use network parameters directly as arepresentation.
3. TRAINING RNNSFor each melodic sequence, we train a generative RNN on
it. The parameters of the trained RNN will be used as a feature to represent the melody. We first train an initialisationon all melodic sequences, and then train on individually
melodic sequences with the initialisation.
3.1 Data
We conduct the experiment on the RWC Music Database(Popular Music) [7]. There is a subjective similarity study[10] undertaken on 80 songs (RWC-MDB-P-2001 No.180) of the RWC Music Database. In this study 27 participants are asked to vote the similarity (on melody, rhythm,
vocals and instruments, respectively) for 200 pairs of clips
after listening to them. Each clip lasts for 30 seconds (starting from the first chorus starting time). For these pairs ofclips, the similarity votes range from 0 to 27. 2 The larger
the vote is, the more similar the clips are. The melodic
similarity matrix is shown in Figure 1, indicating the similarity scores of 200 pairs of clips. The matrix is symmetricbecause if a is similar to b, it means that b is similar to a aswell. There are 400 non-zero values in the matrix (twiceof 200 because of the symmetry).
We use the same 30-second clip as in the subjective
study [10] from each song for training RNNs. We denote the clip from piece ‘RWC-MDB-P-2001 No.X’ asclip X, X∈ [1, 80]. The melodic similarity results of thisstudy [10] are used as the ground truth for evaluation.
3.2 Arranging the training data
We train RNNs using the melody annotation of the RWCMusic Database (Popular Music) from the publicly available AIST Annotation [6]. A melody in the annotation isrepresented as a fundamental frequency sequence in 10 ms
frames as shown in Figure 2(a). We call the frames withfrequencies ‘melody frames’, and the frames without frequencies ‘silent frames’. We convert the frequencies (f )2 The dataset [10] has been publicly available on the web page of the
RWC Music Database at http://staff.aist.go.jp/m.goto/
RWC-MDB/AIST-Annotation/SSimRWC/.

Proceedings of the 19th ISMIR Conference, Paris, France, September 23-27, 2018

765

80

70

60

Clip No.

50(a) A sequence of fundamental frequencies.

40

30

20

10

10

20

30

40

50

60

70

80

Clip No.

Figure 1: The melodic similarity of 200 pairs of clips.

(b) A sequence of pitches

Figure 2: Melodic sequences with different frame hop
sizes. Frames with values of 0 are silent frames.

into pitches (p – indicated by MIDI indices) for melody
frames:fp = 69 + 12 log2
.
(1)
440
The histogram of the pitches in the training set is shownin Figure 3. We focus on pitches in 3 octaves ranging from43 to 78. Frames with pitches beyond this range are considered as silent frames.
3.2.1 Frame hop size
The original frames are arranged in a hop size of 10 ms.
We use a hop size of 50 ms (shown in Figure 2(b)) because RNNs tend to repeat the previous frames with a small
frame hop size.
3.2.2 Skip silent frames
Because of the high ratio of the silent frames (shown in
Figure 2(b)), there will be many invalid training samples
with a sequence of silent frames to predict a silent frame
if we use all frames in the training data. Therefore, we
simply skip all the silent frames to discard those invalid
training samples, resulting in a pitch sequence with only
melody frames (shown in Figure 5(b)).
We aim to look back for 2 seconds to predict the next
frame. With a frame hop size of 50 ms, there are 40 frames
in the input sequence: [xt−N , ..., xt−1 ] → xt , N = 40.

Figure 3: The histogram of the pitches in the dataset.

parameter dimensions. The RNN contains 2 hidden layerswith 64 GRU cells per layer. The output layer is a fullyconnected layer with a softmax activation function. The
inputs are one-hot encoded vectors with a dimension of 37(36 pitches and a silent state). We hope the RNN can fit
the individual pitch sequences as much as possible. In thiscase, overfitting is intended and not a problem any longer;
hence no drop out is applied.
The network is trained by minimising the cross entropy
loss using Adam optimisation with learning rate of 0.001(other parameters of Adam are with default values in tensorflow).

3.2.3 Zero-padding at the beginning

3.4 Initialisation and training on individual clips

We find if the first training sample is [x0 , ..., x39 ] → x40 ,then the generation of the first 40 frames are not modelledin the RNN. In order to generate the whole sequence, we
concatenate a sequence of 40 silent frames in the front ofeach clip, with the first training sample of [xS , ..., xS ] →x0 (xS is the silent frame padding in the front of the clip).

In order to gain a consistent training, we use a fixed initialisation. The initialisation is trained on the training samples from all 80 clips for 100 epochs. Then with this initialisation, we train an individual RNN on each melodic
sequence for 500 iterations. 3 After data arrangement of
Section 3.2, there are around 200-600 training samples for

3.3 Network architecture
We apply a network architecture similar to Megenta [1],but with GRU cells instead of LSTM cells to reduce the3 An iteration means RNN parameters are updated once on a batch oftraining samples. In contrast, an epoch means a full training on all training samples. We use the iteration number to stop training because in thisway RNN parameters are updated for the same times, hence more comparable. However, when to stop training still needs further investigation.

766

Proceedings of the 19th ISMIR Conference, Paris, France, September 23-27, 2018
Initialisation

Individual RNNs

No. of RNNs

1 RNN

80 RNNs

Training data

80 clips

each clip

Batch size

512

64

Early stop

100 epochs

500 iterations

Table 2: RNN training settings.

(a) Batch acc. for initialisation.

(a) Generated pitch sequence.

(b) Batch loss for initialisation.
(b) Original pitch sequence of clip 1.

Figure 5: An identical pitch sequence generated by thetrained RNN.

(c) Batch acc. for training on clip 1. (d) Batch loss for training on clip 1.

Figure 4: Batch accuracies and losses of training for initialisation and training on clip 1 with the initialisation.
every clip. We use a large batch size of 512 for initialisation training because of a big number of training samples,and a smaller batch size of 64 for training for each individual sequence. Training settings are shown in Table 2.
Training for initialisation and training on clip 1 areshown in Figure 4. After training for initialisation, thebatch accuracy reaches 0.7 (Figure 4(a)) and the batch loss
decreases to around 0.8 (Figure 4(b)). After training on
clip 1 with the initialisation, the batch accuracy further increases from 0.7 to 1 (Figure 4(c)); and the batch loss reduces from 0.8 to around 0.1 (Figure 4(d)). With the RNN
trained on clip 1, we can generate an identical melodic sequence, as shown in Figure 5.
3.5 Cosine similarity between RNN parameters
The parameter dimensions of an RNN are shown in Table 3. The total number of parameters is 46, 757.
We reshape matrices to vectors, and concatenate thevectors. The concatenated parameters of the initialisation
RNN and RNNs trained on clip 3 and clip 80 are shown in
Figure 6. The differences in parameters of different RNNs
are subtle. The similarity between two clips is indicatedby the Cosine similarity between their concatenated RNN
parameters. The larger the Cosine similarity is, the moresimilar the clips are.
In the data arrangement stage (see Section 3.2), themelody of a clip (30 seconds) is represented as a sequence of pitches of 600 frames (including silent frames),
as shown in Figure 2(b). We use the Cosine similarity between two pitch sequences as the baseline similarity.

Matrixcell 0/gru cell/gates/kernel
cell 0/gru cell/gates/bias
cell 0/gru cell/candidate/kernel
cell 0/gru cell/candidate/bias
cell 1/gru cell/gates/kernel
cell 1/gru cell/gates/bias
cell 1/gru cell/candidate/kernel
cell 1/gru cell/candidate/bias
fully connected/weights
fully connected/biases
all parameters

Dimension(101, 128)
(128)
(101, 64)
(64)
(128, 128)
(128)
(128, 64)
(64)
(64, 37)(37)
46,757

Table 3: Parameter dimensions.

4. RESULTS ANALYSIS
4.1 Evaluation metric and results
In the subjective similarity study, each clip is compared to
4-6 other clips, usually 5 clips [10]. For example, clip 3 iscompared to clips as shown in Table 4(a). We measure thesimilarity of two clips by computing the Cosine similarity between their RNN parameters. We compare the rankof votes to the rank of similarities for evaluation. For example, as shown in Table 4(a), 8 people vote the melody
of clip 80 is similar to that of clip 3, and 7 people votethe similarity between clip 29 and clip 3. Based on thesevotes we assume clip 80 is more similar to clip 3 than clip
29. Thus, the Cosine similarity between clip 80 and clip
3 should be larger than that between clip 29 and clip 3
C(80, 3) > C(29, 3). We first convert the similarity andvotes into ranks (as shown in Table 4(b)), and then use thepair-wise evaluation metric–Kendall’s tau (τ )– to compare
the ranks. For clip 3, the τ is 0.2 based on similarities between RNN parameters, better than τ = −0.2 based onProceedings of the 19th ISMIR Conference, Paris, France, September 23-27, 2018

767

No.

80

29

59

62

5

Votes

8

7

6

4

3

CRNN

0.99750.99730.997170.9976

0.99725

Cpitch

0.61750.71460.62560.70970.6584(a) Cosine similarities between parameters of clips compared to clip 3.

(a) Parameters of the initialisation RNN

τ

No.

80

29

59

62

5

RVotes

1

2

3

4

5

RRNN

2

3

5

1

4

0.2

5

1

4

2

3

-0.2

Rpitch(b) Ranks of Cosine similarities.

Table 4: Evaluation for clip 3. CRNN and Cpitch are theCosine similarities between parameters and between pitch
sequences, respectively.
(b) Parameters of the RNN trained on clip 3

Similarity

τ

CRNN

0.125

Cpitch0.073

Table 5: Results.

(c) Parameters of the RNN trained on clip 80

Figure 6: Parameters of different RNNs with subtle differences.
similarities between pitch sequences.
The results for 200 pairs of clips are shown in Table 5.
The average τ s are 0.125 and 0.073 based on Cosine similarities between RNN parameters and between pitch sequences, respectively. 4 In the preliminary test, we foundthat there is no improvement in performance by using adimension-reducing technique, such as Principle Component Analysis (PCA), before computing Cosine similarity,
or by using distances between eigenvectors (weighted byeigenvalues) of parameter matrices.
4.2 Visualisation
4.2.1 Similarity v.s. vote
We assume if there are more votes on X than on Y whencomparing to A, then the X should be more similar to A
than Y. However, this may be too strict when votes areclose (8 on X and 7 on Y, for example). In order to showwhether there is a trend that the similarity value is larger
for pairs of clips with a higher vote in general, we show
Cosine similarity v.s. vote plots for RNN parameters andbaseline pitch sequences in Figure 7.
We know the RNN parameters of different clips are very
similar to each other, as shown in Figure 6. Therefore, the4 Using the Euclidean distance provides similar results as using the Cosine similarity: 0.120 and 0.074 for RNN parameters and pitch sequences,respectively.

Cosine similarities between RNN parameters are in a small
range from 0.995 to 0.999 (Figure 7(a)). The Cosine similarities between melodic sequences are in a larger range
from 0.4 to 0.9 (Figure 7(b)). However, neither RNN parameters nor melodic sequences provide a clear trend of
the similarity increasing with number of votes.
4.2.2 t-SNE
To visualise the 80 songs in a low-dimensional space, wefirst reduce the dimension of the features to 5 by PCA, thenfurther reduce it to 2 by t-SNE, with the implementationof [20]. The visualisation based on RNN parameters andpitch sequences is shown in Figure 8. For a clearer visualisation, we only indicate pairs of clips with higher votes(above 9 votes out of 27, as listed in Table 6) by connecting
those pairs with lines.
Because the t-SNE visualisation is not a linear projection from the similarity to the distance on the 2dimensional space, we do not compare the vote against the
distance between two clips in t-SNE visualisation, but focus on the grouping of clips. We observe some interestinggrouping of clips in Figure 8(a): the triangle at the top leftfor (75, 79, 80), and two lines at bottom right connecting(15, 16) and (6,16). In Figure 8(b), no such grouping ofclips can be obviously observed.
5. DISCUSSIONS AND CONCLUSIONS
From the t-SNE visualisation, we observe some interestinggrouping of clips based on RNN parameters (Figure 8(a)).
However, visualisation based on the Cosine similarity between RNN parameters does not show a clear relation between the similarity and the vote (Figure 7(a)). It may

768

Proceedings of the 19th ISMIR Conference, Paris, France, September 23-27, 2018
Cosine similarity between RNN parameters

0.999

80

0.9985

33
60

0.998

28

0.9975

20

60

9

5

10

15

20

Number of votes

74
23

-40

(a) Visualisation based on RNN parameters

Cosine similarity between pitch sequences

-30

70
35
51
68
19

56
50

47
77

45

63

61

39

17

67

38

32
16

6
59

15

73

1
-60
-40

0.9

52

14

27
12
46
42
48
64
37
29 76
44
72
43
11
13
40

41

31

0

65
49

78

0.995

62

66

54
4

24

30

18
8

10

71

22
-20

7

69

55

0.9965
0

26

75
20

0.9955

58

34

0.997

36

3

79
80

0.996

25
21

53

2
5

40

57

-20

-10

0

10

20

30

40

50

(a) Visualisation based on RNN parameters
0.8
400

52

0.7
300

79

0.6

69

55

13

5

8

5

10

15

20

27
12

18

0

54 9

53

No. Pair Vote
1 (79, 80) 23
2 (47, 68) 19
3 (65, 78) 18
4 (6, 16) 17
5 (12, 47) 16
6 (12, 63) 16
7 (15, 16) 16
8 (67, 75) 16
9 (54, 63) 15
10 (72, 75) 15

No. Pair Vote
11 (10, 63) 13
12 (47, 76) 13
13 (51, 63) 13
14 (51, 77) 13
15 (64, 66) 13
16 (7, 49) 12
17 (19, 20) 12
18 (41, 43) 12
19 (42, 44) 12
20 (68, 72) 12

No. Pair Vote
21 (10, 52) 11
22 (7, 20) 10
23 (7, 45) 10
24 (29, 60) 10
25 (47, 67) 10
26 (70, 71) 10
27 (75, 79) 10
28 (75, 80) 10

Table 6: A list of pairs of songs with similarity votes above
9 votes out of 27.

21

22
57
3

61 15 31

60
62

59

63

47

1

74 25
11

48

65

56

50 19 2
73

70

34

33
58
40

-300

16
4

-400
-800

indicate that a direct comparison between RNN parameters is too simple to infer the information in such a large
dimension. Figure 6 also illustrates the difficulties withthe proposed approach, too many parameters with subtle differences. We would like to dig deeper to understand which parameters are most significant for computing
melodic similarity.
Perception studies show that changes in relative scaleor relative duration do not have a major impact on melodic
similarity [24]. The similarity measure should be invariant
to music transformations, such as transposition in pitch andtempo changes [16,23]. The proposed generative RNN canmodel the input pitch sequence, but cannot deal with the

41

30

64

-200

Figure 7: Similarity v.s. vote plot based on different features.

67 49

3724

42

32

-100

17

29

66

(b) Visualisation based on pitch sequences

72

39
14

23

68

Number of votes

28

45
51

7

0

0.4

43

76

35

44

77

80

100

36
26

75

20

0.5

78

46

71

200

38

6
10

-600

-400

-200

0

200

400

600

(b) Visualisation based on pitch sequences

Figure 8: t-SNE visualisation based on different features.

similarity under music transformations. In the future, wewould like to tackle this problem by training RNNs withcoordinate differences instead of absolute coordinates as
inputs, such as intervals and durations instead of pitches
and onsets [16].
We work on the melodic similarity based on theperformance-based representation of melodies, which
seems to complicate the task. We hope we can achieve
more success on symbolic melody representation by usingscore-based representation on a simpler dataset.
In this paper, we propose to represent a melodic sequence by the parameters of its corresponding generative
RNN, and test the utility of the melodic feature (RNN parameters) in the melodic similarity task. The proposed feature contains temporal information within the melodic sequence, and independent of the length of the sequence. We
extend the utility of generative RNNs to use the network
for music similarity analysis rather than music generation.
We expect that the proposed feature (generative RNN parameters) can be used in other tasks, such as musicologicalanalysis and music cognition.

Proceedings of the 19th ISMIR Conference, Paris, France, September 23-27, 2018
6. ACKNOWLEDGEMENT
This work was supported in part by JST ACCEL Grant
Number JPMJAC1602, Japan.
7. REFERENCES[1] Magenta:
Melody RNN. https://github.
com/tensorflow/magenta/tree/master/
magenta/models/melody_rnn.
Accessed:
2018-03-30.
[2] D. Bountouridis, D. G. Brown, F. Wiering, and R. C.
Veltkamp. Melodic Similarity and Applications Using
Biologically-Inspired Techniques. Applied Sciences,7(12), 2017.
[3] G. Brunner, Y. Wang, R. Wattenhofer, and J. Wiesendanger. JamBot: Music Theory Aware Chord Based
Generation of Polyphonic Music with LSTMs. In Proceedings of the 29th International Conference on Tools
with Artificial Intelligence (ICTAI), 2017.
[4] F. Colombo, S. P. Muscinelli, A. Seeholzer, J. Brea,and W. Gerstner. Algorithmic Composition of
Melodies with Deep Recurrent Neural Networks. Computing Research Repository (CoRR), abs/1606.07251,
2016.
[5] J. S. Downie. Evaluating a Simple Approach to Musical Information retrieval: Conceiving Melodic Ngrams as Text. PhD thesis, University of Western Ontario, 1999.
[6] M. Goto. AIST Annotation for the RWC Music
Database. In Proceedings of the 7th International Conference on Music Information Retrieval (ISMIR), pages
359–360, 2006.
[7] M. Goto, H. Hashiguchi, T. Nishimura, and R. Oka.
RWC Music Database: Popular, Classical, and Jazz
Music Databases. In Proceedings of the 3rd International Conference on Music Information Retrieval (ISMIR), pages 287–288, 2002.
[8] M. Grachten, J.-L. Arcos, and R. L. de Mantaras.
Melodic Similarity: Looking for a Good Abstraction
Level. In Proceedings of the 5th International Societyof Music Information Retrievall (ISMIR), 2004.
[9] P. Hanna, P. Ferraro, and M. Robine. On Optimizing the Editing Algorithms for Evaluating Similarity
Between Monophonic Musical Sequences. Journal of
New Music Research, 36(4):267–279, 2007.
[10] S. Kawabuchi, C. Miyajima, N. Kitaoka, andK. Takeda. Subjective Similarity of Music: Data Collection for Individuality Analysis. In Proceedings ofAsia Pacific Signal and Information Processing Association Annual Summit and Conference, pages 1–5,
2012.

769

[11] Q. Le and T. Mikolov. Distributed Representationsof Sentences and Documents. In Proceedings of the
28th International Conference on Machine Learning(ICML), 2014.
[12] S. Madjiheurem, L. Qu, and C. Walder. Chord2Vec:
Learning Musical Chord Embeddings. In Proceedingsof the Constructive Machine Learning Workshop at
30th Conference on Neural Information Processing
Systems (NIPS), 2016.
[13] T. Mikolov, K. Chen, G. S. Corrado, and J. Dean. Efficient Estimation of Word Representations in Vector
Space. In Proceedings of International Conference on
Learning Representations (ICLR) Workshop, 2013.
[14] T. Mikolov, I. Sutskever, K. Chen, G. S. Corrado,and J. Dean. Distributed Representations of Words andPhrases and their Compositionality. In Proceedings ofAdvances in Neural Information Processing Systems
26 (NIPS), pages 3111–3119, 2013.
[15] D. Müllensiefen and K. Frieler. Optimizing Measuresof Melodic Similarity for the Exploration of a Large
Folk Song Database. In Proceedings of the 5th International Society of Music Information Retrievall (ISMIR),
pages 1–7, 2004.
[16] D. Müllensiefen and K. Frieler. Evaluating Different
Approaches to Measuring the Similarity of Melodies.
In et al. V. Batagelj, editor, Data Science and Classification, pages 299–306. Springer, Berlin, 2006.
[17] K. S. Orpen and D. Huron. Measurement of Similarity in Music: A Quantitative Approach for Nonparametric Representations. Computers in Music Research, 4:1 – 44, 1992.
[18] H. Palangi, P. li, Y. Shen, J. Gao, X. He, J. Chen,
X. Song, and R. Ward. Deep Sentence Embedding
Using Long Short-Term Memory Networks: Analysis
and Application to Information Retrieval. IEEE/ACM
Transactions on Audio, Speech and Language Processing (TASLP), 24(4):694–707, 2016.
[19] M. W. Park and E. C. Lee. Similarity Measurement
Method between Two Songs by Using the Conditional
Euclidean Distance. Wseas Transaction On Information Science And Applications, 10(12), 2013.
[20] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel,
B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer,
R. Weiss, V. Dubourg, J. Vanderplas, A. Passos,
D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-Learn: Machine Learning in Python. Journal of Machine Learning Research, 12:2825–2830,
2011.
[21] R. Socher, C. Y. Lin, A. Y. Ng, and C. D. Manning.
Parsing Natural Scenes and Natural Language with Recursive Neural Networks. In Proceedings of International Conference on Machine Learning (ICML), 2011.

770

Proceedings of the 19th ISMIR Conference, Paris, France, September 23-27, 2018[22] B. L. Sturm, J. F. Santos, and I. Korshunova. Folk
Music Style Modelling by Recurrent Neural Networks
with Long Short Term Memory Units. In Extended abstracts for the Late-Breaking Demo Session of the 16th
International Society for Music Information Retrieval
Conference (ISMIR), 2015.
[23] J. Urbano, J. Lloréns, J. Morato, and S. SánchezCuadrado. MIREX 2012 Symbolic Melodic Similarity:
Hybrid Sequence Alignment with Geometric Representations. In Music Information Retrieval Evaluation
eXchange (MIREX), 2012.
[24] M. R. Velankar, H. V. Sahasrabuddhe, and P. A. Kulkarni. Modeling Melody Similarity Using Music Synthesis and Perception. Procedia Computer Science,
45:728 – 735, 2015.
[25] V. Velardo, M. Vallati, and S. Jan. Symbolic Melodic
Similarity: State of the Art and Future Challenges.
Computer Music Journal, 40(2):70–83, 2016.
[26] J. Wu, C. Hu, Y. Wang, X. Hu, and J. Zhu. A Hierarchical Recurrent Neural Network for Symbolic Melody
Generation. Computing Research Repository (CoRR),
abs/1712.05274, 2017.
[27] S. Yazawa, Y. Hasegawa, K. Kanamori, and
M. Hamanaka. Melodic Similarity Based on Extension
Implication-Realization Model. In Music Information
Retrieval Evaluation eXchange (MIREX), 2013.
[28] Y. Zhu, M. Kankanhalli, and Q. Tian. Similarity
Matching of Continuous Melody Contours for Humming Querying of Melody Databases. In Proceedingsof IEEE Workshop on Multimedia Signal Processing,
2002.