Content-based Indexing of Musical Scores

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1 Content-based Indexing of Musical Scores Richard A. Medina NM Highlands University Lloyd A. Smith SW Missouri State University Deborah R. Wagner NM Highlands University Abstract This paper describes a method of automatically creating a content-based index of musical scores. The goal is to capture the themes, or motifs, that appear in the music. The method was tested by building an index of 25 orchestral movements from the classical music literature. For every movement, the system captured the primary theme, or a variation of the primary theme. In addition, it captured 13 of 28 secondary themes. The resulting index was 14% of the size of the database. A further reduction of 2% is possible; however, this discards secondary themes. A listening experiment using five orchestral movements showed that people can reliably recognize secondary themes after listening to a piece of music therefore, it may be necessary to retain secondary themes in a score index. 1. Introduction Content-based music information retrieval (MIR) enables people to locate and retrieve music based on its musical characteristics, rather than on metadata such as composer and title. The potential utility of such systems is attested to by music librarians, who report that library patrons often hum or whistle a phrase of music and ask them to identify and locate a score or recording of the corresponding musical work [7, 10] Score-based Music Information Retrieval Score-based MIR systems operate by accepting a musical query (such as a string of notes) from the user and searching a database of musical scores for a pattern closely matching the query. The returned music may be in any form an audio recording, a midi file, a score, or metadata such as synopses, critiques, or historical notes, but the query is processed against a collection of musical scores. The search is typically carried out by exhaustively matching the query against the database. This has been successful in such systems as Meldex [7], which incorporates a database of 10,000 folk tunes. However, exhaustive search is not likely to scale well to large collections such as thousands of symphonies or other major works. The scaling problem is two-fold. First, as stated above, the search is carried out over the entire database and, therefore, grows in relation to the size of the database. Second, inaccuracies may be introduced into the search in several ways: the user may not correctly remember the musical pattern he or she is trying to recreate, the user may not correctly play, whistle or hum the musical pattern, the musical pattern may be inaccurately captured by the system (especially if it is transcribed from audio input), the database may have coding mistakes in it (especially if it is created by optical music recognition), the user may know a different variant than the one represented in the database (especially in the case of folk music), or the notation in the database may not match the user s performance concept (especially in the case of popular or jazz music). For all these reasons, it is necessary to carry out the search using an algorithm that finds degrees of match [9]. Such approximate search algorithms are much slower than those that look for an exact match of the query Content-based Indexing in MIR Downie and Nelson [4] introduced the use of a contentbased index in music information retrieval. While their index (based on the same folk tune collection used by Meldex) included all notes in the database, a more selective index can be used to reduce the amount of data that is searched. In classical music, the natural unit for indexing is the theme. A theme is a melody that the composer uses as a starting point for musical development. A piece of music may have several themes; by definition, themes Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full cit ation on the first page. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. JCDL 03 May 1-2, 2003, Houston, Texas. Copyright 2000 ACM /00/0000 $

2 will repeat and may be slightly changed ( variations ) by the composer on repetition. Using an index that incorporates musical themes can reduce the search on a collection of classical major works. Furthermore, themes are the musical phrases that a listener is most likely to remember, so such an index focuses the search on the data most likely to match a query Automatic Theme Discovery Theme indices, such as Barlow and Morgenstern s A Dictionary of Musical Themes [2] are well known in the music literature. These compilations are useful for linking themes to their musical works, but they suffer from two major drawbacks. First, they are created manually the author (or authors) of such an index must either listen carefully to each piece of music to be represented, or must comb the literature for analysis by musicologists. Therefore, the index takes a great deal of time and effort to build. Second, a printed index is frozen in time any music written after publication of the index must wait to be included in a later edition. Automatic theme discovery systems attempt to overcome the problems of manual compilation. Because themes are, by definition, musical sequences that are repeated and developed by the composer, these systems operate by finding repeating patterns in music. Liu, et al. [6], for example, search for small repeating melodic sequences, joining them into longer ones. The Melodic Motive Extractor (MME) algorithm, developed by Meek and Birmingham [8], also assembles long repeating patterns from shorter ones. MME then prunes the set of candidate themes using features such as duration, length, and position of first occurrence in the music. This paper describes our method for building an index of musical scores. Like the theme discovery algorithms described above, our method is based on finding repeating melodic sequences, with the goal of capturing the themes of major works in the resulting index. Unlike those systems, ours starts by locating the longest repeating sequences, then deleting substrings of longer patterns. The method was tested by implementing it in software and building an index of 25 orchestral movements from the Baroque, Classical and Romantic periods. Section 2 describes the indexing algorithm and its implementation, while section 3 describes the evaluation experiment. Section 4 presents the results of the experiment, and section 5 discusses those results. Section 6 describes and discusses a listening experiment carried out in order to better interpret the results. Section 7 presents conclusions and ideas for further work. 2. An Algorithm For Building A Musical Score Index This section describes a computational method for building an index from a collection of musical scores. The initial step is to extract a list of repeating melodic patterns from a composition. The strategy is then to isolate the patterns most likely to be themes by removing those determined to be trivial, or that are represented in other patterns. The general procedure is as follows. 1. Find repeating patterns of length equal to or greater than the threshold. a. Ignore patterns that contain only one pitch. b. Ignore patterns that contain only two alternating pitches. 2. Remove all duplicate patterns. 3. Remove patterns that are substrings of longer patterns. 4. Remove variations of patterns that are already captured. The method is organized in two phases extraction and pruning. The first phase (step 1, above) generates a list of repeating patterns within a musical work, while the second phase (steps 2 through 4) consists of a series of pruning stages in which the list is iteratively reduced to its final form. The result is a melodic pattern list for the input musical score. Combining the lists for all the scores produces an index to the collection Pattern Extraction The first step is to assemble a list of repeating melodic sequences. Discovering these sequences is essentially a search for self-similarity in a musical work. Because of this, a self-similarity matrix is used as a structure for extracting repeating patterns. The self-similarity matrix is an n x n bit matrix, where n is the number of notes in the musical work. The matrix indicates where each note exactly matches another note in the music. Comparison is based on the interval and duration properties of each note. Intervals are used to make the analysis independent of key. Matched notes are denoted with a 1 (one) in the matrix, 19

3 while a 0 denotes non-matching notes. Because every note matches itself, the main diagonal is all ones. Descending diagonal ones that are off the main diagonal indicate repeating patterns. The algorithm for creating the self-similarity matrix is illustrated below. 1. Let S be a sequence of intervals of length n 2. Let M be a two dimensional matrix of size n x n 3. Let i 4. For each S i such that i < n, let j 4.1. For each S j such that j < n If S i = S j then M ij 1 Else M ij 0 Figure 1 shows the self-similarity matrix for Fugue No. 7, from The Well Tempered Klavier, by J.S. Bach [1]. For easier reading, the zeros have been replaced by spaces, and 1 s are represented by dots. The long line of dots is the main diagonal. Because the halves of the matrix on either side of the main diagonal are mirror images of one another, it is only necessary to compute and scan half the matrix in searching for repeating patterns. Figure 1. Self-similarity matrix for Fugue No. 7, by J. S. Bach It is presumed that a theme is a melodically interesting phrase with at least some degree of entropy among pitches. Based on this heuristic, the algorithm does not retain patterns that demonstrate little or no melodic variation. Determining whether a pattern contains a single pitch involves parsing the pattern and noting the lack of any change in pitch. In the intervallic representation this is a pattern containing all zeros. Trills are indicated by a single interval that alternates in opposite directions. For our purposes, trills include tympani parts, for example, that contain long patterns of alternating perfect fifths, such as the pattern Repeating patterns extracted using the self-similarity matrix are assembled in a list for further processing. For example, the well-known theme from Beethoven s Symphony No. 5 appears first in measure 1; it repeats later in the score and is entered into the pattern list Pruning The list created from the self-similarity matrix contains all patterns of musical intervals that occur more than once in the musical score. The goal of the pruning phase is to reduce the list into a small set of patterns that contain the themes associated with that score. This is done by eliminating patterns that are: 1) exact duplicates of other previously occurring patterns, 2) substrings of longer patterns, or 3) variations of other patterns. During processing of the matrix, every repeated pattern is recorded individually. If a pattern repeats more than once, there will be a duplicate or duplicates in the pattern list. A duplicate is a pattern that exactly matches another pattern in content and in length (number of intervals). Starting with the first pattern, each pattern is matched against subsequent patterns in the list. When an exact match is found, the duplicate is replaced by a timestamp giving the location (in the score) of the first occurrence of the sequence. Once the end of the list has been reached, the list is sorted by earliest occurrence, as determined by the timestamps. This applies a chronological structure to the list that stresses factors such as when a melody is first introduced into a composition. In subsequent pruning phases, this is useful for determining the importance of a melody in relation to others in the list. The removal of substring patterns entails a process much like the one used to remove duplicates; however, in this stage, a match between two patterns is found by determining if one pattern is a proper substring of the other. If a match is found, the smaller pattern is 20

4 recorded as a substring of the longer pattern and removed. Removing substrings does not discard melodic information the string still appears in the index as part of a longer sequence. With the exception of trills and single note sequences, the index still contains every repeated melodic sequence originally extracted from the self-similarity matrix. The next goal of the procedure is to remove variations of melodic sequences already found. These variations are identified as containing partial substrings of longer patterns. The procedure matches substrings of length greater than or equal to a threshold. The underlying premise is that, because a theme index will be searched using approximate pattern matching [7], it is unnecessary to keep theme variations. Proper substring matching may not give an accurate measure of similarity among patterns that vary by a few notes. For example, the list in Table 1 contains 9 patterns extracted from the self-similarity matrix for Bach s Fugue No. 7. It is clear that patterns F and R share a common substring. The previous stage would not consider these patterns similar because the shorter pattern, R, does not appear in its entirety in F. Figure 2 illustrates the close proximity between the two patterns. Table 1. Sequences from Fugue No. 7 Pattern ID Intervals P O Q F H C K D R Pattern R is a proper substring of F, if its first interval is ignored while comparing the two. In order to capture this partial similarity, variation removal looks for significant parts of patterns that match. This also captures the instance when two partially similar patterns only differ by their surrounding background material. F R Figure 2. Two closely related patterns Each pair of strings is matched to see which ones may be considered variations of others. Through experimentation, the value chosen as a significant match length was 10, or half the length of the shorter of the two strings being matched, whichever is greater. Applying this rule to the set of patterns in Table 1 results in removal of pattern R. The algorithm for variation removal is illustrated below. 1. Let P be a list of k patterns, P 0 P k For each P i such that i < k, i initialized to Let j L 2.2. For each P j such that j < k, and P i > P j 2.3. Let l be the length of P j divided by two If l is less than 10, l If Pj exactly matches a substring of P i of length w, w >= l Remove P j from P This step takes most of the computational time during the pruning process. The key to this stage is the fact that the longer pattern of the two partial matches is retained, and the shorter one removed. It does, however, remove some melodic information. The assumption is that by repeatedly retaining the longer pattern, we are casting a wider net through the list and stand a better chance at retaining the themes of the composition. 3. Evaluation The purpose of the index-building algorithm is to provide a computational method for extracting important melodic patterns from a musical score. This section describes an experiment designed to evaluate its effectiveness Test Data The data set for this experiment was a corpus comprised of 25 classical orchestral scores. The reason for using these works is that they represent large, multifaceted musical compositions that consistently adhere to principles of theme usage. Forming a theme 21

5 index from them is a practical application of an automated score indexing system. Each musical score used in the experiment was digitally encoded as an ASCII text file. All the pieces were drawn from the MuseData virtual score collection, assembled at the Center for Computing Assisted Research in the Humanities (CCARH) [3]. The MuseData collection was used because of its open format [5] and its high quality of encoding. The data set consisted of 6 movements from 4 concerti and 19 movements from 14 symphonies. Composers represented in the test data set include Bach, Mozart, Haydn, and Beethoven. The entire test collection represented approximately 6,000 measures and 225,000 notes. On average, each composition contained 241 measures and 9000 notes Experimental Procedure To implement the algorithm, a Java application was created that accepts a MuseData file as input. The program parses each input file and translates it to a sequence of music nodes. A music node is a compound data structure that specifies a pitch (name and octave), duration, interval (relative to the previous note), and a timestamp relative to the musical score (instrument:measure:beat). Multi-voice compositions are flattened by consecutively stringing together the nodes from each part. A three-part fugue, for example, is converted to a single voice by concatenating the middle part to the upper part, then concatenating the lower part to the end of the middle part. The assumption is that themes are melodic sequences that appear within one voice our algorithm will not find an occurrence of a theme that is split among different instruments. Timing information, however, is preserved so a theme that occurs at the beginning of the second part will be located at the beginning of the composition, rather than one third of the way through. Subsequently, each composition is treated as a single string of nodes. The output is a file containing melodic sequences extracted by the algorithm. Other intermediary output was also recorded in order to observe the behavior of the system after key stages had completed. To verify whether a theme was successfully captured in the index, the primary and secondary themes for the entire data set were manually transcribed from Barlow and Morgenstern s Dictionary of Musical Themes [2] into an intervallic format. These transcribed themes were then compared against the score index. 4. Results Two criteria for evaluating the performance of the algorithm are the successful extraction of themes and reduction of the data that must be searched relative to the size of the entire collection Theme Discovery The first objective of the score-indexing algorithm is to extract the themes of the musical work. A theme may appear in the index as a standalone sequence, or may appear as a substring of a longer sequence. The index building algorithm successfully captures the primary theme in 23 of the 25 musical works in the data set, a 92% discovery rate. The two instances where the theme is not found are due to the fact that the theme, as listed by Barlow and Morgenstern [2], does not repeat. In both of these cases the theme is introduced once at the beginning of the composition and is slightly varied thereafter. These variations do repeat and are captured in the index. For many of the orchestral works in the data set, Barlow and Morgenstern list secondary themes. There were 19 works containing second themes; the algorithm found 9. Additionally, it found 3 of the 7 third themes, and 1 of 2 fourth themes. Figure 3 shows the performance of the algorithm on capturing themes from the musical works in the test data collection. Percentage of Themes Found 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 92% Primary Themes 46% Secondary Themes Figure 3. Theme discovery rate 22

6 4.2. Index Size The second goal of the algorithm was to reduce the amount of searchable data in the test collection. This is essentially a measure of compression. The size of the index is calculated for the entire data set and recorded after various pruning stages in the algorithm. Table 2 shows the number of notes stored in the index during the processing stages. Before pruning, the index is larger than the collection because of the large number of duplicate patterns. The pruning process reduces the note count significantly. Table 2. Size of index during processing Procedure Stage No. Notes Size of collection 225,897 Index before pruning 647,407 Duplicates removed 116,666 Substrings removed 73,036 Variations removed 31,569 Figure 4 shows the index size, as a percentage of the entire collection, at the various processing stages. The first pruning operation removal of duplicate patterns has the largest effect, removing 82% of the original index. The final index is 14% of the size of the collection % overall index. The sequences average 20 notes in length. Table 3. Average no. of patterns for each score at various stages of processing Procedure Stage Avg. # Patterns per Score Index before pruning 1,513 Duplicates removed 247 Substrings removed 143 Variations removed Discussion The index building algorithm successfully captured all primary themes that repeat at least once, and produced an index 14% of the size of the collection. This discussion focuses on the performance of the algorithm on capturing primary and secondary themes, and on further reducing the size of the index Theme Discovery A theme that does not repeat exactly will not be extracted using the approach taken in this investigation. In 2 of the 25 compositions processed, the primary theme was not found because it did not repeat. In both cases, however, a variation of the primary theme was captured. Figure 5 shows the theme from Mozart s Symphony No. 41, Jupiter, 3rd movement, as listed by Barlow and Morgenstern, followed by the variation that was captured by the algorithm; figure 6 shows the interval representations of the same theme and variation (rests are removed from the interval representation) % 32. 3% 14. 0% Index Bef ore Pruning Duplicates Removed Substrings Removed Variations Removed Figure 4. Index size, relative to collection Table 3 shows the average number of patterns for each score at various stages in the processing. Before pruning, the index holds, on average, 1513 entries for each musical score (if trills and single note patterns are included in the index, that number balloons to 19,307 entries for each score). The final index holds, on average, 65 patterns for each musical score in the collection, making for a total of 1324 entries in the Figure 5. Theme and variation from the Mozart s Jupiter Symphony, 3 rd movement Figure 6. Interval representation of theme and variation from Mozart s Jupiter symphony The variation matches the theme for the first 5 intervals, and 5 of the last 6 intervals are the same. The difference occurs in the middle, where the variation 23

7 makes a single jump of a major sixth, while the theme ascends a major sixth in a more roundabout way. The index also retains a variation, rather than the theme, in Beethoven s Violin Concerto, Op. 61, 1st movement. In this case the variation exactly matches the last 10 intervals of the theme. Figure 7 shows the musical notation for the theme and variation; figure 8 shows the interval representation. It is clear, looking at figure 7, that the theme and variation match exactly, starting with measure 3 of the theme and measure 2 of the variation. order of their first occurrence in the score, the primary theme of a given score typically appears near the beginning of the index for that score consistently within the first 10% of sequences listed. Over 80% of the primary themes are within the first 5% of the indexed sequences for that score. Figure 9 shows the distribution of the first appearances among primary themes. The horizontal axis represents each of the 23 primary themes found, sorted by their position of first occurrence in the score. Figure 7. Theme and variation from Beethoven s Violin Concerto Op. 6, 1st Movement Figure 8. Interval representation for theme and variation from Beethoven s Violin Concerto Op. 6, 1 st movement These examples illustrate that, although a primary theme may not repeat exactly, some variation of it is likely to repeat and be represented in the index. The algorithm was less successful at finding secondary themes. We believe the reason for this is that secondary themes, by definition, appear later in the music than primary themes; therefore, the composer has less time to develop them. While two secondary themes found by the algorithm occurred in the first 10% of their respective scores, most made their first appearances later some as late as a third of the way through the score. Furthermore, because secondary themes are usually less important in the overall musical context, they are less likely than primary themes to receive the prominence accorded by exact repetition Reducing the Size of the Index The primary themes, in these works, occur near the beginning of their musical scores all of them are within the first 17% of the score, as determined by measure number. The majority (80%) of them begin within the first two measures of the composition. Because the index building algorithm lists sequences in Theme Figure 9. First appearance of primary themes by measure number. These results are similar to those of Meek and Birmingham [8], who found that position was their most highly weighted feature for finding primary themes. The observation that primary themes occur early in the music leads to the following heuristic for reducing the size of the index: For any given musical score, discard all sequences not in the top 10% of the index for that score. In our data set, this heuristic retains all primary themes that were found, and one of the two primary theme variations, and results in an index approximately 2% of the collection size. It does, however, remove all but two secondary themes. 6. Are Secondary Themes Needed? While the heuristic discussed above is attractive from the standpoint of index size reduction, it produces an index that can be expected to represent only primary themes. This is suitable, if we expect users to use only primary themes in forming musical queries. In order to determine whether it is necessary to retain secondary themes, we would like to analyze musical queries that users have submitted to a classical music 24

8 database over a long period of time. However, we do not have access to that data (indeed, it is unlikely that such data exists), so we carried out a listening experiment to get some indication of how well people can be expected to remember secondary themes after listening to a piece of classical music. The assumption is that, if people can t remember secondary themes shortly after listening to a piece of music, then they will not be able to use them in formulating queries Listening Experiment Participants listened to 5 orchestral movements, played from compact disc on a stereo sound system. After each movement, participants listened to 5 themes played on a piano. One of the themes was the primary theme for that movement, as listed by the Barlow and Morgenstern theme dictionary [2]. The remaining 4 themes were any secondary themes listed in the theme dictionary, and other themes randomly chosen from those listed by the same composer. The order of play for the five themes was randomly set. For example, in the first trial, participants listened to the first movement from Beethoven s Symphony No. 9. They then listened to the first theme from the fourth movement of Beethoven s Piano Sonata No. 1 (Op. 2, No. 1), the second theme from the first movement of Symphony No. 9, the first theme from the first movement of Symphony No. 9, the third theme from the first movement of Beethoven s Symphony No. 4, and, finally the third theme from the first movement of Symphony No. 9. Each theme was played twice on the piano. For each theme, listeners were asked to indicate (by circling Yes or No) whether the theme played on the piano occurred in the symphonic movement they had just listened to. Each trial was carried out on a separate day. The 5 movements used were: Beethoven, Symphony No. 9, movement 1, Bach, Brandenburg Concerto No. 2, movement 1, Mendelssohn, Symphony No. 4, movement 1, Mozart, Symphony No. 40, movement 1, and Tchaikovsky, Symphony No. 6, movement Participants Participants in the experiment were 28 students (16 women and 12 men) in a music appreciation class at New Mexico Highlands University. The class was comprised of a cross section of students, ranging in academic level from freshman (first year) to senior (fourth year). 22 of the students had some musical background in singing or playing an instrument; 6 had no formal musical background. Two were music majors. Participation was optional; students were told their participation, or lack thereof, would not affect their grades. Not all participants took part in all trials the number of listeners in the 5 trials ranged from 20 to Results and Discussion Table 4 shows the number of listeners correctly identifying primary and secondary themes as being present in the orchestral movement they listened to, and extraneous themes as not being present in the movement. Statistical significance was evaluated using a chi-squared test; all results are significant at well below the 1% level. Table 4. Results of listening test Correct Incorrect Primary themes 60 4 Secondary themes Extraneous Themes The results show that, for the Baroque, Classical, and Romantic music used in this test, listeners recognized primary themes more accurately than secondary themes. However, it is clear that people can reliably recognize secondary themes, as well. What we have tested here is, of course, recognition, rather than memory. The fact that people can reliably recognize secondary themes, shortly after listening to a piece of music, does not necessarily mean they remember them well enough to recreate them. We believe it may well be that users will consistently use primary themes in forming musical queries to a classical music database. However, given these results, it is plausible that users may base some queries on secondary themes. Therefore, at this point, we choose to take the conservative approach and retain secondary themes in the musical score index. 7. Conclusion This paper has described a method for building an index of musical scores. Such an index can reduce the amount of searching necessary for processing a user query against a collection of classical musical scores. 25

9 The method is very effective for capturing primary themes; in an experiment using 25 symphonic movements, an implementation of the algorithm captured 23 of the 25 primary themes, and captured variations of the remaining 2 themes. We consider capturing a theme variation a success, because we expect the index to be searched using an approximate matching algorithm [7]. Approximate search is necessary because it is impossible to predict what variation of a theme (possibly caused by errors) a user will enter as a retrieval query. Our algorithm is less successful at capturing secondary themes, finding 13 of the 28 secondary themes listed for the indexed movements by a well-known theme dictionary [2]. We believe the relatively poor performance on secondary themes is caused by the fact that, because secondary themes appear later in the score, the composer has less time to develop them, and is therefore less likely to repeat them exactly as they first appear. Our method relies on extracting exact repetitions of musical patterns, so it will not find patterns that repeat only in variations. In our index building experiment, the resulting index was 14% of the size of the collection. A heuristic that discards all patterns not appearing early in the score reduces the index to 2% of the collection size, but this removes secondary themes. A listening experiment, using 5 orchestral movements, showed that people can reliably recognize secondary themes from music they have just listened to. Therefore, it is plausible that users might base some queries on secondary themes, so it may be necessary to retain secondary themes in the index. Our current goal is to extend the number and style of musical works in our index, to ensure that our results hold up over a wider variety of music. At this point, we are still focusing on classical music; it is clear that the thematic base of most styles of classical music provides a solid basis for indexing, although we are unsure what to expect when analyzing modern styles such as minimalist compositions. A further goal is to build indices of popular music. It is not clear whether a popular music index will capture anything meaningful in terms of user queries, but song hooks may provide such a base. The algorithm itself may be further developed in several ways. First, it may be possible to reduce the size of the index by better identification of variations within the index itself, the goal being to keep only one variation of any melodic sequence in the index. Second, we would like to improve the algorithm s performance on finding secondary themes. This will likely involve some use of approximate matching in the algorithm itself. Reliable location of secondary themes will be useful for musicological applications, even if the eventual decision is to build indices, for music information retrieval, intended to capture only primary themes. Finally, we would like to definitively answer the question of whether it is necessary to keep secondary themes in a music retrieval index. This will require more focused user studies than we have carried out to this point. 8. References [1] Bach, J.S. Prelude and Fugue in Eb Major, The Well- Tempered Klavier, Book 1, Bach-Gesellschaft Edition. MuseData virtual scores. [2] Barlow, H., and Morgenstern, S. A Dictionary of Musical Themes. Crown Publishers, NY, [3] CCARH: Center for Computer Assisted Research in the Humanities. MuseData virtual scores. [4] Downie, J. S., and Nelson, M. Evaluation of a simple and effective music information retrieval method. Proc. ACM SIGIR 2000, 73-80, [5] Hewlett, W. MuseData: Multipurpose representation. In E. Selfridge-Field (ed.), Beyond MIDI: The Handbook of Musical Codes, , MIT Press, Cambridge, MA, [6] Liu, C.C., Hsu, J.L., and Chen, A.L.P. Efficient theme and non-trivial repeating pattern discovering in music databases. Proc. IEEE Intl. Conf. on Data Engineering, 14-21, [7] McNab, R.J., Smith, L.A., Witten, I.H., and Henderson, C.L. Tune retrieval in the multimedia library. Multimedia Tools and Applications 10, , [8] Meek, C. and Birmingham, W. Thematic Extractor. Proc. ISMIR 2001, , [9] Mongeau, M., and Sankoff, D. Comparison of musical sequences. Computers and the Humanities 24, , [10] Salosaari, P., and Jarvlin, K. MUSIR A retrieval model for music. Tech Report RN , University of Tampere,