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					                   10th International Society for Music Information Retrieval Conference (ISMIR 2009)



 THE INTERSECTION OF COMPUTATIONAL ANALYSIS AND MUSIC
MANUSCRIPTS: A NEW MODEL FOR BACH SOURCE STUDIES OF THE
                      21ST CENTURY

                     Masahiro Niitsuma† Tsutomu Fujinami‡ Yo Tomita†
                     †School of Muisc and Sonic Arts, Queen’s University, Belfast
      ‡School of Knowledge Science, Japan Advanced Institute of Science and Technology (JAIST)
                   niizuma@nak.ics.keio.ac.jp, fuji@jaist.ac.jp, y.tomita@qub.ac.uk


                            ABSTRACT                                                discovered? How can a computer assist musicologists in
                                                                                    analysing the information contained in the known sources?
   This paper addresses the intersection of computational                              The main objective of this study is to solve such prob-
analysis and musicological source studies. In musicology,                           lems in historical musicology by addressing the following
scholars often find themselves in the situation where their                          questions:
methodologies are inadequate to achieve their goals. Their
problems appear to be twofold: (1) the lack of scientific                               1. Can computational analysis offer the same conclu-
objectivity and (2) the over-reliance on new source discov-                               sions as those arrived at by historical musicologists?
eries. We propose three stages to resolve these problems, a
                                                                                       2. Are there any oversights in the musicologists’ anal-
preliminary result of which is shown. The successful out-
                                                                                          ysis of the sources?
come of this work will have a huge impact not only on
musicology but also on a wide range of subjects.                                       To achieve our objectives, it is necessary to address the
                                                                                    following issues:
                      1. INTRODUCTION
                                                                                       1. How to define a data structure for storing Bach’s
Recent developments in computer and information tech-                                     manuscripts in digital format;
nology have brought significant changes to the ways in
                                                                                       2. How to extract information from the digitised manu-
which we conduct research in a wide range of domains,
                                                                                          scripts;
and musicology is not an exception.
    Yet in historical musicology the majority of scholars                              3. How to analyse the extracted information.
still conduct their research without making full use of this
technological advancement, thus creating huge potential                                 This paper is structured as follows: Section 2 describes
for future advancement.                                                             the relationship between the proposed methods and ex-
    By nature, their research methods are less scientific, i.e.                      isting scholarly debates in the field; Section 3 discusses
they tend not to, or find it impossible to disclose all the in-                      the research methods to be employed; Section 4 shows a
formation they used in order to arrive at their conclusions,                        preliminary result of the proposed method; Section 5 il-
and hence it is often difficult to verify their findings re-                          lustrates the contribution that the proposed research will
gardless of whether or not there are elements of subjective                         make; and Section 6 offers concluding remarks.
judgment in them.
    There is a separate problem in musicology in that the                                         2. PREVIOUS RESEARCH
majority of source-based studies heavily rely on the redis-
                                                                                    There are numerous research projects dealing with com-
covery of new sources.1 Thus, if a new source is not found,
                                                                                    putation in musicology and different kinds of data formats
there is often little discussion to challenge the existing in-
                                                                                    have been proposed to encode musical data [1–3]. How-
terpretation offered by scholars in the past. Is there really
                                                                                    ever, all of them deal with limited musical information
no way of improving the theories unless a new source is
                                                                                    such as pitch or rhythm derived from printed scores, and
                                                                                    the majority of previous research on computational music
Permission to make digital or hard copies of all or part of this work for           analysis [4–9] is based on those data formats.
personal or classroom use is granted without fee provided that copies are              There is also a certain amount of research related to au-
not made or distributed for profit or commercial advantage and that copies           tomatic music analysis using the signal-processing tech-
bear this notice and the full citation on the first page.                            nique with acoustic sources [10–14], which record musical
 c 2009 International Society for Music Information Retrieval.                      performance from published scores. But if we investigate
  1 Sources refer to manuscript sources, that is written scores by hand.
                                                                                    only published scores, rather than the original manuscripts,
Before the invention of printing, music was preserved either by oral trans-         we miss important information that has been lost in the
mission or by MS copies.                                                            process of creating an edition.


                                                                              519
                                                       Poster Session 3


   Recent journal articles or proceedings of ISMIR [15–                                  Start
                                                                                                                  Data
                                                                                                                extraction
17] includes a considerable number of researches on the
Optical Music Recognition (OMR). Most of them deal with
staff removal algorithm, which eases the preprocessing of                               Physical               Symbolic
                                                                                     manuscript data             data
the digitised images of the manuscripts such as the music
symbol recognition.
   With regard to the research related to manuscript anal-                             Scanning               Computational
                                                                                                                analysis
ysis, Tomita developed a database of variants and errors
which supposedly lists all the extant manuscripts and early
prints of the Well-Tempered Clavier II, a work well known                              Digitised
                                                                                                                  End
                                                                                      image file
for its complex history of compilation, revision and trans-
mission [18]. The database contains all kinds of informa-
tion extracted from manuscripts – not only musical variants
                                                                             Figure 1. Flowchart of the proposed method
but also notational errors and variants that may have been
inherited from its model or may cause errors when fresh
copies were made from it – giving us many insights into                         4. PRELIMINARY EXPERIMENT
how the future database should be developed.
                                                                      4.1 An overview of the preliminary experiment
                                                                      This sections presents a preliminary result of the third stage
                  3. METHODOLOGY
                                                                      described under ”3. Methodology”. Currently, the first and
There are three stages in this project:                               second stages are conducted manually, while the program
                                                                      was developed for the third stage. To demonstrate the per-
   1. To define of a data structure for storing Bach’s                 formance of the latter, the simplest example would be to
      manuscripts in digital format;                                  examine the origin and authenticity of variants. Because
                                                                      WTC II was so popular among Bach’s pupils and admir-
   2. To develop a methodology to automatically extract               ers during and after his lifetime, numerous manuscripts
      data from the digitised images of music manuscripts;            were made, copied and edited, which not only increased
                                                                      the number of errors or variant readings, but also resulted
   3. To develop a methodology to analyse these data to               in introducing contamination to the texts in some sources
      find significant information for musicological study.             [23, 24]. This program produces a source affiliation dia-
                                                                      gram showing how closely these sources were related, tak-
                                                                      ing into account the differences that may be caused either
   In the first instance, a data structure that is appropriate
                                                                      by accident or on purpose while being copied.
to be analysed by computers needs to be defined. This data
                                                                         In this paper, we focus on the sources of Viennese ori-
structure should be designed in such a way that it can en-
                                                                      gin, which are considered to have been originated from a
code all the information extracted from manuscripts – not
                                                                      copy that was brought from Berlin to Vienna in 1777 by
only musical aspects such as pitch or rhythm, but also the
                                                                      Gottfried van Sweieten (1734-1803). How the unique text
physical aspects of the manuscript which may account for
                                                                      of the Viennese sources evolved up has been the principal
the scribe’s unintentional omissions, misplacement, super-
                                                                      interest for musicologists, for this was the state of musical
fluous symbols that were somehow caused by the appear-
                                                                      text which Mozart learned in 1782. In [25], Tomita inves-
ance of its exemplar. This has been investigated with the
                                                                      tigated the Viennese sources, thereby proposing a source
collaboration of musicologists.
                                                                      affiliation diagram of them, an excerpt of which is shown
   Secondly, a method will be developed to harvest the in-
                                                                      in Figure 2.
formation useful for research from the digitised images of
the manuscripts. At the moment, we consider primarily
                                                                      4.2 Preliminary result
the visible information such as the direction of stems or
the position of note-heads. The first task is the recogni-             We describe one approach to this task using the database
tion of each music symbol such as staff line, bar line, note          developed by Tomita [24], an excerpt of which is shown
stem, note head and clef. The Gamera [19] framework will              in Figure 3, where S/N is the serial number given to each
be used for this task.                                                examination point; Bar indicates in which measure(s) the
   Finally, a method to analyse the data will be proposed.            elements are examined; V, bt/pos stands for Voice, Beat
In order to achieve this, powerful machine learning meth-             and Position, respectively; Element specifies the target of
ods such as bagging [20], boosting [21], and random for-              enquiry; Spec. Loc gives graphic representation of infor-
est [22] will be adopted.                                             mation under examination; Classified suggests text-critical
   Figure 1 illustrates how the proposed method operates.             significance.
First, a digitised image file is created by physically scan-              Firstly, the distance between two manuscripts should be
ning the manuscripts. Secondly, symbolic data is extracted            defined. The simplest way is to count the number of differ-
from the digitised image file. Thirdly, computational anal-            ent factors between two manuscripts.
ysis is carried out using the symbolic data.                             In Figure 3, “Q11731” has no different factors from


                                                                520
                10th International Society for Music Information Retrieval Conference (ISMIR 2009)


                                                                         cluster analysis using a set of dissimilarities calculated on
                                                                         the basis of Equation (1). Initially, each manuscript is as-
                                                                         signed to its own cluster and then the algorithm proceeds
                                                                         iteratively, at each stage joining the two most similar clus-
                                                                         ters, continuing until there is just a single cluster. At each
       Nydahl                                                            stage distances between clusters are recomputed by the
                                                                         Lance-Williams dissimilarity update formula according to
                                                                         the complete linkage method.

                                                                                                          Cluster Dendrogram




                                                                                  34
                                   No.




                                                                                       S.M.210
                                   543




                                                                                  32




                                                                                                 Nydahl
                                                                                  30
                                                                                  28
                                                                         Height
Figure 2. Score affiliation diagram of the Well-tempered
Clavier Book II, generated by human analysis (excerpted

                                                                                  26
from [18])




                                                                                                                    No.543
                                                                                  24
                                                                                  22


those of “No.543”, thus the distance between “Q11731”




                                                                                                                                    Q10782




                                                                                                                                             Q11731
and “No.543” is 0. On the other hand, “Q11731” has three
factors which are different from those of “Nydahl”, thus
the distance between “Q11731” and “Nydahl” is 3. How-
ever, such observation dose not reflect the reality suffi-                                                             dist
                                                                                                           hclust (*, "complete")
ciently. To improve the accuracy of observation, we should
consider how easily each factor can change. For instance,
notational factors such as the direction of the stem or po-              Figure 4. Score affiliation diagram of Fugue No.22 in B♭
sition of the note-head are more likely to change than mu-               minor from the Well-tempered Clavier Book II, generated
sical factors such as pitch or duration. Taking this into                by computational analysis
consideration, genealogical distance is defined by the fol-
lowing equation,                                                            Figure 4 illustrates an example of source affiliation di-
                                                                         agram automatically generated by the proposed algorithm.
                       SN
                       X                                                 Manuscripts of Fugues 10, 12 and 14 were used to cal-
   D(M SS1, M SS2) =         αT ypei I(M SS1[i], M SS2[i])   (1)         culate the distance between each manuscript. This result
                       i=1
                                                                         is almost consistent with that of human analysis, while
where, M SS1 and M SS2 denote two different manuscripts,                 the position of No.543 (Berea) is considered to be differ-
M SS[i] denotes the ith content of MSS, αT ypei is the                   ent. This result indicates that this database is sufficient to
weight considering the fluidity of each type of the con-                  achieve a rough classification; but to achieve a more re-
tent, and I(x, y) is the indicator function which returns 0              liable classification or for further analysis, it is necessary
if x = y else 1. In this paper, all αT ypei were equalized,              to develop a new data structure that is suitable for a more
leaving an adjustment of αT ypei as a future task.                       detailed computational analysis. The manual weighting of
                                                                         αT ypei can reflect the expert knowledge of musicologists;
                                                                         however it could also reflect their own subjectivity. To ex-
                                                                         clude it, a method for automatic weighting of these factors
                                                                         should be investigated.
                                                                            There are numerous possibilities of using these databases
                                                                         for analysis and the potential is far-reaching. Figure 5
                                                                         shows biplot of the result of the principle component anal-
                                         Nydahl
                                                                         ysis. This reveals that there exists a large gap between
                                         No.543                          Add.35021 (Bach’s autograph manuscript) and the Vien-
                                                                         nese sources. Figure 6 shows the result of the variable im-
                                                                         portance estimation for the classification of the manuscripts
Figure 3. Database used for the experiment (excerpted                    of Fugue 23 by random forest, where y-axis corresponds
from [18]).                                                              to S/N of the text critical database. This indicates that S/N
                                                                         475, and 136 are important for computer to classify them.
   Secondly, manuscripts are clustered by a hierarchical                 These analyses using appropriate databases are considered


                                                                   521
                                                                                       Poster Session 3




                                                                                                            V475                             V136
                                                                                                            V447                             V242
             −10                   −5                        0                        5                     V340                             V10
                                                                                                            V435                             V295
                                                                                                            V308                             V486
                                                                                                            V465                             V35
      0.4




                                                                                                            V446                             V315




                                                                                               5
                                                                                                            V489                             V171
                                                                                                            V318                             V297
                                                                           V121                             V61                              V447
                                     V502 V343  V165                                                        V430                             V74
                                           Federhofer V36
                                             V475                   V177                V1                  V515                             V11
      0.2




                                  Nydahl                                    V7
                                                                     V181 V220
                           S.M.210.2    V89 V497 V291 V230
                                          V383               V151
                                                       V501V465  V39      V213       Q11731                 V2                               V248
                                                    V319 V444
                                         V470 V451 V422 V293 V242
                                       V278          V250 V345 V67
                                                     V98
                                                   V296 V309
                                                   V406 V254
                                                   V265V129
                                                    V499                V342      Q10782                    V19                              V316
                                          V485 V204 V271 V367 V85 V166
                                              V370 V363 V235 V359 V294 V35
                                                V56 V318 V435 V10
                                                       V264
                                                  V327 V362V21
                                                 V325 V94V60
                                                           V147
                                                                     V471
                                                                  V150
                                              V381 V216 V300 V29 V430
                                               V65 V156 V194 V122 V16
                                                                                     V316                   V93                              V93
                                                V188 V399V28 V163
                                                               V439
                                         V227V308 V494 V224V483V174
                                                    V143 V320V30
                                                             V61
                                                             V45
                                                            V149
                                                            V207
                                                            V360
                                                            V176
                                                            V493
                                                            V457
                                                            V520
                                                V297 V321 V466 V311
                                                            V246
                                                            V335
                                                            V260
                                                            V261
                                                            V423
                                                             V41
                                                             V47
                                             V307 V340 V382V513 V322                  No.543                V195                             V470
                                               V99 V445 V427 V491
                                                 V450 V70
                                                      V75
                                                      V52
                                                      V43
                                                     V105
                                                     V178
                                                     V401 V125
                                                     V341 V366 V292
                                                     V407
                                                     V448
                                                     V144
                                                     V411        V352
                                             V64 V480V413V277V100 V474
                                                     V9V283 V332
                                               V172 V210 V455V155V115
                                               V192V68V282V44V436
                                                                V160
                                                    V141 V458V179
                                                      V302 V253 V131
                                                                V202
                                                              V208
                                                              V180
                                                      V373 V469 V128
                                          V239V74 V284V324V347V198 V62
                                          V133            V337 V101
                                                      V106 V487
                                                      V375 V500
                                                         V175 V117
                                                         V380V135
                                                           V387
                                                          V205 V328
                                                           V33
                                                           V37
                                                           V51
                                                          V110V456
                                                              V228
                                                V431 V426V393V243
                                                          V113 V464
                                                          V154 V66
                                                          V385 5
                                                          V217 V112
                                                              V23
                                                              V20
                                                             V119
                                                             V267
                                                         V351V477 V195
                                                         V379VV90
                                                      V478 V233
                                                         V326V263
                                                         V334V237
                                                        V130V4
                                                        V185V3V22
                                                               V103
                                                               V349
                                                               V305
                                                               V262
                                                               V425
                                                               V127
                                                               V232
                                                               V231
                                                               V124                                         V265                             V15
      0.0




                                                   V134V55V336 V344
                                                         V392V314V92
                                                              V138
                                                  V50V69V421V76V508
                                                 V212 V511V72V437
                                                             V34
                                                              V8V111
                                                              V6V114
                                                             V25
                                                             V40
                                                             V63
                                                             V73
                                                             V53
                                                             V54
                                                             V49
                                                             V58
                                                            V104
                                                             V46
                                                             V83
                                                             V86
                                                             V80
                                                             V78
                                                             V81
                                                             V84
                                                             V96
                                                            V120
                                                            V123
                                                            V140
                                                            V161
                                                            V482
                                                            V484
                                                            V209
                                                            V354
                                                            V357
                                                            V355
                                                            V187
                                                            V189
                                                            V182
                                                            V190
                                                            V184
                                                            V183
                                                            V397
                                                            V395
                                                            V396
                                                            V361
                                                            V173
                                                            V400
                                                            V368
                                                            V369
                                                            V346
                                                            V200
                                                            V201
                                                            V386
                                                            V350
                                                            V384
                                                            V229
                                                            V304
                                                            V306
                                                            V338
                                                            V460
                                                            V374
                                                            V234
                                                            V323
                                                            V403
                                                            V240
                                                            V168
                                                            V312
                                                            V498
                                                            V504
                                                            V509
                                                            V505
                                                            V503
                                                            V512
                                                            V301
                                                            V410
                                                            V419
                                                            V415
                                                            V408
                                                            V420
                                                            V416
                                                            V418
                                                            V298
                                                            V249
                                                            V226
                                                            V273
                                                            V258
                                                            V256
                                                            V259
                                                            V434
                                                             V14
                                                             V24
                                                             V27
                                                            V142
                                                            V414
                                                            V412
                                                            V222
                                                            V274
                                                            V441
                                                            V442                                            V272                             V490




                                                                                               0
                                                             V486
                                                         V251V479V289
                                                       V378
                                                       V376 V244
                                         V152 V219 V461V238V280 V79V481
                                         V95         V2 V82V19
                                                     V97 V158V402 V245
                                                   V516 V139V398
                                                   V286 V452V288 V248
                                                       V270 V365
                                                      V510 V364
                                                      V279V268V91
                                                 V329V330 V463
                                                      V424 V333
                                                      V290 V32V506
                                                      V440V48V507
                                                       V13 V137
                                                           V153
                                                           V492 V108
                                                           V389
                                                           V377
                                                           V428 V109
                                                    V203 V519
                                                    V390 V488 V196
                                                    V518 V371 V107
                                                    V221 V372 V214
                                                    V472 V26V116 V310
                                                       V266 V285
                                                V17      V299 V102 V193
                                                       V495 V223 V252
                                                      V191 V356 V257
                                             V276 V433 V118 V489 V462
                                               V199 V331V303V394 V388
                                                                   V42V225
                                                V88 V467V429V287V255
                                                                   V145
                                                                   V157
                                                                   V241                                     V429                             V288
                                                            V391 V348
                                        V315V432 V409 V339 V206
                                                             V31
                                                            V358
                                                            V170
                                                V447 V446V272
                                                 V476 V404V438
                                                         V317
                                                         V417
                                                        V236 V453
                                                        V295 V281 V71                                       V98                              V285
                                     V148 V496V514 V517 V159
                                                     V313 V218
                                                             V215 V59           V269
                                             V93V405 V38 V169 V468  V211
                                                                   V164                                     V89                              V62
                                    V12          V473 V353V146 V443
                                                          V57
                                                    V77 V449 V162      V87
                                                                                                            V7                               V121
                                     V515 V11                  V171 V197V459
                                                            V126 V167 V275
PC2




                                            V132 V186
      −0.2




                                                     V454
                                                S.M.210.1
                                                                                                            V16                              V115
                                     V15        V490                                                        V69                              V126
                                             V136
                                            V18                      V247
                                                                                                            V162                             V68
                                                                                                            V186                             V497
                                                                                                            V221                             V299
                                                                                                            V224                             V311
      −0.4




                                                                                               −5
                                                                                                            V290                             V159
                                                                                                            V297                             V471

                                                                                                                   0.40   0.50    0.60              0.00       0.02      0.04
                                                                                                                      MeanDecreaseAccuracy                 MeanDecreaseGini
      −0.6




                                                                                               −10
      −0.8




                                                       Add.35021
                                                                                                           Figure 6. Result of variable importance estimation for
             −0.8   −0.6         −0.4         −0.2          0.0          0.2          0.4
                                                                                                           the classification of Viennese sources by a random for-
                                               PC1
                                                                                                           est, where y-axis corresponds to S/N of Fugue 23 shown
                                                                                                           in [18]: for example, V475 is notation difference of rest in
                                                                                                           bar 89; V136 is the existence of accidental in bar32.


                                                                                                              3. The proposed method can be a prototype of an em-
Figure 5. Biplot produced from the output of the principle                                                       pirical research method.
component analysis of the text critical database of Fugue
23
                                                                                                              The result of the proposed research has a good potential
                                                                                                           for becoming a road map for musicological research of the
to bring the objectivity and new findings to historical mu-                                                 future, and empirical research method would offer an al-
sicology.                                                                                                  ternative to the previous research methods often criticised
   Another area of investigation is an automatic handwrit-                                                 for their inherent subjectivism. Consequently, it is hoped
ing analysis. The method for identifying handwriting in                                                    that the majority of previous research may be reworked by
noisy document images [26] cannot directly be applied to                                                   using the proposed methods. In this process, new discov-
music manuscripts. This is because handwriting identifi-                                                    eries can still be made that would shed new light on the
cation needs not only visual information such as curvature                                                 musical works concerned without requiring the rediscov-
(which represents the shape of the curves or bending an-                                                   ery of new sources. Moreover, the results of the proposed
gle) but also multifaceted information such as the purpose                                                 research may also serve as a prototype in other areas of
for which a manuscript was written, the scribe’s habits, the                                               research, such as archaeology, historical literature or other
conditions under which the manuscript was made, and so                                                     social science subjects that involve the study of historical
on. The proposed method is expected to overcome such                                                       sources.
difficulties by taking into account the multifaceted infor-
mation with the appropriate database for computational anal-
ysis.
                                                                                                                                 6. CONCLUSION
                           5. CONTRIBUTION
                                                                                                           In this paper, we have shown the necessity of using the
This research makes main contributions in the following                                                    computational approach in source studies. We also ad-
areas:                                                                                                     dressed the problems of subjective attitudes and its over-
      1. The proposed method will provide a way to verify                                                  reliance on new source discoveries in traditional research
         previous research in historical musicology;                                                       methods in musicology. Three stages that may resolve
                                                                                                           these problems have been discussed. The outcome of this
      2. It will be possible to offer new information about the                                            work should affect not only musicology but also a wide
         sources from the already known sources;                                                           range of subjects.


                                                                                                     522
                10th International Society for Music Information Retrieval Conference (ISMIR 2009)


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 [8] Wai Man Szeto and Man Hon Wong. A graph-                  [20] L Breiman. Bagging predictors. Machine Learning,
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