Volume 1 Building the American Republic A Narrative History to 1877 Harry L. Watson The University of Chicago Press ChiCago and London
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consists of two specialized convolutional networks one. dealing with the sheet image and one dealing with the au. dio spectrogram input In the subsequent layers we fuse. the specialized sub networks by concatenation of the latent. image and audio representations and additional process. ing by a sequence of dense layers For a detailed descrip. tion of the individual layers we refer to Table 1 in Section. 3 4 The output layer of the network and the corresponding. localization principle are explained in the following. a Spectrogram to sheet correspondence In this ex, ample the rightmost onset in spectrogram excerpt Ei j. corresponds to the rightmost note target note j in. 2 2 2 Audio to Sheet Bucket Classification, sheet image Si For the present case the temporal con. text of about 1 2 seconds into the past covers five. The objective for an unseen spectrogram excerpt and a cor. additional notes in the spectrogram The staff image responding staff of sheet music is to predict the excerpt s. and spectrogram excerpt are exactly the multi modal location xj in the staff image For this purpose we start. input presented to the proposed audio to sheet match. ing network At train time the target pixel location xj. with horizontally quantizing the sheet image into B non. in the sheet image is available at test time x j has to overlapping buckets This discretisation step is indicated. be predicted by the model see figure below as the short vertical lines in the staff image above the score. in Figure 2 In a second step we create for each note j in. the train set a target vector tj tj b where each vec. tor element tj b holds the probability that bucket b covers. the current target note j In particular we use soft tar. gets meaning that the probability for one note is shared. between the two buckets closest to the note s true pixel lo. cation xj We linearly interpolate the shared probabilities. based on the two pixel distances normalized to sum up. to one of the note s location xj to the respective closest. bucket centers Bucket centers are denoted by cb in the. b Schematic sketch of the audio to sheet matching task targeted. in this work Given a sheet image Si and a short snippet of au following where subscript b is the index of the respective. dio spectrogram excerpt Ei j the model has to predict the audio bucket Figure 3 shows an example sketch of the compo. snippet s corresponding pixel location xj in the image nents described above Based on the soft target vectors we. design the output layer of our audio to sheet matching net. Figure 1 Input data and audio to sheet matching task work as a B way soft max with activations defined as. dinate xj is the distance of the note head in pixels from yj k. the left border of the image As we work with single staffs. of sheet music we only need the x coordinate of the note yj b is the soft max activation of the output neuron rep. at this point Figure 1a relates all components involved resenting bucket b and hence also representing the region. Summary and Task Description For training we present in the sheet image covered by this bucket By applying the. triples of 1 staff image Si 2 spectrogram excerpt Ei j soft max activation the network output gets normalized to. and 3 ground truth pixel x coordinate xj to our audio to range 0 1 and further sums up to 1 0 over all B output. sheet matching model At test time only the staff image neurons The network output can now also be interpreted. and spectrogram excerpt are available and the task of the as a vector of probabilities pj yj b and shares the. model is to predict the estimated pixel location x j in the same value range and properties as the soft target vectors. image Figure 1b shows a sketch summarizing this task In training we optimize the network parameters by. minimizing the Categorical Cross Entropy CCE loss lj. 2 2 Audio Sheet Matching as Bucket Classification between target vectors tj and network output pj. We now propose a multi modal convolutional neural net X. work architecture that learns to match unseen audio snip lj tj k log pj k 2. pets spectrogram excerpts to their corresponding pixel lo. cation in the sheet image The CCE loss function becomes minimal when the net. work output pj exactly matches the respective soft target. 2 2 1 Network Structure, vector tj In Section 3 4 we provide further information. Figure 2 provides a general overview of the deep network on the exact optimization strategy used 1. and the proposed solution to the matching problem As 1 For the sake of completeness In our initial experiments we started. mentioned above the model operates jointly on a staff im to predict the sheet location of audio snippets by minimizing the Mean. age Si and the audio spectrogram excerpt Ei j related to Squared Error MSE between the predicted and the true pixel coordinate. MSE regression However we observed that training these networks. a note j The rightmost onset in the spectrogram excerpt is much harder and further performs worse than the bucket classification. is the one related to target note j The multi modal model approach proposed in this paper. Figure 2 Overview of multi modal convolutional neural network for audio to sheet matching The network takes a staff image and. a spectrogram excerpt as input Two specialized convolutional network parts one for the sheet image and one for the audio input are. merged into one multi modality network The output part of the network predicts the region in the sheet image the classification bucket. to which the audio snippet corresponds,3 EXPERIMENTAL EVALUATION. This section evaluates our audio to sheet matching model. on a publicly available dataset We describe the experi. mental setup including the data and evaluation measures. the particular network architecture as well as the optimiza. tion strategy and provide quantitative results, Figure 3 Part of a staff of sheet music along with soft tar. get vector tj for target note j surrounded with an ellipse The. two buckets closest to the note share the probability indicated as 3 1 Experiment Description. dots of containing the note The short vertical lines highlight the. bucket borders The aim of this paper is to show that it is feasible to learn. correspondences between audio spectrograms and im, ages of sheet music in an end to end neural network fash. 2 3 Sheet Location Prediction ion meaning that an algorithm learns the entire task purely. from data so that no hand crafted feature engineering is re. Once the model is trained we use it at test time to predict quired We try to keep the experimental setup simple and. the expected location x j of an audio snippet with target consider one staff of sheet music per train test sample this. note j in a corresponding image of sheet music The output is exactly the setup drafted in Figure 2 To be perfectly. of the network is a vector pj pj b holding the prob clear the task at hand is the following For a given au. abilities that the given test snippet j matches with bucket dio snippet find its x coordinate pixel position in a corre. b in the sheet image Having these probabilities we con sponding staff of sheet music We further restrict the audio. sider two different types of predictions 1 We compute to monophonic music containing half quarter and eighth. the center c b of bucket b argmaxb pj b holding the high notes but allow variations such as dotted notes notes tied. est overall matching probability 2 For the second case across bar lines as well as accidental signs. we take in addition to b the two neighbouring buckets. b 1 and b 1 into account and compute a linearly, probability weighted position prediction in the sheet im. age as For the evaluation of our approach we consider the Not. X tingham 2 data set which was used e g for piano tran. x j w k ck 3 scription in 4 It is a collection of midi files already split. k b 1 b b 1, into train validation and test tracks To be suitable for. audio to sheet matching we prepare the data set midi files. where weight vector w contains the probabilities as follows. pj b 1 pj b pj b 1 normalized to sum up to one and. ck are the center coordinates of the respective buckets 2 www etud iro umontreal ca boulanni icml2012. Sheet Image 40 390 Spectrogram 136 40, 5 5 Conv pad 2 stride 1 2 64 BN ReLu 3 3 Conv pad 1 64 BN ReLu. 3 3 Conv pad 1 64 BN ReLu 3 3 Conv pad 1 64 BN ReLu. 2 2 Max Pooling Drop Out 0 15 2 2 Max Pooling Drop Out 0 15. 3 3 Conv pad 1 128 BN ReLu 3 3 Conv pad 1 96 BN ReLu. 3 3 Conv pad 1 128 BN ReLu 2 2 Max Pooling Drop Out 0 15. 2 2 Max Pooling Drop Out 0 15 3 3 Conv pad 1 96 BN ReLu. 2 2 Max Pooling Drop Out 0 15, Dense 1024 BN ReLu Drop Out 0 3 Dense 1024 BN ReLu Drop Out 0 3. Concatenation Layer 2048,Dense 1024 BN ReLu Drop Out 0 3. Dense 1024 BN ReLu Drop Out 0 3,B way Soft Max Layer. Table 1 Architecture of Multi Modal Audio to Sheet Matching Model BN Batch Normalization ReLu Rectified Linear Activation. Function CCE Categorical Cross Entropy Mini batch size 100. 1 We select the first track of the midi files right hand a tolerance of k 1 buckets For example the top 1 bucket. piano and render it as sheet music using Lilypond 3 hit rate counts only those notes where the predicted bucket. b matches exactly the note s target bucket bj The top 2. 2 We annotate the sheet coordinate xj of each note. bucket hit rate allows for a tolerance of one bucket and so. 3 We synthesize the midi tracks to flac audio using on The second measure the normalized pixel distance. Fluidsynth 4 and a Steinway piano sound font captures the actual distance of a predicted sheet location x j. to its corresponding true position xj To allow for an eval. 4 We extract the audio timestamps of all note onsets uation independent of the image resolution used in our ex. As a last preprocessing step we compute log spectrograms periments we normalize the pixel errors by dividing them. of the synthesized flac files 3 with an audio sample rate by the width of the sheet image as x j xj width Si. of 22 05kHz FFT window size of 2048 samples and com This results in distance errors living in range 1 1. putation rate of 31 25 frames per second For dimension We would like to emphasise that the quantitative eval. ality reduction we apply a normalized 24 band logarithmic uations based on the measures introduced above are per. filterbank allowing only frequencies from 80Hz to 8kHz formed only at time steps where a note onset is present At. This results in 136 frequency bins those points in time an explicit correspondence between. We already showed a spectrogram to sheet annotation spectrogram onset and sheet image note head is es. example in Figure 1a In our experiment we use spectro tablished However in Section 4 we show that a time. gram excerpts covering 1 2 seconds of audio 40 frames continuous prediction is also feasible with our model and. This context is kept the same for training and testing onset detection is not required at run time. Again annotations are aligned in a way so that the right. most onset in a spectrogram excerpt corresponds to the 3 4 Model Architecture and Optimization. pixel position of target note j in the sheet image In ad. Table 1 gives details on the model architecture used for. dition the spectrogram is shifted 5 frames to the right to. our experiments As shown in Figure 2 the model is struc. also contain some information on the current target note s. tured into two disjoint convolutional networks where one. onset and pitch We chose this annotation variant with the. considers the sheet image and one the spectrogram audio. rightmost onset as it allows for an online application of our. input The convolutional parts of our model are inspired by. audio to sheet model as would be required e g in a score. the VGG model built from sequences of small convolution. following task, kernels e g 3 3 and max pooling layers The central. 3 3 Evaluation Measures part of the model consists of a concatenation layer bring. ing the image and spectrogram sub networks together Af. To evaluate our approach we consider for each test note j ter two dense layers with 1024 units each we add a B way. the following ground truth and prediction data 1 The true soft max output layer Each of the B soft max output neu. position xj as well as the corresponding target bucket bj rons corresponds to one of the disjoint buckets which in. see Figure 3 2 The estimated sheet location x j and the turn represent quantised sheet image positions In our ex. most likely target bucket b predicted by the model Given periments we use a fixed number of 40 buckets selected as. this data we compute two types of evaluation measures follows We measure the minimum distance between two. The first the top k bucket hit rate quantifies the ratio subsequent notes in our sheet renderings and select the. of notes that are classified into the correct bucket allowing number of buckets such that each bucket contains at most. 3 http www lilypond org one note It is of course possible that no note is present. 4 http www fluidsynth org in a bucket e g for the buckets covering the clef at the. Bucket Distance Distribution 0 05 Train Valid Test. 0 5 Top 1 Bucket Hit Rate 79 28 51 63 54 64,Normalized Pixel Distance. Top 2 Bucket Hit Rate 94 52 82 55 84 36,Ratio of Notes. 0 03 mean N P Dmax 0 0316 0 0684 0 0647,0 3 mean N P Dint 0 0285 0 0670 0 0633. 0 02 median N P Dmax 0 0067 0 0119 0 0112,median N P Dint 0 0033 0 0098 0 0091. 0 1 N P Dmax wb 93 87 76 31 79 01,0 0 0 00 N P Dint wb 94 21 78 37 81 18. 40 30 20 10 0 10 20 30 40 max inter,Bucket Distance. Table 2 Top k bucket hit rates and normalized pixel distances. Figure 4 Summary of matching results on test set Left His NPD as described in Section 3 4 for train validation and test. togram of bucket distances between predicted and true buckets set We report mean and median of the absolute NPDs for both. Right Box plots of absolute normalized pixel distances between interpolated int and maximum max probability bucket predic. predicted and true image position The box plot is shown for both tion The last two rows report the percentage of predictions not. location prediction methods described in Section 2 3 maximum further away from the true pixel location than the width wb of one. interpolated bucket, beginning of a staff As activations function for the inner synthesized midi but played by a human on a piano and. layers we use rectified linear units 10 and apply batch recorded via microphone. normalization 11 after each layer as it helps training and. convergence, Given this architecture and data we optimize the param 4 1 Prediction Example and Discussion. eters of the model using mini batch stochastic gradient de Figure 5 shows the image of one staff of sheet music along. scent with Nesterov style momentum We set the batch with the predicted as well as the ground truth pixel location. size to 100 and fix the momentum at 0 9 for all epochs for a snippet of audio The network correctly matches the. The initial learn rate is set to 0 1 and divided by 10 every spectrogram with the corresponding pixel location in the. 10 epochs We additionally apply a weight decay of 0 0001 sheet image However we observe a second peak in the. to all trainable parameters of the model bucket prediction probability vector A closer look shows. that this is entirely reasonable as the music is quite repet. 3 5 Experimental Results itive and the current target situation actually appears twice. in the score The ability of predicting probabilities for. Figure 4 shows a histogram of the signed bucket distances. multiple positions is a desirable and important property as. between predicted and true buckets The plot shows that. repetitive structures are immanent to music The resulting. more than 54 of all unseen test notes are matched ex. prediction ambiguities can be addressed by exploiting the. actly with the corresponding bucket When we allow for. temporal relations between the notes in a piece by meth. a tolerance of 1 bucket our model is able to assign over. ods such as dynamic time warping or probabilistic models. 84 of the test notes correctly We can further observe that. In fact we plan to combine the probabilistic output of our. the prediction errors are equally distributed in both direc. matching model with existing score following methods as. tions meaning too early and too late in terms of audio. for example 2 In Section 2 we mentioned that training a. The results are also reported in numbers in Table 2 as the. sheet location prediction with MSE regression is difficult. top k bucket hit rates for train validation and test set. to optimize Besides this technical drawback it would not. The box plots in the right part of Figure 4 summarize. be straightforward to predict a variable number of locations. the absolute normalized pixel distances NPD between. with an MSE model as the number of network outputs has. predicted and true locations We see that the probability. to be fixed when designing the model, weighted position interpolation Section 2 3 helps im. In addition to the network inputs and prediction Fig 5. prove the localization performance of the model Table 2. also shows a saliency map 19 computed on the input. again puts the results in numbers as means and medians of. sheet image with respect to the network output 5 The. the absolute NPD values Finally Fig 2 bottom reports. saliency can be interpreted as the input regions to which. the ratio of predictions with a pixel distance smaller than. most of the net s attention is drawn In other words it high. the width of a single bucket, lights the regions that contribute most to the current output. produced by the model A nice insight of this visualiza. 4 DISCUSSION AND REAL MUSIC tion is that the network actually focuses and recognizes the. heads of the individual notes In addition it also directs. This section provides a representative prediction example. some attention to the style of stems which is necessary to. of our model and uses it to discuss the proposed approach. distinguish for example between quarter and eighth notes. In the second part we then show a first step towards match. ing real though still very simple music to its correspond 5 The implementation is adopted from an example by Jan Schlu ter in. ing sheet By real music we mean audio that is not just the recipes section of the deep learning framework Lasagne 7. Spectrogram,Staff Image,Saliency Staff Image,1 0 Bucket Distance 0. Probability,0 6 ground truth,0 4 prediction,0 5 10 15 20 25 30 35. Figure 5 Example prediction of the proposed model The top row shows the input staff image Si along with the bucket borders as thin. gray lines and the given query audio spectrogram snippet Ei j The plot in the middle visualizes the salience map representing the. attention of the neural network computed on the input image Note that the network s attention is actually drawn to the individual note. heads The bottom row compares the ground truth bucket probabilities with the probabilities predicted by the network In addition we. also highlight the corresponding true and predicted pixel locations in the staff image in the top row. The optimization on soft target vectors is also reflected real recording This corresponds to a average normalized. in the predicted bucket probabilities In particular the pixel distance of 0 0402. neighbours of the bucket with maximum activation are also. active even though there is no explicit neighbourhood re. 5 CONCLUSION, lation encoded in the soft max output layer This helps the. interpolation of the true position in the image see Fig 4 In this paper we presented a multi modal convolutional. neural network which is able to match short snippets of. 4 2 First Steps with Real Music audio with their corresponding position in the respective. image of sheet music without the need of any symbolic. As a final point we report on first attempts at working with. representation of the score First evaluations on simple pi. real music For this purpose one of the authors played. ano music suggest that this is a very promising new ap. the right hand part of a simple piece Minuet in G Major. proach that deserves to be explored further,by Johann Sebastian Bach BWV Anhang 114 which. of course was not part of the training data on a Yamaha As this is a proof of concept paper naturally our method. AvantGrand N2 hybrid piano and recorded it using a sin still has some severe limitations So far our approach can. gle microphone In this application scenario we predict only deal with monophonic music notated on a single. the corresponding sheet locations not only at times of on staff and with performances that are roughly played in the. sets but for a continuous audio stream subsequent spec same tempo as was set in our training examples. trogram excerpts This can be seen as a simple version In the future we will explore options to lift these limi. of online score following in sheet music without taking tations one by one with the ultimate goal of making this. into account the temporal relations of the predictions We approach applicable to virtually any kind of complex sheet. offer the reader a video 6 that shows our model following music In addition we will try to combine this approach. the first three staff lines of this simple piece 7 The ra with a score following algorithm Our vision here is to. tio of predicted notes having a pixel distance smaller than build a score following system that is capable of dealing. the bucket width compare Section 3 5 is 71 72 for this with any kind of classical sheet music out of the box with. no need for data preparation,6 https www dropbox com s 0nz540i1178hjp3. Bach Minuet G Major net4b mp4 dl 0, 7 Note our model operates on single staffs of sheet music and requires. 6 ACKNOWLEDGEMENTS, a certain context of spectrogram frames for prediction in our case 40. frames For this reason it cannot provide a localization for the first couple This work is supported by the Austrian Ministries BMVIT. of notes in the beginning of each staff at the current stage In the video. one can observe that prediction only starts when the spectrogram in the and BMWFW and the Province of Upper Austria via the. top right corner has grown to the desired size of 40 frames We kept this COMET Center SCCH and by the European Research. behaviour for now as we see our work as a proof of concept The issue Council ERC Grant Agreement 670035 project CON. can be easily addressed by concatenating the images of subsequent staffs. in horizontal direction In this way we will get a continuous stream of ESPRESSIONE The Tesla K40 used for this research was. sheet music analogous to a spectrogram for audio donated by the NVIDIA corporation. 7 REFERENCES 13 Mark S Melenhorst Ron van der Sterren Andreas. Arzt Agust n Martorell and Cynthia C S Liem A,1 Andreas Arzt Harald Frostel Thassilo Gadermaier. tablet app to enrich the live and post live experience of. Martin Gasser Maarten Grachten and Gerhard Wid, classical concerts In Proceedings of the 3rd Interna. mer Artificial intelligence in the concertgebouw In. tional Workshop on Interactive Content Consumption. Proceedings of the International Joint Conference,WSICC at TVX 2015 06 2015 2015. on Artificial Intelligence IJCAI Buenos Aires Ar, gentina 2015 14 Marius Miron Julio Jose Carabias Orti and Jordi. Janer Audio to score alignment at note level for or. 2 Andreas Arzt Gerhard Widmer and Simon Dixon Au,chestral recordings In Proc of the International. tomatic page turning for musicians via real time ma. Conference on Music Information Retrieval ISMIR, chine listening In Proc of the European Conference. 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Learning ICML 12 pages 1159 1166 2012 Netherlands 2010. 5 Arshia Cont A coupled duration focused architecture 17 Matthew Prockup David Grunberg Alex Hrybyk and. for realtime music to score alignment IEEE Transac Youngmoo E Kim Orchestral performance compan. tions on Pattern Analysis and Machine Intelligence ion Using real time audio to score alignment IEEE. 32 6 837 846 2009 Multimedia 20 2 52 60 2013, 6 Nicholas Cook Performance analysis and chopin s 18 Christopher Raphael Music Plus One and machine. mazurkas Musicae Scientae 11 2 183 205 2007 learning In Proceedings of the International Confer. ence on Machine Learning ICML 2010, 7 Sander Dieleman Jan Schlu ter Colin Raffel Eben Ol. son S ren Kaae S nderby Daniel Nouri Eric Batten 19 Jost Tobias Springenberg Alexey Dosovitskiy. berg Aa ron van den Oord et al Lasagne First re Thomas Brox and Martin Riedmiller Striving for sim. lease August 2015 plicity The all convolutional net arXiv 1412 6806. 8 Zhiyao Duan and Bryan Pardo A state space model for. on line polyphonic audio score alignment In Proc of 20 Verena Thomas Christian Fremerey Meinard Mu ller. the IEEE Conference on Acoustics Speech and Signal and Michael Clausen Linking Sheet Music and Au. Processing ICASSP Prague Czech Republic 2011 dio Challenges and New Approaches In Meinard. Mu ller Masataka Goto and Markus Schedl editors, 9 Jon W Dunn Donald Byrd Mark Notess Jenn Ri Multimodal Music Processing volume 3 of Dagstuhl. ley and Ryan Scherle Variations2 Retrieving and us Follow Ups pages 1 22 Schloss Dagstuhl Leibniz. ing music in an academic setting Communications of Zentrum fuer Informatik Dagstuhl Germany 2012. the ACM Special Issue Music information retrieval,49 8 53 48 2006. 10 Xavier Glorot Antoine Bordes and Yoshua Bengio, Deep sparse rectifier neural networks In International. 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