[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82066-en":3,"doc-seo-82066-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82066,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Tonnetz-Driven Graph Wedgelet for Harmonic Complexity Reduction in Music Scores","A heterogeneous graph representation models symbolic music scores using notes, lyric syllables, and accompaniment events as interconnected structures for both philological and computational analysis. The work studies how to reduce harmonic complexity while preserving task-relevant relations and overall graph structure. A compression scheme for the piano subgraph of vocal-pianistic scores uses binary wedge partitioning trees with a fully adaptive greedy algorithm that recursively minimizes L2 error in a six-dimensional Tonnetz embedding, producing human-readable, playable simplified scores. Experiments on symbolic corpora from three composers evaluate the approach.","arXiv :2607 .08806v 1 [ cs . SD] 9 Jul 2026  \nTonnetz-Driven Graph Wedgelet for Harmonic Complexity  \nReduction in Music Scores  \nEmmanuel Caronna 1 , Elisa Francomano∗1, and Silvia Licciardi 1  \n1 Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo,  \nItaly  \nAbstract  \nHeterogeneous graph built on notes, lyric syllables, and accompaniment events is a natural representation of symbolic music score, providing a substrate for both philological analysis and computational tasks. Music features are therefore well-captured by graph geometry and its properties. This representation has proved effective for analytical tasks as cadence detection, voice separation, and stylistic classification. In the present work, the reduction of harmonic complexity of a music score on graph, by preserving task-relevant information, relation between notes, and graph structure is investigated. A compression scheme for the piano subgraph of vocal-pianistic scores, built on binary wedge partitioning trees, is proposed. The wedges are generated through a fully adaptive greedy algorithm that recursively minimizes the L 2-error within a six-dimensional Tonnetz embedding of musical notes. The partitioning process employs a splitting criterion based on harmonic distance, resulting in regions that accurately reflect the intrinsic harmonic relationships among notes. The reconstructed music scores obtained through piecewise-constant functions and the mean values of the notes inside each wedge are used as anew simplified scores human-readable and playable. Some experiments on a corpus of symbolic music scores of three different composers are performed to assess the proposed approach.  \nKeywords. Symbolic music; Tonnetz; graph; wedge partitioning tree; computational musicology.  \n1 Introduction  \nComputational methods for the music analysis can be categorized depending on the features tobe extracted. Conventional approaches represent music as an audio signal (e.g., a waveform, ora time-frequency representation such as a spectrogram), from which features are identified by signal-processing [1] or deep-learning techniques [2, 3] . Differently, the present paper is focused on the symbolic domain, where the subject is the musical score transformed into a mathematical object, the graph, explicitly encoding notes, rhythm, voices and texts, before any sound realization. Computational analysis of symbolic music has experienced a methodological renewal in the last decade [4, 5], driven by deep learning [3, 6] and music information retrieval [1] . Symbolic formats such as MusicXML [7] and MIDI [8] expose explicit information on pitch, duration, voicing, lyrics, dynamics, and score position. Such granularity has motivated a sustained effort to design representations exploiting it without flattening it into either piano-roll matrices [9, 10] or linear token streams [11, 12] (see Appendix) .  \n∗ Corresponding author: [elisa.francomano@unipa.it](elisa.francomano@unipa.it)  \nAmong the proposed approaches, graph-based representations have emerged as particularly wellsuited to the hierarchical, polyphonic, and temporal nature of a score. It has been used for cadence detection [13], Roman numeral analysis (see Appendix) [14], voice separation [15], expressive performance rendering [16] and composer classification [4] . A particular instance has been proposed in the previous work of the authors [17], where a heterogeneous score-graph has been designed by integrating three types of node:note_voice for the melodic line, syllable for the lyrics, and note_piano for the accompaniment; each one connected by seven relation types encoding: sequential (voice-next-voice, syllable-next-syllable, piano-next-piano), vertical (piano-vert-piano) and cross-modal (syllable-sung_on_head-voice, syllable-sung_onvoice, piano-sung_on-voice) alignment. In the present paper the score-graph construction is adopted.  \nMusic scores contain substantial structural redundancy, es","cbCaipz084ZFUIUG","https://ap.wps.com/l/cbCaipz084ZFUIUG","pdf",29185932,1,17,"English","en",105,"# Introduction\n## Graph-based representations for symbolic music\n## Redundancy and compression in symbolic scores\n## Graph signal processing and Tonnetz embeddings\n# Method\n## Tonnetz-driven graph wedgelet compression\n## Adaptive greedy wedge partitioning and L2 minimization\n# Experiments\n## Dataset, setup, and evaluation","[{\"question\":\"What graph elements are used to represent symbolic music scores in this work?\",\"answer\":\"The representation builds a heterogeneous graph from notes, lyric syllables, and accompaniment events, encoding their relationships so the score becomes a structured mathematical object.\"},{\"question\":\"How does the proposed compression scheme reduce harmonic complexity?\",\"answer\":\"It compresses the piano subgraph using binary wedge partitioning trees, where a fully adaptive greedy algorithm recursively minimizes L2 error within a six-dimensional Tonnetz embedding while maintaining harmonic-distance-aware splits.\"},{\"question\":\"What is the output of the compression, and how is it made useful?\",\"answer\":\"The method reconstructs simplified scores using piecewise-constant functions and mean note values per wedge, yielding human-readable and playable music.\"}]",1784177982,43,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"tonnetz-driven-graph-wedgelet-for-harmonic-complexity-reduction-in-music-scores","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/tonnetz-driven-graph-wedgelet-for-harmonic-complexity-reduction-in-music-scores/82066/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What graph elements are used to represent symbolic music scores in this work?","Question",{"text":74,"@type":75},"The representation builds a heterogeneous graph from notes, lyric syllables, and accompaniment events, encoding their relationships so the score becomes a structured mathematical object.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the proposed compression scheme reduce harmonic complexity?",{"text":79,"@type":75},"It compresses the piano subgraph using binary wedge partitioning trees, where a fully adaptive greedy algorithm recursively minimizes L2 error within a six-dimensional Tonnetz embedding while maintaining harmonic-distance-aware splits.",{"name":81,"@type":72,"acceptedAnswer":82},"What is the output of the compression, and how is it made useful?",{"text":83,"@type":75},"The method reconstructs simplified scores using piecewise-constant functions and mean note values per wedge, yielding human-readable and playable 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