Van Beethoven Research Articles

Graphing Deep Hypermeter in the Scherzo Movement of Beethoven’s Ninth Symphony

Abstract This paper reinterprets my 1992 analysis of the scherzo of Ludwig van Beethoven’s Ninth Symphony using more recently introduced modes of representation: ski-hill graphs, ski-path networks, and metric cubes. It provides a tutorial on the three metric modes of representation, while using those modes to reveal different aspects of the scherzo’s metric form. It presents evidence in support of the proposition that slow pulses and deep hypermeter can “exist,” be aesthetically relevant, and have analytical value.

Genomic Analysis Unlocks Cause Of Beethoven's Death.

American Journal of Medical Genetics Part AVolume 191, Issue 7 p. 1689-1690 THE AJMG SEQUENCE: DECODING NEWS AND TRENDS FOR THE MEDICAL GENETICS COMMUNITY BY ROXANNE NELSON Genomic Analysis Unlocks Cause Of Beethoven's Death First published: 07 June 2023 https://doi.org/10.1002/ajmg.a.62816Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Reference Begg TJA, Schmidt A, Kocher A, et al. 2023. Genomic analyses of hair from Ludwig van Beethoven. Curr Biol; 33(8): 1431– 1447.e22. Volume191, Issue7July 2023Pages 1689-1690 ReferencesRelatedInformation

A vaccine for Beethoven's vulnerable liver.

Dear EJCI Editor, The recent report1 presenting a thorough analysis of Ludwig van Beethoven's genome has made headlines in scientific and non-scientific journals. The famous composer is known to have suffered, among other ailments, from cirrhosis, and the study by Begg et al.1 adds a few exciting new details to this picture. In brief, the authors showed that Beethoven carried a combination of genetic variants (i.e. HFE p.His63Asp and p.Cys282Tyr as well as PNPLA3 p.I148M) that rendered his liver particularly vulnerable to external noxae, here iron, alcohol and caloric overload.2 Hence, regular alcohol consumption, probably combined with rich food over many years is likely to represent the major cause for his chronic liver disease. Interestingly, Begg et al.1 also performed a metagenomic analysis of Beethoven's hair locks and found that in the last months of his life, he might have suffered from hepatitis B virus (HBV) infection. Although the mass media and the authors of the report1 seem to have focused on the analysis of Beethoven's genome, the detection of HBV infection should not be overseen as it might be highly relevant to Beethoven's death, but also to our everyday liver patients. Apparently, the composer experienced a first episode of jaundice 6 years before his death in 1827, possibly a first sign of decompensation. The fact that it took a couple of decades of chronic alcohol consumption on the background of his high-risk genotype to develop clinical liver disease shows the organ's enormous regenerative capacity. This proverbial resilience has been known for a long time and features prominently in the Prometheus saga from 800 BC, which Beethoven refers to in his ballet ‘The Creatures of Prometheus Op. 43’, composed in 1801. One could speculate that during the last months of his life, the composer might have suffered from acute-on-chronic liver failure (ACLF) caused by the HBV infection on top of his alcohol-induced progressive liver damage. This additional insult precipitated the lethal deterioration of liver function (Figure 1). ACLF is a new disease entity,3 defined as acute liver failure in patients with chronic liver diseases. Bajaj et al.4 described ACLF ‘as a potentially reversible condition in patients with chronic liver disease with or without cirrhosis that is associated with the potential for multiple organ failure and mortality within 3 months in the absence of treatment of the underlying liver disease, liver support, or liver transplantation’. The data available in Begg's paper1 are not sufficient to determine if Beethoven suffered from multiple organ failure or only liver failure. Of note, acute viral infections have been identified as precipitating events of ACLF.5, 6 In terms of hepatitis B, acute infection is rare but can result in rapid dysfunction of pre-injured liver, and flares of chronic HBV infection have been described as triggers of ACLF.7 Patients with HBV-ACLF have been reported to suffer from high short-term mortality,8 in line with the data from the metagenomic analyses revealing the viral infection, and Beethoven's rapid demise. Begg's study1 is a major success of molecular genetic analyses. However, we reckon the observation that Beethoven suffered from HBV infection and that ACLF can be triggered by acute viral infections deserves more prominence. This finding might be used as a motivational lever to promote wider acceptance for vaccination against viral infections. Indeed, as highlighted by the pandemic and reviewed recently by Jeng et al.,9 vaccinations represent an effective means to prevent severe viral infections. Regardless of how long Beethoven suffered from HBV infection, one can imagine that prior vaccination against HBV, if it had been available at the time, might have prevented the acute deterioration of his vulnerable liver, which was challenged by the “devil's triangle” of gene variants, environmental toxins, and virus. This represents an important positive message, which is urgently needed in view of the persisting vaccine hesitancy following COVID-19.10 Portrait of Beethoven by Stieler was reproduced in Figure 1 with kind permission of Beethoven Haus Bonn. Open Access funding enabled and organized by Projekt DEAL. The authors have no conflict of interest to declare.

Transfer of meaning from the educator to the student in piano interpretation within the framework of the constructionist perspective

This research analyzes the concept of meaning from a constructionist perspective. From this perspective, while trying to determine how meaning is constructed and conveyed in piano interpretation, the study determined three different categories of meaning as a framework. One can list these categories as aesthetic meaning, symbolic meaning, and pragmatic meaning. In the aesthetic meaning category, music is essentially analyzed in terms of its formal qualities, that is, its immutable characteristics as indicated on the note. Researchers who analyze music based on this category often argue that music carries its meaning. The second category, symbolic meaning, refers to the symbolic meanings attributed to music in relation to the cultural context to which it belongs. Within the framework of this category of meaning, people also consider music in terms of its aesthetic qualities, but the focus is the meanings attributed to music by individuals or societies. The third and final category, pragmatic meaning, is directly related to how one uses music. Within the framework of pragmatic meaning, people base music analysis on the functional uses of music, and they analyze the other two categories accordingly. Here, in line with the brief definitions of the categories of meaning, this study examines the construction and transfer of meaning in piano interpretation with examples from selected works by Ludwig van Beethoven, Frederic Chopin, and Sergei Rachmaninoff. Beethoven’s No. 23 Piano Sonata “Appassionata” is characterized by the concept of contrast based on the fate motif; Chopin’s Op. 31, No. 2 Scherzo is characterized by serenity and calmness; and Rachmaninoff’s Op. 33 Etude No. 8 is characterized based on fairytale-like storytelling. These examples, interpreted according to the requirements of notation and edition, do not vary fundamentally because there is no information on the notes that contribute to the interpretation and explain the subject of the piece. However, the information we have about the composers’ works has shown us that more meaning can be attributed to the work beyond the interpretation suggestions on the notation. These attributed meanings act as a suggestion for the interpreter. However, since interpretation is directly related to the individual’s qualities, these examples of suggestive meaning do not have a given and fixed structure; they vary from person to person.

Alcohol and the death of Ludwig van Beethoven: comparison of general biographies to the medical literature.

Beethoven's autopsy findings of cirrhosis may have been due to alcoholism. This condition may have been underemphasized historically, given its stigma and the incongruence with the often heroic portrayal of Beethoven. We therefore aimed to compare how medical experts and biographers writing for anon-medical audience describe his final illness in the context of alcoholism. English-language biographies were identified using asurvey of biographies of Beethoven and supplemented by the authors. English-language medical publications were identified by searching for "Beethoven" in the PubMed® MEDLINE database. We included studies that mentioned Beethoven's final illness and death. We recorded statements regarding alcohol consumption, alcoholism, or alcohol use disorder, and the role of alcohol in Beethoven's death. The most commonly cited final illness was liver disease. Alcohol use was more frequently mentioned in biographies, but alcoholism less so. Alcohol use was invoked as apossible cause of final illness more frequently by medical publications.

Homes: A Quartet

Abstract This article offers a meditation on the idea of home as expressed by four US poets belonging to different historical periods and socio-cultural backgrounds. At first, the poetic compositions I will discuss may startle readers in ways similar to what happened to Ludwig van Beethoven’s contemporaries as they first listened to his experimental and defamiliarizing late quartets. Emily Dickinson, Jennifer Elise Foerster, Richard Wright, and Agha Shahid Ali populate their homes with volcanoes, lice, faces hidden in gingerbread tins, and half-inch Himalayas. Moving alternately between macroscopic and microscopic dimensions, this article asks provocatively: How is the relation between movement and homemaking staged in these poems? To what extent do these poetic compositions bear the marks of homelessness and of imaginary homes? And finally, what should we make out of this unharmonious wholeness?

Genomic analyses of hair from Ludwig van Beethoven

Ludwig van Beethoven (1770-1827) remains among the most influential and popular classical music composers. Health problems significantly impacted his career as a composer and pianist, including progressive hearing loss, recurring gastrointestinal complaints, and liver disease. In 1802, Beethoven requested that following his death, his disease be described and made public. Medical biographers have since proposed numerous hypotheses, including many substantially heritable conditions. Here we attempt a genomic analysis of Beethoven in order to elucidate potential underlying genetic and infectious causes of his illnesses. We incorporated improvements in ancient DNA methods into existing protocols for ancient hair samples, enabling the sequencing of high-coverage genomes from small quantities of historical hair. We analyzed eight independently sourced locks of hair attributed to Beethoven, five of which originated from a single European male. We deemed these matching samples to be almost certainly authentic and sequenced Beethoven's genome to 24-fold genomic coverage. Although we could not identify a genetic explanation for Beethoven's hearing disorder or gastrointestinal problems, we found that Beethoven had a genetic predisposition for liver disease. Metagenomic analyses revealed furthermore that Beethoven had a hepatitis B infection during at least the months prior to his death. Together with the genetic predisposition and his broadly accepted alcohol consumption, these present plausible explanations for Beethoven's severe liver disease, which culminated in his death. Unexpectedly, an analysis of Y chromosomes sequenced from five living members of the Van Beethoven patrilineage revealed the occurrence of an extra-pair paternity event in Ludwig van Beethoven's patrilineal ancestry.

10. The Influence of Eusebie Mandicevschi on the Formation of the Personality of the Composer Marţian Negrea

Abstract The composer, choir conductor and musicologist, raised from the lands of Bucovina. Eusebie Mandicevschi (1857 - 1829) left posterity a complex musical work: vocal, symphonic, chamber, choral music, prestigious critical studies on Johann Sebastian Bach, Ludwig van Beethoven, Joseph Haydn, Franz Schubert, Johannes Brahms, distinguishing himself, throughout his life, through a sustained and competent pedagogical activity, through a prodigious social activity he was a teacher at the “Akademie für Musik und darstellende Kunst” in Vienna, as an archivist and librarian at the “Gesellschaft der Musikfreunde” in Vienna.

Un Beethoven ibérico: Dos siglos de transferencia cultural ed. by Teresa Cascudo García-Villaraco

Reviewed by: Un Beethoven ibérico: Dos siglos de transferencia cultural ed. by Teresa Cascudo García-Villaraco Walter Aaron Clark Un Beethoven ibérico: Dos siglos de transferencia cultural. Edited by Teresa Cascudo García-Villaraco. (Comares música.) Granada: Comares, 2021. [xi, 397 p. ISBN 9748413690520 (paperback), €33.] Music examples, illustrations, tables, bibliography. Ludwig van Beethoven's legacy is not one that we associate with Spain. At least it is not immediately apparent what sort of influence he and his music might have exercised on Spanish composers, concert artists, and audiences. We associate Beethoven with the genre of the symphony, but symphonic organizations were slow to develop in Spain during the 1800s, and Beethoven's symphonies only gradually gained traction with concert audiences there. And Spanish composers themselves never cultivated the symphony with any notable results. True, they composed an abundance of orchestral music, especially tone poems, ballets, and concertos, many of which have found a secure niche in the canonical repertoire. But one strains to think of a single Spanish symphony that has achieved the stature of Isaac Albéniz's Catalonia, Manuel de Falla's Three-Cornered Hat, or Joaquín Rodrigo's Concierto de Aranjuez. For whatever reason, Spanish composers were simply not drawn to the musical abstractions of the symphony—which is not to say they never composed them. Juan Crisóstomo de Arriaga (1806–1826) was a young composer whose promising career as a symphonist was cut short by a premature demise. And though they are far better known for their zarzuelas and operas, both Tomás Bretón and Ruperto Chapí essayed symphonic works. Joaquín Turina's Sinfonia sevillana (1920) also comes to mind, though it may be the exception that proves the rule, since it is as much a three-movement tone poem as it is a symphony. And yet it should not come as a complete surprise that the Iberian penetration of the Austro-Germanic heritage of which Beethoven was the crowning glory is on full display here. Joseph Haydn was hugely popular in Spain, and his Die Sieben letzten Worte unseres Erlösers am Kreuze was an orchestral work commissioned by the city of Cadiz in 1786. And in the late nineteenth century, Richard Wagner's operas and operatic philosophies were adopted and adapted by many admirers, including Felipe Pedrell, Albéniz, and Enrique Granados, among others. To be sure, this heritage was not confined to symphonies and operas. As this volume makes perfectly clear, the impact of Beethoven's chamber music and piano sonatas was immense, felt first within the salons of the elite before it made its way to concert venues populated by a growing middle class. Thus, Beethoven, a larger-than-life symbol of Viennese classicism and incipient romanticism, is not out of place in Iberian music history, and it was about time that someone undertook to examine his undoubted impact in both Spain and Portugal. That someone is Teresa Cascudo García-Villaraco, a leading musicologist in Spain and professor at the Universidad de La Rioja in Logroño. She assembled a dream team of scholars for this trailblazing collection of essays, which will be of great interest and value not only to Hispanists but also to anyone interested in the global scope of Beethoven interpretation and reception. The editor's insightful introduction concerns issues of reception, discourses, and canonicity relative to Beethoven. As she astutely points out, "Almost two centuries after his death, Beethoven is today the most-programmed composer, an icon of practices associated with 'classical music' and one that constitutes a model for certain attitudes and behaviors, an example of an idea of emancipated humanity that was defined at the end of the eighteenth century" (p. 1, my trans.). She then establishes the necessary tenor and parameters for the volume, which offers a generous collection of twenty essays, divided into nine major parts, by twenty-five scholars. This collection is the outgrowth of a 2020 [End Page 393] conference dedicated to the 250th anniversary of Beethoven's birth and organized by the "Música y Prensa" group of the Sociedad Española de Musicología. Yet, as the editor advises, these...

Silence in Music: L. van Beethoven and J. S. Bach. Aesthetic Approach

Music can bring us to light, when it is not dissonant, not dominated by an aggressive rhythm, by congestion of timbres, or by… consumerism that consumes everything – including our values and tranquility. Spiritual tranquility is a sign of spiritual health; it influences our inner thoughts and emotions, representing an essential aspect in cultivating one’s spiritual life. This is the whisper of the mystical and transcendental Arietta in the last Beehovenian sonata for piano, her secret, variational message: the last part of the last sonata which seems open, unfinished, concluded however with an evanescent melody that searches its identity at unsuspected heights. The aim of the work is to evidence a first analysis of the postures of silence in musical art, and its structure highlights the stylistic characteristics of Beethoven's masterpiece in this sense.

Structural Innovations in the First Movement of Beethoven’s Sonata W. O. O. 47 No. 2 in F minor Kurfürsten (1783)

The article discusses the use of original compositional methods in the first movement of Ludwig van Beethoven’s Piano Sonata W. O. O. 47 No. 2 in F minor “Kurfürsten”, adopted to innovate the sonata on a structural level, but also to offer it a greater variety of characters. The alternation of slow sections with fast ones within the movement, the opening of the work with a slow introduction, repeated in the recapitulation, which was first used by the composer at the age of 13, as an absolute premiere in music history, gave rise, years later, to a masterpiece of the 18th century, the Sonata Op. 13 in C minor “Pathétique”, one of the best known, innovative and impressive works written by him, but also to another important and creative work from the beginning of the 19th century, the Sonata Op. 31 No. 2 in D minor “Tempest”.

Issledovanie differenciacii esteticheskoj identichnosti v istorii zapadnoj muzyki na osnove teorii filosofskoj mysli

Based on T. Adorno's philosophical review, the inner logic of L. van Beethoven's late style and A. Schoenberg's toneless music is explored, and the goal and value of Adorno's tonal history critique are clarified.

РАЗМЫШЛЯЯ НАД КНИГОЙ С. М. ХЕНТОВОЙ «ЛЕВ ОБОРИН»

The article is based on a review of a book by the remarkable and in the second half of the twentieth century exceptionally popular musicologist S. M. Khentova, who, as a student of L. N. Oborin, was a representative of the school of the legendary pianist K. N. Igumnov. Oborin continued the traditions of his teacher both as a performer and as a teacher. Not only great pianists, but also wonderful teachers and concertmasters came out of his class. Oborin’s students were such well-known Russian musicologists as V. Delson and G. Tsypin, who have made a considerable contribution to the formation of Russian performing musicology. Khentova is currently the only biographer of her teacher, who contributed greatly to the formation of Russian pianism. Oborin gained widespread recognition after his triumphant victory at the First International Chopin Competition. In the thirties, it had not only artistic, but also political resonance. Khentova’s book analyses a number of fundamental moments for the formation of Oborin’s performing style. The process of the pianist’s creative formation is explored in the context of the socio-cultural attitudes of the epoch. The problem of the evolution of aesthetic perception of the audience is touched upon. The influence that Igumnov’s school had on the formation of Oborin’s creative attitudes as an interpreter of piano music by L. van Beethoven, P. Tchaikovsky, F. Chopin, S. Prokofiev, etc., as well as the musician’s pedagogical principles, is considered. In this article, all these points are evaluated in terms of modern scientific vision and assessment.

Gluvoća Ludwig Van Beethovena

Ludwig van Beethoven (1770-1827) began experiencing hearing loss in his thirties, which eventually progressed to profound deafness. Physicians and historians have sought for centuries to interpret the original sources from Beethoven's letters, medical documents, and autopsy reports to determine the causes of his deafness and systemic illnesses. This article reviews the current literature on the theories surrounding Beethoven's deafness and medical conditions. It is based on a PubMed® search spanning from 1958 to 2023 and provides a critical analysis of these theories.

Классическая сонатная форма: контекст современного музыкально-педагогического опыта

Importance. The range of issues of fortepiano pedagogy related to the development of the classical sonata form in succession with the composing and performing experience of the pre-classical period is considered. The problem of mastering the modern musical and pedagogical experience in the field of studying the classical sonata form in the fortepiano classroom is solved. Materials and methods. The semiotic approach to the musical text is used as the main methodological principle, as well as historical and cultural commentary and reconstruction of the authentic environment in which the classical sonata form was created and developed. The expediency of using the “quasi-score of the performing concept” in pedagogical communication is shown. The justification of the introduced concept contains various examples of reading the urtext. The proposed methods can be widely used in the sequential process of mastering a large form in an instrumental classroom. Results and Discussion. A useful result of the proposed approach is a meaningful attitude to performance technique as a resource for generating variants of the correct author’s interpretation of a work of art. Despite the fact that the large form is an obligatory part of music pedagogy, practicing musicians face problems of formal and semantic perception of the text in the process of participating in the dialogue environment “teacher – student”, “composer – instrumentalist”. By analogy with the term quasi-scores used in the art criticism analysis of a large form, the concept of “quasi-score of the performing concept” is introduced, which allows to enrich pedagogical communication with a large volume of historical and cultural information tied to the artistic text of the work and the technology of its performance. Concrete examples of the mutual influence of the largest representatives of the composer and performing practice of the 18th century are given and interpreted. Conclusion. The idea of the need to develop the ability of an instrumentalist to understand, hear and reproduce in performing practice the constructs of the musical language generated in the syncretism of the compositional and performing practice of the epochs of Johann Kunau, the Bach family, Domenico Scarlatti, Georg Friedrich Handel, Joseph Haydn, Muzio Clementi, Wolfgang Amadeus Mozart, Ludwig van Beethoven is argued.

Fundamental Analysis of Chick Corea’s Improvisation in Spain (1972)

"Modern jazz can be considered an equal part of modern music, owing to the numerous experiments, at times considered strange or not really agreed by the audience. When talking about modern musical life and the possibilities for making music in a proper manner, no doubt that the value and genius of composers like Wolfgang Amadeus Mozart or Ludwig van Beethoven must be recognized. However, one must also realize that modern life, with its modern, contemporary music is also needed. The great jazz saxophonist, Charlie Parker considered improvisation the middle of the earth, the place where, if only for a few brief moments, one can be the best and the greatest composer in the world. Furthermore, the idea of a song (theme) is the only reason for musicians to come and elaborate together, with variational spontaneity, a unique and maybe unrepeatable musical manifestation. The works of Chick Corea reflect this point of view, as the analysis of the work Spain (1972), discussed in the article bellow, will demonstrate. The work represents the fusion between Spanish music and the compositional methods of modern jazz music, reflecting Corea’s unique style. Improvisation lies at the basis of this composition, offering the musician a multitude of possibilities for expressing his ideas regarding freedom and human nature. Keywords: jazz, piano improvisation, spontaneity, creativity, harmonical knowledge, contemporary "

Becoming Clara Schumann: Performance Strategies and Aesthetics in the Culture of the Musical Canon by Alexander Stefaniak

Reviewed by: Becoming Clara Schumann: Performance Strategies and Aesthetics in the Culture of the Musical Canon by Alexander Stefaniak April L. Prince Becoming Clara Schumann: Performance Strategies and Aesthetics in the Culture of the Musical Canon. By Alexander Stefaniak. Bloomington: Indiana University Press, 2021. [xiii, 308 p. ISBN 9780253058294 (hard-cover), $75; ISBN 9780253058287 (paperback), $20; also available as e-book, ISBN and price vary.] Tables, music examples, endnotes, bibliography, index. Alexander Stefaniak opens his recent monograph with the always astonishing details of Clara Schumann’s musical life: over a thousand concerts performed across sixty years, international acclaim, collaborations with some of the most important musicians of her era, admiring critics, undeniable compositional prowess, and pedagogical acumen. By 1877, the fifty-eight-year-old was at the pinnacle of her career. That same year, the critic L. K. reflected on Schumann’s trajectory in an article for Leipzig’s Signale für die musikalische Welt. L. K. had first heard the performer in 1833. While her earlier performances relied on music that they considered “wild and chaotic,” Schumann’s concerts were now grounded in Johann Sebastian Bach, Ludwig van Beethoven, Robert Schumann, and Felix Mendelssohn-Bartholdy (p. 2). The critic celebrated these programmatic transformations: “The change between ‘Clara Wieck’ and ‘Clara Schumann’ signifies the marriage of the old virtuosity with the classical garb and Verseistigung [spiritualization] of the new” (p. 2). This “marriage” of sorts—between Clara Schumann and the Austro -German canon—guides Stefaniak over the course of his excellent new study. In the past several decades, Clara Schumann scholarship has evolved in exciting trajectories. Current studies show fresh, critical perspectives on all aspects of Schumann’s life. (See Joe Davies, “Introduction: Clara Schumann in the Musicological Imagination,” in Clara Schumann Studies, ed. Joe Davies [Cambridge: Cambridge University [End Page 233] Press, 2021], 1–12.) Stefaniak’s Becoming Clara Schumann situates itself firmly within this community. Engaging eloquently with wide-ranging scholarship, pluralistic primary source materials, concert touring strategies, and programming and compositional practices, Stefaniak offers a fascinating, holistic look into Clara Schumann’s canonical legacy. An important complement to his previous examination of Robert Schumann’s nineteenth-century virtuosities, this new monograph shifts to investigate how Clara Schumann similarly navigated the perils of empty virtuosity and authentic revelation by “inherently infus[ing] pianism with interiority” (p. 11). (See also Alexander Stefaniak, Schumann’s Virtuosity: Criticism, Composition, and Performance in Nineteenth-Century Germany [Bloomington: Indiana University Press, 2016].) Positioning Schumann as both a pragmatic “strategist” and a musical “idealist,” Stefaniak asks us to recognize how performers—perhaps even more so than composers—profoundly shaped canonic ideologies. To be sure, “Schumann invites us to view the canonic tradition not only as a body of musical works but as a dynamic, evolving reality in the everyday professional lives of performers” (p. 281). Organized largely chronologically, each chapter examines a distinct issue related to aspects of Schumann’s career and canonic status. Traversing from her earliest concertizing to her time as a professor in Frankfurt at Dr. Hoch’s Konservatorium, Stefaniak keeps several threads front and center: “canon formation, concepts of interiorit y, Schumann’s gendered public image, and the ways in which she and other performers exercised creative agency” (p. 15). In the first two chapters, Stefaniak examines Schumann’s early concert programming and her 1840s transformation into an authentic interpreter. While this period is sometimes positioned as antithetical to the development of the canonical ideal, Stefaniak guides the reader through compelling music analyses and argues that Weick’s showpieces by Frédéric Chopin, Adolf von Henselt, and Sigismond Thalberg shaped her approaches to resplendent virtuosity. Her strategies were undeniably successful, as relatively quickly “critics heard interiority in the very sound Clara Schumann produced at the piano, regardless of what repertoire she played” (p. 36). Greater attention to aesthetic debates grounds the second chapter, as Stefaniak focuses on the ways Schumann expanded and ratified this association to interiority. Undeniably, her marriage to Robert Schumann positioned her as a crucial part of a composer–interpreter partnership—a musical partnership that was quite calculated in its alignment with the practices of canonic formation. As Robert transformed his compositional approach to gain critical...

Some fascinating developments in mathematics and music

The strength of the bonds between music and mathematics goes without saying. This popular belief hides a subtler misconception, that this relationship involves old-school mathematics: arithmetics in the Greek School (Pythagoras), diophantine approximations in tuning theory (Euler, Rameau), Fourier series for the decomposition of sound signal, and little else. However, there is much more than that and these two sciences still advance hand in hand as of today. This paper will present by way of example three musical situations involving contemporary mathematical topics: Galois theory in a rhythmic canon problem in the field of minimalist music; a graph theory question raised by Ludwig van Beethoven which had to wait almost two centuries for an answer; and a neat word theory theorem discovered in a construction originating in combinations of mystical octaves and fifths in Plato’s Timaeus.

Some fascinating Developments in Mathematics and Music

The strength of the bonds between music and mathematics goes without saying. This popular belief hides a subtler misconception, that this relationship involves old school mathematics: arithmetics in the Greek School (Pythagoras), diophantine approximations in tuning theory (Euler, Rameau), Fourier series for the decomposi-tion of sound signal, and little else. However, there is much more than that and these two sciences still ad-vance hand in hand as of today. This paper will present by way of example three musical situations involving contemporary mathematical topics: Galois theory in a rhythmic canon problem in the field of minimalist mu-sic; a graph theory question raised by Ludwig van Beethoven which had to wait almost two centuries for an answer; and a neat word theory theorem discovered in a construction originating in combinations of mystical octaves and fifths in Plato’s Timaeus.

Analysis of the Similarities between the Third Movement of Beethoven: Piano Sonata "Passion"(OP.57) and the Third Movement of the Piano Concerto NO 5 "Emperors" (OP.73)

Ludwig van Beethoven (1770-1827) was a representative composer in the European classical period. His Piano Sonata "Passion" (OP.57) and Piano Concerto NO.5 "Emperor" (OP.73) are masterpieces in Beethoven's piano music literature. This article will explore the commonness of these two works, which were created in Beethoven's mature period, in terms of creative techniques, musical style, historical status, etc., and strive to deepen the understanding of Beethoven's piano works in his mature period.