Neo-Riemannian Analysis

Независимый исследователь, Российская Федерация, г. Москва. Аннотация В работе представлено доказательство гипотезы Римана в рамках теории хронометрической инвариантности (ТХИ)-расширения общей теории относительности, постулирующего существование динамического скалярного поля времени φ_t. Ключевым элементом является принцип локальной калибровочной инвариантности действия относительно преобразований φ_t → φ_t + C(x). Мы показываем, что данная симметрия влечет за собой унитарность оператора эволюции квантованных возмущений поля φ_t в пространстве Фридмана-Робертсона-Уокера. Спектр соответствующего самосопряженного хроно-гамильтониана Ĥ_HP оказывается дискретным и вещественным. Численное моделирование демонстрирует точное соответствие между собственными значениями E_n оператора Ĥ_HP и мнимыми частями t_n нетривиальных нулей дзета-функции Римана, описываемое соотношением E_n = t_n/(2π). Поскольку спектр самосопряженного оператора вещественен, величины t_n также являются вещественными, что и доказывает гипотезу Римана. Теория предсказывает наличие осцилляций в угловом спектре реликтового излучения на специфических мультипольных моментах ℓ_n ≈ k_n • η_0, что открывает путь для экспериментальной проверки данного подхода. Ключевые слова: гипотеза Римана, дзета-функция Римана, теория хронометрической инвариантности, квантовая теория поля в искривленном пространстве-времени, космологические возмущения, реликтовое излучение.

This article offers original listening strategies for two dimensions of bitonality featured in West Side Story, both implied (but not defined) in Bernstein's writings (1959, 1976): "simultaneous," or the vertical superimposition of clashing strata, and "successive," in which non-stratified tonal events generate tonally ambiguous environments, suggesting more than one key. Bernstein's compositional strategies align with the plot's trajectory: successive bitonality appears when the gangs stalk each other at a distance (centrally in "Prologue," "Dance at the Gym Blues," and "Maria"), with simultaneous bitonality capturing their fateful clash (centrally in "Quintet" and "Tonal Rumble"). Throughout, the analyses apply contemporary theories of tonal transformation (Kaminsky 2004, Rings 2011), scalar dissonance (Martins 2019), and harmonic "divorce" (Temperley 2007,Nobile 2015,De Clercq 2019), amongst others. Finally, I summarize that octatonicism in West Side Story is best contextualized as a processual byproduct of tonal relations, with the seeds sewn in "Prologue.

Essa sequência, aparentemente ingênua, revelou-se presente em inúmeros fenômenos naturais: no crescimento das conchas, na espiral das galáxias, na disposição das sementes de um girassol e até na proporção do corpo humano. A proporção áurea Quando dividimos um número da sequência pelo número imediatamente anterior, obtemos valores que se aproximam de 1,618..., conhecido como o número de ouro ou proporção áurea (φ). Essa proporção foi

The recapitulation in sonata form has a significant role: the crystallization of the primary tonal area through the transposition of the second half of the exposition in a way that it recapitulates in the initial tonality. This procedure is defined as sonata principle, while Hepokoski & Darcy in their sonata theory use the term tonal resolution. However, twentieth-century composers diverge from the use of tonality and harmonic functionality. In modern sonata form, there is not a primary tonal region, which has to return at the closure of the form. On the other side, the compositional structural plan is prioritized over the normative formal procedures and its completion coincides with the end of the form. Therefore, the following hypothesis arises: Should we still explore tonal resolution in modern sonata form recapitulation or the analysis should focus on the structural completion of the compositional plan, which also clarifies the dialogue of the modern composer with the traditional form?

The shift from tonal determinacy to atonality was a gradual process that occurred during the era of the fin de siècle and the first decade of the twentieth century. Often, the particular process embraced an interstitial period where the music integrates tonal with atonal pitch processes, tallying additional challenges to the analytical process.

The robust conventional (tonal) Formenlehre affords us with sufficient tools to negotiate formal structure, formal function, and formal rhetoric. Central to this theoretical stream are L. Meyer’s primary parameters: melody, rhythm, meter, and harmony.

On the other hand, the emancipation of music from its tonal obligations, animated rather unconventional approaches to formal function – composers were inclined to utilise Meyer’s secondary parameters to invoke formal functionality. Scholarly work has proposed a theoretical apparatus that engages secondary parameters to handle cognitive aspects of musical perception, particularly the perceptual boundaries of musical units – a notion essential to the shaping of form.

In the present paper, I consider aspects of form in Desir from Scriabin’s last tonal set, Opus 57. Scriabin invokes harmonic functions through chords borrowed from non-diatonic entities, generating an equivocal tonal environment. While the segmentation process seems to be a straightforward task, the discerning of formal function remains rather ambiguous. To overcome this ambiguity, I employ Howland’s IPSs, a set of form-probing phrase types founded on statistical parameters.

L’essai développe une vision profondément originale de la création, articulant mystique kabbalistique et géométrie riemannienne. Il propose une thèse radicale : la Création est une topologie sacrée, issue non d’un débordement mais d’un repli divin – le Tsimtsum. Ce retrait n’est pas absence, mais pleine condition de l’altérité. L’Infini (Ein Sof) se contracte pour faire émerger un espace fini, fermé mais sans bord : une variété compacte où les Sefirot dessinent les géodésiques de l’être.

La géométrie sacrée proposée repose sur les analogies suivantes :

Tehiru (le vide originel) devient un espace courbe, une sphère ontologique en creux.

Les Sefirot sont des points critiques de lumière, organisant un arbre des géodésiques, structure vivante de l’univers.

La rupture (Shevirat HaKelim) libère la complexité, comme une singularité gravitationnelle inversée.

L’histoire cosmique suit une topologie cyclique, semblable à une bande de Möbius sacrée.

Ce modèle géométrique s’étend à l’humain :

Le Tsimtsum intérieur fonde la conscience : le sujet se constitue par retrait, à l’image du divin.

La pensée suit les courbures de l’arbre séfirotique : Hokhma, Binah, Daat sont des fonctions de stabilisation mentale.

Le langage devient structure géométrique : les lettres sont des vecteurs, la grammaire une connexion affine.

Enfin, cette ontologie courbe renverse nos intuitions :

La limitation est fondatrice, non négative.

La fermeture est condition de la liberté.

L’Infini se révèle non par expansion mais par pliure, comme une lumière se condensant dans une sphère dansante.  L'infini plié L'énigme fondatrice des mystiques-l'enfantement du fini par l'Infini sans dissolutiontrouve dans la Kabbale lourianique sa résolution géométrique. Le Tsimtsoum (retrait divin) y sculpte un espace ontologiquement clos, tandis que les Sefirot en tracent les chemins essentiels. Notre thèse ose ce pas audacieux : la Création est une topologie sacrée, où l'Être se courbe en variété compacte. L'Infini (Ein Sof) ne se contracte point par défaillance, mais par surabondance logique : il engendre la limite comme condition de sa révélation.

The foundational enigma of mystics-how the finite is born from the Infinite without dissolution-finds its geometric resolution in Lurianic Kabbalah. The Tsimtsum (divine withdrawal) sculpts an ontologically closed space, while the Sefirot trace its essential paths. Our thesis dares this bold step: Creation is a sacred topology, where Being curves into a compact manifold. The Infinite (Ein Sof) contracts not from deficiency but from logical superabundance: it begets limitation as the condition of its revelation. The essay presents a deeply original vision of creation, fusing Kabbalistic mysticism with Riemannian geometry. Its core thesis is bold: Creation is a sacred topology, emerging not from divine overflow but from divine withdrawal – Tsimtsum. This retraction is not absence but the active condition of otherness. The Infinite (Ein Sof) contracts to produce a finite, boundaryless but closed space: a compact manifold where the Sefirot trace the geodesics of Being.
The proposed sacred geometry draws the following analogies:
• Tehiru (primordial void) is a curved ontological space, a hollow cosmic sphere.
• The Sefirot are critical light nodes, forming a tree of geodesics, a living skeleton of creation.
• The rupture (Shevirat HaKelim) unleashes complexity, like an inverted gravitational singularity.
• Cosmic history unfolds through a cyclical topology, akin to a sacred Möbius strip.
This geometric framework extends to human consciousness:
• The inner Tsimtsum grounds the ego: consciousness arises by withdrawal, mirroring the divine.
• Thought follows the curvatures of the sefirah-tree: Hokhma, Binah, Daat function as stabilizing cognitive nodes.
• Language becomes a geometric structure: letters are vectors, grammar an affine connection preserving meaning.
Ultimately, this curved ontology overturns classical assumptions:
• Limitation is foundational, not negation.
• Closure is the condition of freedom.
• The Infinite reveals itself not by expansion but by folding, like light condensed into a dancing sphere

Аннотация Мы строим компактный интегральный оператор K z на L 2 (0, ∞), доказываем det(1-K z) = ξ(s)/ξ(1-s), и далее через кластер-экспансию, Borel-сходимость и OS-reflection-positivity восстанавливаем самосопряжённый «Hilbert-Pólya»-оператор, чьи собственные значения соответствуют нулям Римановой дзета-функции, что влечёт ℜs = 1 2. Содержание 1 Оператор K z в L 2 (0, ∞) 1.1 Замыкание квадратичной формы и Friedrichs-продолжение. .. .. . .

Resumo: O presente estudo debruçou-se sobre o conceito de densidade-compressão, proposto por Wallace Berry (1987), com o objetivo de compreender seu comportamento em diferentes situações e apontar algumas propriedades relativas a ele. Esse trabalho se mostra como uma pesquisa teórica, descritiva e experimental, apresentando e discutindo os dados coletados, a fim de fornecer informações que possibilitem um aprofundamento acerca da compreensão do conceito em questão e que abram caminho para novas interpretações e aplicações teóricas.

We present a constructive proof of the Riemann Hypothesis based on the Hilbert-Pólya conjecture. By identifying a self-adjoint operator H, whose spectrum corresponds to the imaginary parts of the nontrivial zeros of the analytically continued Riemann zeta function ζ(s), we demonstrate that all nontrivial zeros lie on the critical line Re(s) = 1 2. The operator is realized through the framework of noncommutative geometry, utilizing the spectral triple (A, H, D) and the thermodynamical time flow on the adele class space. This approach aligns with Alain Connes' construction and provides a spectral interpretation consistent with both known numerical results and analytical properties of ζ(s). The proof concludes with a contradiction argument based on the functional equation and zero distribution statistics.

The lack of attention given to Schenkerian theory by empirical research in music is striking when compared to its status in music theory as a standard account of tonality. In this paper I advocate a different way of thinking of Schenkerian theory that can lead to empirically testable claims, and report on an experiment that shows how hypotheses derived from Schenker’s theories explain features of listener’s perception of key relationships. To be relevant to empirical research, Schenker’s theory must be treated as a collection of interrelated but independent theoretical claims rather than a comprehensive analytical method. These discrete theoretical claims can then lead to hypotheses that we can test through empirical methods. This makes it possible for Schenkerian theory improve our scientific understanding of how listeners understand tonal music. At the same time, it opens the possibility of challenging the usefulness of certain aspects of the theory. This paper exemplifies the emp...

Fork is a framework written in the SuperCollider programming language for algorithmically composing music to chess games in real time in a way that meaningfully conveys the progress of the game in a musically coherent manner. Fork is intended to serve as a dynamic, immersive soundtrack to app-based chess where the players have direct control over the resulting generation, thus turning chess itself into a musical endeavor alongside its normal gameplay. The principles behind Fork straddle the boundary between more traditional note structures and compositional use of uniquely electronic parameters such as timbre and spatialization in musically effective sonification of data.

• Genus: Directional or Progressive Tonality (colloquially: doesn't begin and end in the same key) ○ Species 1: Monotonal works with prolonged off-tonic openings ○ Species 2: "Genuine" non-monotonality. Question: what makes it "genuine"? • Gain practice following and closely reading music-analytical prose-here, prose that describes the global tonal structures of entire works / songs / movements / etc. • Gain practice transitioning between score and prose description, prose description and graphic analysis, and graphic analysis and score. • Gain practice evaluating music-analytical reasoning. I encourage you to read charitably-you should attribute to music analysts the most reasonable and musically astute positions that are compatible with what they've written-but with a healthy amount of skepticism. It's okay to not buy what they're selling, so long as you are prepared to offer reasons for your resistance. • Reflect on how score-study, listening, and performing (not just reading words on the page) can (or must) inform our judgments about the cogency, persuasiveness, compellingness (etc.) of the reasoning. • Gain practice following the dialectical back-and-forth between music analysts who criticize one another's analytical readings. • Pose and attempt to answer the question: What is at stake? Why might it matter, for performing / teaching / composing / etc. whether, for instance, a work is designated as monotonal or non-monotonal? What is the "cash value" of answering that question one way or the other? • Consider the issue of textual motivation for large-scale (non-standard) compositional design. • Deepen our appreciation of some truly lovely chromaticism in Schubert (and to a lesser extent in Beethoven).

Musical Renovism is a theoretical framework that explores the revival and evolution of musical styles by drawing inspiration from different eras and adapting them into something new and distinct. This concept emphasizes the non-linear progression of music history and encourages artists to creatively reinterpret and evolve past styles.

In Music, the concept of Brightness has progressively become a topic of heated debate. According to several authors, when a significant number of Modes is involved in a comparison, it is not possible to exactly establish a brightness hierarchy devoid of inconsistencies and ambiguities. A method to solve the problem is proposed in this paper. Firstly, in order to avoid counter-intuitive solutions, the Brightness of all the Seventh Chords is determined; subsequently, by resorting to a Reference Scale arising from the Overtone Series, all the inconsistencies (e. g. occurrence of Modes yielding the same Absolute Brightness) are removed.

Sampaio Bruno (1857-1915), filósofo e escritor português propôs, no início do século vinte, um sistema de afinação musical heterodoxo que divide a oitava em catorze partes. O sistema é apresentado no opúsculo Théorie exacte et notation finale de la musique e, para o testar, pelo menos um instrumento musical terá sido construído. Esta proposta de divisão da oitava apresenta idiossincrasias distintivas. Aspirando sobretudo a proporcionar alguma luz sobre tais particularidades, o presente artigo aborda três tópicos. Primeiro, expõe alguma investigação associada à busca e compilação de documentação sobre o assunto, assim como do instrumento referido. Segundo, aspira a promover o estudo da proposta de Bruno em si mesma sob uma perspetiva da teoria musical. Finalmente, é realizado um esforço de compreensão de possíveis implicações filosóficas desta teoria, num espírito de sugestão de caminhos, quem sabe úteis a um espectro disciplinar mais amplo.

The document provides an in-depth analysis of J. N. Hummels "Allegro in C Major," using various techniques to reveal its musical structure. Key methods include examining phrase structure and harmonic functions, identifying and tracking motives, analyzing melodic and harmonic intervals, and exploring voice range (ambitus). The analysis highlights the use of rhythmic patterns, scale degrees, and sequences to understand thematic development and harmonic transitions. A special visualization technique is used to explain the harmonic layout of the piece. This detailed approach reveals the compositional techniques Hummel employed, characteristic of the Classical period, and enhances the understanding of the piece's overall musical texture and form.

This article examines how the Tonnetz, widely considered the emblematic diagram of “Western” music theory, emerged in its modern form from a global network of scholars spanning Japan, Germany, and India. Part one consists of four microhistories of transnational connection. The first two focus on Tanaka Shōhei’s 1890 presentation of the Tonnetz as representative of a “mutually civilizing” discourse between Germany and Japan, and Hugo Riemann’s adaptations of Tanaka’s diagram in re-centering Germany’s musicological status. The second two focus on G. S. Khare’s use of the Tonnetz in 1918 to bolster claims of Indian “priority” in the development of tonality, and the influence of Khare’s associates on Tanaka’s later efforts to bolster a Pan-Asianist narrative that cast Japan as the last bastion of an uncolonized Asian spirit. Part two applies a macrohistorical lens in analyzing how these Tonnetze played a constitutive role in the development of musical modernity, which I interpret as an emergent phenomenon of global processes of integration by building on the work of Sebastian Conrad and Sanjay Subrahmanyam. Each of these Tonnetze is thus a “global Tonnetz,” stemming from the drive of each nation to participate in the construction of musical modernity on a global stage. I conclude by acknowledging tensions between my histories of connection and integration, as the former traces threads of causality while the latter embraces emergence. I nevertheless argue in favor of a framework of historical duality that can hold both approaches simultaneously when dealing with global phenomena.

Full version available at UC Press: https://online.ucpress.edu/jams/issue/77/2

Doctor of Philosophy (Music), May 2019, 139 pp., 50 figures, bibliography, 60 titles. Gustav Mahler's Seventh Symphony seems to belie traditional notions of symphonic unity in that it progresses from E minor in the first movement to C major in the Finale. The repertoire of eighteenth and nineteenth century composers such as Haydn, Beethoven, and Brahms indicates that tonal holism is a significant factor for the symphonic genre. In order to reconcile Mahler's adventurous key scheme, this dissertation explores a multidimensional harmonic model that expands upon other concepts like Robert Bailey's double-tonic complex and transformation theory. A multidimensional musical object is a nexus of several interconnected chords that occupy the same functional space (tonic, dominant, or subdominant) and can be integrated into a Schenkerian reading. Mahler's Seventh is governed by a threedimensional tonic object that encompasses the major and minor versions of C, E, and A-flat and the augmented triad that is formed between them. The nature of this multidimensional harmony allows unusual formal procedures to unfold, most notably in the first movement's sonata form. To navigate this particular sonata design, I have incorporated my own analytical terminology, the identity narrative, to track the background harmonic events. The location of these events (identity schism, identity crisis, and identity reclamation) is critical to the entire structure of the Seventh.

In this paper, we attempt to explore mathematical structures of tonal music from the 18th and 19th centuries. We review the known mathematical/musical structures and, noting lacking features of this geometrical construct as a useful model of tonal harmony, we propose generalizations that may be better suited to tonal music. We bring several mathematical devices to bear on the Tonnetz (or Tone Network) in new ways, including Cayley graphs and Coxeter hyperbolic representations. We conclude with three-dimensional geometric models that represent the four-note seventh chords which are ubiquitous in 18th and 19th century music.

A revised version of a paper delivered at the 2006 International Conference on Music Theory in Tallinn, Estonia, and published in the 2008 proceedings of that conference. The revisions in this reading text amount to updating the chordal/analytical notation, as well as correcting some typos.

The document provides an in-depth analysis of D. G. Türk's "Allegro in A Minor," using various techniques to dissect its musical structure. Key methods include examining phrase structure and harmonic functions, identifying and tracking motives, analyzing melodic and harmonic intervals, and exploring voice range (ambitus). The analysis highlights the use of syncopation, rhythmic patterns, scale degrees, and intervals to understand thematic development and harmonic transitions. A special visualization technique is used to explain the harmonic layout of the piece. This detailed approach reveals the intricate compositional techniques Türk employed, characteristic of the early Classical period, and enhances the understanding of the piece's overall musical texture and form.

In a brief but perspicacious study of Mennin\u27 s music in 1954, Walter Hendl describes the composer as a consummate craftsman who devotes great attention to the organization of materials. Although Hendl may not have known Canzona, which had been premiered in 1951 but not published until the year of his essay, the author\u27s statement could well have been written with Mennin\u27s sole piece for band specifically in mind. Not only is every aspect of Canzona integrally related to every other, but the relationships are deployed with a remarkable economy of means

The problem of finding the zeros of functions is one of the important issues in mathematics, and I would not be exaggerating if I said that all of mathematics is based on such problems. Here, curiosity struck me to understand the mechanism or the secret behind these functions. I never expected that this curiosity would lead me to encounter an important function like the Riemann zeta function, starting from the Taylor and Maclaurin series, which at least enabled me to find a function that links the point belonging to a certain domain and the values of this domain with an exponential function, as demonstrated in the proof.

A mind is like a parachute. It only works if it is open. [1] I am grateful to Roger Wibberley and other correspondents following his article in MTO (1) for airing some important questions and providing me with an incentive for this reply. I do plan eventually to produce a more fully revised and corrected expansion of the thesis I set out in "Diatonic ficta" (henceforth DF), (2) incorporating replies to Karol Berger and Peter Urquhart, but this may serve as a partial, interim statement. (3) [2] Cristle Collins Judd began her posting of July 23 to mto-talk ("Wibberley, MTO 2.5," mto-talk 23 July 1996) by addressing not so much Wibberley's solution but his modal premises. In order to restore premises rather than symptoms to the centre of the discussion, I shall first set the Josquin aside. Since some readers may not be familiar with DF and the context in which I used that example, and since none will be able to infer it correctly from Wibberley's article, it might be helpful if I now restate and amplify some parts (only) of the thesis particularly germane to this discussion, and take this opportunity to adjust some areas where my presentation may have proved incomplete or too elliptical. [3] Since I invoke counterpoint so strongly, I had better explain the specific sense in which I use the term. Counterpoint, as defined in DF from Tinctoris and earlier theorists, is concerned not with lines or vague general attributes but with two-voice progressions-what we might call two-part or dyadic harmony. (4) At least up to the late 15th century, the handling of more than two parts was treated by theorists as an extension of those dyadic principles. It is in respecting and reconciling melodic principles and the rules of counterpoint that ficta is necessitated; I have tried to show that ficta needs to be viewed in the context of counterpoint as a whole, and not informed just by precepts specifically labelled as ficta. The list discussion has

's songs have been undeservedly neglected, it is likely because they are in various respects inconsistent in relation to those of other nineteenth-century Lieder composers. 1 Among their technical challenges are wide vocal ranges, extreme dynamic contrasts, and in some cases sheer length; and interpretively, many of the songs present further challenges in the form of chromaticism, enharmonic changes, frequent shifts of tonal focus, and tonal ambiguity. Attempts to comprehend the songs as a body of work can be frustrated by the fact that there are not only different settings of some of the texts, but also different versions of the same setting. 2 The nature of the text, or style of presentation, makes some of the songs seem unwieldy, and a number of the later works are not really songs at all, but rather accompanied recitations. The apparent inconsistencies in Liszt's Lieder derive largely from the composer's penchant for experimentation, which also characterizes his compositions in other genres, as well as his contributions to the field of piano technique and performance. Always inventive and

O estudo tem como objetivo utilizar três métodos de avaliação de similaridades desenvolvidos na psicologia cognitiva na classificação das distâncias e agrupamentos dos acordes diatônicos nas tonalidades maior e menor, levando em consideração as quatro escalas tonais (Jônio,Eólio, Menor Harmônica e Menor Melódica), das vinte e quatro tonalidades, também levando em consideração as quatro escalas tonais, das quarenta e oito séries do Concerto para Violino de Alban Berg e de alguns conjuntos representantes de escalas na teoria musical. Os métodos empregados são: o Modelo de Contraste, que pondera as características comuns e distintas entre os objetos  comparados  (Tversky  1977);  o Alinhamento  Estrutural,  que  classifica  as  similaridades  através  da distinção  entre  dois  tipos  de  diferenças  e  dois  tipos  de  comunalidades  (Gentner;  Markman  1995,  1997; Goldstone 1994; Markman; Gentner 1990, 1993a, 1993b, 1993c, 1996); e a Transformação, que avalia as similaridades através do número de operações necessárias para transformar um objeto em outro (Chater; Hahn 1997; Hahn; Chater; Richardson 2003; Hahn; Richardson; Chater 2001).

the following conditions will be observed: 1. To comply with s56 of the Copyright Act 1994 [NZ], this thesis copy must only be used for the purposes of research or private study. 2. The author's permission must be obtained before any material in the thesis is reproduced, unless such reproduction falls within the fair dealing guidelines of the Copyright Act 1994. Due acknowledgement must be made to the author in any citation. 3. No further copies may be made without the permission of the Librarian of the University of

Introduction 'Strict counterpoint' and 'Palestrina style' are interchangeable terms in current usage. In Bulgarian theory the adjectives 'strict' and 'Palestrinian' are often combined. In the old terminology there are two aspectsla Musica communa (defined by Dimitar Hristov as generally accessible music, 1 according to Neva Krysteva it is a connected style 2) and la Musica reservata (for narrow specialists, elite music-Dimitar Hristov's translation); in Russian terminology the term is строгий стиль, строгое письмо, the German equivalent is Die klassische Vokalpolyphonie, Der strenger Satz, the reciprocal Latin term is stylus a capella ecclesiasticus. 3 We can see different characteristics in distinguishing stylistic features-'classic vocal polyphony,' 'strict composition,' 'vocal church style' and so forth. But these nuances in defining the content are always associated with the creative work of Palestrina. Is it possible for one person to generalize a whole epoch? There is a similar issue with Bach's free style for example, and the answer will inevitably be positive if we follow the analogous link between the name of the most eminent representative of the era and a summarized comprehension of style based on defined compositional techniques. In general, the confirmation of the Palestrina style as 'strict' means that it observes clearly established rules. This first attempt to establish a definition, however, immediately provokes repudiation because the 'clearness' of the techniques in historical and geographical context cannot be guaranteed. There is always a prehistory; a stylistic analogy always exists. We could acknowledge these techniques (at that only relatively) which have comprehensive etymological roots. In this particular case, however, there is no theory of the style by

Attention is drawn to the need for controlling (during encoding) and checking (after encoding) the quality or accuracy of musical data. Some large databases of melodies are now becoming available, and methods of control and checking are presented which are specially suited to these. Two applications are discussed in detail: to Gregorian Chant and to German folksong. An effective method in tonal and modal music is found to be the investigation of~'nelodic progressions which remain unusual even after amalgamation by transposition to a central register.

Attention is drawn to the need for controlling (during encoding) and checking (after encoding) the quality or accuracy of musical data. Some large databases of melodies are now becoming available, and methods of control and checking are presented which are specially suited to these. Two applications are discussed in detail: to Gregorian Chant and to German folksong. An effective method in tonal and modal music is found to be the investigation of~'nelodic progressions which remain unusual even after amalgamation by transposition to a central register.

Este artigo aborda a aplicação da teoria pós-tonal na composição musical, com foco nas classes de conjuntos de classes de notas e nas técnicas de concatenação. O objetivo principal deste estudo é demonstrar como essas abordagens podem ser utilizadas para criar obras coerentes e fluidas, integrando diferentes trechos musicais. A fundamentação teórica deste trabalho baseia-se nas contribuições de autores, como Straus (2013) e Pitombeira (2022). A teoria pós-tonal é apresentada como uma abordagem que utiliza fundamentalmente as classes de conjuntos de classes de notas para criar estruturas melódicas e harmônicas, proporcionando uma intensa coerência interna. A técnica de concatenação é destacada como um processo que envolve uma análise minuciosa das características individuais de cada trecho musical, visando compreender suas similaridades e diferenças, para efetuar a concatenação de forma adequada. Através de um estudo de caso da obra intitulada Buracos, destinada a um quarteto de clarinetes, foram aplicadas as técnicas de concatenação e utilizadas classes de conjuntos de classes de notas para criar ligações melódicas e harmônicas entre os trechos musicais. Os resultados obtidos demonstraram que a utilização dessas abordagens contribuiu para a criação de uma obra coerente e fluída, integrando harmoniosamente os diferentes trechos apresentados. A utilização dessas ferramentas de concatenação proporcionou uma sensação de direção e coesão na música, permitindo ao compositor criar uma narrativa musical envolvente. Este estudo contribui para o enriquecimento do campo da composição pós-tonal, oferecendo ideias e possibilidades criativas para compositores interessados nessa abordagem. Palavras-chave. Teoria pós-tonal, Classes de conjuntos, Planejamento composicional, Ferramentas de concatenação.

The idea that music embodies meaning is largely accepted and uncontroversial. However, the way in which this relationship is articulated is complicated and contributes to music’s ability to project different meanings, especially according to time and place. Such is the case with the British composer Ralph Vaughan Williams’s romance for violin and orchestra, The Lark Ascending (1920). This work contains both musical and extra musical traits that can be interpreted as pastoral and nostalgic. Understanding how these meanings interact through time provides the opportunity for reinterpretation of the work in the present through an environmentally-oriented framework. Previous research regarding The Lark Ascending has specifically focused on aspects such as the work in response to the First World War as well as potential symbolic relationships with George Meredith’s eponymous 1881 poem. The present study establishes The Lark Ascending as a quintessential pastoral work by virtue of its musical content. By considering the circumstances of the work’s creation as well as its subsequent reception, these pastoral traits are then reinterpreted as an expression of nostalgia. This understanding of the work’s nostalgia underpins a new environmentally-oriented reading, one where a contemporary audience is asked to reflect on the emotional or existential distress caused by ecological loss and disruption, and the piece is heard as an elegy for environmental loss and impossible futures.

The idea that music embodies meaning is largely accepted and uncontroversial. However, the way in which this relationship is articulated is complicated and contributes to music’s ability to project different meanings, especially according to time and place. Such is the case with the British composer Ralph Vaughan Williams’s romance for violin and orchestra, The Lark Ascending (1920). This work contains both musical and extra musical traits that can be interpreted as pastoral and nostalgic. Understanding how these meanings interact through time provides the opportunity for reinterpretation of the work in the present through an environmentally-oriented framework. Previous research regarding The Lark Ascending has specifically focused on aspects such as the work in response to the First World War as well as potential symbolic relationships with George Meredith’s eponymous 1881 poem. The present study establishes The Lark Ascending as a quintessential pastoral work by virtue of its musi...

This paper outlines two preliminary studies researching the characterisation of composer style using features automatically extracted from symbolic data, our initial results, and future objectives. Our main research question is whether is it possible to systematically encode musictheoretic constructs in a computational framework in order to yield musicological insights regarding style characteristics and compositional techniques. Our long term goal is to train a computer to be able to make high-level inferences concerning musical style, historical context, genre, composer, and creative influences.

Este artigo visa apresentar alguns procedimentos relevantes de simetrias e voice leadings dentro da linguagem harmônica do compositor brasileiro Moacir Santos, a partir da peça Coisa no.3. Trata-se de uma das obras integrantes do disco Coisas (1965), estreia fonográfica de Moacir que definiria consideravelmente seu estilo e seus processos criativos. De forma geral, o disco se baseia em materiais melódicos e variações motívicas notadamente simples, instrumentação próxima ao estilo cool jazz, presença marcante de percussão afrobrasileira, capacidade de contenção e variação no uso dos recursos orquestrais, além de uma harmonia que oscila entre trechos tonais, modais e pós-tonais. Dentro do álbum, contudo, a exatidão no tratamento de diversos elementos revela uma dimensão ampla de conteúdo musical manipulada por seu autor. É nesse sentido que Coisa no.3 traz um exemplo emblemático de como detalhes específicos de simetrias e voice leadings contribuem para dar sentido ao discurso artístico, conferindo-lhe alto nível de minúcia por trás da superfície econômica.

Este artigo investiga os procedimentos criativos do compositor brasileiro Moacir Santos em Coisa n.2, uma composição de seu álbum Coisas de 1965. Sendo um músico que combinava sua experiência no universo popular com o estudo do repertório erudito, Santos foi um destacado criador no cenário da música brasileira dos anos 1960. Seu estilo mescla elementos de estilos populares, jazz, percussão africana e influências clássicas. Aqui nós enfocamos em sua linguagem harmônica, aplicando ferramentas de análise neorriemanniana e teoria dos conjuntos, buscando demonstrar como os processos harmônicos do artista o situam no universo pós-tonal da música do século XX.

Este artigo investiga os procedimentos criativos do compositor brasileiro Moacir Santos em Coisa n.2, uma composição de seu álbum Coisas de 1965. Sendo um músico que combinava sua experiência no universo popular com o estudo do repertório erudito, Santos foi um destacado criador no cenário da música brasileira dos anos 1960. Seu estilo mescla elementos de estilos populares, jazz, percussão africana e influências clássicas. Aqui nós enfocamos em sua linguagem harmônica, aplicando ferramentas de análise neorriemanniana e teoria dos conjuntos, buscando demonstrar como os processos harmônicos do artista o situam no universo pós-tonal da música do século XX.

This paper intends to construct some reflections on how the use of the poetic text as process of creation of a musical composition can be developed through the rhythmic, sonorous and melodic use of the words, verses and their (possible) musical meaning. Specifically, we use the example of the choral piece Motet em Ré Menor (1966), by the Brazilian composer Gilberto Mendes (1922-2017), a composition based on the concrete poem Beba Coca-Cola (1958) by Décio Pignatari (1927-2012). Some of the problems and issues related to the processes of narrativity and intertextuality, topical meaning and tropification – from the idea of musicking this poem – will be listed and approached in a reflection based on a musical analysis that seeks to depart from the form to the musical meaning relevance.

Structural framing is the reference to initial material at the end of a formal unit; this formal unit might be a theme, section, movement or even a multi-movement work. Structural framing is a special kind of thematic restatement that is fundamentally distinct from recapitulation or apotheosis. Whereas a recapitulation associates the beginning of one section with the beginning of another section, a structural frame associates the beginning of one section with its end. 1 Thus a recapitulation is a re-beginning, an apotheosis is a triumphant arrival, and a structural frame is a closing gesture-a parting 'adieu' that assists the listener in the conceptual encompassment of a formal unit. One occasionally encounters references to 'framing' techniques in the analytical literature. Given their popularity it is surprising to find that no studies focus on framing itself, or address the subtle differences between frames and other types of thematic recurrence. William Rothstein, James Hepokoski and Marianne Kielian-Gilbert are three scholars who invoke the notion of framing. 2 Rothstein, in a chapter on Mendelssohn's Songs Without Words, describes a 'framing device' that is 'obviously meant to invoke an accompanimental prelude and postlude to an actual song' (p. 202). Hepokoski posits an 'introduction-coda frame' as the second of five types of 'deformational procedures' shared by nineteenth-century symphonic modernists. According to him, this procedure 'gives the effect of subordinating "sonata-activity" to the overriding contents of This paper is a modification of 'Structural Framing, Recapitulation, and Mendelssohn's

The main goal of this essay is to analyze Rola Mundo based upon the Pitch-Class Set Theory, providing significant theoretical and perceptive references to the performance. In addition, it shows how the composer uses sets, sub-sets, texture, articulation, dynamics, rhythm, and melody to depict inherent aspects of the text and reveal the poet’s world in its continuous transformation.