Beethoven's early sonatas have already revealed a complex and varied technique that can present significant difficulties for intermediate piano students. In particular, the absence of systematic methodological guidance, as well as the lack of suitable and high-quality repertoire, can result in students struggling to learn Beethoven's piano technique and not being satisfied with the results. By examining and analyzing the theories of great educators, pedagogues, and performers, some of the standard technical patterns are identified and methods of mastering them are summarized. A sampling of related late-elementary level and intermediate level repertoire is identified, providing study material for students starting to learn the Beethoven sonatas, and serving as a guide for their teachers.

For many piano teachers, developing proficient reading skills in their young beginner students is one of the important aspects of weekly lessons yet it can also be one of the most frustrating tasks to undertake. To assist in this process, teachers look to method books to provide structure and an approach to music reading. Two reading approaches are prevalent in the current marketplace and widely used by teachers; the mixed intervallic approach and the middle C approach. The mixed intervallic approach, which stresses reading by interval, pattern and direction, is favoured and endorsed by current pedagogy and is adopted by many method books. This study compared the reading skills of young beginner piano students (ages 7-11) using either the mixed intervallic approach or the middle C approach to see which approach produced more reliable reading skills. Participants performed several music reading tasks to test keyboard identification (verbal), note identification in treble and bass clef (verbal), single note identification in C and G position (playing), broken and solid intervals in C and G position (playing), 3 note patterns and non-patterns in C and G position (playing), and sight reading. I hypothesized that the middle C students would perform better at single note identification while the mixed intervallic students would perform better in interval recognition, pattern recognition and sight reading. The results showed that the middle C students outperformed the mixed intervallic students in all tests except for keyboard identification and 3 note patterns in G position. These findings are surprising as they may indicate that the middle C approach, which is often criticized, is generating reliable reading skills among beginner piano students.

This research aims to trace the influence of McCoy Tyner's style of "intervallic improvisation" on Chick Corea and Kenny Kirkland, as evident in both later pianists' use of triad shapes and patterns based on pentatonic and octatonic scales. While the languages of Chick Corea and Kenny Kirkland were influenced by Tyner, they each subsequently established different harmonic structures and rhythmic devices. Therefore, I describe the stylistic similarity of pentatonic cells based on an intervallic approach to improvisation from one generation to the next with Tyner's improvisational vocabulary found in Kenny Kirkland and Chick Corea. Then, I demonstrate its modernization with octatonic patterns and triad pairs in the jazz tradition via a comparison of the improvisational tendencies of Kirkland and Corea.

A map of connections between musical features and musical expression have been much sought-after. Unveiling a system behind the musical expression humans achieve and perceive intuitively could benefit a range of human activities including musical composition, therapy, and computer science. The present study featured an experiment in which 50 participants rated the expression of valence on a 9-point scale after listening to 10 music samples. The only difference between the samples was the pitch of one note (occurring at various times, octaves and instruments). Each condition featured the note as forming a different interval in regard to the tonic (the first scale degree, and the tonal focal point). The intervals were: minor second, major second, minor third, major third, augmented fourth (the tritone), perfect fifth, minor sixth, major sixth, minor seventh and major seventh. Participants also rated their musical sophistication by answering the 40 questions of the Gold-MSI self-report inventory and a resulting index variable ranging from 40 to 120 was obtained. Statistically significant finds were made and a pattern emerged where minor/augmented intervals code for negative valence and major/perfect intervals code for positive valence. The expression of the minor and major sevenths appeared neutral, but results lacked statistical significance. The musical sophistication of participant was associated with the ability to perceive musical expression of affect. Finally, the term intervallic semiosis was proposed as a designation for the explained functionality of valence coding.

Der Beitrag geht Beschreibungen von Situationen, insbesondere Modulationen, in der theoretischen Literatur des 18. und 19. Jahrhunderts nach, in denen rein intervallische Muster wie chromatische Linien oder symmetrisch divergierende oder konvergierende chromatische Linien als unterstützend oder kollidierend mit standardisierten Kadenzmodellen angesehen werden. / The paper pursues descriptions in the theoretical literature of the 18th and 19th centuries of situations, particularly modulations, where purely intervallic patterns such as chromatic lines or symmetrically diverging or converging chromatic lines, are seen to support, or collide with standardised cadential models.

Selecionamos para análise nesta dissertação os Choros nº4 (1926) e Choros nº7 (1924), obras de câmara compostas por Heitor Villa-Lobos (1887-1959) no período em que o compositor demonstrou grande interesse pela estética modernista que hoje chamamos \"pós-tonal\". Villa-Lobos mesclou em seus Choros - bem como em grande parte de sua obra - elementos do modernismo europeu com outros oriundos da cultura popular brasileira, neste caso em particular o choro urbano carioca das primeiras décadas do século XX. Em síntese, a linguagem utilizada por Villa-Lobos nos dois Choros se aproxima muito da técnica de composição \"em camadas\" recorrente em obras de Stravinsky como A Sagração da Primavera (1913), Petrushka (1911) e O pássaro de fogo (1910). Villa-Lobos utiliza a interação entre materiais harmônicos independentes (estruturas simples geradas individualmente e calcadas em escalas tradicionais não gerenciadas pela tonalidade herdada do classicismo). Em muitos momentos esses materiais escalares estão empilhados formando grandes conjuntos (supercoleções) com oito, nove, dez, onze classes de altura e até o conjunto cromático completo, relacionados por invariâncias entre essas estruturas. Em outras ocasiões esses complexos harmônicos aparecem justapostos, relacionados por transformação intervalar gradativa, operados em torno de classes de altura invariantes e movimentos discretos entre as remanescentes não comuns (prioritariamente por movimentos de tons e semitons), procedimento chamado pelos teóricos da vertente \"neo-Riemanniana\" (como Richard Cohn, Jack Douthett e Peter Steinbach, entre outros) como \"parcimônia\". Notamos também que Villa-Lobos com frequência relaciona essas camadas estratificadas por disposições intervalares simétricas, gerenciando os conjuntos de classes de altura que compõem as partes ou a totalidade harmônica em torno de eixos de simetrias invariantes (reflexão). Notamos ainda invariâncias frequentemente reiteradas em ostinato (simetria por translação), enquanto que variantes remanescentes surgem e desaparecem como segmentos de coleções em outras camadas ao longo do trecho conduzido pelo ostinato, completando a totalidade harmônica por justaposição. A partir desse diagnóstico preliminar, elegemos nesta pesquisa duas correntes analíticas distintas e concomitantes: a simetria intervalar (reflexão e translação) a partir de estudos sobre Teoria dos Conjuntos desenvolvidos essencialmente nos textos de Joseph Straus e João Pedro Oliveira; e a transformação intervalar atuando como regente na relação entre coleções dispostas em rede e na construção de grandes complexos harmônicos (supercoleções), aproximando nossa pesquisa de estudos neo-Riemannianos sobre redes de coleções e parcimônia, em especial os trabalhos desenvolvidos por Dmitri Tymoczko, Richard Cohn, Jack Douthett e Peter Steinbach. / Selected for analysis in this dissertation the Choros No.4 (1926) and Choros No.7 (1924), chamber works for the period of the 1920s, at which time the composer has shown great interest in a tilted to a high content of post- tonal modernist aesthetic harmonic complexity concatenated surface exposure of arguments coming from the Brazilian popular culture, in this particular case referencing the urban carioca choro from the first decades of the twentieth century. In summary, the language used by Villa-Lobos in the two Choros is closely to the composition technique in \'layers\' applied in works such as Stravinsky\'s Rite of Spring (1913), Petrushka (1911) and The Firebird (1910). Villa-Lobos uses the interaction between independent harmonic materials (simple structures generated individually with traditional scales not managed by the tonality inherited of classicism). In many instances these scales are stacked forming large sets (supersets) with eight, nine, ten, eleven pitch-classes or the complete chromatic; structures related by invariances. At other times these harmonic complexes appear juxtaposed, related by gradual intervallic transformations, operated around invariants pitch-class sets and discrete movements between remaining pitch-classes not common (primarily by movements of tones and semitones), a procedure called by the theorists of the \'neo-Riemannian\' (as Richard Cohn, Jack Douthett & Peter Steinbach and others) as \'parsimony\'. We also noticed that Villa-Lobos often relates these stratified layers by symmetrical intervallic arrangements, managing pitch-class sets that make up the parts or whole harmonic around axes of symmetry invariants (reflection). We also noted invariances often repeated on ostinato (translational symmetry), while remnants variants arise and disappear as segments of scales into different layers along the stretch led by ostinato, completing the entirety harmonious by juxtaposition. From this preliminary diagnosis, we choose in this research two distinct and concurrent analytical currents: the intervallic symmetry (invertional and translational) from studies on Pitch-Class Set Theory developed mainly in the writings of Joseph Straus and João Pedro Oliveira; and the intervallic transformation working as conductor in the relationship between scales arranged in network and in building of large harmonics sets (supersets), approaching our research to neo-Riemannian studies about scale networks and parsimony, in particular the texts by Dmitri Tymoczko, Richard Cohn, Jack Douthett & Peter Steinbach.

Selecionamos para análise nesta dissertação os Choros nº4 (1926) e Choros nº7 (1924), obras de câmara compostas por Heitor Villa-Lobos (1887-1959) no período em que o compositor demonstrou grande interesse pela estética modernista que hoje chamamos \"pós-tonal\". Villa-Lobos mesclou em seus Choros - bem como em grande parte de sua obra - elementos do modernismo europeu com outros oriundos da cultura popular brasileira, neste caso em particular o choro urbano carioca das primeiras décadas do século XX. Em síntese, a linguagem utilizada por Villa-Lobos nos dois Choros se aproxima muito da técnica de composição \"em camadas\" recorrente em obras de Stravinsky como A Sagração da Primavera (1913), Petrushka (1911) e O pássaro de fogo (1910). Villa-Lobos utiliza a interação entre materiais harmônicos independentes (estruturas simples geradas individualmente e calcadas em escalas tradicionais não gerenciadas pela tonalidade herdada do classicismo). Em muitos momentos esses materiais escalares estão empilhados formando grandes conjuntos (supercoleções) com oito, nove, dez, onze classes de altura e até o conjunto cromático completo, relacionados por invariâncias entre essas estruturas. Em outras ocasiões esses complexos harmônicos aparecem justapostos, relacionados por transformação intervalar gradativa, operados em torno de classes de altura invariantes e movimentos discretos entre as remanescentes não comuns (prioritariamente por movimentos de tons e semitons), procedimento chamado pelos teóricos da vertente \"neo-Riemanniana\" (como Richard Cohn, Jack Douthett e Peter Steinbach, entre outros) como \"parcimônia\". Notamos também que Villa-Lobos com frequência relaciona essas camadas estratificadas por disposições intervalares simétricas, gerenciando os conjuntos de classes de altura que compõem as partes ou a totalidade harmônica em torno de eixos de simetrias invariantes (reflexão). Notamos ainda invariâncias frequentemente reiteradas em ostinato (simetria por translação), enquanto que variantes remanescentes surgem e desaparecem como segmentos de coleções em outras camadas ao longo do trecho conduzido pelo ostinato, completando a totalidade harmônica por justaposição. A partir desse diagnóstico preliminar, elegemos nesta pesquisa duas correntes analíticas distintas e concomitantes: a simetria intervalar (reflexão e translação) a partir de estudos sobre Teoria dos Conjuntos desenvolvidos essencialmente nos textos de Joseph Straus e João Pedro Oliveira; e a transformação intervalar atuando como regente na relação entre coleções dispostas em rede e na construção de grandes complexos harmônicos (supercoleções), aproximando nossa pesquisa de estudos neo-Riemannianos sobre redes de coleções e parcimônia, em especial os trabalhos desenvolvidos por Dmitri Tymoczko, Richard Cohn, Jack Douthett e Peter Steinbach. / Selected for analysis in this dissertation the Choros No.4 (1926) and Choros No.7 (1924), chamber works for the period of the 1920s, at which time the composer has shown great interest in a tilted to a high content of post- tonal modernist aesthetic harmonic complexity concatenated surface exposure of arguments coming from the Brazilian popular culture, in this particular case referencing the urban carioca choro from the first decades of the twentieth century. In summary, the language used by Villa-Lobos in the two Choros is closely to the composition technique in \'layers\' applied in works such as Stravinsky\'s Rite of Spring (1913), Petrushka (1911) and The Firebird (1910). Villa-Lobos uses the interaction between independent harmonic materials (simple structures generated individually with traditional scales not managed by the tonality inherited of classicism). In many instances these scales are stacked forming large sets (supersets) with eight, nine, ten, eleven pitch-classes or the complete chromatic; structures related by invariances. At other times these harmonic complexes appear juxtaposed, related by gradual intervallic transformations, operated around invariants pitch-class sets and discrete movements between remaining pitch-classes not common (primarily by movements of tones and semitones), a procedure called by the theorists of the \'neo-Riemannian\' (as Richard Cohn, Jack Douthett & Peter Steinbach and others) as \'parsimony\'. We also noticed that Villa-Lobos often relates these stratified layers by symmetrical intervallic arrangements, managing pitch-class sets that make up the parts or whole harmonic around axes of symmetry invariants (reflection). We also noted invariances often repeated on ostinato (translational symmetry), while remnants variants arise and disappear as segments of scales into different layers along the stretch led by ostinato, completing the entirety harmonious by juxtaposition. From this preliminary diagnosis, we choose in this research two distinct and concurrent analytical currents: the intervallic symmetry (invertional and translational) from studies on Pitch-Class Set Theory developed mainly in the writings of Joseph Straus and João Pedro Oliveira; and the intervallic transformation working as conductor in the relationship between scales arranged in network and in building of large harmonics sets (supersets), approaching our research to neo-Riemannian studies about scale networks and parsimony, in particular the texts by Dmitri Tymoczko, Richard Cohn, Jack Douthett & Peter Steinbach.

Dutch composer Peter Schat’s (1935-2003) pursuit of a compositional system that could generate and preserve intervallic relationships, while allowing the composer as much flexibility as possible to manipulate musical material, led him to develop the tone-clock system. Fundamentally comprised of the twelve possible trichords, the tone clock permits each to generate a complete twelve-tone series through the “steering” principle, a concept traced to Boulez’s technique of pitch-class set multiplication. This study serves as an overview of Schat’s tone-clock system and focuses primarily on the effects of the steering function in “Genen” (2000). Furthermore, I expand on the tone-clock system by combining transformational theory with Julian Hook’s uniform triadic transformations and my proposed STEER and STEERS functions, which express the procedures of the steering principle as a mathematical formula. Using a series of transformational networks, I illustrate the unifying effect steering has on different structural levels in “Genen,” a post-tonal composition.

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