Heinrich Baryphonus (1581-1655) and Heinrich Grimm’s (1592/3-1637) didactic treatise, Pleiades musicae (1615/1630), provides a vivid testimony to the state of music education and music theory pedagogy in Protestant Germany in the early seventeenth century. Published initially by Baryphonus for use at the Gymnasium in Quedlinburg and reissued in an expanded format by Grimm for use at the Gymnasium in Magdeburg, the text examines the fundamentals of pitch, intervals, counterpoint, and, in the second edition, triadic theory and composition. Throughout the remainder of the seventeenth century and into the eighteenth century, music theorists including Johann Andreas Herbst (1588-1666), Otto Gibel (1612-1682), and Andreas Werckmeister (1645-1706), used the document as a source for their own musical writings, solidifying its status as a significant contribution to the field of music theory. Recently, scholars such as Carl Dahlhaus, Benito Rivera, and Joel Lester have found value in Pleiades musicae for its role in the early stages of the development of triadic theory and the emergence of harmonic tonality. However, with the exception of the passages on triadic theory, the treatise continues to be relatively unknown. In order to understand the full extent of Baryphonus and Grimm’s contributions to the history of music theory, and to provide a multifaceted context for situating Pleiades musicae in the culture of its time and place of origin, the present study examines both editions of the text from biographical, cultural, educational, philosophical, music-theoretical, and historical perspectives, and includes modern Latin editions and English translations of the two editions of the treatise.

The Czech-born music theorist, Václav Philomathes, wrote the Musicorum libri quattuor in 1512 while attending the University of Vienna. This didactic treatise became one of the most widely published theory treatise of its time with 26 copies of five editions remaining today and covers the topics of Gregorian chant practice, Solmization, Mensural Notation, Choir Practice and Conducting, and Four-voice Counterpoint. Of particular note, is the section on choir practice and conducting, of which there is no equivalent prior example extant today. This dissertation provides a Latin-English translation of Philomathes’s work, as well as produces a critical commentary and comparison of the five editions while positioning the editions within the context of the musico-theoretical background of early-to-mid-16th century scholarship in Central Europe.

How have we come to hear melody as going “up” or “down”? Why does the Western world predominantly adopt spatial terms such as “high” and “low” to distinguish musical notes while other non-Western cultures use non-spatial terms such as “large” and “small” (Bali), or “clear” and “dull” (South Korea)? Have the changing concepts of motion and space in people’s everyday lives over history also changed our understanding of musical space? My dissertation investigates the Western concept of music space as it has been shaped by social change into the way we think about music today. In our understanding of music, the concept of the underlying space is so elemental that it is impossible for us to have any fruitful discourse about music without using inherently spatial terms. For example a term interval in music denotes the distance between two combined notes; but, in fact, two sonic objects are neither near nor far from each other. This shows that our experience of hearing interval as a combination of different notes is not inherent in the sound itself but constructed through cultural and social means. In Western culture, musical sound is often conceptualized through various metaphors whose source domains reflect the society that incubated these metaphorical understandings. My research investigates the historical formation of the conceptual metaphor of music. In particular, I focus on historical formation of the three underlying assumptions we bring to our hearing of music: (1) “high” and “low” notes and motion between them, (2) functionality of musical chords, and (3) reliance on music notation. In each chapter, I contextualize various music theoretical writings within the larger framework of philosophy and social theory to show that our current understanding of musical sound is embedded with the history of Western culture.

It has been said that Pythagoras discovered the perfect musical intervals by chance when he heard sounds of hammers striking an anvil at a nearby smithy. The sounds corresponded to the same intervals Pythagoras had been studying. He experimented with various instruments and apparatus to confirm what he heard. Math, and in particular, numbers are connected to music, he concluded. The discovery of musical intervals and the icon of the musical blacksmith have been familiar tropes in history, referenced in literary, musical, and visual arts. Countless authors since Antiquity have written about the story of the discovery, most often found in theoretical texts about music. However, modern scholarship has judged the narrative as a myth and a fabrication. Its refutation of the story is peculiar because modern scholarship has failed to disprove the nature of Pythagoras’s discovery with valid physical explanations. This report examines the structural elements of the story and traces its evolution since Antiquity to the early modern period to explain how an author interprets the narrative and why modern scholarship has deemed it a legend. The case studies of Nicomachus of Gerasa, Claudius Ptolemy, Boethius, and Marin Mersenne reveal not only how the story about Pythagoras’s discovery functions for each author, but also how the alterations in each version uncover an author’s views on music. / text

O tratado de contraponto, Arte Explicada de Contraponto, do lisboeta André da Silva Gomes, destaca-se na produção teórico-musical brasileira como uma obra que articula o ensino musical europeu, especialmente o português, com aquele praticado no Brasil durante o período colonial. Seu autor, quarto mestre-de-capela da Sé de São Paulo desde 1774, certamente apropriou-se dos principais modelos pedagógicos em voga na segunda metade do século XVIII, em Portugal. A única cópia encontrada de seu tratado recebeu estudos que contribuíram para a divulgação e explicação da maior parte dos preceitos dessa obra, demonstrando seu possível alcance, adquirido ao longo do século XIX. Apesar disso, a questão sobre sua recepção teórica manteve-se aberta, contendo problemas referentes aos modelos teóricos que pudessem ser verificados na obra. O objetivo geral deste trabalho é primeiro, realizar uma consolidação bibliográfica a respeito do ensino teórico-musical em Portugal ao longo dos séculos XVII e XVIII, por um lado, e, vasculhar o caminho teórico encontrado nos tratados musicais europeus que versassem, de modo explícito, sobre as regras de contraponto e as regras do acompanhamento, a fim de se verificar quais desses modelos poderiam ser identificados na obra de Silva Gomes. Como metodologia e, também, delineamento da amplitude do trabalho, elencamos os principais tratados portugueses que se encaixam em uma dessas duas categorias mencionadas, complementados oportunamente por autores espanhóis e italianos, em sua maioria. Através de análises comparativas entre os discursos desses tratados e a obra teórica de Silva Gomes, pudemos verificar a manutenção de certos cânones do ensino de música, provenientes da tradição do contraponto, e enxergar novas possibilidades de interpretação do conteúdo da Arte Explicada, através dos manuais de acompanhamento. Estes, por sua vez, sugerem caminhos aos estudos sobre a recepção teórica brasileira, pautados na tradição de ensino napolitana, cujos modelos possuíram livre trânsito entre os compositores e professores portugueses desde o século XVIII / The treatise on counterpoint Arte Explicada de Contraponto, by Lisboan André da Silva Gomes, stands out in Brazilian theoretical writings as a work which articulates European music teaching, especially Portuguese, with that conducted in Brazil during colonial period. Its author, fourth chapel master of São Paulo\'s cathedral, since 1774, certainly absorbed the main pedagogic models of Portugal in the second half of the 18th century. The only copy found of his treatise has been analyzed in few studies, which contributed to the diffusion and offered explanations for most of its precepts, demonstrating its potential range, acquired along the 19th century. However, its theoretical reception was kept open, presenting some problems regarding the possible theoretical models that could be mapped within the work. The general objective of the present work is, at first, to achieve a bibliographic consolidation concerning music theory teaching in Portugal along 17th and 18th centuries, on one hand, and on the other, to scavenge the theoretical path found in European music treatises that discuss explicitly the rules of counterpoint and accompaniment, in order to verify what are the models which could be identified within the work by Silva Gomes. As methodology and also for bounding the reach of the work, we listed the central Portuguese treatises that fit in one of the above categories, further complemented, majorly, by Spanish and Italian authors. Through comparative analyses between the discourses of such treatises and the theoretical work by Silva Gomes, we were able to verify the abiding of certain canons of music teaching, originated from the tradition of counterpoint, and to look into new possibilities of interpreting the content of Arte Explicada through manuals on accompanying. Those, in turn, suggest directions to further studies about Brazilian theoretical reception, rooted in Neapolitan tradition of teaching models, which transited freely among Portuguese composers and music teachers since the 18th century.

O tratado de contraponto, Arte Explicada de Contraponto, do lisboeta André da Silva Gomes, destaca-se na produção teórico-musical brasileira como uma obra que articula o ensino musical europeu, especialmente o português, com aquele praticado no Brasil durante o período colonial. Seu autor, quarto mestre-de-capela da Sé de São Paulo desde 1774, certamente apropriou-se dos principais modelos pedagógicos em voga na segunda metade do século XVIII, em Portugal. A única cópia encontrada de seu tratado recebeu estudos que contribuíram para a divulgação e explicação da maior parte dos preceitos dessa obra, demonstrando seu possível alcance, adquirido ao longo do século XIX. Apesar disso, a questão sobre sua recepção teórica manteve-se aberta, contendo problemas referentes aos modelos teóricos que pudessem ser verificados na obra. O objetivo geral deste trabalho é primeiro, realizar uma consolidação bibliográfica a respeito do ensino teórico-musical em Portugal ao longo dos séculos XVII e XVIII, por um lado, e, vasculhar o caminho teórico encontrado nos tratados musicais europeus que versassem, de modo explícito, sobre as regras de contraponto e as regras do acompanhamento, a fim de se verificar quais desses modelos poderiam ser identificados na obra de Silva Gomes. Como metodologia e, também, delineamento da amplitude do trabalho, elencamos os principais tratados portugueses que se encaixam em uma dessas duas categorias mencionadas, complementados oportunamente por autores espanhóis e italianos, em sua maioria. Através de análises comparativas entre os discursos desses tratados e a obra teórica de Silva Gomes, pudemos verificar a manutenção de certos cânones do ensino de música, provenientes da tradição do contraponto, e enxergar novas possibilidades de interpretação do conteúdo da Arte Explicada, através dos manuais de acompanhamento. Estes, por sua vez, sugerem caminhos aos estudos sobre a recepção teórica brasileira, pautados na tradição de ensino napolitana, cujos modelos possuíram livre trânsito entre os compositores e professores portugueses desde o século XVIII / The treatise on counterpoint Arte Explicada de Contraponto, by Lisboan André da Silva Gomes, stands out in Brazilian theoretical writings as a work which articulates European music teaching, especially Portuguese, with that conducted in Brazil during colonial period. Its author, fourth chapel master of São Paulo\'s cathedral, since 1774, certainly absorbed the main pedagogic models of Portugal in the second half of the 18th century. The only copy found of his treatise has been analyzed in few studies, which contributed to the diffusion and offered explanations for most of its precepts, demonstrating its potential range, acquired along the 19th century. However, its theoretical reception was kept open, presenting some problems regarding the possible theoretical models that could be mapped within the work. The general objective of the present work is, at first, to achieve a bibliographic consolidation concerning music theory teaching in Portugal along 17th and 18th centuries, on one hand, and on the other, to scavenge the theoretical path found in European music treatises that discuss explicitly the rules of counterpoint and accompaniment, in order to verify what are the models which could be identified within the work by Silva Gomes. As methodology and also for bounding the reach of the work, we listed the central Portuguese treatises that fit in one of the above categories, further complemented, majorly, by Spanish and Italian authors. Through comparative analyses between the discourses of such treatises and the theoretical work by Silva Gomes, we were able to verify the abiding of certain canons of music teaching, originated from the tradition of counterpoint, and to look into new possibilities of interpreting the content of Arte Explicada through manuals on accompanying. Those, in turn, suggest directions to further studies about Brazilian theoretical reception, rooted in Neapolitan tradition of teaching models, which transited freely among Portuguese composers and music teachers since the 18th century.

Ugolino (c. 1380-1457) wrote one of the largest treatises on music theory in the first half of the fifteenth century. This work, the "Declaratio musicae disciplinae," is comprised of five books that cover everything a musician of the era would need to know, from plainchant to harmonic proportions, from musica practica to musica speculativa. However, the treatise has received contradictory interpretations by modern scholars, some viewing it as mainly practical, others as mainly theoretical. I argue that in Book 2, which deals with counterpoint, Ugolino crystallizes the relationship between theory and practice, while offering distinctive contrapuntal practices. Ugolino presents a unique view music's place in the structure of knowledge, one which is highly dependent on Aristotelian philosophy. He posits that music is a science and that it is a branch not of mathematics, as it had traditionally been categorized, but of natural philosophy. This viewpoint shapes the entire treatise and is evident in the book on counterpoint. There, he presents an Italian tradition of teaching counterpoint known as the "regola del grado." Ugolino is the first author to present this tradition entirely in Latin. In addition, he offers an unusual description of musica ficta. In it, he presents a diagram, the "duplex manus," that mixes together both musica recta and musica ficta. Ugolino's work suggests that theory and practice, although arranged hierarchically, need not be in conflict, and that a treatise such as his can be both eminently practical and highly theoretical.