Science, Music, and Mathematics

10.1142/12381 ◽  
2022 ◽  
Keyword(s):  
Music And Mathematics ◽  
And Mathematics

Music and mathematics: Theophrastus against the number-theorists

1977 ◽  
Vol 23 ◽  
pp. 1-15
Author(s):  
Andrew Barker
Keyword(s):  
Good Deal ◽  
Subsequent Publication ◽  
Music And Mathematics ◽  
And Mathematics ◽  
Partial Translation

A long and important fragment of the Περὶ μοψσικῆς of Theophrastus is preserved in Porphyry's commentary on Ptolemy's Harmonics. Both Porphyry and Ptolemy were reedited earlier in this century by Düring, in works which have rightly been taken to supersede the texts of Wallis: and so far as the Theophrastus passage is concerned, we should expect to be able to abandon in Düring's favour the text published by Wimmer, who in effect reprints Wallis, though adopting a few variant readings and emendations from Schneider. But it seems to me that Düring's text is not in all respects an improvement, and that the comments made on it in a subsequent publication by Alexanderson have muddied the waters still further. It is not only a matter of the text: Alexanderson prints also a (partial) translation and an interpretative commentary, and both are open to serious objections. I intend in this paper to deal only with a portion of the fragment, but it is that portion whose argument is the most intricate, and one which ought to shed a good deal of light on central controversies among the musical theoreticians who follow Aristotle. I am not in a position to dispute any of Düring's findings in the manuscripts, but where emendation has in any event proved necessary or where the manuscripts differ among themselves, I hope to show through a study of the content of the argument that the case in favour of Düring is not always closed.

scholarly journals Le Corbusier: architecture, music, mathematics: longing for classicism?

2015 ◽  
Author(s):  
Clara Germana Gonçalves ◽  
Maria João Dos Reis Moreira Soares
Keyword(s):  
Seventeenth Century ◽  
Le Corbusier ◽  
Palabras Clave ◽  
The Will ◽  
Music And Mathematics ◽  
And Mathematics ◽  
Universal Order ◽  
Siglo Xx ◽  
The Universe

Abstract: This paper aims to study the role of the relationships between architecture, music and mathematics in Le Corbusier's thought and work and their relevance in his reinterpretation of classical thinking. It seeks to understand to what extent working with this triad – a foundational and, up until the seventeenth century, dogmatic aspect of architecture in general and of its aesthetics in particular – expresses a will not to break with the fundamental and defining aspects of what could be considered as architectural thought rooted in classical tradition: that which is governed by the will to follow the universal order in the work of art; building a microcosmos according to the macrocosmos; linking, in proportion to one another, the universe, man and architecture. The Modulor presents itself as a manifestation of that will, synthesizing these aspects while proposing itself as an instrument for interdisciplinary thought and practice in which the aforementioned aspects of classical thought are present, clearly and pronouncedly. Le Corbusier’s thought and work presents itself as a twentieth century memory of an ancient and ever present tradition conscious of its struggle for “humanity”. Resumen: Este artículo pretende estudiar el papel de la relación entre arquitectura, música y matemática en el pensamiento y la obra de Le Cobusier y su significado en su reinterpretación del pensamiento clásico. Intenta entender en qué medida con esta triada – aspecto fundacional y hasta el siglo XVII dogmático de la arquitectura, en general, y de su estética, en particular – Le Corbusier expresa su recusa por cortar el vínculo con los aspectos fundamentales y definidores de lo que puede considerarse un pensamiento de tradición clásica en arquitectura: aquel tutelado por la voluntad de seguir el orden universal en la obra de arte – construyendo un microcosmos según un macrocosmos – para así vincular, a través de la proporción, universo, Hombre y arquitectura. El Modulor se presenta como manifestación de esa voluntad, sintetizando estos aspectos y presentándose como un instrumento para un pensamiento y una práctica interdisciplinares en los cuales el pensamiento clásico se encuentra clara y marcadamente presente. El pensamiento de Le Corbusier, través su mirada hacia la relación arquitectura-música-matemática, se presenta, en el siglo XX, como una memoria de una antigua y siempre presente tradición, consciente de su busca por “humanidad”.  Keywords: Le Corbusier; Architecture, music and mathematics; classical thought; Modulor. Palabras clave: Le Corbusier; Arquitectura, música y mathematica; pensamiento clásico; Modulor. DOI: http://dx.doi.org/10.4995/LC2015.2015.791

The Canterbury Tales and the Arabic Frame Tradition

PMLA ◽  
1983 ◽  
Vol 98 (2) ◽  
pp. 237-251 ◽  
Author(s):  
Katharine Slater Gittes
Keyword(s):  
Random Order ◽  
Canterbury Tales ◽  
Art Music ◽  
Arabic Literature ◽  
Confessio Amantis ◽  
Individual Unit ◽  
Music And Mathematics ◽  
And Mathematics ◽  
The Individual ◽  
The Canterbury Tales

The Canterbury Tales is the culmination of a frame tradition that originated and developed in Arabia, not in the West. The Arabic practice of enclosing tales within a frame may be explained by principles of organization peculiar to medieval Arabic literature, art, music, and mathematics: a preference for concreteness, a stress on autonomous elements, and a reliance on external organizing devices. Most Arabic literature emphasizes the individual unit; frames remain open-ended and inconclusive and rarely determine the subject or form of any included part. Although many Western characteristics are present in medieval European frame narratives like the Disciplina Clericalis, the Decameron, and the Confessio Amantis, those works, nonetheless, reveal themselves as continuations of the Arabic tradition. Even the Canterbury Tales, with all its subtle artistry, retains qualities typical of its Arabic ancestors, notably the controlling travelpilgrimage motif, the pointedly random order of tales, and the prominent authorial personality.

Music and mathematics

1945 ◽  
Vol 26 (1) ◽  
pp. 21-21
Author(s):  
G. Warrack
Keyword(s):  
Music And Mathematics ◽  
And Mathematics

Do Mathematicians Have Above Average Musical Skill?

2011 ◽  
Vol 29 (2) ◽  
pp. 203-213 ◽  
Author(s):  
Jennifer Haimson ◽  
Deanna Swain ◽  
Ellen Winner
Keyword(s):  
Reading Ability ◽  
Music Perception ◽  
Music Performance ◽  
Self Report ◽  
Sight Reading ◽  
Modern Language Association ◽  
Doctoral Level ◽  
Music And Mathematics ◽  
Performance Ability ◽  
And Mathematics

accompanying the view that music training leads to improved mathematical performance is the view that that there is an overlap between the kinds of skills needed for music and mathematics. We examined the popular conception that mathematicians have better music abilities than nonmathematicians. We administered a self-report questionnaire via the internet to assess musicality (music perception and music memory) and musicianship (music performance and music creation). Respondents were doctoral-level members of the American Mathematical Association or the Modern Language Association (i.e., literature and language scholars). The mathematics group did not exhibit higher levels of either musicality or musicianship. Among those reporting high music-performance ability (facility in playing an instrument and/or sight-reading ability), mathematicians did not report significantly greater musicality than did the literature/language scholars. These findings do not lend support to the hypothesis that mathematicians are more musical than people with nonquantitative backgrounds.

scholarly journals Musica fibonacciana: Aesthetic and practical approach

New Sound ◽  
2017 ◽  
pp. 70-90
Author(s):  
Rima Povilionienè
Keyword(s):  
Music Composition ◽  
Golden Ratio ◽  
Fibonacci Numbers ◽  
Laws Of Nature ◽  
Fibonacci Sequence ◽  
Number Sequences ◽  
Music And Mathematics ◽  
To Come ◽  
Composition Structure ◽  
And Mathematics

In the sphere of musical research, the intersection of two seemingly very different subject areas-music and mathematics is in essence related to one of the trends of music-attributing the theory of music to science, to the sphere of mathematica. It is regarded the longest-lasting interdisciplinary dialogue. The implication of numerical proportions and number sequences in the music composition of different epochs is closely related to this sphere. A significant role in creating music was attributed to the so-called infinite Fibonacci sequence. Perhaps the most important feature of the Fibonacci numbers, which attracted the attention of thinkers and creators of different epochs, is the fact that by means of the ratio between them it is possible to come maximally close to the Golden Ratio formula, which expresses the laws of nature. On a practical plane, often the climax, the most important part of any composition, matches the point of the Golden Ratio; groups of notes, rhythm, choice of tone pitches, a grouping of measures, time signature, as well as proportions between a musical composition's parts may be regulated according to Fibonacci principles. The article presents three analytical cases-Chopin's piano prelude, Bourgeois' composition for organ, and Reich's minimalistic piece, attempting to render music composition structure to the logic of Fibonacci numbers.

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