{"id":24,"date":"2008-07-17T10:15:15","date_gmt":"2008-07-17T10:15:15","guid":{"rendered":"http:\/\/spheres.edublogs.org\/?page_id=32"},"modified":"2016-10-12T16:35:03","modified_gmt":"2016-10-12T15:35:03","slug":"music-and-numbers","status":"publish","type":"page","link":"https:\/\/www.paulj.myzen.co.uk\/blog\/teaching\/spheres\/lectures\/music-and-numbers\/","title":{"rendered":"2: Music \/ Numbers"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n
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\"leibniz\"‘Music charms us, although its beauty consists only in the agreement of numbers and in the counting, which we do not perceive but which the soul nevertheless continues to carry out, of the beats or vibrations of sounding bodies which coincide at certain intervals.’ (Leibniz, 1714)<\/p><\/blockquote>\n<\/td>\n<\/tr>\n

In this section, we will begin to examine the relationship between numbers and music. Such an association is often manifest in the ways in which music is rhythmically organised, of course – think of the relationship between note values as numerical proportions, or as fractions – but many composers have also sought to apply number relationships to other components of music, such as pitch, dynamic and articulation organisation and, on the macro level, to formal structuring.<\/td>\n<\/tr>\n
The topic will examine the theories and works of a number of composers who have extended the Pythagorean notions of proportion, ratio and the harmonic series, first realised in the music of the medieval and renaissance periods. Such approaches characterise the growing tendency for composers to utilise ‘pre-compositional’ systems, often based on number relationships, in the creation of musical works. Building on relatively simple structural ideas such as the canon, through more complex systems, such as the prolation canon, composers have transferred the observable patterns of ratio from the sonic domain to the temporal domain. Twentieth-century composers who have proposed new ways of working with musical material in these ways include: Henry Cowell, who sought to apply the principles of the harmonic series to elements of rhythmic organisation; Arnold Schoenberg and Anton von Webern, who focused on a quasi-numerical approach to pitch organisation; and Olivier Messiaen, who heralded the much-maligned ‘total serialist’ approach in the 1950s through works such as the Etudes de Rythme<\/em>.<\/td>\n<\/tr>\n
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