Music and Mathematics: From Pythagoras to Fractals

This book is a collection of 10 essays written by different authors on the topic, split into four chapters: ‘Music and mathematics through the history’, ‘The mathematics of musical sound’, ‘Mathematical structure in the music’ and ‘The composer speaks’. Starting from historical remarks (on tuning strings in connection with Pythagorean scales and the theory of rational numbers), the authors move on to the differences between tempered and non-tempered tuning and the Pythagorean comma, before explaining why an octave consisting of 53 rather than 12 tones would be better for tuning. Through the notion of musical cosmology, the reader is led to more scientific aspects of music, namely the analysis of the oscillograph traces – a way to capture music in a manner close to the recording of sounds. For a mathematician, it is interesting to see how the notion of rationality and irrationality and the notion of continued fractions is employed in describing music.
The theory of consonant tones – the tones that sound faintly together with the main tone – is also studied. Later, the way of writing down music is touched: its geometrical aspect as well as its effectiveness. Finally, the authors present the compositional dimension of connections between the two fields, namely the influence of a mathematical approach to the composing process, adding to the common composition techniques the technique of mathematically constructed or “scientific” music. The book presents a comprehensive look at the connections between music and mathematics. While the former is mostly considered as a pure intuitive, aesthetical discipline, the latter is often perceived as a pure technical and logical one. The book suggests, however, that the two disciplines have much in common. This nicely written book would be appreciated by all who want to delve deeper into the connections between the two fields. However, even though the book is written as a collection of essays, the presence of some formulas could mean that the book will be more appreciated by mathematicians interested in music than vice versa.

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