Abstract
This paper gives an overview of the (rather simple) mathematics underlying the theory of tuning musical instruments. Besides demonstrating the fundamental problems and discussing the different solutions (only on an introductory level), we also give Mathematica code that makes it possible to listen to the constructed scales and chords. To really get a “feeling” for the contents of this paper it is very important to hear the tones and intervals that are mentioned. The paper also has the purpose of giving the reader a Mathematica toolkit to experiment with different tunings.
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References
Blackwood, E.: The Structure of Recognizable Diatonic Tunings. Princeton University Press 1985
Lindley, M., Turner-Smith, R.: Mathematical Models of Musical Scales. Bonn: Verlag für systematische Musikwissenschaft 1993
Neuwirth, E.: Musical Temperaments. Transl, from the German by Rita Steblin. With CD-ROM for Windows. (English) Vienna: Springer-Verlag 1997
Neuwirth, E.: Designing a Pleasing Sound Mathematically. Mathematics Magazine. 74, 2001, pp. 91–98
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© 2002 Springer-Verlag Berlin Heidelberg
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Neuwirth, E. (2002). The Mathematics of Tuning Musical Instruments — a Simple Toolkit for Experiments. In: Assayag, G., Feichtinger, H.G., Rodrigues, J.F. (eds) Mathematics and Music . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04927-3_14
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DOI: https://doi.org/10.1007/978-3-662-04927-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07836-1
Online ISBN: 978-3-662-04927-3
eBook Packages: Springer Book Archive