The Applications of Fourier Series Harmonics in Musical Tones
Article Sidebar
-
Fourier Series, Frequency Domain, Musical Tones, Octaves, Spectrum, Time Domain
Abstract
The Fourier Series is considered one of the most important computational tools in mathematics and has widespread usage, specifically in music. The present paper aims at presenting Fourier Series in the context with sound analysis and synthesis. Since Fourier Series decomposes complicated waves into simple sinusoids, that improves our approach to harmonics and thereby the synthesis of sounds. The present discussion how this mathematical method offers to musicians and sound engineers new approaches as to how to generate and evaluate musical tones and sounds. Analyzing various examples, this paper will help to explain the relationship between mathematics and music, with a focus on the role of Fourier analysis in modern music production and its role in creating and designing the new exceptional sound.
Full text article
References
- Cooly, James W., Lewis, Peter A. W., & Welch, Peter D. (1969). "The Cooley, J. W., Lewis, P. A. W., & Welch, P. D. (1969). The Fast Fourier Transform and Its Applications. IEEE, 12(1), 27-34.
- Smith, J. O. (2007). Introduction to Digital Filters with Audio Applications (Vol. 2). Julius Smith.
- Moroney, S. (2023). Introduction to Fourier Analysis and Time-Frequency Analysis of Musical Instruments. Rutgers, The State University of New Jersey-Camden.
- Chowning, J. M. (1973). The Synthesis of Complex Audio Spectra by Means of Frequency Modulation. Journal of the Audio Engineering Society, 21(7), 526-534.
- Lerdahl, F., & Jackendoff, R. S. (1996). A Generative Theory of Tonal Music. MIT Press.
- Rossing, T. D., et al. (2010). The Science of String Instruments. Springer.
- Proakis, J. G. (2007). Digital Signal Processing: Principles, Algorithms, and Applications. Pearson Education India.
- Rudin, W. (1964). Principles of Mathematical Analysis (3rd ed.). McGraw-Hill.
- Osman, A. (2023). Efficient 3D Surface Patch Compression and Reconstruction Using Parametric Descriptions and Transform Techniques. Journal of Pure & Applied Sciences, 22(1), 107–116. https://doi.org/10.51984/jopas.v22i1.2164.
- Bartle, R. G., & Sherbert, D. R. (2000). Introduction to Real Analysis (Vol. 2). John Wiley & Sons.
- Royden, H., & Fitzpatrick, P. M. (2010). Real Analysis. China Machine Press.
- Kolmogorov, A. N., & Fomin, S. V. (1975). Introductory Real Analysis. Courier Corporation.
- Pugh, C. C. (2002). Real Mathematical Analysis. Springer.
- Ashdhir, P., Arya, J., & Rani, C. E. (2021). Exploring the Fundamentals of Fast Fourier Transform Technique and Its Elementary Applications in Physics. European Journal of Physics, 42(6), 065805.
- Duoandikoetxea, J. (2024). Fourier Analysis. American Mathematical Society.
- Loy, G. (2011). Musimathics: The Mathematical Foundations of Music (Vol. 1). MIT Press.
Authors
Copyright (c) 2024 Journal of Pure & Applied Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
In a brief statement, the rights relate to the publication and distribution of research published in the journal of the University of Sebha where authors who have published their articles in the journal of the university of Sebha should how they can use or distribute their articles. They reserve all their rights to the published works, such as (but not limited to) the following rights:
- Copyright and other property rights related to the article, such as patent rights.
- Research published in the journal of the University of Sebha and used in its future works, including lectures and books, the right to reproduce articles for their own purposes, and the right to self-archive their articles.
- The right to enter a separate article, or for a non-exclusive distribution of their article with an acknowledgment of its initial publication in the journal of Sebha University.
Privacy Statement The names and e-mail addresses entered on the Sabha University Journal site will be used for the aforementioned purposes only and for which they were used.
