Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 41, 24 June 2024
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Analyzing musical tones with fourier transformation
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Abstract
This essay delves into the mathematical exploration of musical tones through the application of Fourier Transformation, a pivotal tool in the field of digital signal processing and acoustics. By converting complex musical tones from the time domain to the frequency domain, Fourier Transformation enables the deconstruction of sounds into their constituent frequencies, revealing the unique harmonic structures that contribute to the characteristic timbre of different musical instruments. The focus of this analysis is particularly on the trumpet, chosen for its rich harmonic content and distinctive sound. Through the examination of audio recordings, this study uncovers the fundamental frequency and harmonics of the trumpet, demonstrating how these elements combine to form its unique acoustic fingerprint. The process involves recording, analyzing, and comparing musical tones using software tools like MATLAB and Python, providing an accessible yet profound insight into the intersection of mathematics and music. This essay not only highlights the technical methodology of Fourier Transformation in analyzing musical tones but also explores its practical applications in music theory, digital audio processing, and the broader field of acoustics. The findings underscore the transformative power of mathematical analysis in understanding and appreciating the complex beauty of musical sounds, opening avenues for further research and application in both the scientific and artistic domains.
Keywords
Fourier Transform, Musical Tones, Frequency Spectrum, Timbre Analysis
References
1. Zhu, H., Wen, X., Jin, W., He, Z., and Zeng, Yi. (2015) Oil and gas detection based on deconvolution short-time Fourier transform. Progress in Geophysics, 5, 6.
2. Zhou, H. and Wang, Y. (2008) Fourier transform is used to measure motor speed. University Physics Experiments, 21, 54-56.
3. Yuan, J. (2020) Comparison of Harmony between Timbres of Different Musical Instruments: Application of Fourier Transform in Music. Chinese Writers and Artists, 000(002), 35-35.
4. Smith, J.O. (2007) Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications. W3K Publishing.
5. Brown, J.C. (1991) Calculation of a Constant Q Spectral Transform. Journal of the Acoustical Society of America, 89, 425-434.
6. Chen, J. (2019) Research on music visualization creation method based on Fourier transform. Science and Informatization, 30, 2.
7. Yuan, J. (2020) Comparison of Harmony between Timbres of Different Musical Instruments: Application of Fourier Transform in Music. Chinese Writers and Artists, 000(002), 35-35.
8. Xu, Q. (2017) Musical tone analysis and generation based on Fourier transform. Electronic World, 4, 2.
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of Machine Learning: Integrating machine learning techniques to advance network security - CONFMPCS 2024
- ISBN (Print)
- 978-1-83558-493-4
- ISBN (Online)
- 978-1-83558-494-1
- Published Date
- 24 June 2024
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/41/20240109
- Copyright
- 24 June 2024
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited