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Journal of the Acoustical Society of America / Volume 121 / Issue 5 / JASA EXPRESS LETTERS

Fast automatic inharmonicity estimation algorithm

J. Acoust. Soc. Am. Volume 121, Issue 5, pp. EL184-EL189 (2007); (6 pages)

Jukka Rauhala, Heidi-Maria Lehtonen, and Vesa Välimäki

Helsinki University of Technology, Laboratory of Acoustics and Audio Signal Processing, P.O. Box 3000, FI-02015 TKK, Espoo, Finland.

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A new algorithm is presented for estimating the inharmonicity coefficient of slightly inharmonic stringed instrument sounds. In the proposed partial frequencies deviation method, the inharmonicity is estimated in an intuitive way by minimizing the deviation of the expected partial frequencies compared to the frequencies of the high amplitude peaks in the spectrum. This is done in an iterative process, where the algorithm converges towards the target estimation value. The algorithm is tested using both synthetic and recorded piano tones. The results show that the new algorithm produces accurate results with a small computation cost compared to other methods.

© 2007 Acoustical Society of America

Acknowledgment

This work was financially supported by the Academy of Finland (Project No. 104934). J. R. was supported by the Nokia Foundation, and H.-M. L. was supported by Tekniikan edistämissäätiö and the Emil Aaltonen Foundation.

Article Outline

  1. Introduction
  2. Estimation algorithm
  3. Results and comparison
  4. Conclusion

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KEYWORDS and PACS

Keywords

acoustic analysis, musical acoustics, musical instruments, iterative methods

PACS

  • 43.75.Yy

    Instrumentation and measurement methods for musical acoustics

  • 43.75.Mn

    Pianos and other struck string instruments

ARTICLE DATA

History
Received 20 Nov 2006
Accepted 23 Feb 2007
Revised 19 Feb 2007
Published online 06 Apr 2007
Digital Object Identifier
http://dx.doi.org/10.1121/1.2719043

PUBLICATION DATA

ISSN

0001-4966 (print)  

Publisher

$abstract.society.value is a Member of CrossRef Acoustical Society of America

  1. Askenfelt, A., and Galembo, A. S. (2000). “Study of the spectral inharmonicity of musical sound,” Acoust. Phys. 46(2), 121–132. [ISI]
  2. Bank, B., Avanzini, F., Borin, G. De, Poli, G., Fontana, F., and Rocchesso, D. (2003). “Physically informed signal processing methods for piano sound synthesis: A research overview,” EURASIP J. Appl. Signal Processing 2003(10), 941–952.
  3. Bensa, J., Bilbao, S., Kronland-Martinet, R., Smith III, J O.. , and Voinier, T. (2005). “Computational modeling of stiff piano strings using digital waveguides and finite differences,” Acta. Acust. Acust. 91(2), 289–298.
  4. de Cheveigné, A., and Kawahara, H. (2002). “YIN, a fundamental frequency estimator for speech and music,” J. Acoust. Soc. Am. 111(4), 1917–1930JASMAN000111000004001917000001. [ISI] [MEDLINE]
  5. Fletcher, H., Blackham, E. D., and Stratton, R. (1962). “Quality of piano tones,” J. Acoust. Soc. Am. 34(6), 749–761JASMAN000034000006000749000001. [ISI]
  6. Galembo, A. S., and Askenfelt, A. (1999). “Signal representation and estimation of spectral parameters by inharmonic comb filters with application to the piano,” IEEE Trans. Speech Audio Process. 7(2), 197–203. [Inspec] [ISI]
  7. Järveläinen, H., Välimäki, V., and Karjalainen, M. (2001). “Audibility of the timbral effects of inharmonicity in stringed instrument tones,” Acoust. Res. Letters Online, 2(3), 79–84.
  8. Klapuri, A. (2003). “Multiple fundamental frequency estimation based on harmonicity and spectral smoothness,” IEEE Trans. Speech Audio Process. 11(6), 184–194. [Inspec]


Figures (3) Multimedia (1) Tables (1)

Figures (click on thumbnails to view enlargements)

FIG.1
Structure of the proposed PFD algorithm.

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FIG.2
(Color online) The partial frequency deviation Dk curve at iteration loop rounds (a) 1, (b) 2, (c) 5, (d) 10, (e) 15, and (f) 21, when a recorded Bb0 tone is analyzed (f0 = 32.4 Hz). The corresponding math values at each round are shown in the figures, the final B estimate is 0.0002546.

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FIG.3
(Color online) Inharmonicity estimation test for synthetic piano data with SNR of 40 dB using (a) ICF, (c) ICF+, and (e) PFD. The solid line represents the correct inharmonicity coefficient values for keys 1-35. The same test was done with recorded piano tones( 1 ) by using (b) ICF, (d) ICF+, and (f) PFD. The solid line indicates manually estimated values.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

Multimedia

Tables

Table I. Total running times of test cases, and average RMS errors (synthetic tones) and average RMS deviations (real tones) of the estimated inharmonicity values for the three methods.

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