Musical Intelligence Analysis

  • Rui CheEmail author
  • Xingda Li
  • Dongfang Li
  • Yujing Guan
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 128)


Based on the temperament and physical properties of melody, we exploit splines, Gaussian function and trigonometric functions to construct two sets of stable bases and give the proof of stability. For both constructed function and real music signal,we can obtain the approximation using these bases. Meanwhile, frequency information can be detected exactly by FFT and the approximation is the sum of amplitudes of all frequencies. So, we can get the exact time-frequency music analysis theoretically and our numerical results also prove that well for both kinds of signals.


Short Time Fourier Transform Stable Basis Fundamental Tone Pitch Estimation Amplitude Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zhou, R.: Feature extraction of music content for automatic musictranscription. PH.D thesis, Swiss Federal Institute of Technology (2006)Google Scholar
  2. 2.
    Klapuri, A., Virtanen, T., Holm, J.-M.: Robust multipitch estimation for the analysis and manipulation of polyphonic musical signals. In: Proc. COST-G6 Conference on Digital Audio Effects, Verona, Italy, December 7-9 (2000)Google Scholar
  3. 3.
    Abeysekera, S.S.: Multiple pitch estimation of poly-phonic audio signals in a frequency-lag domain using the bispectrum. In: Proceedings of the IEEE International Symposium on Circuits and Systems, vol. 14(4), pp. 469–472 (2004)Google Scholar
  4. 4.
    Badeau, R., Emiya, V., David, B.: Expectationmaximization algorithm for multi-pitch estimation and separation of overlapping harmonic spectra. In: Proc. IEEE ICASSP, Taipei, Taiwan, pp. 3073–3076 (2009)Google Scholar
  5. 5.
    Godsill, S., Davy, M.: Bayesian harmonic models for musical pitch estimation and analysis. In: Proceedings of the IEEE International Conference on Acoustic, Speech, Signal Processing, vol. 2, pp. 1769–1772 (2002)Google Scholar
  6. 6.
    Christensen, M.G., Stoica, P., Jakobsson, A., Jensen, S.H.: Multi pitch estimation. Signal Processing 88(4), 972–983 (2008)zbMATHCrossRefGoogle Scholar
  7. 7.
    Bach, F., Jordan, M.: Discriminative training of Hidden Markov Models for multiple pitch tracking. In: Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, March 19-23, pp. 489–492 (2005)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MusicNortheast Normal UniversityChangchunP.R. China
  2. 2.Department of MathematicsJilin UniversityChangchunP.R. China

Personalised recommendations