Skip to main content
Log in

Common quantitative characteristics of music melodies — pursuing the constrained entropy maximization casually in composition

  • Moop
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Burkholder J P, Grout D J, Palisca C V. A History of Western Music. New York: W. W. Norton & Co. Ltd., 2014

    Google Scholar 

  2. Li C G. Fundamentals of Music Principles. Beijing: People’s Music Publishing House, 2000

    Google Scholar 

  3. Tymoczko D. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. New York: Oxford University Press, 2011

    Google Scholar 

  4. Andreatta M. From music to mathematics and backwards: introducing algebra, topology and category theory into computational musicology. In: Imagine Math 6. Cham: Springer, 2018. 77–88

    Google Scholar 

  5. Schoenberg A. The Fundamentals of Music Composition. Shanghai: Shanghai Music Publishing House, 1984

    Google Scholar 

  6. Hindemith P. The Craft of Musical Composition. Shanghai: Shanghai Music Publishing House, 2015

    Google Scholar 

  7. Bedford T. Hölder exponents and box dimension for self-affine fractal functions. Constr Approx, 1989, 5: 33–48

    Article  MathSciNet  MATH  Google Scholar 

  8. Hsü K J, Hsü A J. Fractal geometry of music. Proc Natl Acad Sci USA, 1990, 87: 938–941

    Article  MathSciNet  Google Scholar 

  9. Mehr S A, Singh M, Knox D, et al. Universality and diversity in human song. Science, 2019, 366: eaax0868

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61221063, U1736205) and China Science and Technology Museum. Nan NAN was supported by Interdisciplinary Doctoral Program of Xi’an Jiaotong University (Grant No. IDT1707). The authors would like to thank Jicheng FENG, Jie HOU, Qinping GAO, Xi YANG, Bin LV, Yi ZHONG, Hui TIAN, Keju WANG, Zheng LIU, Lankui HAN of Xi’an Conservatory of Music for collaborating on the Concert for Bridging Art and Science that gives inspiration on this research, Jingchun WANG of CRISP, Chenxu WANG, Xiping MA, Xiaodi FANG, Ru WEN of Xi’an Jiaotong University for insightful discussions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaohong Guan.

Additional information

Supporting information Videos and other supplemental documents. The supporting information is available online at https://info.scichina.com and https://link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

Supplementary Materials (SM) for

11432_2021_3366_MOESM1_ESM.pdf

Common quantitative characteristics of music melodies — pursuing the constrained entropy maximization casually in composition

11432_2021_3366_MOESM2_ESM.pdf

Common quantitative characteristics of music melodies — pursuing the constrained entropy maximization casually in composition

Supplementary material, approximately 23.4 MB.

Supplementary material, approximately 6.10 MB.

Supplementary material, approximately 974 KB.

Supplementary material, approximately 875 KB.

Supplementary material, approximately 1.68 MB.

Supplementary material, approximately 35.6 MB.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nan, N., Guan, X., Wang, Y. et al. Common quantitative characteristics of music melodies — pursuing the constrained entropy maximization casually in composition. Sci. China Inf. Sci. 65, 174201 (2022). https://doi.org/10.1007/s11432-021-3366-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-021-3366-4

Navigation