Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Music statistics: uncertain logistic regression models with applications in analyzing music

  • Published:
Fuzzy Optimization and Decision Making Aims and scope Submit manuscript

Abstract

In the realm of data analysis, traditional statistical methods often struggle when faced with ambiguity and uncertainty inherent in real world data. Uncerainty theory, developed to better model and interpret such data, offers a promising alternative to conventional techniques. In this paper, we establish logistic regression models to initiate music statistics based on uncertainty theory. In particular, we will classify the music into different types named Baroque, Classical, Romantic, and Impressionism based on four characteristics: harmonic complexity, rhythmic complexity, texture complexity, and formal structure, with the help of the uncertain logistic models proposed. This theoretical framework for music classification provides a nuanced understanding of how music is interpreted under conditions of ambiguity and variability. Compared with the probabilistic counterpart, our approach highlights the versatility of uncertainty theory and provides researchers one much more feasible method to analyze the often-subjective nature of music reception, as well as broadening the potential applications of uncertainty theory.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availibility

All data generated or analyzed during this study are included in this paper.

Code Availability

All the codes implemented during this study are available from the corresponding author on reasonable request.

References

  • Abarca, J. A. L. (2023). Four axioms for a theory of rhythmic sets and their implications. Online Journal of Music Sciences, 8(2), 226–237.

    Article  Google Scholar 

  • Perez, A., et al. (2023). How do artificial neural networks classify musical triads? a case study in eluding bonini’s paradox. Cognitive Science, 47(1), e13233.

    Article  Google Scholar 

  • Dawson, M. R., et al. (2020). Artificial neural networks solve musical problems with fourier phase spaces. Scientific Reports, 10(1), 7151.

    Article  MathSciNet  Google Scholar 

  • Johnson, R. A., & Wichern, D. W. (2020). Applied Multivariate Statistical Analysis. Hoboken: Pearson Prentice Hall.

    Google Scholar 

  • Li, A., & Lio, W. (2024). Bayesian inference in the framework of uncertainty theory. Journal of Ambient Intelligence and Humanized Computing, 15, 1–8.

    Article  Google Scholar 

  • Lio, W., & Liu, B. (2020). Uncertain maximum likelihood estimation with application to uncertain regression analysis. Soft Computing, 24(13), 9351–9360.

    Article  Google Scholar 

  • Liu, B. (2007). Uncertainty theory. Berlin: Springer.

    Book  Google Scholar 

  • Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.

    Google Scholar 

  • Ruditsa, R. (2021). Relative musical pitch in formal definition. In: Proceedings of the worldwide music conference 2021: Volume 2, Springer, pp 3–17.

  • Schuijer, M. (2008). Analyzing atonal music: Pitch-class set theory and its contexts (Vol. 60). New York: University Rochester Press.

    Book  Google Scholar 

  • Yang, X., & Liu, B. (2019). Uncertain time series analysis with imprecise observations. Fuzzy Optimization and Decision Making, 18(3), 263–278.

    Article  MathSciNet  Google Scholar 

  • Yao, K., & Liu, B. (2018). Uncertain regression analysis: An approach for imprecise observations. Soft Computing, 22(17), 5579–5582.

    Article  Google Scholar 

  • Ye, T., & Liu, B. (2022). Uncertain hypothesis test with application to uncertain regression analysis. Fuzzy Optimization and Decision Making, 21(2), 157–174.

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was support by supported by the National Natural Science Foundation of China (Grant No. 11901145).

Author information

Authors and Affiliations

  1. School of Mathematics, Physics and Information, Shaoxing University, Shaoxing, 312000, Zhejiang, People’s Republic of China

    Jue Lu, Lianlian Zhou & Anshui Li

  2. Cai Yuanpei School of Art and Design, Shaoxing University, Shaoxing, 312000, Zhejiang, People’s Republic of China

    Wenxing Zeng

Authors
  1. Jue Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lianlian Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenxing Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anshui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anshui Li.

Ethics declarations

Conflict of interest

The authors declare that they have no Conflict of interest.

Ethics approval

This paper does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix A Index Explanation

  1. (i)

    Harmonic Complexity(HC)

    1. (a)

      Level 1: Basic diatonic harmony, predominately using primary chords (I, IV, V). Minimal chromaticism or modulation.

    2. (b)

      Level 2: Simple diatonic progressions with occasional secondary dominants and modulations to closely related keys. Some use of non-diatonic chords.

    3. (c)

      Level 3: Moderate use of chromaticism, including secondary dominants, modal interchange, and more frequent modulations to related and distant keys. Begins to explore altered chords.

    4. (d)

      Level 4: High use of chromaticism, including complex chord substitutions, frequent modulations including to distant keys, and extensive use of non-traditional harmonies such as augmented sixth chords and altered chords.

    5. (e)

      Level 5: Extremely complex harmonic language, extensive use of dissonance, atonality, polytonality, or serialism. Frequent use of highly chromatic or completely non-diatonic structures.

  2. (ii)

    Rhythmic Complexity(RC)

    1. (a)

      Level 1: Very simple and repetitive rhythms, predominantly using basic note values like whole, half, and quarter notes without syncopation.

    2. (b)

      Level 2: Includes some rhythmic variety and mild syncopation. Use of dotted notes and ties, still primarily straightforward rhythms.

    3. (c)

      Level 3: Moderate rhythmic complexity with more frequent use of syncopation, compound meters, and some asymmetrical meters. Varied rhythmic patterns and combinations.

    4. (d)

      Level 4: Complex rhythms involving frequent syncopation, mixed meter, and irregular meters. Use of complex tuplets and intricate rhythmic layering.

    5. (e)

      Level 5: Extremely complex rhythmic structures, extensive use of polyrhythms and polymeters, advanced syncopation, and frequent changes in time signature. Complex cross-rhythms common.

  3. (iii)

    Texture Complexity(TC)

    1. (a)

      Level 1: Predominantly monophonic texture. Single melodic line without accompaniment or only minimal accompaniment.

    2. (b)

      Level 2: Simple homophonic texture, featuring a clear melody with chordal accompaniment. Limited counterpoint or polyphony.

    3. (c)

      Level 3: Textural variety including homophony and polyphony. Use of counterpoint may be more evident. Some layers or independent lines might be introduced.

    4. (d)

      Level 4: Rich polyphonic or heterophonic textures, with multiple independent lines interweaving. Complex counterpoint common, with significant interaction between lines.

    5. (e)

      Level 5: Extremely dense and complex textures, extensive use of polyphony, counterpoint, and/or heterophony. May include layered textures using modern techniques and electronic effects.

  4. (iv)

    Formal Structure(FS)

    1. (a)

      Level 1: Very simple structures such as strophic form or basic binary or ternary forms. Minimal development or thematic transformation.

    2. (b)

      Level 2: Clear forms such as standard binary, ternary, or simple sonata/rondo forms with some thematic development and clear sectional divisions.

    3. (c)

      Level 3: More complex forms with developed themes, such as sonata form with moderate development sections, theme and variations, or compound ternary forms.

    4. (d)

      Level 4: Advanced structures with extensive development and transformation of material. Includes complex sonata forms, through-composed forms, or intricate rondo forms.

    5. (e)

      Level 5: Highly sophisticated structural forms that may include large-scale cyclic forms, innovative or avant-garde structures, or highly integrative forms that blur traditional boundaries.

Appendix B Data set

The data used in this paper will be provided in the following tables.

Table 4 Data set
Full size table
Table 5 Data set
Full size table
Table 6 Data set
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, J., Zhou, L., Zeng, W. et al. Music statistics: uncertain logistic regression models with applications in analyzing music. Fuzzy Optim Decis Making 23, 637–654 (2024). https://doi.org/10.1007/s10700-024-09436-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10700-024-09436-8

Keywords

Search

Navigation