Statistical learning and the uncertainty of melody and bass line in music


Autoři: Tatsuya Daikoku aff001
Působiště autorů: Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany aff001;  Centre for Neuroscience in Education, Department of psychology, University of Cambridge, Cambridge, United Kingdom aff002
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: 10.1371/journal.pone.0226734

Souhrn

Statistical learning is the ability to learn based on transitional probability (TP) in sequential information, which has been considered to contribute to creativity in music. The interdisciplinary theory of statistical learning examines statistical learning as a mechanism of human learning. This study investigated how TP distribution and conditional entropy in TP of the melody and bass line in music interact with each other, using the highest and lowest pitches in Beethoven’s piano sonatas and Johann Sebastian Bach’s Well-Tempered Clavier. Results for the two composers were similar. First, the results detected specific statistical characteristics that are unique to each melody and bass line as well as general statistical characteristics that are shared between the melody and bass line. Additionally, a correlation of the conditional entropies sampled from the TP distribution could be detected between the melody and bass line. This suggests that the variability of entropies interacts between the melody and bass line. In summary, this study suggested that TP distributions and the entropies of the melody and bass line interact with but are partly independent of each other.

Klíčová slova:

Bioacoustics – Entropy – Learning – Markov models – Music cognition – Neurophysiology – Statistical distributions – Conditional entropy


Zdroje

1. Saffran JR, Aslin RN, Newport EL. Statistical learning by 8-month-old infants. Science (80-). 1996. doi: 10.1126/science.274.5294.1926 8943209

2. Cleeremans A, Destrebecqz A, Boyer M. Implicit learning: News from the front. Trends Cogn Sci. 1998;2: 406–416. doi: 10.1016/s1364-6613(98)01232-7 21227256

3. Perruchet P, Pacton S. Implicit learning and statistical learning: one phenomenon, two approaches. Trends Cogn Sci. 2006;10: 233–238. doi: 10.1016/j.tics.2006.03.006 16616590

4. Yumoto M, Daikoku T. Basic function. Clinical Applications of Magnetoencephalography. 2016. doi: 10.1007/978-4-431-55729-6_5

5. Daikoku T. Time-course variation of statistics embedded in music: Corpus study on implicit learning and knowledge. PLoS One. 2018;13. doi: 10.1371/journal.pone.0196493 29742112

6. Wiggins GA. Consolidation as Re-Representation: Revising the Meaning of Memory. Front Psychol. 2019; 1–22. doi: 10.3389/fpsyg.2019.00001

7. Wiggins GA. Creativity, information, and consciousness: The information dynamics of thinking. Phys Life Rev. 2018;1: 1–39. doi: 10.1016/j.plrev.2018.05.001 29803403

8. Berry D., Dienes Z. Implicit learning: Theoretical and empirical issues. Hove, England: Lawrence Erlbaum; 1993.

9. Reber AS. Implicit learning and tacit knowledge. An essay on the cognitive unconscious. New York: Oxford University Press; 1993.

10. Perkovic S, Orquin JL. Implicit Statistical Learning in Real-World Environments Leads to Ecologically Rational Decision Making. Psychol Sci. 2017;29: 34–44. doi: 10.1177/0956797617733831 29068761

11. Daikoku T, Takahashi Y, Tarumoto N, Yasuda H. Auditory statistical learning during concurrent physical exercise and the tolerance for pitch, tempo, and rhythm changes. Motor Control. 2018;22. doi: 10.1123/mc.2017-0006 28872415

12. Daikoku T, Yatomi Y, Yumoto M. Statistical learning of an auditory sequence and reorganization of acquired knowledge: A time course of word segmentation and ordering. Neuropsychologia. 2017;95. doi: 10.1016/j.neuropsychologia.2016.12.006 27939187

13. Daikoku T, Takahashi Y, Tarumoto N, Yasuda H. Motor Reproduction of Time Interval Depends on Internal Temporal Cues in the Brain: Sensorimotor Imagery in Rhythm. Front Psychol. 2018;9: 1–11. doi: 10.3389/fpsyg.2018.00001

14. Daikoku T, Yatomi Y, Yumoto M. Implicit and explicit statistical learning of tone sequences across spectral shifts. Neuropsychologia. 2014;63. doi: 10.1016/j.neuropsychologia.2014.08.028 25192632

15. Daikoku T, Yatomi Y, Yumoto M. Statistical learning of music- and language-like sequences and tolerance for spectral shifts. Neurobiol Learn Mem. 2015;118. doi: 10.1016/j.nlm.2014.11.001 25451311

16. Tsogli V, Jentschke S, Daikoku T, Koelsch S. When the statistical MMN meets the physical MMN. Sci Rep. 2019;9: 5563. doi: 10.1038/s41598-019-42066-4 30944387

17. Koelsch S, Busch T, Jentschke S, Rohrmeier M. Under the hood of statistical learning: A statistical MMN reflects the magnitude of transitional probabilities in auditory sequences. Sci Rep. 2016;6: 1–11. doi: 10.1038/s41598-016-0001-8

18. Daikoku T. Neurophysiological markers of statistical learning in music and language: Hierarchy, entropy, and uncertainty. Brain Sci. 2018;8. doi: 10.3390/brainsci8060114 29921829

19. Raphael C, Stoddard J. Functional Harmonic Analysis Using Probabilistic Models. Comput Music J. 2004;28: 45–52. doi: 10.1162/0148926041790676

20. Brent MR. Speech segmentation and word discovery: a computational perspective. Trends Cogn Sci. 1999;3: 294–301. doi: 10.1016/s1364-6613(99)01350-9 10431183

21. Temperley D. 8—Computational Models of Music Cognition. In: Deutsch DBT-TP of M ( Third E, editor. Academic Press; 2013. pp. 327–368. https://doi.org/10.1016/B978-0-12-381460-9.00008-0

22. Rohrmeier M, Rebuschat P. Implicit Learning and Acquisition of Music. Top Cogn Sci. 2012;4: 525–553. doi: 10.1111/j.1756-8765.2012.01223.x 23060126

23. Dubnov S. Information Dynamics and Aspects of Musical Perception. The Structure of Style, ISBN 978-3-642-12336-8. Springer-Verlag Berlin Heidelberg, 2010, p. 127. 2010. doi: 10.1007/978-3-642-12337-5_7

24. Wang W. Machine Audition: Principles, Algorithms and Systems: Principles, Algorithms and Systems. Information Science Reference; 2010.

25. Servan-Schreiber E, Anderson JR. Learning Artificial Grammars With Competitive Chunking. J Exp Psychol Learn Mem Cogn. 1990;16: 592–608. doi: 10.1037/0278-7393.16.4.592

26. Perruchet P, Vinter A. PARSER: A Model for Word Segmentation. J Mem Lang. 1998;39: 246–263. https://doi.org/10.1006/jmla.1998.2576

27. Pearce MT, Wiggins GA. Auditory Expectation: The Information Dynamics of Music Perception and Cognition. Top Cogn Sci. 2012;4: 625–652. doi: 10.1111/j.1756-8765.2012.01214.x 22847872

28. Pearce M, Wiggins G. Improved Methods for Statistical Modelling of Monophonic Music. J New Music Res. 2004;33: 367–385. doi: 10.1080/0929821052000343840

29. Daikoku T, Yatomi Y, Yumoto M. Pitch-class distribution modulates the statistical learning of atonal chord sequences. Brain Cogn. 2016;108. doi: 10.1016/j.bandc.2016.06.008 27429093

30. Agres K, Abdallah S, Pearce M. Information-Theoretic Properties of Auditory Sequences Dynamically Influence Expectation and Memory. Cogn Sci. 2018;42: 43–76. doi: 10.1111/cogs.12477 28121017

31. Shannon CE. A Mathematical Theory of Communication. Bell Syst Tech J. 1948;27: 623–656.

32. Friston K. The free-energy principle: A unified brain theory? Nat Rev Neurosci. 2010;11: 127–138. doi: 10.1038/nrn2787 20068583

33. Applebaum D. Probability and Information: An Integrated Approach. 2nd ed. Cambridge: Cambridge University Press; 2008. doi: 10.1017/CBO9780511755262

34. Pearce M. Expectation in melody. 2006; 377–405.

35. Manzara LC, Witten IH, James M. On the Entropy of Music: An Experiment with Bach Chorale Melodies. Leonardo Music J. 1992;2: 81–88. doi: 10.2307/1513213

36. Witten IH, Manzara LC, Conklin D. Comparing Human and Computational Models of Music Prediction. Comput Music J. 1994;18: 70–80. doi: 10.2307/3680523

37. Cox G. On the Relationship Between Entropy and Meaning in Music: An Exploration with Recurrent Neural Networks. 2010.

38. Daikoku T. Entropy, Uncertainty, and the Depth of Implicit Knowledge on Musical Creativity: Computational Study of Improvisation in Melody and Rhythm. 2018;12: 1–11. doi: 10.3389/fncom.2018.00097 30618691

39. Hasson U. The neurobiology of uncertainty: implications for statistical learning. Phil Trans R Soc B. 2017;372: 20160048. doi: 10.1098/rstb.2016.0048 27872367

40. Nastase S, Iacovella V, Hasson U. Uncertainty in visual and auditory series is coded by modality-general and modality-specific neural systems. Hum Brain Mapp. 2014;35: 1111–1128. doi: 10.1002/hbm.22238 23408389

41. Harrison LM, Duggins A, Friston KJ. Encoding uncertainty in the hippocampus. Neural Networks. 2006;19: 535–546. doi: 10.1016/j.neunet.2005.11.002 16527453

42. Omigie D, Stewart L. Preserved statistical learning of tonal and linguistic material in congenital amusia. Front Psychol. 2011;2: 1–11. doi: 10.3389/fpsyg.2011.00001

43. Omigie D, Pearce MT, Stewart L. Tracking of pitch probabilities in congenital amusia. Neuropsychologia. 2012;50: 1483–1493. doi: 10.1016/j.neuropsychologia.2012.02.034 22414591

44. Omigie D, Pearce MT, Williamson VJ, Stewart L. Electrophysiological correlates of melodic processing in congenital amusia. Neuropsychologia. 2013;51: 1749–1762. doi: 10.1016/j.neuropsychologia.2013.05.010 23707539

45. Daikoku T. Implicit learning in the developing brain: An exploration of ERP indices for developmental disorders. Clin Neurophysiol. 2019. https://doi.org/10.1016/j.clinph.2019.09.001

46. Daikoku T. Depth and the Uncertainty of Statistical Knowledge on Musical Creativity Fluctuate Over a Composer’s Lifetime. Frontiers in Computational Neuroscience. 2019. p. 27. Available: https://www.frontiersin.org/article/10.3389/fncom.2019.00027 31114493

47. Daikoku T. Method and apparatus for analyzing characteristics of music information. United States of America; US20190189100, 2019. Available: https://patentscope.wipo.int/search/en/detail.jsf?docId=US244367418&tab=NATIONALBIBLIO&fbclid=IwAR3cy6qM_YpE_sQebTYc0ixnGTfuprzEiLxxb4Qbe1bKHlhlh5UZSgZDEWM

48. Daikoku T, Okano T, Yumoto M. Relative difficulty of auditory statistical learning based on tone transition diversity modulates chunk length in the learning strategy. In Proceedings of the Biomagnetic. Proc Biomagn. 2017;22–24: p.75. doi: 10.1016/j.nlm.2014.11.001

49. Elmer S, Lutz J. Relationships between music training, speech processing, and word learning: a network perspective. 2018; 1–9. doi: 10.1111/nyas.13581 29542125

50. François C, Chobert J, Besson M, Schön D. Music Training for the Development of Speech Segmentation. Cereb Cortex. 2012; 1–6. doi: 10.1093/cercor/bhs180 22784606

51. Francois C, Schön D. Musical expertise boosts implicit learning of both musical and linguistic structures. Cereb Cortex. 2011;21: 2357–2365. doi: 10.1093/cercor/bhr022 21383236

52. Hansen NC, Pearce MT. Predictive uncertainty in auditory sequence processing. Front Psychol. 2014;5: 1–17. doi: 10.3389/fpsyg.2014.00001

53. Przysinda E, Zeng T, Maves K, Arkin C, Loui P. Jazz musicians reveal role of expectancy in human creativity. Brain Cogn. 2017;119: 45–53. doi: 10.1016/j.bandc.2017.09.008 29028508

54. Paraskevopoulos E, Kuchenbuch A, Herholz SC, Pantev C. Statistical learning effects in musicians and non-musicians: An MEG study. Neuropsychologia. 2012;50: 341–349. doi: 10.1016/j.neuropsychologia.2011.12.007 22197571

55. Tishby N, Polani D. Information Theory of Decisions and Actions. Perception-Action Cycle. 2011; 601–636. doi: 10.1007/978-1-4419-1452-1_19

56. Schmidhuber J. Developmental robotics, optimal artificial curiosity, creativity, music, and the fine arts. Conn Sci. 2006;18: 173–187. doi: 10.1080/09540090600768658

57. Daikoku T. Musical Creativity and Depth of Implicit Knowledge: Spectral and Temporal Individualities in Improvisation. Front Comput Neurosci. 2018;12: 1–27. doi: 10.3389/fncom.2018.00001

58. Daikoku T. Computational models and neural bases of statistical learning in music and language: Comment on “Creativity, information, and consciousness: The information dynamics of thinking” by Wiggins. Phys Life Rev. 2019. https://doi.org/10.1016/j.plrev.2019.09.001

59. Hauser MD, Chomsky N, Fitch WT. The Faculty of Language: What Is It, Who Has It, and How Did It Evolve? Science (80-). 2002;298: 1569 LP–1579. doi: 10.1126/science.298.5598.1569 12446899

60. Jackendoff R, Lerdahl F. The capacity for music: What is it, and what’s special about it? Cognition. 2006;100: 33–72. doi: 10.1016/j.cognition.2005.11.005 16384553

61. Daikoku T, Yumoto M. Single, but not dual, attention facilitates statistical learning of two concurrent auditory sequences. Sci Rep. 2017;7. doi: 10.1038/s41598-017-10476-x 28860466

62. Daikoku T, Takahashi Y, Futagami H, Tarumoto N, Yasuda H. Physical fitness modulates incidental but not intentional statistical learning of simultaneous auditory sequences during concurrent physical exercise. Neurol Res. 2017;39. doi: 10.1080/01616412.2016.1273571 28034012

63. Rohrmeier M, Cross I. Statistical Properties of Tonal Harmony in Bach’s Chorales. Proc 10th Intl Conf Music Percept Cogn. 2008;6: 123–1319. Available: http://icmpc10.psych.let.hokudai.ac.jp/%5Cnhttp://www.mus.cam.ac.uk/files/2009/09/bachharmony.pdf

64. Daikoku T. Tonality Tunes the Statistical Characteristics in Music: Computational Approaches on Statistical Learning. Frontiers in Computational Neuroscience. 2019. p. 70. Available: doi: 10.3389/fncom.2019.00070 31632260

65. Daikoku T, Yumoto M. Concurrent statistical learning of ignored and attended sound sequences: An MEG study. Fronstiers, Hum Neurosci. 2019;under revi.

66. Wagenaar W. Generation of random sequences by human subjects: A critical survey of literature. Psychol Bull. 1972;77: 65–72.

67. Bains W. Random number generation and creativity. Med Hypotheses. 2008;70: 186–190. doi: 10.1016/j.mehy.2007.08.004 17920778

68. Yumoto M, Daikoku T. Neurophysiological Studies on Auditory Statistical Learning [in Japanese] 聴覚刺激列の統計学習の神経生理学的研究. Japanese J Cogn Neurosci. 2018;20: 38–43.

69. Daikoku T, Ogura H, Watanabe M. The variation of hemodynamics relative to listening to consonance or dissonance during chord progression. Neurol Res. 2012;34. doi: 10.1179/1743132812Y.0000000047 22642826

70. Friston K. A theory of cortical responses. Philos Trans R Soc B Biol Sci. 2005;360: 815–836. doi: 10.1098/rstb.2005.1622 15937014

71. Albrecht J, Shanahan D. The Use of Large Corpora to Train a New Type of Key-Finding Algorithm. Music Percept An Interdiscip J. 2013;31: 59 LP–67. doi: 10.1525/mp.2013.31.1.59


Článek vyšel v časopise

PLOS One


2019 Číslo 12