Statistical Properties in Jazz Improvisation Underline Individuality of Musical Representation
Abstract
:1. Introduction
1.1. Statistical Learning: A Mathematical Model of a Learning System in the Brain
1.2. Corpus Study in Music: Classical and Jazz Music
1.3. Computational Modeling of Musical Improvisation
1.4. Study Purpose
2. Study 1
2.1. Methods
2.2. Results
2.2.1. Time-Course Variation in Musical Improvisation
W. J. Evans
H. J. Hancock
M. Tyner
2.2.2. Difference in Statistical Characteristics between Pieces of Music and between Musicians
2.3. Discussion
2.3.1. Time-Course Variation of Statistics in Musical Representation
2.3.2. Statistical Characteristics that Depend on Music and Musician
2.3.3. Improvisation
3. Study 2
3.1. Methods
3.2. Results
3.2.1. 0th-Order Markov Model
3.2.2. First-Order Markov Model
3.3. Discussion
3.3.1. Relationships among Sequences
3.3.2. Relationships among Improvisers
3.3.3. Statistical Learning in Psychological and Computational Studies
4. Conclusions
Supplementary Materials
Funding
Acknowledgments
Additional Information
Conflicts of Interest
References
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Improvisors | Titles |
---|---|
W. J. Evans | Autumn Leaves from Portrait in Jazz, 1959 |
Israel from Explorations, February 1961 | |
I Love You Porgy from Waltz for Debby, June 1961 | |
Stella by Starlight from Conversations with Myself, 1963 | |
Who Can I Turn To from Bill Evans at Town Hall, 1966 | |
Some Day My Prince Will Come from the Montreux Jazz Festival, 1968 | |
A Time for Love from Alone, 1969 | |
H. J. Hancock | Cantaloupe Island from Empyrean Isles, 1964 |
Maiden Voyage from Flood, 1975 | |
Some Day My Prince Will Come from The Piano, 1978 | |
Dolphin Dance from Herbie Hancock Trio ’81, 1981 | |
Thieves in the Temple from The New Standard, 1996 | |
Cotton Tail from Gershwin’s World, 1998 | |
The Sorcerer from Directions in Music, 2001 | |
M. Tyner | Man from Tanganyika from Tender Moments, 1967 |
Folks from Echoes of a Friend, 1972 | |
You Stepped Out of a Dream from Fly with the Wind, 1976 | |
For Tomorrow from Inner Voice; 1977 | |
The Habana Sun from The Legend of the Hour, 1981 | |
Autumn Leaves from Revelations, 1988 | |
Just in Time from Dimensions from Dimensions, 1984 |
a. W. J. Evans | |||||||||||
Model 1 | Model 2 | ||||||||||
Hierarchy | Variable | B | SE B | β | VIF | CI | B | SE B | β | VIF | CI |
Third | 0,2,3,5 | −171.28 | 66.20 | −0.76 * | 1.00 | 4.08 | −144.06 | 42.75 | −0.64 * | 1.05 | 3.33 |
0,−3,−4,−6 | 627.99 | 214.37 | 0.55 * | 1.05 | 6.85 | ||||||
R2 | 0.49 | 0.80 | |||||||||
F | 6.69 * | 12.71 * | |||||||||
Forth | 0,1,3,4,6 | −317.34 | 97.30 | −0.83 * | 1.00 | 3.92 | |||||
R2 | 0.62 | ||||||||||
F | 10.64 * | ||||||||||
b. M. Tyner | |||||||||||
Model 1 | Model 2 | ||||||||||
Hierarchy | Variable | B | SE B | β | VIF | CI | B | SE B | β | VIF | CI |
Second | 0,−2,−5 | 172.15 | 38.79 | 0.89 ** | 1.00 | 6.37 | 191.08 | 20.78 | 0.99 ** | 1.06 | 5.51 |
0,5.7 | −485.35 | 127.57 | −0.41 * | 1.06 | 7.89 | ||||||
R2 | 0.76 | 0.93 | |||||||||
F | 19.70 ** | 43.63 ** |
a Eigenvalue, percentages of variance and cumulative variance. | ||||||||
Total | Variance * | Cumulative * | ||||||
Component 1 | 10.79 | 51.40 | 51.40 | Component 1 | ||||
Component 2 | 5.91 | 28.15 | 79.55 | Component 2 | ||||
Component 3 | 1.37 | 6.52 | 86.07 | Component 3 | ||||
Component 4 | 1.21 | 5.76 | 91.84 | Component 4 | ||||
b. Eigenvectors for the principal components | ||||||||
Component 1 | Component 2 | Component 3 | Component 4 | |||||
W. J. Evans | Autumn leaves | 0.71 | −0.62 | 0.09 | −0.18 | |||
Israel | 0.85 | −0.46 | −0.12 | 0.02 | ||||
I Love You Porgy | 0.78 | −0.15 | 0.34 | −0.39 | ||||
Stella by Starlight | 0.68 | −0.61 | 0.12 | −0.16 | ||||
Who Can I Turn To | 0.82 | −0.08 | 0.52 | −0.12 | ||||
Some Day My Prince Will Come | 0.60 | −0.71 | 0.07 | 0.19 | ||||
A Time for Love | 0.73 | −0.56 | −0.12 | 0.20 | ||||
H. J. Hancock | Cantaloupe Island | 0.39 | 0.72 | 0.24 | 0.38 | |||
Maiden Voyage | 0.71 | −0.14 | −0.64 | 0.23 | ||||
Some Day My Prince Will Come | 0.78 | 0.14 | −0.47 | −0.38 | ||||
Dolphin Dance | 0.71 | −0.57 | −0.11 | 0.34 | ||||
Thieves in the Temple | 0.69 | 0.62 | 0.12 | 0.12 | ||||
Cotton Tail | 0.79 | −0.30 | 0.21 | 0.13 | ||||
The Sorcerer | 0.63 | −0.73 | 0.01 | 0.15 | ||||
M. Tyner | Man fromTanganyika | 0.72 | 0.48 | −0.06 | −0.42 | |||
Folks | 0.69 | 0.53 | −0.32 | −0.01 | ||||
You Stepped Out of a Dream | 0.66 | 0.69 | 0.03 | 0.23 | ||||
For Tomorrow | 0.73 | 0.62 | 0.03 | −0.03 | ||||
The Habana Sun | 0.51 | 0.76 | 0.03 | 0.23 | ||||
Autumn Leaves | 0.85 | 0.37 | −0.13 | −0.31 | ||||
Just in Time | 0.86 | 0.38 | 0.20 | 0.18 |
0th-Order | 1st-Order |
---|---|
0 | 2,0 |
1 | −2,0 |
−1 | 2,4 |
2 | −2,−4 |
−2 | −2,−5 |
3 | −2,−7 |
−3 | 3,0 |
4 | −3,−5 |
−4 | 3,7 |
5 | −4,−7 |
−5 | 5,3 |
7 |
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Daikoku, T. Statistical Properties in Jazz Improvisation Underline Individuality of Musical Representation. NeuroSci 2020, 1, 24-43. https://doi.org/10.3390/neurosci1010004
Daikoku T. Statistical Properties in Jazz Improvisation Underline Individuality of Musical Representation. NeuroSci. 2020; 1(1):24-43. https://doi.org/10.3390/neurosci1010004
Chicago/Turabian StyleDaikoku, Tatsuya. 2020. "Statistical Properties in Jazz Improvisation Underline Individuality of Musical Representation" NeuroSci 1, no. 1: 24-43. https://doi.org/10.3390/neurosci1010004