Statistics in MusicologyCRC Press, 15 juil. 2003 - 312 pages Traditionally, statistics and music are not generally associated with each other. However, ...intelligent... music software, computer digitization, and other advanced techniques and technologies have precipitated the need for standard statistical models to answer basic musicological questions. Statistics In Musicology presents an unprecedented introduction to statistical and mathematical methods developed for use in music analysis, music theory, and performance theory. It explores concrete methods for data generation and numerical encoding of musical data and serves as a practical reference for a wide audience, including statisticians, mathematicians, musicologists, and musicians. |
Table des matières
CHAPTER 1 Some mathematical foundations of music | 1 |
CHAPTER 2 Exploratory data mining in musical spaces | 23 |
CHAPTER 3 Global measures of structure and randomness | 81 |
CHAPTER 4 Time series analysis | 107 |
CHAPTER 5 Hierarchical methods | 139 |
CHAPTER 6 Markov chains and hidden Markov models | 169 |
CHAPTER 7 Circular statistics | 187 |
CHAPTER 8 Principal component analysis | 205 |
CHAPTER 9 Discriminant analysis | 221 |
CHAPTER 10 Cluster analysis | 233 |
CHAPTER 11 Multidimensional scaling | 247 |
List of figures | 255 |
| 265 | |
| 281 | |
| 287 | |
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Expressions et termes fréquents
algorithm ARCADELT ARGERICH ASKENAZE b₁ BACH BACH BACH BACH SCARLATTI BARTOK bandwidths BARTOK Béla Bartók Beran Boxplots BRENDEL CAPOVA Chernoff faces CHOPIN clusters coefficients compositions correlation corresponding Cortot and Horowitz courtesy of Zentralbibliothek covariance matrix Das Wohltemperierte Klavier decomposition defined Definition DEMUS dimension discriminant rule distance entropy estimated euclidian finite function GIANOLI harmonic harpsichord HAYDN hidden Markov models HISMOOTH instance intervals J.S. Bach KATSARIS kernel KLIEN KRUST KUBALEK linear Linear discriminant analysis log2 Markov chain Mazzola measure melodic indicator metric modulo 12 MOZART observed obtained ORTIZ outliers parameter performances periodogram piano pitch principal components regression sample SCARLATTI BARTOK PROKOFFIEFF Schumann Schumann's Träumerei Scriabin skewness smoothing Sonata sound wave specific spectral density statistics structure Symbol plot TAKEMITSU tempo curves Theorem topological dimension values variance vector wavelet Webern Wohltemperierte Klavier x(ti Zentralbibliothek Zürich