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Mathematics and Computation in Music
A Categorical Generalization of Klumpenhouwer Networks
other
Author(s):
Alexandre Popoff
,
Moreno Andreatta
,
Andrée Ehresmann
Publication date
(Online):
June 16 2015
Publisher:
Springer International Publishing
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Adjoint functors
Daniel Kan
(1958)
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The Topos of Music
Guerino Mazzola
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Morphisms of generalized interval systems andPR-groups
Thomas Fiore
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Thomas Noll
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Ramon Satyendra
(2013)
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Author and book information
Book Chapter
Publication date (Print):
2015
Publication date (Online):
June 16 2015
Pages
: 303-314
DOI:
10.1007/978-3-319-20603-5_31
SO-VID:
1958dd43-2edd-4bb6-9eff-67f83bdf002c
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Book chapters
pp. 3
A Structural Theory of Rhythm Notation Based on Tree Representations and Term Rewriting
pp. 16
Renotation from Optical Music Recognition
pp. 29
Foundations for Reliable and Flexible Interactive Multimedia Scores
pp. 42
Genetic Algorithms Based on the Principles of Grundgestalt and Developing Variation
pp. 52
Describing Global Musical Structures by Integer Programming on Musical Patterns
pp. 64
Improved Iterative Random Walk for Four-Part Harmonization
pp. 73
Location Constraints for Repetition-Based Segmentation of Melodies
pp. 85
Modeling Musical Structure with Parametric Grammars
pp. 97
Perfect Balance: A Novel Principle for the Construction of Musical Scales and Meters
pp. 109
Characteristics of Polyphonic Music Style and Markov Model of Pitch-Class Intervals
pp. 115
A Corpus-Sensitive Algorithm for Automated Tonal Analysis
pp. 122
Finding Optimal Triadic Transformational Spaces with Dijkstra’s Shortest Path Algorithm
pp. 128
A Probabilistic Approach to Determining Bass Voice Leading in Melodic Harmonisation
pp. 137
Hypergestures in Complex Time: Creative Performance Between Symbolic and Physical Reality
pp. 149
Generating Fingerings for Polyphonic Piano Music with a Tabu Search Algorithm
pp. 161
Logistic Modeling of Note Transitions
pp. 173
Evaluating Singer Consistency and Uniqueness in Vocal Performances
pp. 179
A Change-Point Approach Towards Representing Musical Dynamics
pp. 187
Structural Similarity Based on Time-Span Sub-Trees
pp. 193
Cross Entropy as a Measure of Musical Contrast
pp. 199
Symbolic Music Similarity Using Neuronal Periodicity and Dynamic Programming
pp. 207
Applications of DFT to the Theory of Twentieth-Century Harmony
pp. 219
Utilizing Computer Programming to Analyze Post-Tonal Music: Contour Analysis of Four Works for Solo Flute
pp. 231
A Statistical Approach to the Global Structure of John Cage’s Number Piece $${Five}^5$$ F i v e 5
pp. 237
Exact Cover Problem in Milton Babbitt’s All-Partition Array
pp. 245
Constructing Geometrical Spaces from Acoustical Representations
pp. 257
Geometry, Iterated Quantization and Filtered Voice-Leading Spaces
pp. 267
Using Fundamental Groups and Groupoids of Chord Spaces to Model Voice Leading
pp. 279
All-Interval Structures
pp. 291
Unifying Tone System Definitions: Ordering Chromas
pp. 303
A Categorical Generalization of Klumpenhouwer Networks
pp. 315
The Spinnen-Tonnetz: New Musical Dimensions in the 2D Network for Tonal Music Analysis
pp. 323
Probabilistic Segmentation of Musical Sequences Using Restricted Boltzmann Machines
pp. 335
¿El Caballo Viejo? Latin Genre Recognition with Deep Learning and Spectral Periodicity
pp. 349
Can a Musical Scale Have 14 Generators?
pp. 361
On the Step-Patterns of Generated Scales that are Not Well-Formed
pp. 373
Triads as Modes within Scales as Modes
pp. 385
Greek Ethnic Modal Names vs. Alia Musica’s Nomenclature
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