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作者	Agust©Ưn-Aquino, Octavio Alberto, author.

题名 Computational counterpoint worlds : mathematical theory, software, and experiments / Octavio Alberto Agust©Ưn-Aquino, Julien Junod, Guerino Mazzola.

目录
1.	Prolegomena on Counterpoint	1
1.1.	Counterpoint's Many Voices	1
1.2.	Consonances, Dissonances, and the Fourth	2
1.3.	Point Against Point	2
1.4.	First-Species Counterpoint	3
1.5.	Three Creativity Walls	4
2.	First-Species Model	5
2.1.	Dichotomies	5
2.2.	Counterpoint Dichotomies	10
2.2.1.	Musical Meaning of the Operations with Counterpoint Intervals	12
2.3.	Counterpoint Symmetries	14
2.4.	The Counterpoint Theorem	16
2.4.1.	Some Preliminary Calculations	17
2.4.2.	Hichert's Algorithm	20
3.	The Case of the Twelve-Tone Scale	27
3.1.	Neuronal Evidence for the Polarity Function	27
3.1.1.	The EEG Test	28
3.1.2.	Analysis by Spectral Participation Vectors	30
3.1.3.	Isolated Successive Intervals	30
3.1.4.	Polarity	31
3.1.5.	Music and the Hippocampal Gate Function	32
3.2.	The Counterpoint Theorem Revisited	35
3.3.	The Perspective from the Reduced Strict Style	35
3.4.	The Antipodality of Fuxian and Ionian Dichotomies	37
3.5.	The Fuxian and Riemann Dichotomies	38
4.	Graphs	41
4.1.	Counterpoint Worlds	42
4.2.	Strict Digraphs	45
4.3.	Quotient Digraphs	50
4.3.1.	Vertex Partitions	50
4.3.2.	Component Connections	51
4.3.3.	Homogeneous Digraphs	57
5.	Morphism Enumeration	67
5.1.	Backtracking	69
5.2.	Reducing the Problem Size	71
5.2.1.	Avoiding Redundancy	71
5.2.2.	Limiting Combinations	74
5.2.3.	Pruning the Search Tree	76
5.3.	Procedure	80
5.3.1.	Constructing the Strict Digraphs	82
5.3.2.	Constructing the Quotient Digraphs	82
5.3.3.	Constructing the Component Trees	85
5.3.4.	Populating the Mapping Tree	85
5.3.5.	Populating the Combinations Map	87
5.3.6.	Filtering the Quotient Structures	92
5.3.7.	Listing Valid Mappings	95
5.3.8.	Generating Strict Mappings	96
5.4.	Discussion	97
5.4.1.	Complexity	97
5.4.2.	Global Morphisms	99
6.	Experimentation	101
6.1.	Rubato	102
6.1.1.	Installation	102
6.1.2.	Quick Start	103
6.2.	Recipes	106
6.2.1.	Random Generation	106
6.2.2.	Composition	109
6.2.3.	Transformation	110
6.2.4.	Extensions	112
6.3.	Rubettes	115
6.3.1.	Counterpointiser	115
6.3.2.	DeCounterpointiser	117
6.3.3.	BollyWorld	119
6.3.4.	BollyCarlo	120
6.3.5.	BollyComposer	120
6.3.6.	BollyMorpher	121
6.3.7.	AnaBollyser	122
6.3.8.	Midi File In	123
6.3.9.	Midi File Out	123
6.3.10.	Score Play	124
6.3.11.	Voice Splitter	125
6.3.12.	Voice Merger	125
7.	Quasipolarities and Interval Dichotomies	127
7.1.	Introductory Remarks	127
7.2.	Characterization of Quasipolarities	128
7.3.	Calculation of Strong Dichotomies	129
8.	Towers of Counterpoint	135
8.1.	The Category of Strong Dichotomies	135
8.2.	Towers of Counterpoint	137
8.3.	Dense Consonances and Dissonances	143
9.	A Categorical Look at Gesture Theory	149
9.1.	Gestures over Topological Categories	149
9.1.1.	Digraphs Associated with Topological Categories	150
9.1.2.	Toward Hypergestures: The Topological Category of Gestures with Body in a Topological Category	151
9.1.3.	Functoriality with Respect to the Underlying Topological Category	153
9.2.	Constructing Gestures from Morphisms	154
9.2.1.	Interpreting Diagrams as Gestures	156
9.2.2.	Gestures with Bodies in Factorization Categories	157
9.2.3.	Homological Extensions Are Gestures	159
10.	Hypergesture Homology for Counterpoint	161
10.1.	Singular Homology for Hypergestures	161
10.1.1.	Chain Modules for Singular Hypergesture Homology	163
10.1.2.	Boundary Homomorphisms	164
10.2.	Homological Interpretation of the Counterpoint Model	170
10.2.1.	Hypergestural Singular Homology	171
10.2.2.	A Classical Example of a Topological Category from Counterpoint	171
10.2.3.	The Meaning of H1 for Counterpoint	176
10.2.4.	Concluding Comments	178
	Mathematical Basics	179
A.1.	Sets and Relations	179
A.2.	Graph Theory	181
A.3.	Groups and Rings	183
A.4.	Modules	185
A.5.	Topology	186
A.6.	Categories	187
A.6.1.	Basic Definitions	187
A.6.2.	Subfunctors and Sieves	191
A.6.3.	Subobjects and Object Classifiers	191
A.6.4.	Adjoint Functors	192
A.6.5.	Topoi	192
A.	Guide to Counterpoint Worlds	193
B.1.	Discrete Digraphs	194
B.2.	Forests	195
B.3.	Stars	195
B.4.	Grids	196
B.5.	Unknown Digraphs	197
	Strict Digraphs	199
	References	207
	Index	213

复本

馆藏地	索书号	处理状态
Innovative Univ. Library	MT55 .A39 2015	AVAILABLE

载体形态	x, 220 pages : illustrations (some color), music ; 25 cm.
Content Type	text txt rdacontent.
载体类型	unmediated n rdamedia.
Carrier Type	volume nc rdacarrier.
丛编	Computational music science.
	Computational music science.
Summary	This is the first book bringing together recent developments and perspectives on mathematical counterpoint theory in detail. The authors include recent theoretical results on counterpoint worlds, the extension of counterpoint to microtonal pitch systems, the singular homology of counterpoint models, and the software implementation of contrapuntal models.
Contents	Prolegomena on counterpoint -- First-species model -- The case of the twelve-tone scale -- Graphs -- Morphism enumeration -- Experimentation -- Quasipolarities and interval dichotomies -- Towers of counterpoint -- A categorical look at gesture theory -- Hypergesture homology for counterpoint -- Mathematical basics -- A guide to counterpoint worlds.
Bibliography	Includes bibliographical references (pages 207-211) and index.
主题	Counterpoint -- Mathematics.
	Computer music -- History and criticism.
其它责任者	Junod, Julien, author.
	Mazzola, G. (Guerino), author.
国际标准书号	331911235X
	9783319112350

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