Music Representation and Transformation in Software: Structure and Algorithms in Python

Preface
	Introduction
	The Origin of this Book
	Prerequisites and Approach
	What this Book is Not About
	Intended Audience
		Students
		Instructors
		Practitioners
		Experienced Researchers
	Regarding the Musical Examples
	About the Software
	Acknowledgements
Contents
Part 1: Representation
	1 Software Modeling and Object-Oriented Design
		1.1 Object-Oriented Design by Example
		1.2 A Concise Introduction to Python Classes
			Properties
			Multiple Inheritance
		1.3 What Can Go Wrong in Object-Oriented Design
			Over Abstraction
			Concurrency and Side-effects
			Still Requires Good Practice
		1.4 The Meaning of Music Representation
	2 The Chromatic Scale and the Diatonic Foundation
		2.1 The Pythagorean Scale
		2.2 Just Intonation and Equal-Tempered Chromatic Scales
			2.2.1 The Chromatic Scale Representation
		2.3 Tones, Pitches, and the Diatonic Foundation
			2.3.1 Diatonic Tone Representation
			2.3.2 DiatonicToneCache
			2.3.3 Diatonic Pitch Representation
		2.4 Exercises
	3 Intervals
		3.1 What is a Music Interval?
			3.1.1 Compound Intervals
			3.1.2 Interval Inversion
		3.2 Interval Analytics
			3.2.1 Negative Intervals
			3.2.2 Interval Reduction
			3.2.3 Inversions
			3.2.4 Interval Addition
			3.2.5 Afterword on Interval Operators
		3.3 Interval Representation and Implementation
			3.3.1 Negation, Inversion, and Reduction
			3.3.2 Interval Addition and Operator Overloading
			3.3.3 Exceptions
			3.3.4 Computing Start and End Pitches
		3.4 Examples
		3.5 Exercises
	4 Modality, Tonality, and Scales
		4.1 Modality and Tonality
			4.1.1 A Traditional Approach to Modality
			4.1.2 An Intervallic Approach to Modality
			4.1.3 Counterexamples
			4.1.4 Modes, Derived Modalities and Modal Index
		4.2 Modality and Tonality Representation
			4.2.1 Defining and Creating Modality
			4.2.2 System Modalities
			4.2.3 Modality Factory
			4.2.4 Modal Index, Incremental Intervals, and Tonal Scale
			4.2.5 Tonality Representation
			4.2.6 Pitch Scales
		4.3 Exercises
	5 Time in Music
		5.1 Three Notions of Time in Music, an Introduction
		5.2 Whole Note Time: Measuring Time in Fractions
		5.3 Time Signature and Tempo
			5.3.1 Time Signature
			5.3.2 Tempo
		5.4 Whole Time / Actual Time Conversions
		5.5 Whole Time / Beat Time Conversion
		5.6 Representational Considerations
			5.6.1 Whole Note Time Representation
			5.6.2 Position and Duration
			5.6.3 Beat Position
			5.6.4 TimeSignature and Tempo classes
			5.6.5 The Time Conversion Algorithms
		5.7 Exercises
	6 The Note and Note Aggregates
		6.1 Notes and Their Aggregative Partners
			6.1.1 The Note
			6.1.2 Beams
			6.1.3 Tuplets
		6.2 Representation
			6.2.1 The Note Inheritance Hierarchy
			6.2.2  Semantic Clarifications
		6.3 Algorithms
			6.3.1 Accessing Notes
			6.3.2 Adding a Note
			6.3.3 Reversing a Melody
		6.4 Exercises
	7 Chords
		7.1 A Brief Introduction to Chords
			7.1.1 Tertian Chord Types
			7.1.2 Secundal Chord Types
			7.1.3 Quartal Chord Types
			7.1.4 Secondary Chord Types
		7.2 Chord Template and Chord Representation
			7.2.1 Template and Chord Class Design
			7.2.2 Chord Construction
		7.3 Chord Categories: Syntax and Examples
			7.3.1 Tertian Chords
			7.3.2 Secundal Chords
			7.3.3 Quartal Chords
			7.3.4 Secondary Chords
		7.4 Exercises
	8 Instruments
		8.1 A Simple Genealogical Model for Instruments
		8.2 A Software Model for an Instrument Catalog
		8.3 The Instrument Catalog Class Model
			8.3.1 Articulations
			8.3.2 Accessing Instrument Data
			8.3.3 The Instrument Catalog as Persistent Data
			8.3.4 Instrument Catalog Initialization
		8.4 Exercises
	9 Score Representation
		9.1 What is a Musical Score?
		9.2 Score as a Class Model
			9.2.1 Voices and Lines
			9.2.2 Event Sequences for Tempo, Time Signature, and Dynamics
			9.2.3 What Happened to Key Signature?
			9.2.4 Putting It All Together
		9.3 Time-Based Note Search
			9.3.1 Red-Black Trees
			9.3.2 Notes and Intervals
			9.3.3 Interval Search Trees
			9.3.4 Finding all Notes Sounding in an Interval
			9.3.5 Finding All Notes Starting in an Interval
			9.3.6 Adding Note Search to Score
		9.4 Score Management
			9.4.1 Interval Tree Update using the Observer Pattern
		9.5 Final Remarks
		9.6 Exercises
	10 Rendering Score to MIDI
		10.1 An Introduction to MIDI
			10.1.1 Tracks, Channels, and Messages
			10.1.2 Time Representation in MIDI
			10.1.3 MIDI Messages
		10.2 Mapping a Score to a MIDI File
		10.3 Time Conversions
		10.4 Score to MIDI Conversion Algorithms
		10.5 Converting a Line to a MIDI File
		10.6 Exercises
	11 Variable Dynamics and Tempo
		11.1 What are Variable Dynamics and Tempo?
			11.1.1 An Introduction to Variable Dynamics and Tempo
		11.2 Functions and Graphs
			11.2.1 The Piecewise Linear Function
			11.2.2 The Stepwise Function
			11.2.3 The Constant Function
			11.2.4 Generic Univariate Function
			11.2.5 Domain Reset with Affine Transformations
		11.3 Using Functions for Variable Tempo
			11.3.1 Tempo Functions and the TempoEventSequence
			11.3.2 Tempo Functions, MIDI Generation and Time Conversion
		11.4 Using Variable Dynamics Functions
			11.4.1 Details on Variable Dynamics Functions
			11.4.2 Computing MIDI Velocity Events
		11.5 Exercises
	12 Further Representations
		12.1 Harmonic Context
			12.1.1 HarmonicContext and HarmonicContextTrack Representations
		12.2 A Syntax for Constructing Music Structures
			12.2.1 The Music Parser
			12.2.2 A Music Syntax
				Text Structure
				Harmonic Notation
				Note Notation
				Beams and Tuplets
				User-Defined Modalities
			12.2.3Invoking the Parser in Code
		12.3 LiteScore
		12.4 Exercises
Part 2: Music Transformations
	13 An Introduction to Music Transformations
		13.1 What is a Music Transformation?
		13.2 Outline on Transformations
		13.3 A Word on Machine Learning
		13.4 Moving Forward
	14 A Constraint Engine for Pitch Assignment
		14.1 Constraint Programming
		14.2 Music Constraints and Solution Spaces
		14.3 Music Constraint Programming Elements
			14.3.1 PMaps
			14.3.2 Constraints
			14.3.3 Types of Constraints
				Unary Constraints
				Binary Constraints
				Mulit-Actor Constraints
			14.3.4 Invoking the Pitch Constraint Solver
		14.4 Examples
		14.5 Final Thoughts
	15 Shift: A Transform for Key Change
		15.1 An Overview of the Shift Transform
		15.2 Structural Design of the Shift Transform
		15.3 Tonal and Pitch Functions
			15.3.1 Tonal Functions
			15.3.2 CrossTonalityShiftTonalFunction
			15.3.3 GeneralPitchFunction
			15.3.4 CrossTonalityShiftPitchFunction
		15.4 The Shift Transform
			15.4.1 Problem Context and Interface
			15.4.2 The Main Loop
			15.4.3 Clarifying Shifting with Mode Change
			15.4.4 Clarifying Shift with Secondary Chords
		15.5 Examples
			15.5.1 Simple Key Shift using Intervals
			15.5.2 Shift with Modality Change
			15.5.3 Modality and Modal Index Change
			15.5.4 Modulating Sequence
		15.6 Final Thoughts
	16 Reflection: A Transform for Melodic Inversion
		16.1 An Overview of Melodic Reflection
		16.2 Permutations
			16.2.1 Definition and Permutation Composition
			16.2.2 Using Permutations
		16.3 Class Structures for the Reflection Transform
		16.4 Scalar Reflection
			16.4.1 Scalar Reflection Details
			16.4.2 TDiatonicReflection
			16.4.3 Examples of Scalar Reflection
		16.5 Chromatic Reflection
			16.5.1 Chromatic Reflection Details
			16.5.2 TChromaticReflection
			16.5.3 Examples of Chromatic Reflection
		16.6 Final Thoughts
	17 Reshape: A Transform for Melodic Shaping
		17.1 Introduction
		17.2 A Model for Shaping Functions
			17.2.1 Shaping Functions
			17.2.2 The Pitch Range Interpreter
		17.3 A Representation for Shaping Functions and Pitch Interpreters
			17.3.1 The Pitch Range Interpreters, Description and Examples
			17.3.2 Shaping Classes, Description and Examples
		17.4 Melodic Forms and Constraints
		17.5 The Reshape Transform
			17.5.1 The TReshape Transform API
		17.6 Examples
		17.7 Final Thoughts
	18 Harmonic Transcription: Preserving Melody over Harmonic Change
		18.1 Introduction
		18.2 Melodic Analysis for Similarity
			18.2.1 Harmonic Role Analysis
			18.2.2 Melodic Contour Analysis
			18.2.3 Software Design
		18.3 Further Constraining the Search Space
			18.3.1 The Melodic Window
			18.3.2 Melodic Variance (Tunnel)
		18.4 The Harmonic Transcription Transform
		18.5 Examples
		18.6 Final Thoughts
	19 Retrograde: Reversing a Melody
		19.1 Introduction
		19.2 The Retrograde Transform
			19.2.1 The Retrograde Transform Design
			19.2.2 The Retrograde Transform API
		19.3 Examples
		19.4 Final Thoughts
	20 Melodic Search and Pattern Substitution
		20.1 Melodic Search
			20.1.1 Melodic Search Options
			20.1.2 Melodic Search Technical Details
				Search Setup
				Search Algorithm Overview
				Finer Details
			20.1.3 Melodic Search API
			20.1.4 Melodic Search Examples
		20.2 The Melodic Pattern Substitution Transform
			20.2.1 The Foundations of Melodic Pattern Substitution
			20.2.2 An Approach to Melodic Pattern Substitution
			20.2.3 Harmonic Context Expression Rules
			20.2.4 The Melodic Pattern Substitution API
		20.3 Examples
		20.4Final Thoughts
	21 Dilation: Musical Expansion and Contraction
		21.1 A Discussion on Dilation
			21.1.1 Dilation Dynamics
			21.1.2 The Dilation Transform API
		21.2Examples
		21.3 Final Thoughts
	22 The Step Shift Transform and Sequences
		22.1 An Introduction to Step Shift
		22.2 Step Shift Dynamics
			22.2.1 Pitch Remap
			22.2.3 Simple Chord Remap
			22.2.3 Secondary Chords
			22.2.4 The Step Shift API
		22.3 Examples
		22.4 Final Thoughts
	23 Final Thoughts
		23.1 The Quest for a Broader Musical Synthesis
		23.2 The Quest for Real-time Synthesis
		23.3 Automated Score Analysis
		23.4 Forward
Appendices
	A. Modality Varieties
		A.1. Diatonic Modalities
		A.2. Pentatonic Modalities
		A.3. Octatonic Modality
		A.4. Whole Tone Modality
		A.5. Blues Modality
	B. OrderedMap
	C. The Observer Pattern
	D. Chords
		D.1. Tertian Chords
		D.2. Secundal Chords
		D.3. Quartal Chords
	E. A Brief Introduction to XML
		E.1. Tags, Elements, and Attributes
		E.2. Data Structuring
		E.3. Reading an XML File with Python
	F. Binary Search Trees
	G. Processing Constraints: The Design of a Pitch Constraint Engine
		G.1. Two Straight Forward Solutions
			G.1.1 Depth-First Search
			G.1.2 Breadth-First Search and Chains
		G.2. Improvements on the Constraint Solution Algorithm
Bibliography