Musical Theory and Audio Synthesis

[mayzee]

anyone recommend any (preferably free) ebooks on musical theory and audio synthesis...

Starting to poke some programs into making sound but I feel like I should know a bit more about the theory... DJings given me plenty of experience of what sounds 'right' but I want to know more about why it sounds right...

ta

M

[Luka]

yeah i found this book in an op shop and was about to buy it for a friend as a bday present as his folks bought him a nice new synth. upon opening it i realised it was extacly everything i wanted to know.



Terry Burrows 'Total Keyboard' Carlton Books UK 2000


Runs through quick history of piano and synths, artists and styles. Teaches keyboard techniques , fingering and timing, basic notes through to chords (includes a chord reference dictionary), scales and keys, generalisations of styles of music in notes, midi and a bit more.

Also recomend doing some basic piano lessons too (even out of a book) and practice thought tedious is the best way. even if you are playing stupid tunes or scales again and again and again.. it all helps your ear and brain to keyboard relationship

[audiostatic]

The entire musictheory.net website packaged for offline viewing. Simply expand the archive, open the "musictheory.net" folder, and click on "START.html" to view this website's content without an Internet connection.

http://www.musictheory.net/downloads/offline.zip

noise sculpture

"How to make a noise: sound design and synthesiser programming", the most comprehensive guide to synthesiser programming, is now available (and it is free).

www.noisesculpture.com/index.php

Subtractive Synthesis

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Contents

   1. Terms and Abbreviations used
   2. Basic Subtractive Synthesis
   3. Oscillators and Waveforms
   4. Filters
   5. Envelopes
   6. Modulation
   7. Advanced Waveforms
   8. Applying Principles to Other Synthesizers 

Subtractive Synthesis

Physical Audio Signal Processing

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# Preface

    * Book Series Overview
    * Acknowledgments 


# Acoustic Modeling with Delay

    * Delay Lines
          o A Software Delay Line 
    * Acoustic Wave Propagation Simulation
          o Traveling Waves
          o Damped Traveling Waves
          o Converting Propagation Distance to Delay Length
          o Spherical Waves from a Point Source
          o Reflection of Spherical or Plane Waves
          o An Acoustic Echo Simulator
          o Program for Acoustic Echo Simulation 
    * Lossy Acoustic Propagation
          o Exponentially Decaying Traveling Waves
          o Dispersive Traveling Waves
          o Summary 
    * Digital Waveguides
          o Physical Outputs 
    * Tapped Delay Line (TDL)
          o Example Tapped Delay Line
          o Transposed Tapped Delay Line
          o TDL for Parallel Processing
          o General Causal FIR Filters 
    * Comb Filters
          o Feedforward Comb Filters
          o Feedback Comb Filters
          o Feedforward Comb Filter Amplitude Response
          o Feedback Comb Filter Amplitude Response
          o Equivalence of Parallel Combs to TDLs
          o Equivalence of Series Combs to TDLs
          o Time Varying Comb Filters 
    * Feedback Delay Networks (FDN)
          o FDN and State Space Descriptions
          o Single-Input, Single-Output (SISO) FDN
          o FDN Stability 
    * Allpass Filters
          o Allpass from Two Combs
          o Nested Allpass Filters
          o More General Allpass Filters
          o Example Allpass Filters
          o Gerzon Nested MIMO Allpass 
    * Allpass Digital Waveguide Networks
          o Signal Scattering
          o Digital Waveguide Networks 
    * Exercises
    * Problems
    * Problems 


# Artificial Reverberation

    * The Reverberation Problem
          o Exact Reverb via Transfer-Function Modeling
          o Complexity of Exact Reverberation
          o Possibility of a Physical Reverb Model 
    * Perceptual Aspects of Reverberation
          o Perception of Echo Density and Mode Density
          o Perceptual Metrics for Ideal Reverberation
                + Energy Decay Curve
                + Energy Decay Relief 
    * Early Reflections
    * Late Reverberation Approximations
          o Desired Qualities in Late Reverberation
          o Schroeder Allpass Sections
          o Nested Allpass Filters 
    * A Schroeder Reverberator called JCRev
    * FDN Reverberation
          o History of FDNs for Artificial Reverberation
          o Choice of Lossless Feedback Matrix
                + Householder Feedback Matrix
                + Most General Lossless Feedback Matrices
                + Triangular Feedback Matrices 
          o Choice of Delay Lengths
                + Mean Free Path
                + Mode Density Requirement 
          o Achieving Desired Reverberation Times
          o Delay-Filter Design
                + First-Order Delay-Filter Design 
          o Tonal Correction Filter
          o FDNs as Digital Waveguide Networks
          o Further Extensions for FDN Reverberation
                + Spatialization of Reverberant Reflections
                + Distribution of Mode Frequencies
                + Reverberation Time vs. Frequency
                + The Digital Waveguide Mesh for Reverberation 
    * Digital Waveguide Reverberators
    * Time Varying Reverberators
    * Exercises
    * Problems
    * More Problems 


# Time-Varying Delay Effects

    * Variable Delay Lines
    * Delay-Line Interpolation
          o Linear Interpolation
          o First-Order Allpass Interpolation
                + Minimizing the Transient Response of First-Order Allpass Interpolation 
    * Large Delay Changes
    * Specific Time-Varying Delay Effects
          o Flanging
                + Flanger Speed and Excursion
                + Flanger Depth Control
                + Flanger Inverted Mode
                + Flanger Feedback Control
                + Summary of Flanging 
          o Phasing
          o Phasing with First-Order Allpass Filters
                + Classic Analog Phase Shifters
                + Classic Virtual Analog Phase Shifters 
          o Phasing with 2nd-Order Allpass Filters
                + Allpass Phaser Architecture
                + Allpass Phaser Parameters
                + Allpass Phaser Notch Distribution 
          o Vibrato Simulation
          o Doppler Effect
                + Vector Formulation 
          o Doppler Simulation
                + Doppler Simulation via Delay Lines
                + Time-Varying Delay-Line Reads
                + Multiple Read Pointers
                + Multiple Write Pointers
                + Stereo Processing
                + System Block Diagram 
          o Chorus Effect
          o The Leslie
                + Rotating Horn Simulation
                + Leslie Free-Field Horn Measurements
                + Separating Horn Output from Base Leakage 
          o Rotating Woofer-Port and Cabinet Simulation
          o Miscellaneous Effects
                + Doubling Simulation
                + Slap Back 
    * Exercises
    * Delay Line Interpolation Problems 


# Plucked String Instruments

    * Ideal Vibrating String
          o Wave Equation
          o Wave Equation Applications
          o Traveling-Wave Solution
          o Sampled Traveling-Wave Solution
          o Wave Impedance 
    * Rigid Terminations
          o Velocity Waves at a Rigid Termination
          o Force Waves at a Rigid Termination 
    * Moving Rigid Termination
    * The Ideal Plucked String
    * The Ideal Struck String
    * The Damped Plucked String
          o Computational Savings 
    * Frequency-Dependent Damping
          o Length $ 3$ FIR Loop Filter
          o Length $ 3$ FIR Loop Filter Controlled by ``Brightness'' and ``Sustain''
          o One-Zero Loop Filter
          o The Karplus-Strong Algorithm
          o Loop Filter Design 
    * The Stiff String
    * The Externally Excited String
          o Equivalent Forms
                + Summary 
    * Loop Filter Identification
    * Plucked/Struck String Pitch Estimation
    * Coupled Strings
          o Horizontal and Vertical Transverse Waves
          o Coupled Horizontal and Vertical Waves
          o Asymmetry of Horizontal/Vertical Terminations
          o Coupled Strings
          o Longitudinal Waves 
    * Nonlinear Distortion
    * Amplifier Feedback
    * Commuted Synthesis of Strings
          o Further Reading in Commuted Synthesis 
    * Body-Model Factoring
    * Exercises
    * Problems 


# Piano

    * Introduction
    * The Piano String
          o Dispersion Filter Design 
    * Commuted Piano Synthesis
          o Excitation Factoring
          o String Interface
          o Coupled Piano Strings
          o Commuted Synthesis of String Reverberation
          o High Key Numbers
          o Force-Pulse Filter Design 
    * Further Reading in Piano Synthesis
    * Exercises
    * Piano Modeling Problems 


# Woodwinds

    * Single-Reed Instruments
          o Digital Waveguide Single-Reed Implementation
          o A View of Single-Reed Oscillation
          o Single-Reed Theory
                + Scattering-Theoretic Formulation
                + Computational Methods 
          o Practical Details 
    * Tonehole Modeling
          o The Clarinet Tonehole as a Two-Port Junction
          o Tonehole Filter Design
          o The Tonehole as a Two-Port Loaded Junction 
    * Exercises 


# Bowed Strings

    * Digital Waveguide Bowed-String
    * The Bow-String Scattering Junction
    * Further Extensions
    * Exercises
    * Nonlinear Commuted Synthesis of Bowed Strings
          o Nonlinear Commuted Model
          o Nonlinear Bow Friction
          o Friction Impulse Detection
          o Pulsed Noise
          o Simulation Results
          o Prognosis
          o Appendix: Selected Software Items 


# Brasses

    * Modeling the Lips and Mouthpiece
    * Bell Models 


# Conclusion
# History of Enabling Ideas

    * Early Musical Acoustics
    * Modal Expansions
    * Mass-Spring Resonators
    * Sampling Theory
    * Physical Digital Filters
          o Analog Computers
          o Finite Difference Methods
          o Transfer Function Models
          o Wave Digital Filters 
    * Voice Synthesis
          o Dudley's Vocoder
          o Vocal Tract Analog Models
          o Singing Kelly-Lochbaum Vocal Tract
          o Linear Predictive Coding of Speech 
    * String Models
    * Karplus-Strong Algorithms
    * Digital Waveguide Models
    * Conclusion 


# Physics, Mechanics, and Acoustics

    * Newton's Laws of Motion
          o Newton's Three Laws of Motion
          o Mass
          o Gravitational Force
          o Hooke's Law
          o Applying Newton's Laws of Motion 
    * Work = Force times Distance = Energy Expended
    * Potential Energy in a Spring
          o Kinetic Energy of a Mass 
    * Energy in the Mass-Spring Oscillator
    * Energy Conservation
          o Energy Conservation by Newton's Second Law 
    * Momentum
    * Conservation of Momentum
    * Young's Modulus
    * Young's Modulus as a Spring Constant
    * String Tension
    * Moment of Inertia
    * Radius of Gyration
          o Rectangular Cross-Section
          o Circular Cross-Section 
    * Particle Velocity of a Gas
    * Volume Velocity of a Gas
    * Gas Pressure is Confined Kinetic Energy
    * Bernoulli Equation
    * Bernoulli Effect
    * Air Jets
    * Acoustic Intensity
    * Acoustic Energy Density
    * Speed of Sound in Air
    * Air Absorption
    * Problems 


# String Wave Equation

    * Non-Stiff String
    * Wave Momentum 


# Digital Waveguide Theory

    * The Ideal Vibrating String
    * The Finite Difference Approximation
          o FDA of the Ideal String 
    * Traveling-Wave Solution
          o Traveling-Wave Partial Derivatives
          o Traveling-Wave Partial Derivatives by the Chain Rule
          o Wave Velocity
          o d'Alembert Derived
          o Converting Any String State to Traveling Slope-Wave Components 
    * Sampled Traveling Waves
          o Digital Waveguide Model
          o Digital Waveguide Interpolation
          o Relation to the Finite Difference Recursion 
    * The Lossy 1D Wave Equation
          o Loss Consolidation
          o Frequency-Dependent Losses
          o Well Posed PDEs for Modeling Damped Strings
          o Digital Filter Models of Damped Strings
          o Lossy Finite Difference Recursion
                + Frequency-Dependent Losses 
    * The Dispersive 1D Wave Equation
          o Higher Order Terms 
    * Alternative Wave Variables
          o Spatial Derivatives
          o Force Waves
          o Wave Impedance
          o State Conversions
          o Power Waves
          o Energy Density Waves
          o Root-Power Waves
          o Total Energy in a Rigidly Terminated String 
    * Scattering at Impedance Changes
          o Kelly-Lochbaum Scattering Junctions
          o One-Multiply Scattering Junctions
          o Normalized Scattering Junctions
          o Junction Passivity 
    * Waveguide Transformers
    * Loaded Waveguide Junctions
    * Two Coupled Strings
          o Two Ideal Strings Coupled at an Impedance
          o Coupled Strings Eigenanalysis 
    * Digital Waveguide Mesh
          o The Rectilinear 2D Mesh
          o Dispersion
          o Recent Developments
          o 2D Mesh and the Wave Equation
          o The Lossy 2D Mesh
          o Diffuse Reflections in the Waveguide Mesh 
    * FDNs as Digital Waveguide Networks
          o Lossless Scattering
          o Normalized Scattering
          o General Conditions for Losslessness 
    * Digital Waveguide Theory Problems 


# Digital Waveguide Filters

    * Ladder Waveguide Filters
    * Half-Rate Waveguide Filters
    * Conventional Ladder Filters
    * Power-Normalized Waveguide Filters 


# Delay Line Interpolation

    * Lagrange Interpolation
          o Relation of Lagrange and Sinc Interpolation
          o Lagrange Interpolation Optimality
          o Explicit Formula for Lagrange Interpolation Coefficients
          o Lagrange Interpolation Coefficients for Orders 1, 2, 3
          o Matlab Code for Lagrange Interpolation
          o Polynomial Parametrization of Interpolating Filter $ h_\Delta $
          o Farrow Structure for Variable Delay FIR Filters 
    * Thiran Allpass Interpolators
          o Thiran Allpass Interpolation in Matlab or Octave
          o Frequency Responses of Thiran Allpass Interpolators for Fractional Delay 
    * Bandlimited Interpolation
          o Theory of Ideal Bandlimited Interpolation
          o From Theory to Practice
          o Implementation
          o Quantization Issues
                + Choice of Table Size
                + Choice of Interpolation Resolution 
          o Summary of Windowed Sinc Interpolation 
    * Periodic Sinc Interpolation
    * Linear Interpolation as a Filter
          o Convolution Interpretation
          o Frequency Response of Linear Interpolation
                + The Triangular Pulse as a Convolution of Two Rectangular Pulses
                + Fourier Transforming the Triangular Pulse 
          o Special Cases 


# Introduction to Lumped Models

    * Impedance
          o Dashpot
          o Ideal Mass
          o Ideal Spring 
    * One-Port Network Theory
          o Series Combination of One-Ports
          o Parallel Combination of One-Ports
          o General One-Ports
          o Passive One-Ports
          o Simulation Diagrams 
    * Finite Difference Approximation
    * Bilinear Transformation
          o Finite Differences vs. the Bilinear Transform
          o Application of the Bilinear Transform
                + Practical Considerations 
    * Higher Order Models
    * ``Traveling Waves'' in Lumped Systems
          o Scattering Theory for Traveling Waves
          o Physical Interpretation
          o General Reflectance 


# Passive Impedances

    * Passive Reflectances
    * Passive String Terminations
          o Reflection Transfer Function 
    * The Guitar Bridge
          o Building a Synthetic Guitar Bridge Admittance
                + Method 1
                + Method 2
                + Matlab for Method 1
                + Matlab for Method 2 
    * Positive Real Functions
          o Relation to Stochastic Processes
          o Relation to Schur Functions
          o Relation to functions positive real in the right-half plane
          o Special cases and examples
          o Minimum Phase (MP) polynomials in $ z$
          o Miscellaneous Properties 


# Finite Difference Schemes

    * Finite Difference Schemes
    * Convergence
          o Consistency
          o Well Posed Initial-Value Problem
                + A Class of Well Posed Damped PDEs
                + Proof that the Third-Order Time Derivative is Ill Posed 
          o Stability of a Finite Difference Scheme
          o Lax-Richtmyer equivalence theorem
          o Passivity of a Finite Difference Scheme
          o Summary
          o Convergence in Audio Applications 
    * Characteristic Polynomial Equation
    * Von Neumann Analysis 


# Waveguide and FDTD Equivalence

    * Introduction
          o Finite Difference Time Domain (FDTD) Scheme
          o Digital Waveguide (DW) Scheme
          o FDTD and DW Equivalence 
    * State Transformations
    * Excitation Examples
          o Localized Displacement Excitations
          o Localized Velocity Excitations
          o More General Velocity Excitations
          o Additive Inputs
          o Interpretation of the Time-Domain KW Converter 
    * State Space Formulation
          o FDTD State Space Model
          o DW State Space Model
                + DW Displacement Inputs
                + DW Non-Displacement Inputs
                + Input Locality 
          o Boundary Conditions
                + Resistive Terminations
                + Boundary Conditions as Perturbations
                + Reactive Terminations
                + Interior Scattering Junctions 
          o Lossy Vibration
          o State Space Summary 
    * Computational Complexity
    * Summary
    * Future Work
    * Acknowledgments 


# Wave Digital Filters

    * Wave Digital Elements
          o A Physical Derivation of Wave Digital Elements
                + Reflectance of a General Lumped Waveguide Termination
                + Reflectances of Elementary Impedances
                + Choosing Waveguide Impedance to Simplify Element Reflectance
                + Digitizing Elementary Reflectances via the Bilinear Transform 
          o Summary of Wave Digital Elements
          o Wave Digital Mass
          o Wave Digital Spring
          o Wave Digital Dashpot
          o Limiting Cases
          o Unit Elements 
    * Adaptors for Wave Digital Elements
          o Two-Port Parallel Adaptor for Force Waves
                + Compatible Port Connections 
          o General Parallel Adaptor for Force Waves
                + Alpha Parameters
                + Reflection Coefficient, Parallel Case
                + Physical Derivation of Reflection Coefficient
                + Reflection Free Port 
          o Two-Port Series Adaptor for Force Waves
          o General Series Adaptor for Force Waves
                + Beta Parameters
                + Reflection Coefficient, Series Case
                + Physical Derivation of Series Reflection Coefficient
                + Series Reflection Free Port 
    * Wave Digital Modeling Examples
          o ``Piano hammer in flight''
                + Extracting Physical Quantities 
          o Force Driving a Mass
                + A More Formal Derivation of the Wave Digital Force-Driven Mass 
          o Force Driving a Spring against a Wall
          o Spring and Free Mass
          o Mass and Dashpot in Series
                + Checking the WDF against the Analog Equivalent Circuit 
          o Wave Digital Mass-Spring Oscillator
                + Oscillation Frequency
                + Linearly Growing State Variables
                + Why this can't happen in reality
                + Energy-Preserving Parameter Changes (Mass-Spring Oscillator)
                + Exercises in Wave Digital Modeling 


# The Digital Waveguide Oscillator

    * Additive Synthesis
    * Digital Sinusoid Generators
    * The Second-Order Waveguide Filter
    * Application to FM Synthesis
    * Digital Waveguide Resonator
    * State-Space Analysis
    * Eigenstructure
          o Damping and Tuning Parameters
          o Eigenvalues in the Undamped Case 
    * Summary
    * Matlab/Octave Programs 


# Transfer Function Models

    * Outline
    * Sampling the Impulse Response
    * Pole mapping
    * Filter Design Methods
    * Modal Expansion
          o Parallel Second-Order Expansion
          o Delay Loop Expansion 


# Resonator Factoring

    * Mode Extraction Techniques
          o Amplitude response peak measurement
          o Weighted digital filter design
          o Linear prediction
          o Sinusoidal modeling
          o Late impulse-response analysis 
    * Inverse Filtering
          o Empirical Notes on Inverse Filtering Experiments
          o Matlab Code for Inverse Filtering 
    * Sinusoidal Modeling of Mode Decays
    * Parallel Body Filterbank Design
    * Approximating the Shortened Excitation as a Noise Burst
    * Body Factoring Example 


# Nonlinear Elements

    * Memoryless Nonlinearities
          o Clipping Nonlinearity
          o Arctangent Nonlinearity
          o Cubic Soft Clipper
          o Series Expansions
                + Arctangent Example 
          o Spectrum of a Memoryless Nonlinearities
                + The Square Law
                + Power Laws
                + Spectrum of the Arctangent Nonlinearity 
          o Cubic Soft-Clipper
          o Practical Advice 


# Synthesis Tool Kit (STK) Intro

    * Installing and Testing the STK
    * Customizing the STK for Development
          o STK Subdirectory Overview
          o Compiling the STK Library and Demos 
    * Testing Out a New STK Project
    * Compiling and Debugging from Emacs 


# Debugging STK Programs in gdb

    * An example .gdbinit file.
    * Preparing your Program for Debugging
    * Executing gdb from the command line
    * Executing gdb from Emacs
    * Useful commands in gdb
    * Dealing with C++ in gdb
    * Miscellaneous tricks in gdb under Emacs 


# Selected STK Modules

    * Non-Interpolating Delay Line
          o DLineN.h
          o DLineN.cpp 
    * Linearly Interpolated Delay Line
          o DLineL.h
          o DLineL.cpp 
    * Allpass-Interpolated Delay Line
          o DlineA.h
          o DlineA.cpp 
    * Finite Impulse Response (FIR) Digital Filters
          o FIR.cpp
          o FIR.h 


# Programming Examples

    * Simple Plucked String
          o Listing of test main program: main.cpp
          o SimpString.h
          o SimpString.cpp
          o Description of the SimpString object 
    * More Practical Plucked String
          o Header file for main program: gtr.h
          o Main program: gtr.cpp
          o Guitar.h
          o Guitar.cpp
          o Plucked3.h
          o Plucked3.cpp
          o Bowed String Synthesis Example
                + Structure of a basic bowed string model
                + Improving the basic model
                + Researchers working on bowed strings 


# Resources on the Internet
# Sound Examples
# Citations by Topic

    * Network Theory
    * Basic Circuit Theory
    * Laplace Transform Analysis
    * Finite Differences
    * Use of Finite Differences in Instrument Modeling
    * Modal Analysis
    * Modal Synthesis
    * Wave Digital Filters
    * Digital Waveguide Filters and Models
    * Ladder and Lattice Filters
    * Virtual Analog Synthesis
    * String Modeling
    * Nonlinear String Modeling
    * Vacuum Tube Modeling
    * Coupled Strings
    * Psychoacoustics for String Modeling (Perception of Parameter Errors)
    * Piano String Modeling
    * Piano Hammer Modeling
    * Clavichord Modeling
    * Bell Modeling
    * Wave Digital Piano-Hammer
    * Commuted Piano Synthesis
    * Bowed Strings
    * Woodwinds
    * Horns
    * Brass Instruments
    * Brass Instrument Excitation
    * Flue Instruments
    * Conical Acoustic Tubes
    * Artificial Reverberation
    * Waveguide Mesh
    * Feedback Delay Networks
    * Voice
    * Filter Design
    * Filter Design in Digital Waveguide Models
    * IIR Digital Filter Implementation
    * Minimum Phase FIR Filter Design
    * Linear Prediction
    * Ladder and Lattice Digital Filters
    * Audio Signal Processing
    * Applications of Frequency-Warping in Audio Signal Processing
    * General Computer Music and Sound Synthesis
    * General Musical Acoustics
    * General Acoustics
    * Physics of Waves
    * Interpolation
    * Farrow Interpolation Structure
    * Splines
    * TIIR Filters
    * Musical Instrument Controllers
    * Model-Based Audio Compression
    * Software Tools
    * Elementary Signal Processing
    * Intermediate to Advanced Signal Processing
    * Intermediate Signal Processing
    * Math Reference 

Physical Audio Signal Processing

Modular Synthesizers

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    1 Introduction

        1.1 The Purpose of this Document 
        1.2 Acknowledgements 

    2 Oscillator Waveform Modification

        2.1 Sync 
        2.2 Frequency Modulation Techniques 
        2.3 Wave Shaping 
        2.4 Vector Synthesis 
        2.5 Wave Sequencing 
        2.6 Audio-Rate Crossfading 
        2.7 Wave Terrain Synthesis 
        2.8 VOSIM 
        2.9 FOF Synthesis 
        2.10 Granular Synthesis 

    3 Filter Techniques

        3.1 Resonant Filters as Oscillators 
        3.2 Serial and Parallel Filter Techniques 
        3.3 Audio-Rate Filter Cutoff Modulation 
        3.4 Adding Analog Feel 
        3.5 Wet Filters 

    4 Noise Generation

        4.1 White Noise 
        4.2 Brown Noise 
        4.3 Pink Noise 
        4.4 Pitched Noise 

    5 Percussion

        5.1 Bass Drum Synthesis 
        5.2 Snare Drum Synthesis 
        5.3 Synthesis of Gongs, Bells and Cymbals 
        5.4 Synthesis of Hand Claps 

    6 Additive Synthesis

        6.1 What is Additive Synthesis? 
        6.2 Resynthesis 
        6.3 Group Additive Synthesis 
        6.4 Morphing 
        6.5 Transients 
        6.7 Which Oscillator to Use 

    7 Physical Modeling

        7.1 Introduction to Physical Modeling 
        7.2 The Karplus-Strong Algorithm 
        7.3 Tuning of Delay Lines 
        7.4 Delay Line Details 
        7.5 Physical Modeling with Digital Waveguides 
        7.6 String Modeling 
        7.7 Woodwind Modeling 
        7.8 Related Links 

    8 Speech Synthesis and Processing

        8.1 Vocoder Techniques 
        8.2 Speech Synthesis 
        8.3 Pitch Tracking 

    9 Using the Logic Modules

        9.1 Complex Logic Functions 
        9.2 Flipflops, Counters other Sequential Elements 
        9.3 Asynchronous Elements 
        9.4 Arpeggiation 

    10 Algorithmic Composition

        10.1 Chaos and Fractal Music 
        10.2 Cellular Automata 
        10.3 Cooking Noodles 

    11 Reverb and Echo Effects

        11.1 Synthetic Echo and Reverb 
        11.2 Short-Time Reverb 
        11.3 Low-Fidelity Echo and Reverb 

    12 Distortion Effects

        12.1 Distortion using Nonlinearities 
        12.2 Multiband Distortion 
        12.3 Polynomial Distortion 
        12.4 Distortion using Time-Variant Systems 

    13 Frequency and Pitch Shifting

        13.1 Frequency Shifting 
        13.2 Pitch Shifting 

    14 Spatialization 
    15 Emulating Classic Synths

        15.1 General Guidelines 
        15.2 Yamaha DX7 
        15.3 Octave Cat 
        15.4 ARP Odyssey 
        15.5 Casio 
        15.6 Hallsey Mark 1 and 2 
        15.7 Other Emulations 

Modular Synthesizers

F.M. Synthesis

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Contents

   1. Definitions
   2. What is FM?
   3. What is DX-FM?
   4. What are Operators and Algorithms?
   5. Critical relationship between "M" and "C"
   6. Non-coincident and Coincident Series
   7. Series generated by M:C
   8. Modulation Amount
   9. Two Modulators
  10. Tips for using F.M.
  11. FM Synthesizers 

F.M. Synthesis

Gordon Reid SoundonSound synth secrets is good

have fun

[motek]

good one
thanks

[edwardgeorge]

if you want to spend quite a bit of money *THE* book to get is "The Computer Music Tutorial" by Curtis Roads.
10 years old and it's still pretty much the benchmark